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SAFETY ANALYSIS OF STRUCTURAL FOUNDATIONS BUILT ON ABANDONED SOLID WASTE SITES
BY
IBRAHIM, MUSA OBAJI PG/PhD/11/59375
DEPARTMENT OF CIVIL ENGINEERING FACULTY OF ENGINEERING
UNIVERSITY OF NIGERIA, NSUKKA
SEPTEMBER 2015
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APPROVAL
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APPROVAL
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DEDICATION This thesis is dedicated to Almighty God, the author of eternal salvation, for making it possible
for me to reach the concluding stage of this course.
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ACKNOWLEDGEMENTS
First and fore-most, I like to thank the Almighty God for keeping me alive and making it
possible for me to complete this study. I wish to express my gratitude to my supervisor Professor
N.N. Osadebe who amidst tight schedule gave me prompt attention, supervision and
encouragement especially during the tough times of the study. I equally appreciate the patience
and support of my wife and the entire members of my family.
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TABLE OF CONTENTS
Approval i
Approval ii
Dedication iii
Acknowledgments iv
Table of Contents v
List of Tables ix
List of Figures xi
List of Plates xiii
List of Symbols/Abbreviations and Units xiv
Abstract xvii
CHAPTER ONE INTRODUCTION 1
1.1 Background 3
1.2 Statement of problem 7
1.3 Aim of the study 10
1.4. Objectives of study 10
1.5 Significance of the study 10
1.6 Delimitation of the study 11
1.7 Limitations of the study 12
1.8 Research questions 12
1.9 Organization of this study 13
CHAPTER TWO LITERATURE REVIEW 15
2.1 Properties of solid waste soil 15
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2.1.1 Classification of municipal solid waste 16
2.1.2 Compression characteristics of ASWSS 18
2.1.3 Shear Strength Characteristics of ASWSS 20
2.2 ASWSS as foundation soil 21
2.2.1 Spatial variation in ASWSS 24
2.2.2 Characteristic and representative values 25
2.3 Safety analysis of ASWSS 28
2.3.1 Risk and reliability analysis 30
2.4 Classification of geotechnical category 35
CHAPTER THREE PLAN AND METHODOLOGY 39
3.1 Location of study area 40
3.2 Design of study 46
3.3 Population and sampling technique 47
3.4 Instruments for data collection and administration 49
3.5 Procedures and methods of data analysis 50
3.5.1 Determination of engineering properties 50
3.5.2 Design values of soil data 51
3.5.3 Evaluation of reliability index and probability of failure 53
3.5.4 Reliability analysis using Hasofer-Lind approach (FORM) 53
3.5.5 Solution of reliability index equation 57
3.5.6 Reliability analysis of Monte Carlo Simulation (MCS) 60
3.5.7 Regression Analysis of ASWSS and Natural Soil properties 64
CHAPTER FOUR RESULTS AND DISCUSSION 68
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4.1 Graphical representation of test result 69
4.1.1 Atterberg limits test results 69
4.1.2 Compaction test results 82
4.1.3 Consolidation and triaxial tests results 89
4.1.4 Specific gravity and sieve analysis results 102
4.2 Chemical analysis of ASWSS and NS 109
4.3 Organic matter content 135
4.4 X – ray diffraction test 139
4.5 Student’s t –test of triaxial test results 141
4.6 T – test atterberg limits, compaction and specific gravity test results 161
4.7 Evaluation of design data 184
4.7.1 Trimmed upper and extended lower mean (ASWSS) 190
4.7.2 Design values of soil properties and load effects 194
4.8 Determination of foundation width 197
4.9 Estimation of settlement value 202
4.10 Reliability of foundation design by Monte Carlo Simulation 203
4.11 Reliability of foundation design by first order reliability method (FORM) 208
4.12 Influence of foundation dimensions on the reliability of foundation design 213
4.13 Classification of ‘expected performance’ of foundation design 220
4.14 Geotechnical properties of ASWSS and NS 224
4.15 Design values 226
4.16 Safety indices of ASWSS and NS 227
4.17 Performance classification of ASWS S 228
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CHAPTER FIVE CONCLUSION AND RECOMMENDATIONS 230
5.1 Summary 230
5.2 Conclusion 231
5.3 Recommendations 233
References 236
Appendix A: Safety Analysis using first order reliability method FORM 5 248
Appendix B: Determination of foundation width using MATLAB 250
Appendix C: Results of laboratory determination of geotechnical properties of
ASWSS and NS 251
Appendix D: Application of t –table in the computation of t values 261
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LIST OF TABLES
TABLE PAGE
2.1 Australia draft solid waste classification 18
2.2 Coefficient of variation for some common field measurements 23
2.3 Probability of failure for various distribution of performance function 35
2.4 Geotechnical categories related to geotechnical hazards and vulnerability
levels 37
4.1 Results of x – ray diffraction test (ASWSS) 140
4.2 Student’s t – test of triaxial test results 143
4.3 Student’s t – test of atterberg limits test results 162
4.4 T – test of compaction test results 174
4.5 Student’s t –test of specific gravity test results 180
4.6 Triaxial test results including estimated values at 4.0 and 4.5 m 189
4.7 Descending order of data in table C.4 site A/1 (ASWSS) 191
4.8 Trimmed – upper and extended lower values of data in table 4.15 192
4.9 Descending order of data in table C.4 site A/2 (ASWSS) 192
4.10 Trimmed upper and extended lower values of data in Table 4.9 192
4.11 Sample mean (µ), standard deviation () and coefficient of
variation (Cov) of soil data 193
4.12 Population mean for zones 195
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4.13 Characteristic values of soil data 196
4.14 Evaluated foundation widths using soil data of site 1 in zone A
on table C.4 199
4.15 Evaluated foundation widths using soil data of site 2 in zone A 200
4.16 Evaluated foundation width using data of site 1 of Zone B 200
4.17 Evaluated foundation width using soil data of site 2 in zone B 201
4.18 Evaluated foundation widths using soil data of site 1 in zone C 201
4.19 Evaluated foundation widths using soil data of site 2 in zone C on 202
4.20 Reliability indices and probability of failures for selected Loads,
foundation depths and foundation widths by monte carlo simulation 205
4.21a Mean values and standard deviation of aswss properties 209
4.21b Mean values and standard deviation of NS properties 210
4.22 Reliability indices and probability of failures for selected loads,
Foundation depths, and foundation width by first order reliability
method (FORM 5) 210
4.23 Standard classification of ‘expected performance’ of foundation design 220
4.24 Classification of ‘expected performance’ of spread foundation design 221
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LIST OF FIGURES
FIGURE PAGE
2.1(a) Probability densities for soil resistance and loads 33
2.1(b) Probability density for margin of safety 33
3.1a Map of Kaduna State showing the sampled areas in red verge 41
3.1b Map of part of Kaduna town showing test points 42
3.3 Plot of Resistance and Load showing the definition of
reliability index 55
4.1 Variation of liquid limit, plastic limit, plasticity index and shrinkage
limit with depth 70
4.2 Variation of maximum dry density and optimum moisture content
with depth 83
4.3 Variation of total settlement with depth 90
4.4 Variation of cohesion, angle of internal resistance and unit weight
of soil with depth 93
4.5 Variation of specific gravity with depth 103
4.6 Variation of clay and silt content with depth 106
4.7 Variation of sulphate, chloride, carbonate and calcium/magnesium
with depth in wet season 111
4.8 Variation of sulphate, chloride, carbonate and calcium/magnesium
with depth in dry season 123
4.9 Variation of organic matter content with depth 136
4.10 Influence of foundation depth increase on reliability of foundation
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design 214
4.11 Influence of foundation width increase on reliability of foundation
design 217
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LIST OF PLATES
PLATE PAGE
1 Site 1 of Zone A at Tudun Wada, Kaduna Nigeria 43
2 Site 2 of Zone A at Malali, Kaduna Nigeria 43
3 Site 1 of Zone B at Sabo, Kaduna Nigeria 44
4 Site 2 of Zone B at Kakuri, Kaduna Nigeria 44
5 Site 1of Zone C at Costain, Kaduna Nigeria 45
6 Site 2 of Zone C at Nassarawa, Kaduna Nigeria 45
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LIST OF SYMBOLS/ABBREVIATIONS AND UNITS
SYMBOL/ABBREVIATION TERM UNIT
LRFD Load and Resistance Factor Design
ASD Allowable Stress Design
WSD Working Stress Design
AASHTO American Association of State Highway
and Transportation Officials
LSD Limit State Design
Sc, Sq, & Sγ. Shape Factors
dc, dq, & dγ Depth Factors
NC, Nq & Nɤ Bearing Capacity Coefficients
γ Unit Weight of Soil kN/m3
B Foundation Width M
R Soil capacity (Resistance) kN/m2
Q Load kN/m2
µ Mean Value
σ Standard Deviation
Cov Covariance
FORM First Order Reliability Method
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FOSM First Order Second Moment
SLS Serviceability Limit State
E ( ) Expected Value
YL Life Load Factor
YD Dead Load Factor
Reliability Index
Pf Probability of failure
Ø Angle of internal resistance degrees
C Cohesion kN/m2
SWSS Solid Waste Site Soil
NS Natural Soil
RBD Reliability Based Design
\
MCS Monte Carlo Simulation
E Load Effects kN/m2
Ed Design Load Effects kN/m2
Rd Design Soil Resistance kN/m2
ULS Ultimate Limit State
F Factor of Safety
Pij Correlation Coefficient between i and j
βo Regression Intercept
β1 Regression Slope
ε Regression Error Term
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Z Foundation depth
SPT Standard Penetration Test Blows/ft
CPT Cone Penetration Test MN/m2
VST Vane Shear Test kN/m2
DMT Dilatometer Test kN/m2
PMT Pressuremeter Test kN/m2
LL Liquid Limit %
PL Plastic Limit %
PI Plasticity Index %
LS Shrinkage Limit %
OMC Optimum Moisture Content %
MDD Maximum Dry Density g/cm3
GS Specific Gravity
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ABSTRACT This study adopted experimental design to investigate the suitability of abandoned solid waste site soil (ASWSS) as a foundation material for building construction. Measurements of geotechnical properties of stratified random soil samples of ASWSS and adjoining natural soil (NS) at depths 1.5, 2.0, 2.5, 3.0 and 3.5 m were obtained from six test points in Kaduna, Nigeria. The soil samples were subjected to sieve analysis, Atterberg limits (liquid limit, plastic limit, plasticity index and shrinkage limit), compaction, consolidation, triaxial, specific gravity tests as well as chemical characterization. Data treatment of ASWSS was carried out by applying 15% upper trim and 15% lower extended mean. These were done to forestall the effects of ‘reinforced earth scenario’ (unusual high strength spots caused by mix matrices of soil and fibrous materials) and unnoticed randomly distributed weak spots. Design data were evaluated in accordance with the provision of European code (Eurocode 7). The responses of ASWSS and NS to loadings were investigated by carrying out spread foundation designs on both of them using the same loading and geometric conditions. The two sets of designs were subjected to safety measurements by first order reliability method and Monte Carlo simulation respectively. The comparative reliability of ASWSS and NS with respect to structural loading was obtained in forms of reliability index and probability of failure. Significant differences in the geotechnical properties of ASWSS and NS were observed. The liquid and plastic limits of ASWSS fell in the ranges of 28 – 32% and 25 – 37% respectively. The angles of internal resistance ranged from 7 - 15º for ASWSS and 8 º - 17º for NS. Clay and silt accounted for up to 90% of ASWSS in some cases while as low as 9 kN/m2 cohesion was recorded. The composition of organic matters in ASWSS was found to be in the range of 2.1 – 5% while that of calcium/magnesium ranged between 106 mg/kg and 1000 mg/kg. Corrosive agents of sulphate and carbonate were found in the ranges of 235 – 903 mg/kg and 20 – 50 mg/kg respectively. The main mineral composition was quartz (silicon oxide), rutile (titanium oxide) and stolzite (lead tungsten oxide). Design values of cohesion, angle of internal resistance and unit weight of soil were obtained in the ranges of 9.5 – 12 kN/m2, 7 - 20º and 12.9 – 14.3 kN/m3 respectively for ASWSS. The safety of foundation designs on ASWSS and NS was obtained in terms of reliability index and probability of failure. Despite the record of small probability of failure of 0.00013, corresponding to reliability index of 3.75, there were few cases of zero reliability indices corresponding to probability of failure of 0.5 on ASWSS. These values placed ASWSS in the category of ‘hazardous to high’ safety index in the standard performance classification formats. Sulphate resistant cement, large reinforced concrete basement or foundations covering large areas and a minimum foundation depth of 2.0 m are recommended for all structural foundations built on abandoned solid waste sites.
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CHAPTER ONE
INTRODUCTION
In most geotechnical engineering work concerning Solid Waste Sites, efforts seemed to
have been directed mainly towards discovering the mechanical properties of solid waste
site soil (SWSS) in order to determine the safe and reliable landfill inclination slopes and
consequently landfill capacity. In other words, landfill structure is the main focus and its
safe design the concern. However, the high cost and quest for municipal space for
infrastructural development invariably calls for judicious management and use of
available ones by optimizing the benefits derivable from all lands including old landfills.
A higher scale of this phenomenon is clearly and currently observed in most areas with
the resultant economy of space almost over-emphasized in the affected wards.
Establishing the geotechnical properties of SWSS is primary to the use of landfill for any
engineering purpose though geotechnical investigation results by their very terms do not
portray absolute conclusion of the elements they speak of, especially in their precise
order. Spatial and geotechnical uncertainties exist significantly in different forms.
In addition to the wide ranges of approximations attending the practice, assessment of
SWSS properties is categorically fraught with uncertainties in obtaining representative
samples, time –dependent variations in soil characteristics and different or almost
incompatible reactions of layers of SWSS to the applied stress values as a result of the
heterogeneity of waste composition. These uncertainties are either compensated for,
using relevant probabilistic and statistical theories or designs and engineering judgments
are made based on incomplete geotechnical information and traditional factor of safety
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which by nature lacks logical competence to address the inconsistency posed by these
wide ranges of uncertainties. Structural and mechanical engineering practices which deal
with specified material geometries and qualities have their uncertainties arising from the
prediction of tolerances to which the structural members may be built and also the
stresses and environmental conditions to which they may be exposed (Phoon, 2008).
However the practice is different in geotechnical engineering. Geological materials are
investigated in their natural state and their conditions are, of necessity, inferred from
measurements carried out on limited sample sizes (Baecher and Christian, 2003). The
uncertaintities therefore, arise from the accuracy and completeness with which the
geotechnical properties are discovered and the prediction of the mobilized resistance of
soil and rock materials. Reliability-based design incorporates interalia, the principles of
probability, statistics and other mathematical solutions to give expressions and make
allowances for uncertain elements in the use of evaluated soil properties for foundation
design.
Due to social and economic reasons, strong preference has become an important element
in the settlement pattern of most of the world cities. This has created an informal
polarization of settlement and uneven distribution of population among the various wards
that make up the townships. Undoubtedly, waste generation has followed the same
pattern.
A study of this nature therefore, is most desirable at a time when pressures on land
acquisition, coupled with lack of strict regulation, have driven individuals, public and
private outfits into indiscriminate use of abandoned solid waste site soil (ASWSS) for
various purposes. This study comes in to equip the public with the knowledge of the
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varying risk levels involved and the required geotechnical procedures to adopt in the use
of ASWSS for different developments.
1.1 Background
The first rational system of reference for the classification of geological materials
behaviour and interpretation of observations/experience developed out of a scientific
approach launched by Karl Terzaghi (1883-1963) in 1925 to study varying responses of
soil and rock under differently specified stress characterization using the knowledge of
physical science and engineering mechanics (Baecher and Christian 2003). From here
geotechnical engineering took off and went through series of technological refinements to
arrive at the present geotechnical reliability which is the integration and extension of the
works of Freudenthal (1947), Purgsley (1955) and Cornell (1969).
These pioneers of geotechnical engineering warned that the results of laboratory tests,
their own observation/assertions or anybody’s else do not advance conclusive narrative,
since applying finite efforts to discover the state of an engineering site as laid down by
nature obviously involves a number of unpleasant approximations and uncertainties
which must be quantified and compensated for using reliability based methods. In
practical terms, reliability deals with the relationship between the loads a system has to
carry and its ability to carry those loads (Baecher and Christian 2003). The interaction
between the load and resistance becomes uncertain if the quantitative evaluation of the
load and resistance variables bears any uncertain elements. The widest and simplest
expression of reliability is in the form of reliability index and probability of failure which
may be related mathematically.
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There has been an intensive search for a design model that has sufficient probabilistic and
statistical robustness to address soil properties and model variability in geotechnical
engineering until 1978 when load and resistance factor design (LRFD) method was
discovered in the proposal submitted by Ravindra and Galambos (1978). Their
submission which received approval for publication in the first edition of load and
resistance factor design manual for steel construction, published in 1986, formed the
basis for the development of a safety control format for steel structures in United States
(US) codes. The code clearly defines the material capacity as the resistance and the
aggregate stress to be imposed on the structure as the load.
This period was actually preceded by the period of implicit consensus and understanding
that the traditional methods (allowable and working stress designs) were not capable of
meeting the technical challenges posed by the model and soil properties uncertainties.
According to Phoon (2008), ‘LRFD is used in a loose way to encompass methods that
require all limit states to be checked using a specific multiple-factor format involving
load and resistance factor’. It started as partial factor design approach (DA) in Europe;
limit state design (LSD) in Canada and LRFD in United States, where practical
application of the model and development of its code have been recorded. It is
noteworthy to say that the European design approach (DA) has undergone tremendous
reliability-based refinement both in code calibration and design modeling that resulted in
the recent design standard called Eurocode 7.
The National Research Council (2006) report acknowledged the fact that the inherent and
unavoidable uncertainties resulting from soil properties measurements and model
imprecision, and how they affect design decisions, need to be assessed by modern and
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improved methods, simplified enough to attract world-wide acceptance. The very attempt
to evaluate the reliability of a system is an acceptance of the fact that it is unrealistic to
attain absolute reliability if uncertain elements have been identified in the system and
thus making probabilistic analysis imperative.
Three philosophical issues here may be identified: the readiness of geotechnical
engineering community to redirect the mind set towards a reliability based design format
that has a good portion of its concept based on probabilistic analysis; the need to reduce
the mathematical complexity in reliability-based design (RBD) to a simplified model that
can be handled by non-specialist in numerical and statistical analysis and lastly the
reliability based calibration of comprehensive multiple factor formats that capture the
variability in the sources of uncertainties (Robert et al, 2008).
RBD was introduced to civil engineering in form of structural reliability theory by
Freudenthal (1947) and Pugsley (1955). Like any other new concept, it was developed to
improve the management of failure tendencies by carrying out design based on certain
criteria that consistently reduce the probability of failure to its acceptable minimum.
However, the mathematical rigour involved in the application of the theory even in
simple designs, made the concept unpopular. Several attempts were made towards
simplifying RBD theory, but the most popular was the one by Cornell (1969) where he
reformulated Gaussian equation into a model requiring just the second moment statistical
descriptors (mean and covariance) of uncertain material parameters to evaluate the
reliability index equation.
At this stage, however, the solution of Cornell’s equation was still found inconsistent
when the performance function of factor of safety was replaced by that of margin of
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safety, though their limit state equations were mechanically equivalent. Hasofer and Lind
(1974) addressed this problem by proposing an equation of uncertain elements containing
dimensionless variables whose mean value and standard deviation are zero and unity
respectively. They redefined reliability index whose geometric interpretation is the linear
displacement between the closest point on the failure surface and the point defined by the
expected values of the variables
The probability characteristics exhibited by inherent spatial variability in ASWSS
properties make it exceptionally suitable for probability-based reliability treatment. It is
clear that of all the sources of uncertainties, the natural random soil heterogeneity appears
to have the worst effect on the failure mechanism of structural foundation soil. This fact
and the deviation of the actual failure surface from its theoretical domain may be
dramatic for ASWSS.
The earlier solution of reliability equations ‘postulates an existence of average response
that depends on the average values of the soil properties’ (Phoon et al. 2003). This
average response is assumed to be characteristically identical with that observed from a
corresponding homogenous field having the same properties as the average properties of
randomly heterogeneous soil. However recent works have revealed the possibility of the
deviation of actual failure surface from its theoretically evaluated domain to a weaker
part of material formation and thereby rendering the evaluated average strength of soil
material higher than the actual mobilized strength. This has a serious consequence on
design.
It is understandable that a comprehensive description of a random geological formation
that mimics the exact spatial heterogeneity of its materials is not realistic. The progress
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now, therefore, is the evolution of models and standards like Eurocode 7, first and second
order reliability methods (FORM and SORM), Monte Carlo simulation (MCS), cross
correlation structure (CCS), cross-spectral density matrix (CSDM) etcetera, that reduce
approximations and give description of random fields more accurately (Baecher and
Christian, 2003 and Hema and Emil, 2015)..
1.2 Statement of Problem
The management of solid waste, though not totally neglected, has witnessed several but
failed attempts to make it worthwhile especially in most part of the developing world. In
the absence of engineered repositories, relevant SWSS management skills and controlled
disposal points, waste is indiscriminately disposed at open dumps situated at low lying
areas or undeveloped and unused land masses usually not in close proximity to dwelling
places (Ramaiah, et al., 2010). However, municipal expansion and proliferation of social
and economic activities soon render such dump sites an environmental misnomer with
subsequent abandonment of the use and re-allocation of it for infrastructural development
ultimately. Not enough is seen in the treatment of SWSS by composting, and the high
water content makes incineration critically seasonal.
Where professionals are involved, thorough investigation of ASWSS is often
recommended with the result revealing most of the time the anticipated weakness in soil
data. Upon this weakness has been based the argument against the use of ASWSS and in
favour of the search for alternative sites most of the time. Traditionally, the empirical
expression of these risk levels (weakness) coherently and numerically is what has been
absent. This is the solution provided by the recent development in geotechnical reliability
and with the risk level of ASWSS explicitly, though not unanswerably, presented by a
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tested and approved risk controlling model, ASWSS designs and decision making are
made simple. This study was intended to make its impact in this direction.
The use of ASWSS for development, whether the preference of the developers or not, is a
widely known practice despite the structural foundation failures recorded in the practice
in the recent times. Developments on ASWSS require more than adherence to the
mandatory provisions of building codes. The design details should be the product of
tested and approved risk controlling techniques like reliability – based method. Many
catastrophic and fatal failures of landfill structures and waste dumps were recorded
between 1997 and 2005 world-wide, resulting into the death of over 600 people and
mobilization and redistribution of over 1.5 million m3 of waste (Gandolla et al., 1979; Eid
et al., 2000; Blight, 2004 and Merry et al., 2005). The environmental damage caused by
these catastrophes, most of which were reported to have occurred in developing nations,
was almost irreparable (Blight, 2008). One of the most recent and surprising cases was
the 2011 failure of a students workshop cited on an ASWSS in a tertiary institution
having a notable civil Engineering department in Nigeria.
In the face of the current scarcity of municipal land, old and abandoned Solid Waste Sites
may not be allowed to waste without development. On the other hand, if failures are
recorded despite claims of adequate site investigation and propriety of designs, it means
something has to be done to acknowledge and accept the peculiarities of SWSS that
require relevant statistical and reliability treatment of its soil data to make it a fair
representation of both the tested sample and untested mass in the parent population. Until
this is done, there will continue to be the tendency of either the design of structural
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foundation members below its failure level or elusive selection of factor of safety in a
defensible and uneconomical manner.
Results obtained from modern methods (especially Monte Carlo simulation) have
revealed worrisome discrepancies between the average response of spatially variable soils
and the response of corresponding homogenous soil (Phoon et al 2003). For instance,
Nobahar and Popescu (2000) and Griffiths et al. (2002) discovered up to 30% decrease in
the mean value of bearing capacity of spatially variable soils having coefficient of
variation of 50%, compared with the bearing capacity of corresponding homogenous soil
with the same average soil properties.
An increase of 12% in the average settlement of spatially variable soil having coefficient
of variation of 42% was equally discovered by Paice et al. (1996) over the settlement of
corresponding homogenous geological formation having equivalent mean soil properties.
The summary results of the work of Popescu et al. (1997) projected up to 20% increase in
pore-water pressure for a non-homogenous soil deposit having coefficient of variation of
40%, over that of corresponding homogenous soil deposit with equivalent mean soil
properties.
The technical issues raised by these uncertainties constituted the target of some of the
recent works. It is obvious, however, that not all the modern methods have what it takes
to address the effect of these discrepancies in the use of soil data for design and analysis.
While appreciating the efforts of these researchers and those mentioned earlier, one
question remains unanswered and that is ‘how can the combined efforts of these
researchers be harnessed to solve the obvious problem of variability in geotechnical
reliability?’’ This is part of the focus of this study.
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1.3 Aim of the Study
The aim of the study was to explore the contrasting responses of ASWSS and adjoining
NS to structural loading so as to establish the peculiar geotechnical characteristics of
ASWSS.
1.4 Objectives of the Study
The specific objectives were
i. To obtain the properties of ASWSS and adjourning Natural Soil (NS) for
comparison with those reported in similar and recent works of other areas.
ii. To obtain design values of soil properties using Eurocode 7 and reliability
methods for both ASWSS and adjourning natural ground.
iii. To evaluate the reliability indices and probabilities of failure of foundation
designs for both ASWSS and adjourning natural soil in all cases using reliability
based computer program (FORM5).
iv. To categorize, from the results of ii and iii, the safety indices of ASWSS
foundation designs and the proportion of deviation from those of the natural
adjourning soil and make recommendations regarding the use of ASWSS for
developments.
1.5 Significance of the Study Despite large scale investigation of random fields for representative values, shear strength
characteristics and values so far reported in literature fall in an amazingly wide range as a
result of SWSS field variation in its geotechnical character. The design engineer will
therefore be in dilemma as to which value to adopt. Lack of the application of modern
and effective probability-based reliability methods in establishing the engineering
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behaviour of ASWS is partly responsible for the wrong selection of design data used in
the prediction of failure zones that are higher than the actual field values.
The design process of this study is illustrative and its results the direct products of
reliability-based handling of ASWSS and thus may be reliably applied in judgments and
decision making concerning the loads to be imposed on ASWSS sites. This will also save
the community, developers and a relevant professional body further loses from ASWSS
structural foundation failures and the embarrassment of being associated with such
failures in the practice.
1.6 Delimitation of the Study
The application of only the geotechnical aspect of foundation design based on Eurocode
7, Monte Carlo simulation and first order reliability method defined the analytical
boundary of the study. The structural component of foundation design which requires
second order reliability method (SORM) was not included.
A total of six abandoned solid waste sites (ASWSS), two in Kaduna North; two in
Kaduna South and two in the land between, were selected for study. This is due to the
facts of literature that have shown appreciable similarity among the results of studies
conducted on ASWSS. A depth range of 1.5 to 3.5m were selected for material sampling
and a scheme of geotechnical investigation was designed to include the
conduct/determination of: unit weight of soil, water content, direct shear box tests,
atterberg limits, triaxial compression tests, grain-size distribution, consolidation and
compaction test. Direct and indirect application of some of these measurements were
made in relevant models while others were used in comparative assessment of the states
of ASWSS and NS.
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Bearing capacity measurement is conspicuously absent from the list, and this is due to the
fact that there was no intention of considering stress imposition on ASWSS soil by
highway structures, though that may be a possible dimension of consideration.
Furthermore, special attention is often given to heterogeneous soil outcrop and
exceptionally weak formation in both design and construction of highways.
1.7 Limitations of the Study An overall or system reliability (SYSREL) evaluation requires the analysis of both the
geotechnical and structural components of foundation structure. A higher order reliability
method, however, is required for the structural analysis and this was not included in this
study because of lack of requisite knowledge of the author in structural reliability theory
and practice.
1.8 Research Questions To provide a direction and focus to the execution of this study the following research
questions are generated
(i) What are the differences between the engineering properties of ASWSS and those
of the adjourning natural soil and how do they compare with those reported in
literature?
(ii) What procedures are employed to arrive at the appropriate design values of soil
data?
(iii) How do the reliability indices and probabilities of failure of ASWSS compare
with those of corresponding natural soil in each case of design method?
(iv) What are the tolerances and levels of safety indices of ASWSS on the standard
expected performance classification table?
1.9 Organization of this Study
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This study is divided into five chapters, the first of which presents the problem and
current situation of ASWSS and advances some modern techniques and approaches in
design and statistical treatment of data to address it. It highlights the evolution and
improvement trend of these approaches and generates their application objectives to
achieve the overall purpose of the study within the defined measurement and analytical
ambits. It is concluded with a note on the potential weakness of the study, scholarly
limitations of the author, benefits and beneficiaries of the results of the study. The second
chapter describes mainly the published principles and practical approaches to a realistic
characterization of ASWSS and corresponding design methodologies that take into
account the randomly variable distribution of its soil character. In this section, the
principles of reliability-based design, their theoretical basis and validity and the
feasibility of their practical application are well discussed.
The third chapter relates to the plan for the execution of the study and contains briefs
under the following subheadings; design, subjects, instrumentation and
procedure/methods of data analysis. The fourth chapter presents a procedural model of
ASWSS data statistics and employs first order and Monte Carlo Simulation reliability to
predict the expected responses of ASWSS and its corresponding NS under differently
specified stress characterization. The fifth chapter is a brief that summarizes the salient
features of the study including key findings from modern design and analytical efforts to
discover the true state of ASWSS. It is concluded with relevant proposals on the possible
geotechnical and statistical solutions to the problems associated with the use of
ASWSS for developments.
32
CHAPTER TWO LITERATURE REVIEW
In a study of this nature, a review of existing knowledge, theories and outcomes of other
people’s works is unanswerably necessary. This chapter presents the published works
and results of other scholars and researchers and the relation which their procedures and
findings bear to this study in the following order of subsections:
• Properties of ASWSS;
• ASWSS as foundation soil;
• Safety analysis of ASWSS and
• Classification of reliability of ASWSS.
In this chapter the engineering phenomena taking place in the life of ASWSS, the
characteristics of its geotechnical properties and the factors modifying them are well
33
described. The purpose of this chapter, inter alia, is to establish a vocabulary for the
entire study and present brief accounts of new approaches to safety analysis of ASWSS
that address the problem posed by its inconsistent composition.
2.1 Properties of Solid Waste Soil The term waste refers to those materials that have negative value to its current owner
especially in its current form and location (Baccini and Brunner, 1991; Tchobanoglous et
al., 1993). Municipal solid waste entails wastes generated within a town, city or districts
and excludes those from commercial, industrial and building construction or demolition
processes. They are mainly the tangible by-products of domestic and council activities.
In a health conscious and organized society, solid wastes are found in strategically
located and designated dump sites called sanitary or landfills. These sanitary fills may be
owned and privately operated to accept waste only from the owner (on site) or operated
on behalf of municipal authorities and licensed to accept wastes from generators other
than owner (landfill). However in a poorly managed system, they may be found in
arbitrary and uncontrolled locations within or outside residential areas. Its unique
geotechnical properties which result from wide range of its material composition are of
primary importance in describing its engineering behavior. These properties may be
examined in three basic perspectives namely, classification, compressibility and shear
strength characteristics.
2.1.1 Classification of municipal solid waste Solid Waste classification is a system that allows the separation of Solid Waste
composition into its material types, identified in percentage by weight and could be
related or compared with similar data from different sources. A number of classification
systems obviously exist, but the basis for a choice of classification appears to be the
34
purpose and nature of composition. For the purpose of management and pollution control,
wastes may be classified according to the composition of its waste stream, disposal routes
and generating source. A comprehensive sample of this mode of classification is shown
in Australia Draft Solid Waste Classification of September 1993 in Table 2.1 For the
purpose of engineering services Solid Waste may be classified based on compositional
characteristics, aging level and degradation potential with reference to a particular
location in space or time along the continuum. When information is required on
variability characteristics of geotechnical properties of ASWSS due to degradation and
compressibility, then Landva and Clerk (1990) classification of SWSS into organic and
inorganic constituents becomes most relevant.
The material properties and grain size of a soil allow it to be assigned to one of the
limited number of classification groups namely clay, silt, sand, gravel and stone. The
particle size distribution curve actually reveals the composition of these groups in a
particular soil mass. However, there are larger particles in ASWSS than are commonly
found in soil and which are capable of influencing test results. Approximately then, two
approaches to the classification of material composition of ASWSS are necessary in
engineering measurement. The first approach is the general classification in which soil
component is treated as a single material. The second approach is the classification of soil
material portion into its standard groups, that is, stone, gravel, silt and clay.
35
Table 2.1: Australia Draft Solid Waste Classification (Tchobanoglous et al., 1993)
Proc./Disposal Route Waste Stream Principal Source
Sub-stream 1 Secondary Source
Sub-stream 2 Measurement/Transport mode
Sub-stream 3 Material Composition
1 Recycling A: Municipal Waste 1 Domestic waste 0 All, Weighbridge 0 Mixed 2 Composting 2 Other Domestic 1 Cars, station wagons 1 Paper/cardboard 3 Incineration 3 Other Council 2 Utes, p/vans, sgl axle
Trailers 2 Food/kitchen
4 Landfill 3 Ige utes, multiple axle Trailers
3 Garden
5 On-site B: Commercial. & Industrial.
0 Unknown 4 Open trucks, Gross wt < 5t
4.1 Wood
A Agriculture 5 Open trucks, 5t < Gr wt < 12t
4.2 Trees > 150mm dia
B Mining 6 Open trucks, Gross wt > 12t
5 Tyres
C Manufacturing 7 Compactors, bins<8m3
6 Glass
D Electricity, Gas and Water
8 Compactors, bins 8 – 12m3
7 Plastic
F Wholesale and Retail Trade
9 Compactors, bins 12 – 19m3
8.1 Ferrous – mixed
G Transport and Storage
10 Compactors, bins 19 – 32m3
8.2 Ferrous – car
HIJ Services sector 11 Compactors, bins >32m3
9.1 Special –Other
K Community services (hlth, ed)
12 Other 9.2 Special –Sewage sldg
L Recreation, Tourism 9.3 Special –Dusty waste C: Building. and
Demolition. X Waste processing Facility
9.4 Putrescible/Organic (K)
9.5 Asbestos (N220) 9.6 Clinical & Pharm. (R) 10 Clean fill (mixed) 10.1 Bricks 10.2 Concrete 10.3 Carpet 10.4 Plaster board 10.5 Non-ferrous-Al. 10.6 Non-ferrous-Other 10.7 Ceramics 10.8 Clean excavated
Matl 11 Other segregated
2.1.2 Compression characteristics of ASWSS The results of Bjarngard and Edgers (1990) analysis of settlement data from twenty four
(24) case histories explained the settlement pattern of ASWSS in three chronological
36
stages. In the first stage (immediate settlement), stress dependent primary settlement
occurs quickly within 300 days of stress application in reaction to the compression of
SWSS under loading conditions.
A linear relation with gentle slope is observed between strain and logarithmic time in this
settlement curve. This initial phase of settlement occurs in both new and old SWSS fills
and continues for a period of about one year after which decomposition in recent deposits
is activated. Acute degradation of organic composition sets in, with the resultant
production of leachate and gas, causing the development of destabilizing pore pressures.
The continuation of this phenomenon leads to a secondary phase of creep and non-stress
dependent long-term settlement. This phase accounts for the greatest part of SWSS
settlement and may be sustained for many years. Extraction of leachate and gas at this
stage especially in an engineered repository system may be carried out if the fill is to be
considered as the foundation ground for engineering structure.
In the absence of fresh deposits (in the case of abandonment) and after a sufficiently long
period of time (20 years and above), there is a drop in settlement scale (third stage) and a
linear strain/logarithmic time scale relation develops again with a minimal slope due to
gradually ending process of decomposition. Depending on the magnitude of loading , the
creep of non-degradable but compressible materials and residual decomposition of
organic substances may induce further but small scale settlement and progressive
redistribution of stresses at this stage. From the analysis of these three stages of
settlement, Bjarngard and Edgers (1990) modeled the settlement of SWSS as follows:
= ∆
+ () ()
()+ ()
()
() 2,1
37
Where = settlement, = initial thickness of landfill, = initial effective stress,∆ =
stress increment, = compression index (slope of strain versus logarithmic effective
stress), ∝ = coefficient of mechanical secondary compression and ∝ = coefficient
of secondary compression due to residual decomposition.
2.1.3 Shear strength characteristics of ASWSS The shear strength of ASWS is that property that binds its element together and enables it
to remain in equilibrium when its surface is not level as a result of a combination of inter
particle attraction and resistance to inter particle slip and mass deformation (Smith, 1998;
Bowles 1996). Shear strength which is often correlated to its parameters of cohesion and
angle of internal resistance, is of primary importance in describing the strength
characteristics of ASWSS.
It is often expressed using coulomb failure criterion as (Smith and Smith, 1998)
= ∅ + 2.2
Where = ℎ ℎ ,
= ,
∅ = ℎ
= ℎ
However the heterogeneous composition, time-dependent and inconsistent properties of
SWS have made its shear strength evaluation from field and laboratory measurements
difficult and costly.
Generally, the common approaches include triaxial compression test, shear box test, in-
situ tests (like CPT, SPT, etc) and back computation from plate loading test. The
conventional application of these test methods and their resulting data in ASWSS
38
investigation and foundation design has proved to be inadequate, unreliable and most of
the time bears no meaningful correlation with the field realities (Mitchell, 1993 and
Kavazanjian, 2001). This explains why foundation failures are recorded in ASWSS
despite claims of investigation. The question then is ‘what must be done to obtain design
input data that mimics approximately the geotechnical characters of ASWS’. The answer
to this question which is the focus of this study as well as of many other researches
currently going on in the area is provided in the next section.
2.2 ASWSS as Foundation Soil In training and practice, we have often considered significant randomness in the spatial
variation and distribution of geological materials; however, our presumed randomness is
that of our knowledge and models and not of geological formation (Baecher and
Christian, 2003). Geological formation is only random to the extent to which we are
ignorant of its actual and true physical conditions. The spatial order of geological
deposition is fixed once it has been made and cannot be shuffled except by seismicity and
very low rate modification due to weather fluctuations. This goes to show that probability
is actually not in nature but in our modeling of nature (Baecher and Christian, 2003).
Since our knowledge of nature is neither accurate nor complete, there is need to deal with
geotechnical uncertainties with some elements of randomness to make statistical
solutions applicable in the subject.
The statistics of geotechnical data therefore is a combination of the statistics of measured
parameters influenced by its sample size and the statistics of relative frequencies of
occurrences of random variables whose actual spatial order is not precisely known. The
gap between our perceived geotechnical properties of an investigated site and its true
physical conditions lies in (a) measurement and data representation errors resulting in
39
poor data representativeness (b) statistical imprecision associated with the use of
insufficient statistical raw data and (c) model imperfection resulting in inability to mimic
the exact physical behavior of geomaterials.
Quantitative evaluation of soil properties has revealed a great deal of variability in the
engineering behavior of geomaterials even within a particular site. Gregory and John
(2008) noted that ‘the wide ranges of the reported values are only suggestive of
conditions at a specific site’. Furthermore these observers (Gregory et al. 2008)
considered it appropriate to think about the impact of variability on safety by developing
the reliability index as:
=
= 1 2.3
Where = reliability index, = margin of safety (resistance minus load),
= Factor of safety (resistance divided by load), [.] = expected and standard
deviation. In this primary definition of reliability index, however, the two equations are
not identical except = 1 implying that = 0 also.
Equation 2.3 is theoretically an expression of the gap between expected performance and
failure state in number of standard deviations. The extent to which soil properties vary is
illustrated in Table 2.2 (Phoon and Kulhawy 2008).
Table 2.2: Coefficient of variation for some common field measurements (Phoon and
Kulhawy, 1996)
Test type Property Soil type Mean Units Cov(%) CPT Qt Clay 0.5 – 2.5 MN/m2 < 20 Qc Clay 0.5 – 2 MN/m2 20 – 40 Qc Sand 0.5 – 30 MN/m2 20 – 60 VST su Clay 5 – 400 kN/m2 10 – 40 SPT N Clay and sand 10 – 70 Blows/ft 25 – 50 A reading Clay 100 – 450 kN/m2 10 – 35
40
A reading Sand 60 – 1300 kN/m2 20 – 50 B reading Clay 500 – 880 kN/m2 20 – 60 DMT B reading Sand 350 – 2400 kN/m2 20 – 60 ID Sand 1 – 8 15 – 65 KD Sand 2 – 30 20 – 50 ED Sand 10 – 50 MN/m2 10 – 35 PL Clay 400 – 2800 kN/m2 20 – 50 PMT PL Sand 1600 - 3500 kN/m2 15 – 65 EPMT Sand 5 – 15 MN/m2 8 – 30 Wn Clay and silt 13 – 100 % 6 – 30 WL Clay and silt 30 – 90 % 6 – 30 WP Clay and silt 15 – 15 % –a Laboratory Index
PI Clay and silt 10 – 40 % –a
LI Clay and silt 10 % < 10 , Clay and silt 13 – 20 KN/m2 10 – 40; Dr Sand 30 – 70 % 50 – 70b
It is important to note that the variability in SWSS properties is much higher than those of
Phoon and Kulhawy’s (1996) report.
Table 2.2 shows unbelievably large values of coefficient of variations of measured soil
properties at a particular site. These values which are in their tens of percentage
correspond to reliability indices between one and two and have such high equivalent
probabilities of failure that are not reflected in any of the recorded rates of failure of
foundations or engineering structures.
Gregory and John (2008) attributed this inconsistency to spatial averaging and
measurement noise in natural soil. Where concern is focused on the application of the
mean value of natural soil properties in a particular geomaterial volume, low measured or
evaluated values are balanced by high ones and hence a consistent reduction in the
variance of the average is observed as volumes of measurements of geomaterial get
larger. Gregory and John (2008) rightly observed that ‘averaging reduces uncertainty’.
41
However this is only true if the volume of soil involved in foundation failure is similar to
the tested volume.
Measurement noise implies that variation of any degree in soil property data is a function
of actual variability in geological formation and measurement imprecision (random
error). In all cases, the random error has negative impact on the precision with which
average values may be estimated, though not in any way correlated to the spatial and
time-dependent variations in the properties of the natural geological formation.
2.2.1 Spatial variation in ASWSS In addition to inherent variability in soil properties, ASWSS is fraught with inconsistency
due to varieties of non-soil composition and their attendant influence on the measurement
of geotechnical characteristics of waste fills. In practice, the convention is to carry out
laboratory tests on soil sample passing through sieve number 4 in order to eliminate
‘larger than gravel’ materials capable of giving false measurement indication. Spatial
variation in ASWSS can be characterized in detail, but only with a large number of
observations which normally are not available (Gregory and John, 2008). A smooth
deterministic trend may be used to model spatial variation but in combination with
residuals about the trend. This model is described probabilistically by Gregory and John
(2008) as
= + 2.4
Where () is the actual soil property at location x (in multiple or single dimension),
() Is a smooth trend at and
() is the residual deviation from the trend.
42
In the same vein and in the absence of large number of observations to do otherwise, the
authors (Gregory and John, 2008) described the residuals as random variable of zero
mean and some variance:
= [− 2.5
in which () is the variance of the residual.
From the equation 2.4 and 2.5, the notion of the analyst is that spatial variation in the
properties of heterogeneous soil is probabilistically distributed between the trend of
variation and the residual variation about the trend.
2.2.2 Characteristic and representative values In the face of wide ranges of variability of properties of ASWSS, one of the most critical
decisions to make is that of selecting a representative value. The European standard (EN
1990) gave the definition of characteristic value of an action (loading) as ‘its main
representative value’ and this is specified as ‘ a mean value, an upper or lower value, or a
nominal value’ (Denys and Trevor, 2008). For a randomly variable and normally
distributed load, Denys and Trevor (2008) prescribe the characteristic value
corresponding to 95% fractile as:
= + 1.645 = 1 + 1.645 2.6
with the representative values of actions as: = 2.7
where = characteristic value of an actions (loading)
= Mean value
() = Coefficient of variation
= 1.0 or , or
with , and as combining factors with the non- leading variable actions
to account for persistent and transient design situations, the frequent value ( (
43
Qk) and the quasi-permanent value ( Qk). The values of these factors , and
are supplied in EN1990 especially in cases of snow and wind loads. In foundation design
calculation, the variable loads are much less significant than in many structural designs,
hence, a combination factor of unity is often applied, making the representative
actions equal to characteristic actions
The characteristic value of material property is defined by EN1990 as ‘the value
having a prescribed probability of not being attained in a hypothetical unlimited test
series ‘. EN1990 equally specified that ‘the characteristic value should be defined as the
5% fractile’. Assuming a normal distribution, the characteristic value is expressed as
= − 1.645 = (1 − 1.645 2.8
where is the mean value, is the standard deviation and is the coefficient
of variation of the unlimited test series, , and the coefficient 1.645 provides 5% fractile
of the results (Trevor and Denys , 2008). This definition of characteristic value and the
resulting equation 2.7 make a great deal of sense in structural analyses and design, where
the volume of structural element being designed and the tested volume are identical.
However, the wide margin of disparity between the soil volume involved in geotechnical
failures and the tested geomaterial volume may result in the predicted value of
violating the true and physical lower limit of an engineering field if equation 2.7 and its
definition are applied in geotechnical analyses. In ASWSS which is inherently variable
both in composition and properties, the occurrence of a limit state is influenced by the
mean strength value of soil, evaluated only from the relevant slip surface. The specified
5% fractile by EN1990 therefore, is not the 5% fractile of the tested soil samples but of
the mean strength value of only the soil mass governing that limit state. Further to the
44
above SWSS geotechnical peculiarity, the mean and standard deviation values arising
from limited test results and those of the land mass governing the limit state occurrence,
may be grossly divergent, leading to the violation of the lower bound if EN1990
definition is applied in its ordinary meaning. Hence EN1990 defines the characteristic
value of a soil property as ‘a cautious estimate of the value affecting the occurrence of the
limit state.’
Beside the application rule that ‘if statistical methods are used, the characteristic value
governing the occurrence of the limit state under consideration is not greater than 5%
fractile, Eurocode 7 provides no clue as how a ‘cautious estimate’ should be arrived at.
However, a historical expression of characteristic value of soil property,
= −
√ 2.9
by student (1908) was simplified by Schneider (1997) as = − 0.5 2.10 Where = mean value of soil property = Standard deviation = Student value (which is estimated from the number, N, of test values and the
anticipated confidence level).
A practical rule proposed by Duncan (2000) is that conservative estimates of the worst
( ) and best ( ) values should be made based on the level of variability of soil
property, and the standard deviation obtained from the expression
= − /6 2.11
The characteristic value may then be calculated from equation 2.8
( = 1 − 1.645 )
2.3 Safety Analysis of ASWSS
45
The summary requirements of all design codes are that structural and foundation designs
and their execution should ensure that all actions and conditions of use and operation are
sustained with acceptable levels of reliability and cost effectiveness.
In pursuance of this, Europeans standards, that is Europäische Norms (EN 1990) has
adopted the concept of limit state design to ensure that a state beyond which structures,
foundations or their elements no longer fulfills any of the operational design criteria is
satisfactorily unlikely. Two limit states are considered in this regard. They are ultimate
limit state (ULS) and serviceability limit state (SLS).
Ultimate limit state, Trevor and Denys (2008) define as ‘those situations involving safety,
such as the collapse of a structure or other forms, including excessive deformation in the
ground prior to failure, causing failure in the supported structure, or where there is a risk
of danger to people or severe economic loss.’ According to the same authors (Trevor and
Denys, 2008), ‘serviceability limit state corresponds to those conditions beyond which
the specified requirements of the structure or structural elements are no longer met.’In
foundation work and designs the description of geomaterial behavior at the instance of
limit state is paramount in ensuring that the occurrence of limit state is satisfactorily
avoided.
Traditionally, avoidance of ULS and SLS are often done separately using different
calculation models, but the difference actually lies in the fact that the strength properties
of soil are used to analyses failure mechanism as a check on ULS violation, while soil
compressibility and deformation analyses check the SLS violation. In foundation design
ultimate limit state is typically represented by the ultimate bearing capacity of the soil
while SLS pertains to performance requirements and is checked by applying a partial
46
factor of unity to characteristic service loads and load effects. This limit states definitions
and the reliability-based evaluation of design values of action effects and soil tolerances,
establish the safe region of ASWSS designs.
2.3.1 Risk and reliability analysis Risk-based decisions are made more accurately if the probabilities of potential outcomes
of undesirable events can be predicted and the magnitude of their consequences
quantified with precision. Such decision making begins with the assignment of a measure
of probability of occurrence to an uncertain event, followed by the attempt to estimate the
magnitude of the associated adversity. Risk, even in the ordinary usage, is defined in
terms of uncertain scenario and the consequences of its occurrence, that is
= , = , 2.12
It has the sense of an event in view, the probability of that event materializing and the
consequences of the event’s materialization. The definition and measurement of risk
differ from one discipline to another. In health management for instance, risk is the
probability that people will contact certain disease in the circumstance of vulnerability. It
is the fractional measure of the adversely affected, out of those exposed to such pathogen.
Risk in this circumstance is modeled as equal to probability, that is
= = 2.13
In insurance policy administration, the risk in respect of an insured vehicle against total
loss in the event of theft is equal to the total cost of replacing it. Here risk is modeled as
equal to consequence, that is
= = 2.14
However, in the contexts of engineering, risk is defined as the product of probability and
consequence, that is
47
= = 2.15
(Baecher and Christian 2003).
These definitions appear simple, but their integration into analytical and design models of
engineering facilities is something else.The term ‘acceptable risk level’ has been used
several times to make the various application of risk assessment exhibit regularities, but
not even the government of united state acting through her congress has been able to
define ‘acceptable risk levels’ for civil infrastructure (Baecher and Christian 2003). This
appears to have been left to the professional discretion of relevant regulatory agencies.
Generally, lower risk levels are commonly associated with higher costs, but the
interesting flexibility in engineering is the fact that risk levels may be lowered
considerably to mitigate the huge consequences of failure or raised to achieve economy.
In civil engineering, risk is often evaluated in terms of probability of failure. The
uncertainty in the ability of a system to carry its designed load is reflected in the
difference or harmony between the expected and observed performance of the system
during the reference period of interaction. This ability, which includes the uncertaintities
in the determination of both the force effects and ground resistance, is commonly
expressed in the form of reliability index or probability of failure. However the
uncertaintities in the determination of the load (Q) and resistance (R) have made their
values uncertain and thus having such statistical descriptors as mean , expected value
( [ ]), standard deviation , coefficient of variation Ω =
, variance , correlation
coefficient ρ and covariance cov[ ].
48
Irrespective of the probability distribution of the load () and the ground resistance (),
two performance functions are applicable in geotechnical reliability analysis. They are
margin of safety and factor of safety, with
= − 2.16
and
= / 2.17
Applying equation 2.16 in the definition of reliability index, the mean value and variance
of are − 2.18
and = + - 2 2.19
respectively.
Reliability index which expresses the linear departure of from its failure surface
( = ) in units of standard deviation is defined as
=
=
−
–
− 2
2.20
This definition of β is typically illustrated in Figure 2.1a for probability densities of
and and in Figure 2.1b for margin of safety ( ).
Prob
abili
ty d
ensi
ty fu
nctio
n (P
df)
Load
()
49
Distribution of & Figure 2.1a Probability densities for &
Figure 2.1b Probability density for
However, if the performance function of factor of safety is used then
= 2.21
Failure occurs when the value of F is unity, that is = 1 and a reliability index is
expressed as = − 1 2.22
Expressing the ratio of two uncertain elements as in the case of equations 2.21 and 2.22 is
obviously more difficult to solve than when their difference is simply required. Baecher
and Christian (2003) reported that ‘some researchers have assumed that R and are log
normally distributed (that is, the logarithm of R and are normally distributed) so that
the logarithm of their ratio becomes the differences between their logarithms.’ The
expression for in this regard becomes identical with Equations 2.20 - 2.21. In design
( )
Failure zone (i.e. probability of failure pf)
50
and analysis, the performance of a geotechnical structure is described by either or
called the performance function. The statistical distribution of either or is important
in the evaluation of the reliability index .
A normal case of distribution is applicable when or logarithm of is normally
distributed, that is, in a sequence of observed or logarithm of the values cluster
around a central one, with smaller deviations of additive nature occurring more
frequently than larger ones (Kottegoda and Rosso, 1997; Baecher and Christian, 2003).
When evaluated from Equation 2.22 and in terms of , lognormal case is applies, that
is, a multiplicative effect of deviations from the central value is observed. Gamma
distribution applies if additive nature of the squares of errors is observed while
symmetrically triangular gives rise to a triangular case of distribution (Baecher and
Christian 2003; Kottegoda and Rosso, 1997). Table 2.3 gives values of the probability of
failure for some distributions of performance function and for a range of reliability index.
Table 2.3: Probability of failure for various distribution of performance function
(Baecher and Christian, 2003)
Probability of failure
Reliability index
Normal distribution
Triangular distribution
Ω = 0.05 Ω = 0.10 Ω = 0.15
0.0 5.000 x 10 – 1 5.000 x 10 – 1 5.100 x 10 – 1 5.199 x 10 – 1 5.297 x 10 – 1 0.5 3.085 x 10 – 1 3.167 x 10 – 1 3.150 x 10 – 1 3.212 x 10 – 1 3.271 x 10 – 1 1.0 1.586 x 10 – 1 1.751 x 10 – 1 1.583 x 10 – 1 1.571 x 10 – 1 1.551 x 10 – 1 1.5 6.681 x 10 – 2 7.513 x 10 – 2 6.236 x 10 – 2 5.713 x 10 – 2 5.111 x 10 – 2 2.0 2.275 x 10 – 2 1.684 x 10 – 2 1.860 x 10 – 2 1.437 x 10 – 2 1.026 x 10 – 2 2.5 6.210 x 10 – 3 0.0 4.057 x 10 – 3 2.298 x 10 – 3 1.048 x 10 – 3 3.0 1.350 x 10 – 3 0.0 6.246 x 10 – 4 2.111 x 10 – 4 4.190 x 10 – 5 3.5 2.326 x 10 – 4 0.0 6.542 x 10 – 5 9.831 x 10 – 6 4.415 x 10 – 7 4.0 3.167 x 10 – 5 0.0 4.484 x 10 – 6 1.977 x 10 – 7 6.469 x 10 – 10 4.5 3.398 x 10 – 6 0.0 1.927 x 10 – 7 1.396 x 10 – 9 4.319 x 10 – 14
Log Normal distribution
51
5.0 2.867 x 10 – 7 0.0 4.955 x 10 – 9 2.621 x 10 – 12
The results showed on table 2.3 reveals a non-consistent relationship between and
for the various distributions. For small values of , however the probability of failure
exhibits just little difference. Generally, the assumption of a Normal distribution is rather
conservative for most range of reliability index, and this explains why most designers opt
for Normal distribution especially when it is difficult to ascertain the exact distribution of
performance function.
2.4 Classification of Geotechnical Category EN 1990 presents three classes of consequences of failure with the introduction of three
Geotechnical categories accounting for their varying degree of safety. These are
Geotechnical categories 1 (GC1), 2 (GC2) and 3 (GC3) for low, medium and high
consequences of failure respectively. Geotechnical category 1 relates to simple structures
requiring basic and empirical design procedures and qualitative site analysis to achieve
the required reliability. The general expectation here is that of negligible consequences of
failure but where the ground condition, for instance, poses risk to property and life, this
part of the structure may be assigned a higher category to cater for the risk.
Geotechnical category 2 relates to structures requiring quantitative data to achieve the
necessary reliability, from a thoroughly investigated normal ground not prone to
exceptional risk or difficulty. Eurocode 7 partial factor design and first order reliability
methods may be employed in both design and safety assessment procedures.
Geotechnical category 3 relates to large structures and exceptionally difficult site
conditions, prone to high risk of failure. Eurocode 7 recommends extra provisions to
cater for the associated abnormal risk in addition to the provisions of Eurocode 7 which
are the minimum requirements.
52
Table 2.4: Geotechnical Categories related to geotechnical hazards and vulnerability
levels (Orr and Farrell, 1999)
GC1 GC2 GC3 Expertise required Person with
appropriate comparable experience
Experienced qualified person
Experienced geotechnical specialist
Geotechnical investigations
Qualitative investigations including trial pits
Route investigations involving borings, field and laboratory tests
Additional more sophisticated investigations and laboratory tests
Design procedures Prescriptive measures and simplified design procedures, e.g. design bearing pressures based on experience or published presumed bearing pressures. Stability or deformation calculations may not be necessary
Routine calculations for stability and deformations based on design procedures in EC7
Conventional: Examples of structures
• Simple 1 and 2 storey structures and agricultural
• Spread and pile foundations
• Walls and other retaining structures
• Very large building
• Large bridges • Deep excavations • Embankments on
53
buildings having maximum design column load of 250kN and maximum design wall load of 100kN/m
• Retaining walls and excavation supports where ground level difference does not exceed 2m
• Small excavations for drainage/pipes .
• Bridge piers and abutments
• Embankments and earthworks
• Ground anchors and other support systems
• Tunnels in hard, non-fractured rock
soft ground • Tunnels in soft or
highly permeable ground
It is not surprising that Eurocode 7 is silent on the detail reliability requirements of the
Geotechnical categories since the local authorities in the possession of local knowledge
have the prerogative of national or local guidance.
However, from the understanding that a reliability index lower than 2.5 is seldom used in
design, except for minor and unimportant structures and the fact that EN 1990 specifies a
target reliability index of 3.8 for representative structures for a reference period of fifty
(50) years, it suffices to suggest reliability indices of 2.5, 3.5 and 4.5 for Geotechnical
categories 1,2 and 3 respectively. This means that the assignment of a structure to a
particular Geotechnical category may be done to achieve cost effectiveness or higher
level of reliability as the case may be. However, not all parts of a structure need be
assigned the same category. Any exceptionally difficult part like poor or difficult
supporting ground may be assigned a higher Geotechnical category. The essence of the
54
classification based on Geotechnical category presented by EN 1990 is to make provision
and cater for material and design conditions capable of posing risk of failure.
CHAPTER THREE PLAN AND METHODOLOGY
Applying conventional and simple methods in describing the properties of homogenous
formation makes much sense. However, in a complex and heterogeneous field of soil and
non-soil material composition like ASWSS, such methods obscure the geotechnical
identity of the tested sample while erratic departure of the interpolated properties from
their actual field values of unobserved locations results. Employing geotechnical
reliability in characterizing and designing on such fields is, no doubt, rigorously based.
However, the current simplification of reliability – based design (RBD) is gradually
giving it an emerging structure that is quite accessible to practical application. Additional
tools and effort are required to meet the challenges of the compositional nature of
ASWSS. This chapter highlights the proposed scheme of execution and distribution of
such efforts in the following subsections:
• Location of study area
• Design of study
55
• Population and sampling techniques
• Instruments for data collection and administration
• Procedures and methods of data analysis
3.1 Location of Study Area The study was conducted in Kaduna, the capital city of Kaduna state. Housing well, over
one and half million (1,500,000) people of diverse ethnic background, Kaduna is one of
the oldest cities of the Northern Nigeria. The township spans about twenty-eight
kilometers (28km) in length and about nineteen kilometers (19km) in breadth having a
total land area of about fifty three thousand hectares (53,000ha). It is topographically
shaped into a trough with Kaduna North and Kaduna South Local Government Areas
(LGAs) occupying the two peaks of the trough respectively. River Kaduna runs along the
lower region of the trough, dividing the township into two parts. The life styles of the
residents of Kaduna North and Kaduna South LGAs are not exactly identical as a result
of ethnic, religious and socio-economic differences and so also waste generation and
environmental health consciousness. For the purpose of this study, the township was
divided into three zones with Kaduna North and Kaduna South LGAs forming zones A
and B respectively while the area along the lower region of the trough forms zone C.
Two sites, 1 and 2 were selected for zone A, with site 1 in Tudun-wada and site 2 in
Malali. Two sites were equally selected for zone B; site 1 in Sabo and Site 2 in Kakuri.
Zone C has its first site in Costain while the second in Nassarawa. All the sites were older
than 20 years. Site 1 of zone A is a 33year old and abandoned solid waste dump site
56
situated inside a tertiary institution. It is the site of the failed students workshop structure
originally designed to house mechanical engineering facilities. Its long years of
abandonment have given it a surface value akin to that of natural ground. These sampled
areas are shown in Figures 3.1a and 3. 1b while the actual locations of the trial pits are
shown in Plates 1 – 6.
57
58
59
Plate 1: Site 1 of Zone A at Tudun Wada, Kaduna Nigeria
Plate 2: Site 2 of Zone A at Malali, Kaduna Nigeria
60
Plate 3: Site 1 of Zone B at Sabo, Kaduna Nigeria
Plate 4: Site 2 of Zone B at Kakuri, Kaduna Nigeria
61
Plate 5: Site 1 of Zone C at Costain, Kaduna Nigeria
Plate 6: Site 2 of Zone C at Nassarawa, Kaduna Nigeria
3.2 Design of Study The study was targeted mainly at old and abandoned SWSS and as such fresh and most of
the serving ones did not fall in the category. All the selected sites for the study were
62
either old and abandoned or sufficiently surrounded by developments to be considered for
abandonment in the near future. The spread of the test sites was specifically developed to
capture the diversities in the inhabitants’ ethnic, cultural, religious and socio-economic
settings and the possible reflection in waste generation and consequently in the
degradation of soil properties.
It is obvious that the evaluation of load effects and soil resistances are often coupled in
both structural and geotechnical engineering but the properties, geometry and spatial
distribution of geomaterials are, most of the time, poorly discovered. The ancient
observational method applied in monitoring the impact of uncertainties in the response of
structural foundation soil is quite compatible with the current geotechnical reliability. The
general concern is how the geotechnical reliability can be applied in ASWSS
investigation and design with confidence. A choice of combination of methods is
necessary from the wide range of approaches available from the libraries of geotechnical
reliability literature.
The study was developed to steer a middle course between a rigorous mathematical
presentation, typical of statistical approach and a purely observational and practical
assessment upon which geotechnical engineering discipline was founded. The current
acceptance and application of moderate statistical methods in geotechnical engineering
has dismissed the fear that further complexity in mathematical treatment of soil data
would render the field and laboratory efforts towards predicting and inferring the
geotechnical state of soil materials to mere statistical exercise.
63
The field investigation revealed among other things, the extent to which the natural
ground properties had been altered by the presence of ASWSS and the approach to this
study therefore was designed in the following order:
• assessment of the properties of ASWSS and adjoining natural ground;
• evaluation of design values of ASWSS and natural soil properties;
• reliability-based evaluation of safety indices using computer programs MATHLAB, and
FORM5 respectively and
• comparative classification of safety indices of ASWSS and adjoining natural ground.
3.3 Population and Sampling Techniques The reaction of ASWSS under leading is important in this study; hence all the properties
relating to the strength and compressibility were investigated. These included the
conduct/determination of particle size distribution, unit weight of soil, water content,
Atterberg limits, direct shear box test, triaxial test, compaction test, small and large scale
consolidation tests. In most research works the constraints of such resources as skill,
finance, and time make the study of every element in a population almost impossible.
This is especially so with geotechnical and spatial observations. A population sample is
necessarily selected for study in order to obtain the estimates of population parameters or
characterize the entire population distribution without observing and measuring every
element in the sampled population (Baecher and Christian, 2003). Interestingly the
enterprise of sampling is a common feature in many scientific and engineering
endeavours and as such similar situations are met in different activities. The underlying
factor is the development of a sampling plan that models the population properties of
interest to an acceptable precision. Baecher and Christian (2003) define sampling plan as
64
‘a program of action for collecting data from a sampled population’. In all cases attempt
is made towards maximizing the utility of the adopted sampling plan.
The subjects of geotechnical observations often display spatial or even temporal structure
and hence the elements are expectedly not identically distributed. From the description
and understanding of ASWSS, it is sufficient to assume that ASWSS has a heterogeneous
population over any area of occupation, but can be stratified into subpopulations that are
individually consistent. In this regard, the three zones (A, B and C) mentioned in
subsection 1 of this chapter constitute the population strata with each stratum internally
and consistently unique in terms of material composition. A plan of ‘Stratified Random
Sampling’ whereby precise estimate of the properties of stratum made from random
sampling was applied.
The mean of the total sampled population is (Thompson 2002).
= 1
3.1
Where the population mean, m is is the number of strata, h denotes the stratum, N is the
size of sampled population, Nh is the size of the hth stratum and is the mean of the
stratum. An estimate of the variance of the total population is
= 1
+ 3.2 Where is the sample variance, since the sample from each stratum is simple random
the estimate of the variance within each can be obtained from (Baecher and Christian
2003).
65
= 1
− 1
− 3.3 Where is the sample variance, n the sample population size and sample value.
3.4 Instruments for Data Collection and Administration Erroneous interpretation of subsurface geology may result from a combination of natural
variability and inconsistency in the properties and composition, misrepresentation of soil
data due to wrong measurement indications, model and transcription errors and
inadequate representativeness. A chosen instrument for data acquisition must be such as
reduces the probability of occurrence of any or all of the sources of errors in addition to
that resulting from erroneous or insufficient data about the end result of the physical
phenomena that form and modify the geological materials in ASWSS.
The summary of a large literature on the assessment of ASWSS shear strength
characteristics is that the indicated penetration resistance of in situ tests does not have a
meaningful correlation with the actual shear strength of ASWSS (Mitchell 1993). On the
other hand, the apparently large strain sustained by ASWSS without reaching failure
point in a triaxial test which is generally efficient for the evaluation of shear strength has
made the test method independently unreliable for ASWSS since strength in this case
relates directly to levels of strain. A combination of triaxial/shear box and other related
laboratory tests and assessment of the properties of ASWSS of the study area were
employed. .
3.5 Procedures and Methods of Data Analysis Most of the misrepresentation of soil data from the investigation of a complex field like
solid waste sites comes mainly from wrong methods of properties assessment and data
handling. ASWSS is mostly heterogeneous in outcrop and must be treated as such in all
66
evaluations except otherwise revealed by field examination. A chosen method of data
acquisition should be such that addresses field situations. A soil mass may be layered by
different soil groups (sand, silt, clay etcetera) or Φ-c values. The thickness of each
stratum is important in evaluating the mean values of the properties. It is misleading to
average values of properties of different strata without accounting for the geometry or
proportion of each stratum in the soil mass. Rational and empirical approaches have been
employed to establish methods for evaluating the shearing resistance of soil. Each
method seems to be based on certain field situation. This principle is very much useful
and is adopted in difficult engineering fields like ASWSS.
3.5.1 Determination of engineering properties Repeated observations and laboratory check measurements help to detect blunders or
mistakes. Out of the repeated observations and measurements any single value that
appears out of order is usually assumed to contain mistakes and hence expunged from the
set. A simple mean of the remaining measurements is taken as the value of the measured
property. In the design of this study, observations and determination of soil properties are
made at every 0.5m interval of depth. Bowles (1997) noted that ‘an increase in shear
strength with depth could be approximated by addition of soils with the same Φ and γ
properties but increased cohesion.’ However if a number of thin layers of Φ - c soils are
encountered, Bowles (1997) recommends that the average value of the measured property
be obtained thus:
= + + + − − − +
∑
∅ = ∅ + ∅ + ∅ ± − − − − − − − − ∅
∑
67
Where = cohesion in stratum of thickness Hi, ΦI = angle of internal friction in stratum
of thickness, Φ may be zero.
In the same way, the mean unit weight of Soil (γ) may be obtained thus:
γ = γ + γ + γ − − − + γ
∑
3.5.2 Design values of soil data According to Eurocode 7, ultimate limit state (ULS) design calculation should ensure that
the action effects, , does not in anyway exceed the design resistance, that is
≤ 3.7 Eurcode also recommends that the SLS calculation should ensure that the design action
effect, (e.g. settlement), should be below the allowable maximum deformation .
ℎ , ≤ 3.8 Denys and Trevor (2008) noted that ‘While using the partial factor method in ULS
calculation and assuming the geometrical parameters are not factored, the and may
be obtained either by applying partial action and partial material factors, and
respectively, to representative loads, and characteristic soil strengths, or partial
action effects and the resistances calculated using unfactored representative loads and
characteristic soil strengths’. That is
= ,
, 3.9 and
= ,
, 3.10
or
= , , 3.11 and
= , , / 3.12
68
The study adopted Duncan (2000) expression for computing the standard deviation
from the best value and the worst value as indicated in equation 2.11, that is,
= −
6 .
The characteristic value of soil property is obtained using equation 2.8 which is indicated
as = − 1.645= 1 − 1.645.
In a similar way the characteristic and representative values of action effects is obtained
from equations 2.6 and 2.7 respectively.
3.5.3 Evaluation of reliability index and probability of failure
Evaluation of reliability index and probability of failure begins from the formulation of
relevant limit state equations with the characteristic values of soil properties and the
representative values of action effects.
FORM and MCS analysis were performed for spread foundation in drained conditions of
ASWS and hence the action effect and bearing resistance for these conditions are (Trevor
and Denys, 2008).
E = Fu = G + Q 3.13
The mean value of the bearing resistance being
= = = + ɤ + 0.5ɤɤɤɤ 3.14
µR = + ɤ + 0.5ɤɤɤɤ 3.15
3.5.4 Reliability analysis using Hasofer – lind approach (FORM) Reliability analysis using FORM and its extension by the Rosenblueth (1975) Point-
estimate methods is hinged on two assumptions that are not entirely valid within the
ambit of both theoretical and practical application of reliability theory. One of the
69
assumptions is that it is possible to carry out the linear extrapolation of the moments of
the failure criterion from an origin defined by the mean values of the variable (it is
estimated from the evaluation of partial derivatives). The second is assuming the form of
the distribution of the statistical moments of performance function (factor of safety or
margin of safety ) to compute probability of failure Pf and reliability index , whereas
the distribution is not even known.
Hasofer- Lind addressed these problems by reformulating the equations of the uncertain
quantities in terms of dimensionless variables having zero mean value and standard
deviation of unity. This gives rise to a different definition of reliability index which is
geometrically interpreted as the distance between the point defined by the expected
values of the variables and the closest point on the failure surface.
If there are η uncertain variables while is defined in terms of its mean value µxi and its
standard deviation , we can define a primed and dimensionless variable as
=
−
3.16
= +
Applying this to the basic reliability case of a system having a resistance R and under a
loading effect of Q, then
= −
3.17
= −
3.18
In a case of uncorrelated and and applying a particular moment of failure function
like that of margin of
70
, = − = − + − = 0 3.19
Appling this expression, a plot of the failure criterion using the reduced variables as the
axis is shown in Figure 3.3
The distance (d) between the origin and failure surface is given as
= −
+
= 3.20
The evaluation of reliability index consists in finding the point along the failure surface
at which the value of is minimal. It must be noted however that the failure surface is
not always linear; it may be convex or concave.
R1
Figure 3.3 Plot of Resistance () and load () showing the definition of reliability index
The Hasofer – Lind formulation has the merit that it does not require that the distribution
of the failure function be found.
In multidimensional space of more than two variables as seen in the evaluation of bearing
capacity of soil
= +
+ … … … . . + ″ = ( x ) 3.21
Failure surface Q1
d
Origin R1
71
Where I is the vector of and indicates the transpose of a matrix or vector. The
problem then is the minimization of with the constraint that g () = 0 is satisfied. This
is what the evaluation of reliability index entails.
The above minimization (subject to the stated constraint) by Lagrange Multiplier
approach yields.
= = ∑ ∗, ∂
∂∗
∑ ∂∂
∗
3.22
The superscript or subscript star indicates that the evaluation of the derivative is done at
the closest point on the failure surface. Taylor series approach equally minimized
identically with the Lagrange Multiplier Approach, as
= =
= −
∑ ∗∂
∂∗
∑ ∂∂
∗
3.22
3.5.5 Solution of reliability index equation
It is understood from equations4.1 ( g ) and 4.1(ℎ) that the subscript or superscript star
means that the equations must be evaluated at the nearest point on the failure surfaces.
The issue is finding this point on the failure surface. In a linear failure line it is simply the
perpendicular offset from the failure line to the origin. However not all failure criteria are
linear as observed earlier. In the Lagrange Multiplier Approach, Baecher and Christian
(2003) define the gradient of the failure function in terms of the primed variables, that is
72
= ∂g
∂X,
∂g
∂X … … … … … … … …
∂g∂X
3.24
They went further to observe that since g (X1) = 0 at the point to be found, minimizing d
is equivalent to minimizing L in the following equation
= + λ = ( ) + λg X 3.25
Where λ is the Lagrangian multiplier having zero value at the solution point, making the
minimum value of and to be the same. For or d to be of minimum value, all their
partial derivatives must equate to zero, that is
∂∂
= 0 ∂g
∂ = 0 3.26
Baecher and Christian (2003) normalized the expression for G in equation 3.16 into a unit
rector where
=
()
3.27
and
= ∂g
∂ .
∑ ∂g∂
3.28
Therefore the coordinates of the failure point at which the unit vector α is evaluated is
∗= − ∗ 3.29
Ang and Tang (1990) used Rackwitz algorithm to itemize the procedure for solving for
in equation 4 (ℎ) above into six interactive steps as follow:
Step 1. The solution of starts from assuming the initial values of . This is usually
taken as the mean values of the variables. For example, in bearing capacity computation
xi will be the mean values of the angle of internal resistance of the soil(Ø), the cohesion
() and the unit weight of the soil ().
73
Step 2. This step consists in obtaining the partial derivative of the failure function with
respect to each variable. The mean values are substituted into the equation to obtain an
absolute value of each partial derivative. For insistence
∂g∂ =
∂g∂ , 3.30
represents the partial derivative (with respect to cohesion ) of the failure function
involving the general bearing capacity equation. This is done also for and and the
mean values are substituted to obtain the value of each derivation that is and
=
Φ
The values for are also obtained as
= ∑()
=
Φ
Φ = Φ
Φ
=
Φ
=
Φ
Step 3: The values for , and are substituted in the expression for the new
transformed design point
∗ = − to obtain a simplified expression for ∗
containing only the
unknown variable .
Step 4: The expression in step 3 above is substituted into the general failure equation
74
(∗, ∗
, … . . , … ) = 0 and the value for is obtained using FORM5 or
MATLAB.
Step5: With a known value for , the new coordinates for the failure point are obtained as
∗ = − Step 6: Steps 2 to 5 are repeated, replacing the initial value of xi with the new ones obtained from = − until convergence is achieved. For this thesis, a performance function of margin of safety (M) is chosen. Therefore the
failure criterion is expressed as
- Qγ = M derived from limit state equation
- Qγ = 0 Where = factor for resistance
= factor for load effects = resistance effect = load combination
3.5.6 Reliability analysis by Monte Carlo simulation (MCS)
The current advancement and refinement in reliability engineering are inter alia
responsible for the fast migration from intuitive and gut feeling decision making to that
based on verifiable scientific analysis of relevant material/system operation data.
Among the recent variety of statistical methods of reliability analysis, Monte Carlo
simulation is one of those noted for its simplicity and high prediction precision.
The first mention of Monte Carlo simulation was at Los Alamos National Laboratory
where atomic scientists developed the techniques to study the random diffusion of
neutrons in an atomic bomb program. The model was named after the city in Monaco
(PC, 2015).
MCS may be used to carry out simulation of fundamentally stochastic processes as well
as solving non-stochastic problem with random variable (Baecher and Christian, 2003). It
is used in structural reliability to model the behavior of a load carrying component from
the statistical distributions of simulated failure and safety points.
*
75
It is easily noted that structures designed and constructed to higher reliability levels may
not be cost effective while those with higher probability of failure are simply unsafe.
Among many factors on which reliability indices depend, ground conditions and their
wide scatter are notably prominent especially in ASWSS. This accounts for the grossly
misleading results of conventional methods of ASWSS properties assessment and
evaluation.
MCS method requires the use of a computer for deterministic evaluation of a simulation
function at a large number of points. The sequence of these pseudo random and
uniformly distributed numbers may be generated from a linear congruential algorithm (I1,
I2, - - - - - Ii, Ii +1 , - - - - , In ) in which Ii + 1 = a Ii + c (mod m) 3.31
The ‘mod m ‘in equation 3.31 indicates that the function is to be evaluated to modulo m
in which the result is divided by m and only the remainder retained while a and c are
constants (Beacher and Christian, 2003)
In engineering application, m may be chosen to be the maximum value of uncertain
variable and must be carefully selected with a and c to ensure sufficiently long and non
repeating sequence that enables the generation of large number of points while
maintaining some semblance of field range of the variable.
In a simplified application of the algorithm, c = 0 so that the value of any generated
point depends only on the previous one and constant a. In a function of uncorrelated
variables the criterion to be satisfied, as in ultimate limit state (ULS) simulation may be
defined as ≤ and the probability of failure Pfuls is the ratio of the number of times
in which the ultimate limit state is violated to the total number of simulation, that is
Pfuls is the ratio of Nfuls to N (Trevor and Denys, 2008), that is
76
=
3.32
It may equally be checked that the evaluated settlement Ed does not exceed the maximum
allowable value Cd, and thus SLS criterion to be satisfied is Ed ≤ Cd (Eurocode 7, 1990).
In the SLS simulation, the number of occurrence for which Ed > Cd, (Pfsls, is counted
against the total number of SLS simulations (N) and the estimated failure probability, Pfsls
is the ratio of NfSLS to N, (Trevor and Denys, 2008), that is
=
3.33
The application of MCS in these ways assume statistical independence of the uncertain
variables, which is practicably invalid with soil properties, and may result in
underestimation of the probabilities of potential outcomes of unfavorable events. In many
official applications, the uncertain soil variables are correlated and MCS must therefore
be structured to generate correlated sequence (Baecher and Christian 2003; Phoon, 2008).
Correlated Random Number
Thousands of generated numbers for each of n random variable may be related to another
set of variable. If X and Y are related to each other and consist of n random variables
with standard Normal distribution, their correlation matrix k may be written as
=
1 − − − −
1 − − − −
− − − − 1
in which Pij is the correlation coefficient between i and j and can be factored into an
upper triangular matrix S and its lower triangular transpose ST and thus, STS = K
(Baecher and Christian, 2003). In Morgan and Henrion (1990) simplified model, that is
77
exclusively typical of two variable, it is shown by Cholesky decomposition that if x1 and
x2 are a pair of Normally distributed and correlated variables y1 and y2 are
=
= + 1 − 3.34
Baecher and Christian (2003) noted that for each sample, two random numbers, x and y
with standard normal distribution may be generated while a third random number Z that
is correlated to x may be generated using Cholesky decomposition:
= . + 1 − 3.35
and the values for x1 and x2 for the sample are then
= + . 3.36
= + . 3.37
These computed values of x1 and x2 are used to generate one sample of margin of safety
M from
= −
Where
= mean margin of safety
= mean resistance
and = mean force effects
Reliability index for uncorrelated force effects and resistance is given by
=
=
3.38
However, if R and E are correlated then
78
=
=
3.39
Where = correlation coefficient between R and E
,
= variance of R and E
= standard deviation of M.
3.5.7 Regression analysis of ASWSS and NS properties
The large volume of tests required in principle to characterize an engineering site in detail
far exceeds what may be practically, financially or temporarily acquired (Baecher and
Christian). It is more convenient to apply a tested mathematical model in defining the
properties of unobserved locations of a spatial field. The simplest way to observe the
trend of a set of observed soil data is to plot its horizontal or vertical extent and run a line
along its mean trend. The uneven nature of residual variation of the plot about the
interpolated mean trend is a measure of uncertainty in the interpolation and this variance
reduces and the interpolated trend approximates the data plot more closely as the fitted
mathematical model (straight line, quadratic curve or polynomial) becomes more refined.
The statistical interpretation of the mean, standard deviation and correlation coefficient
are no accurate means of distinguishing two sets of measurements of the same data in the
same order of spatial variation. In their usual form of data combination, spatial details are
lost to the detriment of the adopted analytical model, not withstanding whether
numerical, graphical or statistical approaches are employed. What is needed therefore is a
mathematical relationship that captures the relevant statistical descriptions and allows the
prediction of one variable for a known value of the other (Baecher and Christian 2003).
Regression analysis meets this demand more rationally in geotechnical observations.
79
The undrained strength of ASWSS increases with pre-consolidation pressure as one goes
down the depth. If observed data exist to establish the quantitative relationship between
undrained strength and depth of stratum, this fact and the information generated from
data can be used to formulate a mathematical relationship that would allow the pattern of
increase in undrained strength of ASWSS to be modeled with increase in depth. This is
precisely what regression analysis does.
Regression in its simplest, univariate and linear form is often started with an initial
assumption of a straight line relationship and thus takes the form
= + + 3.40
Where is an observed random variable, is an observed random variable and and
are unknown parameters called regression coefficients with as the intercept and as
the slope while is the error term and represents the difference between and
deterministic component and (Kottegoda and Rosso; 1997).
In estimating the parameters, Kottegoda and Rosso (1997) recommends that it is more
convenient to minimize the absolute deviations from the straight line by minimizing the
sum of squared deviations from the mean to solve for the parameters (this brings the
solution to the method of least squares) and that from equation 3.40 the sum of the
squares horizontal or vertical deviations from the population regression line having
intercept and slope is given by
= ε
= (y− β − β)
3.41
Minimizing the sum of squared deviations means equating the respective partial
derivatives to zero, that is,
∂
∂β= − 2 ∑
(− − ) = 0 3.4.2
80
and ∂
∂β= − 2 ∑
(− − ) = 0 3.43
since the equations are linear, the simultaneous solutions of the least square equations are
= ∑ –∑
(∑
)/ ∑
(∑ )/
= ∑ ( )
∑ ( ) 3.44
= ∑ = 1 ⁄ − ∑
= 1 =⁄ − 1 3.45
Where = ∑ ⁄
= ∑ ⁄
Kottegoda and Rosso (1997) equally defined the simplified terms of the sum of squares
and cross products for faster solution of regression equations as
= ∑ = 1 ( − )2 = ∑
2 = 1 − ∑
= 1 ⁄ 3.46
= ∑ = 1 ( − )2 = ∑
2 = 1 − ∑
= 1
⁄ 3.47
=
= 1
– − =
∑ − ∑
∑ ⁄ 3.48
The expression for the slope parameter can be obtained from =
3.49
While the intercept still remain as
= ∑ = 1 ⁄ − 1 ∑
= 1 ⁄ = − 1
The error term (ε) in = + 1+ ε may be obtained by averaging the value over a
set of observed values of and such mean value applied approximately in further
predictions. On the extreme note, it is possible to carry out another regression analysis to
discover or establish the distribution of the error term. This may be necessary in precise
81
geotechnical observations and where the error term is occurring in significant magnitude
and exhibiting random or erratic scatter along the population regression line.
CHAPTER FOUR
RESULTS AND DISCUSSION
The failure of structural foundations develops in different forms. It often starts from an
isolated yielding event that triggers off sequence of subsequent failure mechanisms. In all
cases and regardless of components interdependencies, the contribution of the bearing
soil as an individual component is investigated by examining its various geotechnical
properties which generally define the strength status. ASWSS reliability studies therefore
begin with the determination of these geotechnical properties, followed by the estimation
of the probabilities of their state leading to failure.
The distribution of properties of engineering materials exhibit variations at different
scales depending on the material types and phenomena governing the variability. Where
the scale of scatter is large, decision making becomes difficult and the consequences of
unreliable judgment may be severe.
The pattern of variations may be investigated by establishing the relationship between
pairs of observed data especially where there is an inclusion of data that has not been
82
significantly altered. . In this way statistical description of a random field may be given
more comprehensively and accurate engineering information may be usefully derived
from such statistical data via reliability-based procedures. These procedures are often
structured to capture the remnant of field realities and data that have escaped the
conventional and empirical field and laboratory examinations.
The ability of the procedures to generate true and sufficiently large representatives of
field population makes it adequate in describing the uncertain field. The capabilities of
such engineering project sites with respect to loadings can be accurately evaluated and
presented in forms of reliability indices and probabilities of failure by relevant models.
Derived mainly from laboratory tests this chapter presents the geotechnical properties of
ASWSS under study and their range of applications in models of quantitative safety
analysis.
4.1 Graphical Representation of Test Results The mean results of laboratory determination of geotechnical properties of ASWSS and
NS from three replicates are shown in Appendix C, but their sequences of distribution
and variation in relation to changes in foundation depth need be represented graphically.
4.1.1 Atterberg limits test results Atterberg limits tests determine the various values of water content at which changes in
strength and compressibility occur (Smith and Smith, 1998). The results of Atterberg
limits tests shown in Table C.1 of Appendix C were used to give graphical
representations of the variation of individual parameter (Liquid Limit LL, Plastic Limit
PL, Plasticity Index PI and Shrinkage Limit LS) with depth as shown in Figure 4.1(a) –
(x)
83
Z
NS ASWSS
1.5 49 40 2 32 44 2.5 33 40 3 35 52 3.5 29 28
Figure 4.1 (a) Variation of LL of *Site A/1 with depth.
Z NS ASWSS
1.5 35.09 35.5 2 30.95 37.17 2.5 26.97 25.54 3 34.31 36.11 3.5 28.17 25
Figure 4.1 (b) Variation of PL of Site A/1 with depth.
0
10
20
30
40
50
60
1.5 2 2.5 3 3.5
Liqui
d Lim
it (%
)
Foundation Depth (m)
NS
ASWSS
0
5
10
15
20
25
30
35
40
1.5 2 2.5 3 3.5
Plas
tic Li
mit
(%)
Foundation Depth (m)
NS
ASWSS
84
*Site A/1 is zone A site 1
Z NS ASWSS
1.5 13.91 4.5 2 1.05 6.83 2.5 6.03 4.5 3 0.69 15.89 3.5 0.83 3
Figure 4.1 (c) Variation of PI of Site A/1 with depth.
Z NS ASWSS 1.5 10 4.29 2 10.71 5 2.5 10 5.71 3 10.71 8.57 3.5 10.71 10
Figure 4.1 (d) Variation of LS of Site A/1 with depth.
02
4
6
8
10
12
14
16
18
1.5 2 2.5 3 3.5
Plas
ticity
Inde
x (%
)
Foundation Depth (m)
NS
ASWSS
0
2
4
6
8
10
12
1.5 2 2.5 3 3.5
Shrin
kage
Lim
it (%
)
Foundation Depth (m)
NS
ASWSS
85
Z NS ASWSS
1.5 39 42 2 36 44 2.5 34 40 3 38 50 3.5 36 35
Figure 4.1 (e) Variation of LL of *Site A/2 with depth.
Z NS ASWSS
1.5 29 36.5 2 28 37.55 2.5 28 35 3 33 36.5 3.5 27.15 28.2
Figure 4.1 (f) Variation of PL of Site A/2 with depth.
*Site A/2 is zone A site 2
Z NS ASWSS
1.5 10 5.5
0
10
20
30
40
50
60
1.5 2 2.5 3 3.5
Lliqu
id Li
mit
(%)
Foundation Depth (m)
NS
ASWSS
0
5
10
15
20
25
30
35
40
1.5 2 2.5 3 3.5
Plas
tic Li
mit
(%)
Fondation Depth (m)
NS
ASWSS
0
2
4
6
8
10
12
14
16
Plas
ticity
Inde
x (%
)
NS
ASWSS
86
2 8 6.45 2.5 6 5 3 5 13.5 3.5 8.85 6.8
Figure 4.1 (g) Variation of PI of Site A/2 with depth.
Z NS ASWSS 1.5 10.91 4.45 2 10.5 6 2.5 10.25 8.27 3 10.25 8.05 3.5 10.05 10.05
Figure 4.1 (h) Variation of LS of Site A/2 with depth.
Z NS ASWSS
1.5 37 32 2 37 35 2.5 48 33 3 36 34 3.5 34 34
0
10
20
30
40
50
60
1.5 2 2.5 3 3.5
Liqui
d Lim
it (%
)
Foundation Depth (m)
NS
ASWSS
0
2
4
6
8
10
12
1.5 2 2.5 3 3.5
Shrin
kage
Lim
it (%
)
Foundation Depth (m)
NS
ASWSS
87
Figure 4.1 (i) Variation of LL of *Site B/1 with depth.
Z NS ASWSS 1.5 26.67 27.78 2 32.58 29.29 2.5 31.01 29.29 3 28.22 27.92 3.5 25.54 30.49
Figure 4.1 (j) Variation of PL of Site B/1 with depth.
*Site B/1 is zone B site 1
Z NS ASWSS
1.5 20.33 4.22 2 4.42 5.71
2.5 16.99 3.71 3 7.78 6.08
3.5 8.46 3.51
0
5
10
15
20
25
30
35
1.5 2 2.5 3 3.5
Plas
tic Li
mit
(%)
Foundation Depth (m)
NS
ASWSS
0
5
10
15
20
25
1.5 2 2.5 3 3.5
Plas
ticity
Inde
x (%
)
Foundation Depth (m)
NS
ASWSS
88
Figure 4.1 (k) Variation of PI of Site B/1 with depth.
Z NS ASWSS
1.5 7.86 8.57 2 8.57 9.29 2.5 9.29 8 3 8.57 8.57 3.5 8.57 8.57
Figure 4.1 (l) Variation of LS of Site B/1 with depth.
Z NS ASWSS 1.5 32 29.19 2 33 28.55 2.5 32 26.29 3 30 28.72 3.5 33 28.72
Figure 4.1 (m) Variation of LL of Site *B/2 with depth.
7
7.5
8
8.5
9
9.5
1.5 2 2.5 3 3.5
Shrin
kage
Lim
it (%
)
Foundation Depth (m)
NS
ASWSS
0
5
10
15
20
25
30
35
1.5 2 2.5 3 3.5
Liqui
d Lim
it (%
)
Foundation Depth (m)
NS
ASWSS
89
Z NS ASWSS
1.5 27.75 29.19
2 29 28.55
2.5 25.72 26.29
3 27.65 28.72
3.5 27.65 28.72
Figure 4.1 (n) Variation of PL of Site B/2 with depth.
*Site B/2 is zone B site 2
Z NS ASWSS
1.5 4.25 0.81 2 4 5.45 2.5 6.28 6.71 3 2.35 5.28 3.5 5.35 5.28
Figure 4.1 (o) Variation of PI of Site B/2 with depth.
23
24
25
26
27
28
29
30
1.5 2 2.5 3 3.5
Plas
tic Li
mit
(%)
Foundation Depth (m)
NS
ASWSS
0
1
2
3
4
5
6
7
8
1.5 2 2.5 3 3.5
Plas
ticity
Inde
x (%
)
Foundation Depth (m)
NS
ASWSS
90
Z NS ASWSS 1.5 8.55 9.28 2 9.75 8.29 2.5 8.55 8.57 3 8.57 8.5 3.5 8.57 8.55
Figure 4.1 (p) Variation of LS of Site B/2 with depth.
Z NS ASWSS 1.5 42 38 2 38 40 2.5 36 38 3 36 39 3.5 38 39
Figure 4.1 (q) Variation of LL of Site *C/1 with depth.
Z NS ASWSS
7.5
8
8.5
9
9.5
10
1.5 2 2.5 3 3.5
Shrin
kage
Lim
it (%
)
Foundation Depth (m)
NS
ASWSS
29
30
31
32
33
34
35
3637
Plas
tic Li
mit
(%)
NS
ASWSS
3334353637383940414243
1.5 2 2.5 3 3.5
Liqui
d Lim
it (%
)
Foundation Depth (m)
NS
ASWSS
91
1.5 35.25 33.5 2 34.5 36.5 2.5 32 32 3 30.95 33.5 3.5 32.55 33.72
Figure 4.1 (r) Variation of PL of Site C/1 with depth.
*Site C/1 is zone C site 1
Z NS ASWSS 1.5 6.75 4.5 2 3.5 3.5 2.5 4 6 3 5.03 5.5 3.5 5.45 5.28
Figure 4.1 (s) Variation of PI of Site C/1 with depth.
Z NS ASWSS
0
1
2
3
4
5
6
7
8
1.5 2 2.5 3 3.5
Plat
icity
Inde
x (%
)
Foundation Depth (m)
NS
ASWSS
7.5
8
8.5
9
9.5
Shrin
kage
Lim
it (%
)
NS
ASWSS
92
1.5 9.25 7.95 2 8.85 8.71 2.5 8.57 8.77 3 8.9 8.75 3.5 8.55 8.55
Figure 4.1 (t) Variation of LS of Site C/1 with depth.
Z NS ASWSS 1.5 36 40 2 38 37 2.5 35 39 3 34 37 3.5 35 34
Figure 4.1 (u) Variation of LL of *Site C/2 with depth
.
Z NS ASWSS 1.5 29.15 28 2 28.45 27.5 2.5 27.15 28.85
3132333435363738394041
1.5 2 2.5 3 3.5
Liqui
d Lim
it (%
)
Foundation Depth (m)
NS
ASWSS
23
24
25
26
27
28
29
30
31
1.5 2 2.5 3 3.5
Plas
tic Li
mit
(%)
NS
ASWSS
93
3 30.25 26.62 3.5 26.4 25.5
Figure 4.1 (v) Variation of PL of Site C/2 with depth.
*Site C/2 is zone C site 2
Z NS ASWSS
1.5 6.85 12 2 9.55 9.5 2.5 7.85 10.15 3 3.75 10.38 3.5 8.6 8.5
Figure 4.1 (w) Variation of PI of Site C/2 with depth.
Z NS ASWSS 1.5 8.25 7.25 2 7 8.15 2.5 9.15 6.27 3 6.75 7.75
0
2
4
6
8
10
12
14
1.5 2 2.5 3 3.5
Plas
ticity
Inde
x (%
)
Foundation Depth (m)
NS
ASWSS
0123456789
10
1.5 2 2.5 3 3.5
Shrin
kage
Lim
it (%
)
Foundation Depth (m)
NS
ASWSS
94
3.5 7.15 8.05
Figure 4.1 (x) Variation of LS of Site C/2 with depth.
Figures 4.1 (a) – (x) revealed no pattern of variations of LL, PL, PI or LS with foundation
depth that may be ascribed to the differences in material composition of ASWSS and NS.
The patterns of variation of LL and PL with depth appear to exhibit appreciable closeness
for ASWSS and NS while those of PI and LS are significantly divergent. Although there
are indications of scanty presence of outliers, generally ASWSS has higher values of PI
than NS. The indication of this is that ASWSS contains finer soil particles than NS and
consequently less in grading.
4.1.2 Compaction test results Compaction is the process whereby stress is mechanically applied to a soil mass to cause
densification by the expulsion of air from the voids between the soil particles. This
engineering principle is widely employed in strengthening runways, subgrades of roads
and embankments (Smith and Smith, 1998). Densities achieved by compaction are
termed as dry densities and expressed in mg/m3, while the moisture content at which
maximum dry density is achieved is known as the optimum moisture content (Smith and
Smith, 1998). The compaction tests result of this study are shown in Table C.2 of
Appendix C while their variations with depths are graphically represented in Figure
4.2(a) – (l).
95
Z NS ASWSS
1.5 1.67 1.56 2 1.67 1.48 2.5 1.39 1.57 3 1.33 1.71 3.5 1.48 1.51
Figure 4.2 (a) Variation of maximum dry density of site A/1 with depth.
Z NS ASWSS 1.5 22.47 20 2 18 20.86 2.5 20 18.32 3 26.51 25 3.5 25 17
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
1.5 2 2.5 3 3.5
Max
imum
Dry
Den
sity
(g/c
m3 )
Foundation Depth (m)
NS
ASWSS
0
5
10
15
20
25
30
1.5 2 2.5 3 3.5
Opt
imum
Moi
stur
e Co
nten
t (%
)
Foundation Depth (m)
NS
ASWSS
96
Figure 4.2(b) Variation of optimum moisture content of site A/1
with depth.
Z NS ASWSS 1.5 1.76 1.67 2 1.82 1.55 2.5 1.7 1.6 3 1.65 1.5 3.5 1.68 1.58
Figure 4.2 (c) Variation of maximum dry density of site A/2 with
depth.
Z NS ASWSS 1.5 19.25 22 2 20.22 20 2.5 25.75 23 3 20.15 25 3.5 19 19
00.20.40.60.8
11.21.41.61.8
2
1.5 2 2.5 3 3.5
Max
imum
Dry
Den
sity
(g/c
m3 )
Foundation Depth (m)
NS
ASWSS
0
5
10
15
20
25
30
1.5 2 2.5 3 3.5
Opt
imum
Moi
stur
e Co
nten
t (%
)
Foundation Depth (m)
NS
ASWSS
97
Figure 4.2(d) Variation of optimum moisture content of site A/2
with depth.
Z NS ASWSS 1.5 1.85 1.93 2 1.96 1.8 2.5 1.93 1.65 3 1.81 1.57 3.5 1.88 1.7
Figure 4.2 (e) Variation of maximum dry density of site B/1 with
depth.
Z NS ASWSS 1.5 15.05 10.56 2 14.46 18.36 2.5 12.79 19.17 3 19.54 17.97 3.5 16.38 15.55
0
0.5
1
1.5
2
2.5
1.5 2 2.5 3 3.5
Max
imum
Dry
Den
sity
(g/c
m3 )
Foundation Depth (m)
NS
ASWSS
0
5
10
15
20
25
1.5 2 2.5 3 3.5
Opt
imum
Moi
stur
e Co
nten
t (%
)
Foundation Depth (m)
NS
ASWSS
98
Figure 4.2(f) Variation of optimum moisture content of site B/1 with depth.
Z NS ASWSS
1.5 1.71 1.68 2 1.79 1.67 2.5 1.48 1.56 3 1.7 1.66 3.5 1.65 1.65
Figure 4.2 (g) Variation of maximum dry density of site B/2 with depth.
Z NS ASWSS
1.5 22.56 20.72 2 20.17 20.68 2.5 18.27 18.18 3 17.7 19.27 3.5 16.32 16.35
0
5
10
15
20
25
1.5 2 2.5 3 3.5
Opt
imum
Moi
stur
e Co
nten
t (%
)
Foundation Depth (m)
NS
ASWSS
00.20.40.60.8
11.21.41.61.8
2
1.5 2 2.5 3 3.5
Max
imum
Dry
Den
sity
(g/c
m3 )
Foundation Depth (m)
NS
ASWSS
99
Figure 4.2(h) Variation of optimum moisture content of site B/2 with depth.
Z NS ASWSS 1.5 1.8 1.67 2 1.84 1.9 2.5 1.79 1.83 3 1.67 1.72 3.5 1.54 1.52
Figure 4.2 (i) Variation of maximum dry density of site C/1with
depth.
Z NS ASWSS 1.5 20.2 18.33 2 19 19.27 2.5 18.84 18.38 3 18.9 19.2 3.5 19.1 19
00.20.40.60.8
11.21.41.61.8
2
1.5 2 2.5 3 3.5
Max
imum
Dry
Den
sity
(g/c
m3 )
Foundation Depth (m)
NS
ASWSS
17
17.5
18
18.5
19
19.5
20
20.5
1.5 2 2.5 3 3.5
Opt
imum
Moi
stur
e Co
nten
t (%
)
Foundation Depth (m)
NS
ASWSS
100
Figure 4.2(j) Variation of optimum moisture content of site C/1with depth.
Z NS ASWSS 1.5 1.8 1.94 2 1.92 1.9 2.5 1.9 1.82 3 1.88 1.79 3.5 1.76 1.72
Figure 4.2 (k) Variation of maximum dry density of site C/2with
depth.
Z NS ASWSS
1.5 16.83 15.5 2 15.56 16.2 2.5 14.2 17.22 3 16.25 17 3.5 16.35 17
Figure 4.2(l) Variation of optimum moisture content of site C/2
with depth.
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.95
2
1.5 2 2.5 3 3.5
Max
imum
Dry
Den
sity
(g/c
m3 )
Foundation Depth (m)
NS
ASWSS
02468
101214161820
1.5 2 2.5 3 3.5
Opt
imum
Moi
stur
e Co
nten
t (%
)
Foundation Depth (m)
NS
ASWSS
101
When compacting efforts of soil is stepped up, soil voids are reduced and maximum dry
density (MDD) appreciates with consequent reduction in optimum moisture content
(OMC), (Smith and Smith, 1998). Figure 4.2 shows no significant changes in the MDD
with depth and almost same values for both ASWSS and NS are depicted for various
foundation depths. OMC, however, showed slightly downward trend with foundation
depth and appreciable similarity between ASWSS and NS for a given amount of
compaction.
4.1.3 Consolidation and Triaxial tests results Total settlement (ΡC) is the aggregate of stress dependent initial compression, primary
consolidation and secondary consolidation. As a rule in foundation design ΡC must not be
greater than 25 mm. The values of ΡC for ASWSS and NS of this study are shown in
Table C.3 of Appendix C while those of triaxial test results (C, ∅ and ) are shown in
Table C.4 of Appendix C. The variations of these parameters with foundation depths are
represented in Figures 4.3 and 4.4 respectively.
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
Tota
l Set
tlem
ent (
m)
NS
ASWSS
102
Z NS ASWSS 1.5 0.0002 0.0004 2 0.0002 0.0002 2.5 0.0002 0.0003 3 0.0003 0.0005 3.5 0.0003 0.0002
Figure 4.3 (a) Variation of total settlement of site A/1with depth.
Z NS ASWSS 1.5 0.0002 0.0003 2 0.0003 0.0005 2.5 0.0002 0.0002 3 0.0003 0.0004 3.5 0.0002 0.0003
Figure 4.3 (b) Variation of total settlement of site A/2with depth.
Z NS ASWSS
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
1.5 2 2.5 3 3.5
Tota
l Set
tlem
ent (
m)
Foundation Depth (m)
NS
ASWSS
0
0.0005
0.001
0.0015
0.002
0.0025
Tota
l Set
tlem
ent (
m)
NS
ASWSS
103
1.5 0.0005 0.0004 2 0.0003 0.0004 2.5 0.0002 0.0003 3 0.0022 0.0003 3.5 0.0003 0.0004
Figure 4.3 (c) Variation of total settlement of site B/1with
depth.
Z NS ASWSS
1.5 0.0004 0.0003 2 0.0003 0.0004 2.5 0.0003 0.0002 3 0.0002 0.0003 3.5 0.0002 0.0002
Figure 4.3 (d) Variation of total settlement of site B/2 with
depth.
Z NS ASWSS 1.5 0.0002 0.0005 2 0.0003 0.0005
0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
0.00035
0.0004
0.00045
1.5 2 2.5 3 3.5
Tota
l Set
tlem
ent (
m)
Foundation Depth (m)
NS
ASWSS
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
Tota
l Set
tlem
ent (
m)
NS
ASWSS
104
2.5 0.0002 0.0003 3 0.0003 0.0004 3.5 0.0003 0.0002
Figure 4.3 (e) Variation of total settlement of site C/1 with
depth.
Z NS ASWSS 1.5 0.0002 0.0004 2 0.0003 0.0003 2.5 0.0002 0.0003 3 0.0003 0.0002 3.5 0.0002 0.0003
Figure 4.3 (f) Variation of total settlement of site C/2 with
depth .
Z NS ASWSS 1.5 28 10 22 27 16 2.5 24 10 3 22 15 3.5 19 12
0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
0.00035
0.0004
0.00045
1.5 2 2.5 3 3.5
Tota
l Set
tlem
ent (
m)
Foundation Depth (m)
NS
ASWSS
0
5
10
15
20
25
30
1.5 22 2.5 3 3.5
Cohe
sion
(kN/
m2 )
Foundation Depth (m)
NS
ASWSS
105
Figure 4.4(a) Variation of cohesion of site A/1 with depth.
Z NS ASWSS
1.5 13 11 2 10 9 2.5 15 7 3 8 10 3.5 9 9
Figure 4.4(b) Variation of angle of internal resistance of site
A/1with depth.
Z NS ASWSS
1.5 15.9 15.78 2 16.8 13.97 2.5 16.8 14.19 3 15.67 15.21 3.5 16.24 16.01
0
2
4
6
8
10
12
14
16
1.5 2 2.5 3 3.5
Angl
e of
Inte
rnal
Re
sista
nce
(°)
Foundation Depth (m)
NS
ASWSS
0
2
4
6
8
1012
14
16
18
1.5 2 2.5 3 3.5
Unit
Wei
ght (
kN/m
3 )
Foundation Depth (m)
NS
ASWSS
106
Figure 4.4(c) Variation of unit weight of site A/1 with
depth.
Z NS ASWSS
1.5 24 10 2 25 14 2.5 19 15 3 25 14 3.5 22 13
Figure 4.4(d) Variation of cohesion of site A/2 with depth.
Z NA ASWSS
1.5 14 10 2 12 10 2.5 13 9 3 15 8 3.5 16 9
0
5
10
15
20
25
30
1.5 2 2.5 3 3.5
Cohe
sion
(kN/
m2 )
Foundation Depth (m)
NS
ASWSS
0
24
6
8
10
1214
16
18
1.5 2 2.5 3 3.5
Angl
e of
Inte
rnal
Res
istan
ce (°
)
Foundation Depth (m)
NA
ASWSS
107
Figure 4.4(e) Variation of angle of internal resistance of site
A/2 with depth.
Z NS ASWSS
1.5 17.14 15.96 2 16.24 14.42 2.5 15.9 14.72 3 16.58 15.98 3.5 16.12 16.32
Figure 4.4(f) Variation of unit weight of site A/2 with
depth.
Z NS ASWSS
1.5 25 9 2 17 18 2.5 18 19 3 22 12 3.5 28 13
13
13.5
14
14.5
15
15.5
16
16.5
17
17.5
1.5 2 2.5 3 3.5
Unit
wei
ght (
kN/m
3 )
Foundation depth (m)
NS
ASWSS
0
5
10
15
20
25
30
1.5 2 2.5 3 3.5
Cohe
sion
(kN/
m2 )
Foundation Depth (m)
NS
ASWSS
108
Figure 4.4(g) Variation of cohesion of site B/1 with depth.
Z NS ASWSS
1.5 16 12 2 13 13 2.5 14 13 3 16 13 3.5 15 15
Figure 4.4(h) Variation of angle of internal resistance of site B/1
with depth.
Z NS ASWSS
1.5 15.8 16.58 2 16.4 13.98 2.5 16.6 14.87 3 16.6 16.35 3.5 16.68 16.35
0
2
4
6
8
10
12
14
1618
1.5 2 2.5 3 3.5
Angl
e of
Inte
rnal
Res
istan
ce (°
)
Founation Depth (m)
NS
ASWSS
12.5
13
13.5
14
14.5
15
15.5
16
16.5
17
1.5 2 2.5 3 3.5
Unit
Wei
ght (
kN/m
3 )
Foundation Depth (m)
NS
ASWSS
109
Figure 4.4(i) Variation of unit weight of site B/1 with depth.
Z NS ASWSS
1.5 20 12 2 24 9 2.5 19 10 3 22 12 3.5 22 13
Figure 4.4(j) Variation of cohesion of site B/2with depth.
Z NS ASWSS
1.5 11 12 2 13 9 2.5 13 10 3 14 12 3.5 16 13
0
5
10
15
20
25
30
1.5 2 2.5 3 3.5
Cohe
sion
(kN/
m2 )
Foundation Depth (m)
NS
ASWSS
0
2
4
6
8
10
12
14
16
18
1.5 2 2.5 3 3.5
Angl
e of
Inte
rnal
Res
istan
ce (°
)
Foundation Depth (m)
NS
ASWSS
110
Figure 4.4(k) Variation of angle of internal resistance of site B/2
with depth.
Z NS ASWSS 1.5 15.89 15.98 2 16.22 15.5 2.5 16.22 14.98 3 16.24 16.1 3.5 16.4 16.3
Figure 4.4(l) Variation of unit weight of site B/2 with
depth.
Z NS ASWSS
1.5 28 10 2 26 9 2.5 25 11 3 20 10 3.5 19 12
Figure 4.4(m) Variation of cohesion of site C/1 with depth.
14
14.5
15
15.5
16
16.5
17
1.5 2 2.5 3 3.5
Unit
Wei
ght (
kN/m
3 )
Foundation Depth (m)
NS
ASWSS
0
5
10
15
20
25
30
1.5 2 2.5 3 3.5
Cohe
sion
(kN/
m2 )
Foundation Depth (m)
NS
ASWSS
111
Z NS ASWSS
1.5 13 13 2 13 13 2.5 14 13 3 15 13 3.5 16 14
Figure 4.4(n) Variation of angle of internal resistance of site
C/1with depth.
Z NS ASWSS
1.5 15.9 16.2 2 16.82 14.98 2.5 16.8 15.8 3 16.84 16.24 3.5 16.84 16.24
0
2
4
68
10
12
14
16
18
1.5 2 2.5 3 3.5
Angl
e of
Inte
rnal
Res
istan
ce (°
)
Foundation Depth (m)
NS
ASWSS
14
14.5
15
15.5
16
16.5
17
1.5 2 2.5 3 3.5
Unit
Wei
ght (
kN/m
3 )
Foundation Depth (m)
NS
ASWSS
112
Figure 4.4(o) Variation of unit weight of site C/1 with depth.
Z NS ASWSS
1.5 23 11 2 18 13 2.5 22 11 3 19 12 3.5 23 10
Figure 4.4(p) Variation of cohesion of site C/2with depth.
Z NS ASWSS
1.5 12 9 2 14 11 2.5 13 10 3 15 12 3.5 16 11
0
5
10
15
20
25
1.5 2 2.5 3 3.5
Cohe
sion
(kN/
m2 )
Foundation Depth (m)
NS
ASWSS
0
2
4
6
8
10
12
14
16
18
1.5 2 2.5 3 3.5
Angl
e of
Inte
rnal
resis
tanc
e (°)
Foundation Depth (m)
NS
ASWSS
113
Figure 4.4(q) Variation of angle of internal resistance of site C/2 with depth.
Z NS ASWSS
1.5 15.51 13.89 2 16.01 14.22 2.5 16.2 12.92 3 16.24 13.9 3.5 16.3 14.28
Figure 4.4(r) Variation of unit weight of site C/2 with depth.
Total settlement of ASWSS and NS falls below the maximum allowable value for all the
foundation depths. However erratic changes in value were observed between the depths
of 1.5m and 3.0m while significant downward trend begins to be noticed from the depth
of 3.0m. This scenario is true for both ASWSS and NS. Impressively enough, none of the
settlement values exceeded 0.0025m, indicating that degradation process is at its
completion stage for ASWSS that are over twenty years of abandonment.
The values C, ∅ and of ASWSS are generally lower than those of NS. These
geotechnical strength parameters of soil simply indicate that NS is better in strength
characteristics than ASWSS. In most cases the differences are large but the two sets of
data exhibit similarity from the depth of 3.5m for most of the observed data as shown in
Figures 4.4 (a) - (r).
0
2
4
6
8
10
12
14
16
18
1.5 2 2.5 3 3.5
Unit
Wei
ght (
kN/m
3
Foundation Depth (m)
NS
ASWSS
114
There is no definite pattern of variation of the parameters with foundation depth that can
be explained by the compositional differences between ASWSS and NS though their
values are extremely divergent in most cases. A number of outliers may be observed but
their occurrences make it difficult to think of expunging them. It is simply not certain
whether they are outliers or not, so it is safer to treat them as real data.
4.1.4 Specific gravity and sieve analysis results
Results of specific gravity tests are used in the evaluation of total settlement, void ratio
and degree of saturation. However, sieve analysis was carried out to determine the
percentage of clay and silt in the soil mass. These results (specific gravity and sieve
analysis) are shown in Tables C.5 and C.6 of Appendix C respectively while their
variations with depth are graphically represented in Figures 4.5 and 4.6 respectively.
Z NS AWSS
1.5 2.21 1.64 2 2.36 2.04 2.5 2.47 2.14 3 2.54 2.26 3.5 2.66 2.45
Figure 4.5 (a) Variation of specific gravity of site A/1 with
depth.
0
0.5
1
1.5
2
2.5
3
1.5 2 2.5 3 3.5
Spec
ific G
ravi
ty
Foundation Depth (m)
NS
AWSS
115
Z NS ASWSS
1.5 2.56 1.88 2 2.6 2.17 2.5 2.64 2.48 3 2.66 2.56 3.5 2.65 2.64
Figure 4.5 (b) Variation of specific gravity of site A/2 with depth.
Z NS ASWSS
1.5 2.55 2.52 2 2.55 2.54 2.5 2.56 2.56 3 2.63 2.56 3.5 2.67 2.58
Figure 4.5 (c) Variation of specific gravity of site B/1 with
depth.
0
0.5
1
1.5
2
2.5
3
1.5 2 2.5 3 3.5
Spec
ific G
ravi
ty
Foundation depth (m)
NS
ASWSS
2.4
2.45
2.5
2.55
2.6
2.65
2.7
1.5 2 2.5 3 3.5
Spec
ific G
ravi
ty
Foundation Depth (m)
NS
ASWSS
116
Z NS ASWSS 1.5 2.58 1.78 2 2.65 1.92 2.5 2.65 2.2 3 2.67 2.58 3.5 2.67 2.6
Figure 4.5 (d) Variation of specific gravity of site B/2 with
depth.
Z NS ASWSS
1.5 2.58 2.5 2 2.65 2.57 2.5 2.67 2.58 3 2.67 2.64 3.5 2.69 2.66
0
0.5
1
1.5
2
2.5
3
1.5 2 2.5 3 3.5
Spec
ific G
ravi
ty
Foundation Depth (m)
NS
ASWSS
2.4
2.45
2.5
2.55
2.6
2.65
2.7
2.75
1.5 2 2.5 3 3.5
Spec
ific G
ravi
ty
Foundation Depth (m)
NS
ASWSS
117
Figure 4.5 (e) Variation of specific gravity of site C/1with depth.
Z NS ASWSS
1.5 2.57 2.14 2 2.6 2.25 2.5 2.67 2.4 3 2.67 2.61 3.5 2.69 2.63
Figure 4.5 (f) Variation of specific gravity of site C/2with
depth.
Z NS ASWSS
1.5 32.64 43.8 2 53.86 64.7 2.5 42 71.48 3 68.68 89.92 3.5 63.84 70.86
0
0.5
1
1.5
2
2.5
3
1.5 2 2.5 3 3.5
Spec
ific G
ravi
ty
Foundation Depth (m)
NS
ASWSS
0102030405060708090
100
1.5 2 2.5 3 3.5
Clay
& S
ilt co
nten
t (%
)
Foundation Depth (m)
NS
ASWSS
118
Figure 4.6 (a) Variation of clay & silt content of site A/1 with depth.
Z NS ASWSS 1.5 30.74 45.77 2 28.91 48.92 2.5 42.48 58.12 3 60.4 60.25 3.5 56.52 56.55
Figure 4.6 (b) Variation of clay & silt content of site A/2 with depth.
Z NS ASWSS
1.5 38.22 48.14 2 20.56 65.9 2.5 19.64 23.64 3 50.78 55.02 3.5 35.12 45.7
0
10
20
30
40
50
60
70
1.5 2 2.5 3 3.5
Clay
& S
ilt C
onte
nt (%
)
Foundation Depth (m)
NS
ASWSS
0
10
20
30
40
50
60
70
1.5 2 2.5 3 3.5
Clay
& S
ilt C
onte
nt (%
)
Foundation depth (m)
NS
ASWSS
119
Figure 4.6 (c) Variation of clay & silt content of site B/1with depth.
Z NS ASWSS
1.5 38 40.44 2 42.2 62.68 2.5 30.35 70.04 3 22.5 62.66 3.5 38.27 68.72
Figure 4.6 (d) Variation of clay & silt content of site B/2with
depth.
Z NS ASWSS 1.5 36.4 52.5 2 32.46 50.68 2.5 40.47 65.44 3 28.74 58.32 3.5 30.04 62.62
0
10
20
30
40
50
60
70
80
1.5 2 2.5 3 3.5
Clay
& S
ilt C
onte
nt (%
)
Foundation Depth (m)
NS
ASWSS
0
10
20
30
40
50
60
70
1.5 2 2.5 3 3.5
Clay
& S
ilt C
onte
nt (%
)
Foundation Depth (m)
NS
ASWSS
120
Figure 4.6 (e) Variation of clay & silt content of site C/1with depth
.
Z NS ASWSS
1.5 32.35 42.36 2 27.2 28.85 2.5 28.45 39.48 3 32.31 52.43 3.5 30.46 56.44
Figure 4.6 (f) Variation of clay & silt content of site C/2with depth.
The results of these tests are quite relevant in foundation designs. It gives the design
Engineer an idea about the possible interaction of the bearing soil with structural loads as
well as the general grading level of the engineering site. Up to 80% of the tested samples
of ASWSS have specific gravity (Gs) value lower than 2.60 and this placed that
proportion of soil in the range of organic clay to bog peat. The graphs of specific
gravity/depth (Figure 4.5) generally showed positive variations of Gs with depth but
having gentle slopes with depth 3.0m having the highest value for all observed sequences
of ASWSS data. ASWSS and NS exhibit similarity in the trend of variation with depth,
though the values of Gs of NS are consistently higher than those of ASWSS.
0
10
20
30
40
50
60
1.5 2 2.5 3 3.5
Clay
& S
ilt co
nten
t (%
)
Foundation Depth (m)
NS
ASWSS
121
Figure 4.6 showed wide margins of clay/silt contents between NS and ASWSS though
their trends of variations with foundation depth are quite similar. Up to 45% difference
between ASWSS and NS clay/silt composition is recorded at some corresponding depths,
however, with those of ASWSS constantly higher. The occurrence of clay/silt does not
follow a particular pattern in relation to the depth of foundation. It increases with depth in
some cases and in others it decreases.
4.2 Chemical Analysis of ASWSS and NS The average response of spatially variable soils differs significantly from the response of
corresponding homogenous soils having equivalent mean properties. The discovery of
only the mechanical properties of ASWSS therefore, may be insufficient and
inconclusive in judgment and in addressing the problem.
A program of fundamental chemical analysis of soil was drawn to assess the
concentration of the compounds of sulphate, chloride, carbonate, bicarbonate, pH,
organic matter and minerals content in the tested soil samples. Wet and dry seasons were
selected separately for sampling and testing in some cases because in wet season the
downward washing of leachate results in higher concentration of the compounds at lower
depths. However, the results are generally expected to be lower in concentration than in
dry season because of dilution resulting from high moisture content. The sampling and
tests of these compounds in both dry and wet seasons give a better and balanced chemical
analysis of soil. The results of these tests are shown in Table C.7 of Appendix C while
the graphical representation of their variation with depth for both wet and dry seasons
are shown in Figures 4.7 and 4.8 respectively.
122
Z NS ASWSS 1.5 264.45 473.18 2 271.81 491.81 2.5 274.15 584.1 3 282.43 686.13 3.5 289.5 691.82
Figure 4.7 (a) Variation of sulphate of site A/1 with depth in wet
season.
Z NS ASWSS
1.5 280.64 522.63 2 376.9 568.6 2.5 390.55 605.32 3 430.63 612.1 3.5 472.39 620.1
Figure 4.7 (b) Variation of chloride of site A/1 with depth in wet
season.
0
100
200
300
400
500
600
700
800
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation Depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
123
Z NS ASWSS 1.5
28.8
2 26.8 26 2.5 29.95 20.33 3 33.1 35.2 3.5 32.16 38.16
Figure 4.7(c) Variation of carbonate of site A/1 with depth in wet
season.
Z NS ASWSS
2 233 899 2 201 886 2.5 188 543 3 165 297 3.5 134 189
Figure 4.7(d) Variation of * ∑Ca+Mg of site A/1 with depth in wet
season.
*∑Ca+Mg is the combination of Calcium and Magnesium
0
5
10
15
2025
30
35
40
45
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation Depth (m)
NS
ASWSS
0100200300400500600700800900
1000
2 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
124
Z NS ASWSS 1.5 224.41 436.44 2 266.83 501.6 2.5 241.5 578.15 3 268.42 586.42 3.5 286.53 596.33
Figure 4.7 (e) Variation of sulphate of site A/2with depth in wet season.
Z NS ASWSS 1.5 320.5 643.2 2 338.77 658.32 2.5 386.76 784.1 3 440.19 786.37 3.5 489.1 799.1
Figure 4.7 (f) Variation of chloride of site A/2 with depth in wet
season.
0
100
200
300
400
500
600
700
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
800
900
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
125
Z NS ASWSS
1.5 30.22 27.2 2 36.19 28.1 2.5 37.55 30.67 3 32.2 33.8 3.5 40 40.67
Figure 4.7(g) Variation of carbonate of site A/2 with depth in wet
season .
Z NS ASWSS 1.5 289 776 2 233 654 2.5 178 498 3 167 201 3.5 150 188
Figure 4.7(h) Variation of ∑Ca+Mg of site A/2 with depth in wet
season.
0
5
10
15
20
25
30
35
40
45
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
800
900
1.5 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Foundation depth (m)
NS
ASWSS
126
Z NS AWSS 1.5 234.12 399.25 2 243.55 452.46 2.5 265.1 477.1 3 285.6 484.7 3.5 292.56 495.18
Figure 4.7 (i) Variation of sulphate of site B/1with depth in wet
season.
Z NS ASWSS 1.5 299.6 499.4 2 320.15 538.45 2.5 338.6 555.67 3 415.2 620.19 3.5 440.88 699.42
Figure 4.7 (j) Variation of chloride of site B/1 with depth in wet
season.
0
100
200
300
400
500
600
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation Depth (m)
NS
AWSS
0
100
200
300
400
500
600
700
800
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
127
Z NS ASWSS
1.5 31.23 28.9 2 30.88 36.88 2.5 32.6 38.7 3 38.3 39.22 3.5 39.1 40.3
Figure 4.7(k) Variation of carbonate of site B/1 with depth in wet
season.
Z NS ASWSS
1.5 290 556 2 207 322 2.5 188 178 3 167 121 3.5 143 199
Figure 4.7(l) Variation of ∑Ca+Mg of site B/1 with depth in wet
season.
0
5
1015
20
25
30
35
40
45
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation depth (m)
NS
ASWSS
0
100
200
300
400
500
600
1.5 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
128
Z NS ASWSS 1.5 249.73 399.6 2 256.4 468.31 2.5 295.66 474.1 3 250.17 552.19 3.5 259.22 560.15
Figure 4.7 (m) Variation of sulphate of site B/2with depth in wet
season.
Z NS ASWSS 1.5 320.32 568.32 2 335.59 658.1 2.5 430.66 740.19 3 442.72 821.22 3.5 450.33 866.32
Figure 4.7 (n) Variation of chloride of site B/2 with depth in wet
season.
0
100
200
300
400
500
600
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation Depth (m)
NS
ASWSS
0100200300400500600700800900
1000
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation depth (m)
NS
ASWSS
129
Z NS ASWSS
1.5 27.6 28.8 2 29.89 20.13 2.5 30.35 32.1 3 33.22 36.8 3.5 36.48 39.5
Figure 4.7(o) Variation of carbonate of site B/2 with depth in wet
season.
Z NS ASWSS 1.5 278 659 2 231 440 2.5 178 308 3 144 187 3.5 107 154
Figure 4.7(p) Variation of ∑Ca+Mg of site B/2with depth in wet season.
0
5
10
15
20
25
30
35
40
45
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation Depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
1.5 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
130
Z NS ASWSS
1.5 267.5 389.15 2 284.1 499.1 2.5 222.1 542.1 3 275.15 578.55 3.5 246.44 588.42
Figure 4.7 (q) Variation of sulphate of site C/1with depth in wet
season.
Z NS ASWSS
1.5 315.22 420.67 2 329.18 496.18 2.5 330.72 542.15 3 356.84 599.3 3.5 415.1 620.1
Figure 4.7 (r) Variation of chloride of site C/1 with depth in wet
season.
0
100
200
300
400
500
600
700
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation Depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
131
Z NS ASWSS
1.5 27 27.3 2 25.23 29.3 2.5 28.45 30.19 3 32.1 23.25 3.5 38.73 40
Figure 4.7 (s) Variation of carbonate of site C/1 with depth in wet
season.
Z NS ASWSS
1.5 195 443 2 187 200 2.5 144 176 3 143 143 3.5 122 108
Figure 4.7(t) Variation of ∑Ca+Mg of site C/1with depth in wet
season.
0
5
10
15
20
2530
35
40
45
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation Depth (m)
NS
ASWSS
050
100150200250300350400450500
1.5 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
132
Z NS ASWSS
1.5 220.55 235.1 2 242.2 245.2 2.5 240.17 265.44 3 256.68 269.67 3.5 280.99 298.3
Figure 4.7 (u) Variation of sulphate of site C/2with depth in wet
season.
Z NS ASWSS 1.5 353.1 356.78 2 388.9 422.13 2.5 420.95 443.17 3 467.3 587.67 3.5 488.76 595.1
Figure 4.7 (v) Variation of chloride of site C/2 with depth in wet
season.
0
50
100
150
200
250
300
350
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation Depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
133
Z NS ASWSS
1.5 20.22 24.6 2 24.68 29.9 2.5 29.16 29.92 3 28.15 30.35 3.5 39.7 40
Figure 4.7 (w) Variation of carbonate of site C/2 with depth in wet
season.
Z NS ASWSS
1.5 180 389 2 167 339 2.5 133 218 3 121 155 3.5 120 106
Figure 4.7(x) Variation of ∑Ca+Mg of site C/2with depth in wet
season.
05
10
15
20
25
30
35
40
45
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation Depth (m)
NS
ASWSS
0
50
100
150
200
250
300
350
400
450
1.5 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Fou ndation Depth (m)
NS
ASWSS
134
Z NS ASWSS
1.5 400.63 903.65 2 283.13 789.13 2.5 270.22 673.16 3 254.55 469.1 3.5 230.22 336.22
Figure 4.8(a) Variation of sulphate of site A/1with depth in dry
season.
Z NS ASWSS
1.5 617.1 972.3 2 454.96 648.62 2.5 429.6 459.39 3 342.85 344.86 3.5 320.54 322.45
Figure 4.8(b) Variation of chloride of site A/1with depth in dry
season.
0100200300400500600700800900
1000
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation Depth (m)
NS
ASWSS
0
200
400
600
800
1000
1200
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation depth (m)
NS
ASWSS
135
Z NS ASWSS 1.5 50 50.1 2 46.17 48.9 2.5 42.15 42.33 3 30.62 33.62 3.5 29.88 30.19
Figure 4.8(c) Variation of carbonate of site A/1with depth in dry
season.
Z NS ASWSS
1.5 233 50.1 2 200 48.9 2.5 176 42.33 3 108 33.62 3.5 77 30.19
Figure 4.8(d) Variation of ∑Ca+Mg of site A/1with depth in dry
season.
0
10
20
30
40
50
60
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation Depth (m)
NS
ASWSS
0
50
100
150
200
250
1.5 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Foundation depth (m)
NS
ASWSS
136
Z NS ASWSS
1.5 390.3 698.3 2 362.33 664.23 2.5 345.45 555.45 3 268.1 489.1 3.5 386.22 370.24
Figure 4.8(e) Variation of sulphate of site A/2with depth in dry
season.
Z NS ASWSS
1.5 560.76 768.7 2 450.66 656.12 2.5 324.96 495.22 3 340.45 348.9 3.5 270.54 275.66
Figure 4.8(f) Variation of chloride of site A/2with depth in dry
season.
0
100
200
300
400
500
600
700
800
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation Depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
800
900
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
137
Z NS ASWSS
1.5 49.56 50.32 2 46.35 47.35 2.5 31.73 34.77 3 31.22 33.28 3.5 26.49 28.6
Figure 4.8(g) Variation of carbonate of site A/2with depth in dry
season.
Z NS ASWSS
1.5 176 1001 2 102 897 2.5 87 822 3 80 444 3.5 55 287
Figure 4.8(h) Variation of ∑Ca+Mg of site A/2with depth in dry
season.
0
10
20
30
40
50
60
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundatin Depth (m)
NS
ASWSS
0
200
400
600
800
1000
1200
1.5 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
138
Figure 4.8(i) Variation of sulphate of site B/1with depth in dry season.
Z NS ASWSS 1.5 395.15 699.23 2 300.66 615.68 2.5 296.53 598.45 3 280.56 586.43 3.5 288 488.43
Z NS ASWSS 1.5 500.31 692.23 2 500.27 520.27 2.5 446.5 463.45 3 315.11 322.1 3.5 310.1 310.15
Figure 4.8(j) Variation of chloride of site B/1with depth in dry
season.
0
100
200
300
400
500
600
700
800
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
800
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
139
Z NS ASWSS
1.5 43.77 692.23 2 40.09 520.27 2.5 36.67 463.45 3 30.24 322.1 3.5 23 310.15
Figure 4.8(k) Variation of carbonate of site B/1with depth in dry
season.
Z NS ASWSS 1.5 192 667 2 180 434 2.5 171 219 3 100 177 3.5 83 136
Figure 4.8(l) Variation of ∑Ca+Mg of site B/1with depth in dry
season.
0
100
200
300
400
500
600
700
800
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
800
1.5 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
140
Z NS ASWSS
1.5 382.56 494.62 2 355.34 395.33 2.5 363.45 368.46 3 294 295.11 3.5 259.35 288.62
Figure 4.8(m) Variation of sulphate of site B/2with depth in dry
season.
Z NS ASWSS 1.5 488.67 498.69 2 342.25 344.25 2.5 322.06 342.3 3 268.33 288.73 3.5 254.89 276.9
Figure 4.8(n) Variation of chloride of site B/2with depth in dry season.
0
100
200
300
400
500
600
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation Depth (m)
NS
ASWSS
0
100
200
300
400
500
600
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
141
Z NS ASWSS
1.5 48.65 48.97 2 46.45 47.5 2.5 30.28 33.24 3 29.66 30.76 3.5 25.86 28.95
Figure 4.8(o) Variation of carbonate of site B/2with depth in dry
season.
Z NS ASWSS 1.5 189 545 2 166 407 2.5 143 227 3 98 188 3.5 67 146
Figure 4.8(p) Variation of ∑Ca+Mg of site B/2with depth in dry season.
0
10
20
30
40
50
60
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation Depth (m)
NS
ASWSS
0
100
200
300
400
500
600
1.5 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Foundation depth (m)
NS
ASWSS
142
Z NS ASWSS
1.5 346 676 2 340.1 640.12 2.5 324.65 435.68 3 296.11 398.11 3.5 249.66 389.42
Figure 4.8(q) Variation of sulphate of site C/1with depth in dry
season.
Z NS ASWSS
1.5 495 697.15 2 320.64 532.45 2.5 320.17 321.67 3 260.83 288.49 3.5 239.68 26.88
Figure 4.8(r) Variation of chloride of site C/1with depth in dry
season.
0
100
200
300
400
500
600
700
800
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation Depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
800
1.5 2 2.5 3 3.5
Cchl
orid
e (m
g/kg
)
Foundation Depth (m)
NS
ASWSS
143
Z NS ASWSS 1.5 49.88 50.44 2 48.89 50.1 2.5 45.35 48.35 3 24.09 29.63 3.5 20.86 20.86
Figure 4.8(s) Variation of carbonate of site C/1with depth in dry
season.
Z NS ASWSS 1.5 170 877 2 165 552 2.5 129 328 3 109 200 3.5 56 183
Figure 4.8(t) Variation of ∑Ca+Mg of site C/1with depth in dry
season.
0
10
20
30
40
50
60
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation Depth (m)
NS
ASWSS
0100200300400500600700800900
1000
1.5 2 2.5 3 3.5
∑Cca
+Mg
(mg/
kg)
Foundation Depth (9m)
NS
ASWSS
144
Z NS ASWSS
1.5 322.1 634.22 2 315.15 620.19 2.5 223.37 577.66 3 234 539.13 3.5 200.54 520.56
Figure 4.8(u) Variation of sulphate of site C/2with depth in dry
season.
Z NS ASWSS
1.5 589 599 2 584.67 588.99 2.5 563.85 567.73 3 420.31 423.5 3.5 340.12 344.12
Figure 4.8(v) Variation of chloride of site C/2with depth in dry
season.
0
100
200
300
400
500
600
700
1.5 2 2.5 3 3.5
Sulp
hate
(mg/
l)
Foundation Depth (m)
NS
ASWSS
0
100
200
300
400
500
600
700
1.5 2 2.5 3 3.5
Chlo
ride
(mg/
kg)
Foundation depth (m)
NS
ASWSS
145
Z NS ASWSS
1.5 46.9 48.99 2 46.72 47.6 2.5 42.33 46.77 3 40.33 45.28 3.5 32.66 34.66
Figure 4.8(w) Variation of carbonate of site C/2with depth in dry
season.
Z NS ASWSS 1.5 196 448 2 192 278 2.5 128 192 3 119 156 3.5 87 115
Figure 4.8(x) Variation of ∑Ca+Mg of site C/2with depth in dry season.
Chemical characterization is one of the most important investigations of ASWSS. It
revealed the chemical compositions of ASWSS in its various quantities expressed in
milligrams/liter (mg/l) or milligrams/kilogram (mg/kg). Figure 4.7 and 4.8 showed the
0
10
20
30
40
50
60
1.5 2 2.5 3 3.5
Carb
onat
e (m
g/l)
Foundation depth (m)
NS
ASWSS
050
100150200250300350400450500
1.5 2 2.5 3 3.5
∑Ca+
Mg
(mg/
kg)
Foundation Depth (m)
NS
ASWSS
146
results of this characterization for ASWSS and NS at different depths in both wet and dry
seasons. Sulphate, chloride and carbonate contents vary positively with foundation depth
in wet season. However the direct opposite of this scenario is observed in dry season,
confirming the fact that high concentration of these compounds are found at lower depths
in wet season as a result of downward washing of leachate. Calcium and magnesium
composition decrease with depth in dry and wet seasons because of their inability to be
washed down easily in solution. Sulphate, chloride, and calcium/magnesium occur in
harsh proportions that violate WHO/EPA allowable maximum value in many cases of
ASWSS tests. However appreciable similarity both in quantity and variation with depth is
are observed for chloride contents of ASWSS and NS in wet and dry season
4.3 Organic Matter Content The amount of organic matter present in SWSS is a measure of its level of degradation.
The value is expressed as a percentage of the total mass of the soil sample. Higher values
are indications of further degradation and consolidation. Foundation soil cannot be said to
be stable where degradation is very much in progress. This is why World Health
Organisation (WHO) and Environmental Protection Agency (EPA) have set a ceiling of
5% of organic matter content in any proposed engineering soil. Table C. 8 of Appendix C
shows the results of organic matter content test of ASWSS of this study while Figure 4.9
shows its variation with foundation depth.
Z ASWSS
0.5
1
1.5
2
2.5
3
3.5
4
Org
anic
Mat
ter C
onte
nt (%
)
ASWSS
147
1.5 3.27 2 3.65 2.5 3.22 3 2.89 3.5 2.1
Figure 4.9 (a) Variation of organic matter content of site A/1 with depth.
Z ASWSS
1.5 4.06 2 3.88 2.5 3.45 3 2.78 3.5 2.33
Figure 4.9 (b) Variation of organic matter content of site A/2 with depth.
Z ASWSS 1.5 5.01
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1.5 2 2.5 3 3.5
Org
anic
Mat
ter C
onte
nt (%
)
Foundation Depth (m)
ASWSS
0
1
2
3
4
5
6
Org
anic
Mat
ter C
onte
nt (%
)
ASWSS
148
2 4.89 2.5 4.51 3 3.88 3.5 2.9
Figure 4.9 (c) Variation of organic matter content of site B/1with depth.
Z ASWSS
1.5 3.88 2 3.22 2.5 2.8 3 2.56 3.5 2.04
Figure 4.9 (d) Variation of organic matter content of site B/2with depth.
00.5
11.5
22.5
33.5
44.5
1.5 2 2.5 3 3.5
Org
anic
Mat
ter C
onte
nt (%
)
Foundation Depth (m)
ASWSS
0
1
2
3
4
5
6
Org
anic
Mat
ter C
onte
nt (%
)
ASWSS
149
Z ASWSS 1.5 4.87 2 4.66 2.5 4.32 3 2.99 3.5 2.36
Figure 4.9 (e) Variation of organic matter content of site C/1with depth.
Z ASWSS
1.5 4.55 2 4.05 2.5 3.81 3 2.7 3.5 2.09
Figure 4.9 (f) Variation of organic matter content of site C/2with
4.4 X – Ray Diffraction Test
The test was conducted to find out the mineral composition of ASWSS. This is important
because the behaviour of soil under stress may largely be influenced by its mineral
00.5
11.5
22.5
33.5
44.5
5
1.5 2 2.5 3 3.5
Org
anic
Mat
ter C
onte
nt (%
)
Foundation Depth (m)
ASWSS
150
contents. Some minerals have high swelling and shrinkage potentials in the presence or
absence of water and the knowledge of this is important in foundation designs. The
X – Ray Diffraction test of this study was conducted only for ASWSS and the results are
shown in Table 4.1
Table 4.1 Results of X- Ray Diffraction Test (ASWSS)
NO
ZONE
01 02 03
A, B & C Mineral name Quartz Rutile Stolzite
Compound
name
Silicon Oxide Titanium Oxide Lead Tungsten
Oxide
PDF name Silicon Oxide Titanium Oxide Lead Tungsten
Oxide
Empirical O2Si O2Ti O4PbW
151
formula
Chemical
formula
SiO2 TiO2 Pb(WO4)
Crystal system Hexagonal Tetragonal Tetragonal
Alpha (º) 90.0000 90.0000 90.0000
Beta (º) 90.0000 90.0000 90.0000
Gamma (º) 120.0000 90.0000 90.0000
Status Alternate
pattern
Marked as
deleted by
ICDU
Alternate
pattern
Quality Indexed (I) Calculated (C) Indexed (I)
PDF is computer program file name
4.5 Student’s T - Test of Triaxial Test Results T – Test is a means by which the standard deviation of the difference between the means
of two sets of data is expressed. It is clear therefore that the higher the value the more
obvious the difference, and conversely, lower values are indications of high uncertainty
about the difference. T – test requires an initial expectation called null hypothesis which
the experiment is designed to test. The null hypothesis in this case can be that ‘we expect
differences’ between ASWSS and NS properties or that there are ‘no differences’
between them. However, it does not make sense to expect ‘differences’ if the scale of
such differences cannot be predicted. The null hypothesis in this case therefore, is that
152
there are ‘no differences’ between ASWSS and NS properties and the t – test simply
shows the level of consistency of data with this expectation or its departure from it.
Student’s t - test was used to compare the differences between the means of ASWSS and
NS data (C, ∅ and ) in relation to the variation in the data sets. The results were used to
determine the level of significance of the difference between the two means. In this
process the number of degrees of freedom had to apply, which in the case of geotechnical
data is the number of independent variables that yield the estimates, less the number of
parameters used in the intermediate steps (Wikipedia, 2014). The implication of this is
that if the number of replicates of an observed data is n, then the number of degrees of
freedom is n - 1. This is applied in the computation of t - values of this analysis, and since
data were observed at 1.5, 2.0, 2.5, 3.0 and 3.5 m depths, n = 5 and the number of degrees
of freedom = n – 1 = 5 - 1= 4. This means that ASWSS has number of degrees of
freedom of 4 and NS has number of degrees of freedom of 4 and hence their combined
number of degrees of freedom is 8.
For any computed value of t in this analysis, the t – table was entered for number of
degrees of freedom of 8 and for a minimum confidence level of 95% or 0.05. The
tabulated t – table value at this level of confidence was compared with the computed
value. If the computed value is higher than the t – table value, then the difference
between those ASWSS and NS data is significant, but if it is lower, the difference is not
significant, implying that the occurrence of the difference might have been a subject of
chance. This t – test results shown in Table 4.2 were obtained by computing the t values
using the t – table shown in Table D. 1 of Appendix D.
153
Table 4.2a: Student’s T-Test of Triaxial Test Results Zone: A Site: 1
ASWSS () /
NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
10 28
Replicate 2 (2.0 m depth)
16 27
Replicate 3(2.5 m depth)
10 24
Replicate 4 (3.0 m depth)
15 22
Replicate 5 (3.5 m depth)
12 19
∑
63 120 Total (=sum of the 4 replicate values)
5 5 12.6 24 Mean (=total/ )
∑
825 2,934 Sum of the squares of each replicate value
∑
3,969 14,400 Square of the total∑ . It is not the same as
∑
∑
793.8 2,880
∑
31.20 54.0 ∑ = ∑ −
∑
7.8 13.5 = ∑/ − 1
=1
1 +2
2 4.26 is the variance of the difference
between the means
154
2.06 = √ (the standard deviation of the difference between the means)
=1− 2
t = 5.53 Very highly significant
Table 4.2b: Student’s T-Test of Triaxial Test Results Zone: A Site: 1
ASWSS (∅) (ᵒ)
NS (∅) (ᵒ)
Remark Level of Significance
Replicate 1 (1.5 m depth)
11 13
Replicate 2 (2.0 m depth)
9 10
Replicate 3(2.5 m depth)
7 15
Replicate 4 (3.0 m depth)
10 8
Replicate 5 (3.5 m depth)
9 9
∑
46 55 Total (=sum of the 4 replicate values)
5 5 9.2 11 Mean (=total/ )
∑
432 639 Sum of the squares of each replicate value
∑
2,116 3,025 Square of the total∑ . It is not the same as
∑
∑
423.2 605
∑
8.8 34 ∑ = ∑ −
∑
2.2 8.5 = ∑/ − 1
=1
1 +2
2 2.14
is the variance of the difference between the means
1.46 = (the standard deviation of the
difference between the means)
=1− 2
t = 1.23 Not significant
155
Table 4.2c: Student’s T-Test of Triaxial Test Results Zone: A Site: 1
ASWSS () /
NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
15.78 15.90
Replicate 2 (2.0 m depth)
13.97 16.80
Replicate 3(2.5 m depth)
14.19 16.80
Replicate 4 (3.0 m depth)
15.21 15.67
Replicate 5 (3.5 m depth)
16.01 16.24
∑
75.16 81.41 Total (=sum of the 4 replicate values)
5 5 15.03 16.28 Mean (=total/ )
∑
1,133.19 1,326.58 Sum of the squares of each replicate value
∑
5,649.03 6,627.59 Square of the total∑ . It is not the same as
∑
∑
1,129.81 1,325.52
∑
3.38 1.06 ∑ = ∑ −
∑
0.845 0.265 = ∑/ − 1
=1
1 +2
2 0.222
is the variance of the difference between the means
0.47 = (the standard deviation of the
difference between the means)
=1− 2
t = 2.66 Significant
Table 4.2d: Student’s T-Test of Triaxial Test Results Zone: A
156
Site: 2 ASWSS ()
/ NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
10 24
Replicate 2 (2.0 m depth)
14 25
Replicate 3(2.5 m depth)
15 19
Replicate 4 (3.0 m depth)
14 25
Replicate 5 (3.5 m depth)
13 22
∑
66 115 Total (=sum of the 4 replicate values)
5 5 13.2 23 Mean (=total/ )
∑
886 2,671 Sum of the squares of each replicate value
∑
4,356 13,225 Square of the total∑ . It is not the same as
∑
∑
871.2 2,645
∑
14.8 26 ∑ = ∑ −
∑
3.7 6.5 = ∑/ − 1
=1
1+
2
2
2.04 is the variance of the difference
between the means
1.43 = (the standard deviation of the
difference between the means)
=1− 2
t = 6.85 Very highly significant
Table 4.2e: Student’s T-Test of Triaxial Test Results Zone: A Site: 2
ASWSS (∅) (ᵒ)
NS (∅) (ᵒ)
Remark Level of Significance
Replicate 1 (1.5 m depth)
10 14
157
Replicate 2 (2.0 m depth)
10 12
Replicate 3(2.5 m depth)
9 13
Replicate 4 (3.0 m depth)
8 15
Replicate 5 (3.5 m depth)
9 16
∑
46 70 Total (=sum of the 4 replicate values)
5 5 9.2 14 Mean (=total/ )
∑
426 990 Sum of the squares of each replicate value
∑
2,116 4,900 Square of the total∑ . It is not the same as
∑
∑
423.2 980
∑
2.8 10 ∑ = ∑ −
∑
0.7 2.5 = ∑/ − 1
=1
1 +2
2 0.64
is the variance of the difference between the means
0.8 = (the standard deviation of the
difference between the means)
=1− 2
t = 6 Very highly significant
Table 4.2f: Student’s T-Test of Triaxial Test Results Zone: A Site: 2
ASWSS () /
NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
15.96 17.14
Replicate 2 (2.0 m depth)
14.42 16.24
Replicate 3(2.5 m depth)
14.72 15.90
Replicate 4 (3.0 m 15.98 16.58
158
depth) Replicate 5 (3.5 m depth)
16.32 16.12
∑
77.40 81.98 Total (=sum of the 4 replicate values)
5 5 15.48 16.40 Mean (=total/ )
∑
1,201.04 1,345.08 Sum of the squares of each replicate value
∑
5,990.76 6,720.72 Square of the total∑ . It is not the same as
∑
∑
1,198.15 1,344.14
∑
2.89 0.94 ∑ = ∑ −
∑
0.72 0.24 = ∑/ − 1
=1
1 +2
2 0.19
is the variance of the difference between the means
0.44 = (the standard deviation of the
difference between the means)
=1− 2
t = 2.09 Significant
Table 4.2g: Student’s T-Test of Triaxial Test Results Zone: B Site: 1
ASWSS () /
NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
9 25
Replicate 2 (2.0 m depth)
18 17
Replicate 3(2.5 m depth)
19 18
Replicate 4 (3.0 m depth)
12 22
Replicate 5 (3.5 m depth)
13 28
∑
71 110 Total (=sum of the 4 replicate values)
159
5 5 14.2 22 Mean (=total/ )
∑
1,079 2,506 Sum of the squares of each replicate value
∑
5,041 12,100 Square of the total∑ . It is not the same as
∑
∑
1,008.2 2,420
∑
70.8 86 ∑ = ∑ −
∑
17.70 21.5 = ∑/ − 1
=1
1 +2
2 7.84
is the variance of the difference between the means
2.8 = (the standard deviation of the
difference between the means)
=1− 2
t = 2.79 Significant
Table 4.2h: Student’s T-Test of Triaxial Test Results Zone: B Site: 1
ASWSS (∅) (ᵒ)
NS (∅) (ᵒ)
Remark Level of Significance
Replicate 1 (1.5 m depth)
12 16
Replicate 2 (2.0 m depth)
13 13
Replicate 3(2.5 m depth)
13 14
Replicate 4 (3.0 m depth)
13 16
Replicate 5 (3.5 m depth)
15 15
∑
66 74 Total (=sum of the 4 replicate values)
5 5 13.2 14.8 Mean (=total/ )
∑
876 1102 Sum of the squares of each replicate value
4,356 5,476 Square of the
160
∑
total∑ . It is not the same as
∑ ∑
871.2 1,095.2
∑
4.8 6.8 ∑ = ∑ −
∑
1.2 1.7 = ∑/ − 1
=1
1 +2
2 0.58
is the variance of the difference between the means
0.76 = (the standard deviation of the
difference between the means)
=1− 2
t = 2.11 Significant
Table 4.2i: Student’s T-Test of Triaxial Test Results Zone: B Site: 1
ASWSS () /
NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
16.58 15.80
Replicate 2 (2.0 m depth)
13.98 16.40
Replicate 3(2.5 m depth)
14.87 16.60
Replicate 4 (3.0 m depth)
16.35 16.60
Replicate 5 (3.5 m depth)
16.35 16.68
∑
78.13 82.08 Total (=sum of the 4 replicate values)
5 5 15.63 16.42 Mean (=total/ )
∑
1226.10 1347.94 Sum of the squares of each replicate value
∑
6,104.30 6,737.13 Square of the total∑ . It is not the same as
∑
∑
1,220.86 1,347.43
161
∑
5.24 0.51 ∑ = ∑ −
∑
1.31 0.13 = ∑/ − 1
=1
1 +2
2 0.288 is the variance of the difference
between the means
0.54 = √ (the standard deviation of the difference between the means)
=1− 2
t = 1.46 Not significant
Table 4.2j: Student’s T-Test of Triaxial Test Results Zone: B Site: 2
ASWSS () /
NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
9 20
Replicate 2 (2.0 m depth)
10 24
Replicate 3(2.5 m depth)
11 19
Replicate 4 (3.0 m depth)
12 22
Replicate 5 (3.5 m depth)
14 22
∑
56 107 Total (=sum of the 4 replicate values)
5 5 11.2 21.4 Mean (=total/ )
∑
642 2,305 Sum of the squares of each replicate value
∑
3,136 11,449 Square of the total∑ . It is not the same as
∑
∑
627.2 2,289.8
∑
14.8 15.2 ∑ = ∑ −
∑
3.7 3.8 = ∑/ − 1
=1
1 +2
2 1.5
is the variance of the difference between the means
162
1.22 = (the standard deviation of the
difference between the means)
=1− 2
t = 8.36 Very highly significant
Table 4.2k: Student’s T-Test of Triaxial Test Results Zone: B Site: 2
ASWSS (∅) (ᵒ)
NS (∅) (ᵒ)
Remark Level of Significance
Replicate 1 (1.5 m depth)
12 11
Replicate 2 (2.0 m depth)
9 13
Replicate 3(2.5 m depth)
10 13
Replicate 4 (3.0 m depth)
12 14
Replicate 5 (3.5 m depth)
13 16
∑
56 67 Total (=sum of the 4 replicate values)
5 5 11.2 13.4 Mean (=total/ )
∑
638 911 Sum of the squares of each replicate value
∑
3,136 4,489 Square of the total∑ . It is not the same as
∑
∑
627.2 897.8
∑
10.8 13.2 ∑ = ∑ −
∑
2.7 3.3 = ∑/ − 1
=1
1 +2
2 1.2
is the variance of the difference between the means
1.095 = (the standard deviation of the
difference between the means)
=1− 2
t = 2.0 Significant
163
Table 4.2l: Student’s T-Test of Triaxial Test Results Zone: B Site: 2
ASWSS () /
NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
15.98 15.89
Replicate 2 (2.0 m depth)
15.50 16.22
Replicate 3(2.5 m depth)
14.98 16.22
Replicate 4 (3.0 m depth)
16.10 16.24
Replicate 5 (3.5 m depth)
16.30 16.40
∑
78.86 80.97 Total (=sum of the 4 replicate values)
5 5 15.77 16.19 Mean (=total/ )
∑
1,244.91 1,311.37 Sum of the squares of each replicate value
∑
6,218.90 6,556.14 Square of the total∑ . It is not the same as
∑
∑
1,243.78 1,311.23
∑
1.13 0.14 ∑ = ∑ −
∑
0.28 0.04 = ∑/ − 1
=1
1 +2
2 0.064
is the variance of the difference between the means
0.25 = (the standard deviation of the
difference between the means)
=1− 2
t =1.68 Not significant
Table 4.2m: Student’s T-Test of Triaxial Test Results Zone: C
164
Site: 1 ASWSS ()
/ NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
10 28
Replicate 2 (2.0 m depth)
9 26
Replicate 3(2.5 m depth)
11 25
Replicate 4 (3.0 m depth)
10 20
Replicate 5 (3.5 m depth)
12 19
∑
52 118 Total (=sum of the 4 replicate values)
5 5 10.4 23.6 Mean (=total/ )
∑
546 2,846 Sum of the squares of each replicate value
∑
2,704 13,924 Square of the total∑ . It is not the same as
∑
∑
540.8 2,784.8
∑
5.2 61.2 ∑ = ∑ −
∑
1.3 15.3 = ∑/ − 1
=1
1+
2
2
3.32 is the variance of the difference
between the means
1.82 = (the standard deviation of the
difference between the means)
=1− 2
t = 7.25 Very highly significant
Table 4.2n: Student’s T-Test of Triaxial Test Results Zone: C Site: 1
ASWSS (∅) (ᵒ)
NS (∅) (ᵒ)
Remark Level of Significance
Replicate 1 (1.5 m depth)
13 13
165
Replicate 2 (2.0 m depth)
13 13
Replicate 3(2.5 m depth)
13 14
Replicate 4 (3.0 m depth)
13 15
Replicate 5 (3.5 m depth)
14 16
∑
66 71 Total (=sum of the 4 replicate values)
5 5 13.2 14.2 Mean (=total/ )
∑
872 1015 Sum of the squares of each replicate value
∑
4,356 5,041 Square of the total∑ . It is not the same as
∑
∑
871.2 1,008.2
∑
0.8 6.8 ∑ = ∑ −
∑
0.2 1.7 = ∑/ − 1
=1
1 +2
2 0.38
is the variance of the difference between the means
0.62 = (the standard deviation of the
difference between the means)
=1− 2
t = 1.61 Not significant
Table 4.2o: Student’s T-Test of Triaxial Test Results Zone: C Site: 1
ASWSS () /
NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
16.20 15.90
Replicate 2 (2.0 m depth)
14.98 16.82
Replicate 3(2.5 m depth)
15.80 16.80
Replicate 4 (3.0 m 16.24 16.84
166
depth) Replicate 5 (3.5 m depth)
16.24 16.84
∑
79.46 83.20 Total (=sum of the 4 replicate values)
5 5 15.89 16.64 Mean (=total/ )
∑
1,263.96 1,385.13 Sum of the squares of each replicate value
∑
6,313.89 6,922.24 Square of the total∑ . It is not the same as
∑
∑
1,262.78 1,384.45
∑
1.18 0.68 ∑ = ∑ −
∑
0.295 0.17 = ∑/ − 1
=1
1 +2
2 0.093
is the variance of the difference between the means
0.30 = (the standard deviation of the
difference between the means)
=1− 2
t = 2.5 Significant
Table 4.2p: Student’s T-Test of Triaxial Test Results Zone: C Site: 2
ASWSS () /
NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
11 23
Replicate 2 (2.0 m depth)
13 18
Replicate 3(2.5 m depth)
11 22
Replicate 4 (3.0 m depth)
12 19
Replicate 5 (3.5 m depth)
10 23
∑
47 105 Total (=sum of the 4 replicate values)
167
5 5 9.4 21 Mean (=total/ )
∑
655 2,227 Sum of the squares of each replicate value
∑
2,209 11,025 Square of the total∑ . It is not the same as
∑
∑
441.8 2,205
∑
213.2 22 ∑ = ∑ −
∑
53.3 5.5 = ∑/ − 1
=1
1 +2
2 11.76
is the variance of the difference between the means
3.43 = (the standard deviation of the
difference between the means)
=1− 2
t = 3.38 Highly significant
Table 4.2q: Student’s T-Test of Triaxial Test Results Zone: C Site: 2
ASWSS (∅) (ᵒ)
NS (∅) (ᵒ)
Remark Level of Significance
Replicate 1 (1.5 m depth)
9 12
Replicate 2 (2.0 m depth)
11 14
Replicate 3(2.5 m depth)
10 13
Replicate 4 (3.0 m depth)
12 15
Replicate 5 (3.5 m depth)
11 16
∑
53 70 Total (=sum of the 4 replicate values)
5 5 10.6 14 Mean (=total/ )
∑
567 990 Sum of the squares of each replicate value
2,809 4,900 Square of the
168
∑
total∑ . It is not the same as
∑ ∑
561.8 980
∑
5.2 10 ∑ = ∑ −
∑
1.3 2.5 = ∑/ − 1
=1
1 +2
2 0.76
is the variance of the difference between the means
0.87 = (the standard deviation of the
difference between the means)
=1− 2
t = 3.91 Highly significant
Table 4.2r: Student’s T-Test of Triaxial Test Results Zone: C Site: 2
ASWSS () /
NS () /
Remark Level of Significance
Replicate 1 (1.5 m depth)
13.89 15.51
Replicate 2 (2.0 m depth)
14.22 16.01
Replicate 3(2.5 m depth)
12.92 16.20
Replicate 4 (3.0 m depth)
13.90 16.24
Replicate 5 (3.5 m depth)
14.28 16.30
∑
69.21 80.26 Total (=sum of the 4 replicate values)
5 5 13.84 16.05 Mean (=total/ )
∑
959.20 1,288.75 Sum of the squares of each replicate value
∑
4,790.02 6,441.67 Square of the total∑ . It is not the same as
∑
∑
958.00 1,288.33
169
∑
1.2 0.42 ∑ = ∑ −
∑
0.3 0.105 = ∑/ − 1
=1
1 +2
2 0.081
is the variance of the difference between the means
0.28 = (the standard deviation of the
difference between the means)
=1− 2
t = 7.9 Very highly significant
Significance in statistics means probably true, and in application, significance level
expresses how likely an implication of data pattern may be due to chance. Significance
level of 0.05 (95%) for instance means that the findings deduced from data pattern has
five percent chance of not being true. This is the minimum level of acceptance for most
engineering and scientific judgments based on statistical data.
Out of the eighteen tested cases of triaxial test results, six were in ‘very highly
significant’, two in ‘highly significant’, six in ‘significant’ and four in ‘not significant’
levels. A total of fourteen out of eighteen cases were in different significance levels
showing that seventy eight percent (78%) of the tests indicate that there exists differences
between these ASWSS and NS Properties (, ∅ and ).
4.6 T – Test of Atterberg Limits, Compaction and Specific Gravity Test Results The t – tests of Atterberg Limits, compaction and specific gravity test results were carried
out on zonal basis, with the five replicates of each of the two sites of a zone adding up to
make a total of ten replicates in the zone. The conduct and results of these tests are shown
in Tables 4.3, 4.4 and 4.5.
170
Table 4.3a: Student’s T-Test of Atterberg Limits Test Results Zone: A
ASWSS (LL) %
NS (LL) %
Remark Level of Significance
Replicate 1 40 49 Replicate 2 44 32 Replicate 3 40 33 Replicate 4 52 35 Replicate 5 28 29 Replicate 6 42 39 Replicate 7 44 36 Replicate 8 40 34 Replicate 9 50 38 Replicate 10 35 36
∑ 415 361 Total (=sum of the 4
replicate values)
41.5 10 17,649 36.1 Mean (=total/ )
∑
172,225
13,293
Sum of the squares of each replicate value
∑
17,222.5
130,321
Square of the total∑ . It is not the same as
∑
∑
426.5
13,032.1
∑
47.39
260.9 ∑ = ∑ −
∑
7.738
29.99
= ∑/ − 1
=1
1 +2
2
2.78
is the variance of the difference between the means
2.78
= (the standard deviation of the
difference between the means)
=1− 2
t = 1.94 Significant
171
Table 4.3b: Student’s T-Test of Atterberg Limits Test Results Zone: B
ASWSS (LL) %
NS (LL) %
Remark Level of Significance
Replicate 1 32 37 Replicate 2 35 37 Replicate 3 33 48 Replicate 4 34 36 Replicate 5 34 34 Replicate 6 30 32 Replicate 7 34 33 Replicate 8 33 32 Replicate 9 34 30 Replicate 10 34 33
∑
333
352 Total (=sum of the 4 replicate values)
10 10 33.3 35.2 Mean (=total/ )
∑
11,107 12,620 Sum of the squares of each replicate value
∑
110,889 123,904 Square of the total∑ . It is not the same as
∑
∑
11,088.9 12,390.4
∑
18.1 229.6 ∑ = ∑ −
∑
2.01 25.51 = ∑/ − 1
=1
1 +2
2
2.75
is the variance of the difference between the means
1.66
= (the standard deviation of the
difference between the means)
=1− 2
t = 1.14 Not significant
Table 4.3c: Student’s T-Test of Atterberg Limits Test Results Zone: C
ASWSS (LL) %
NS (LL) %
Remark Level of Significance
Replicate 1 38 42
172
Replicate 2 40 38 Replicate 3 38 36 Replicate 4 39 36 Replicate 5 39 38 Replicate 6 40 36 Replicate 7 37 38 Replicate 8 39 35 Replicate 9 37 34 Replicate 10 34 35
∑
381
368 Total (=sum of the 4 replicate values)
10 10 38.1 36.8 Mean (=total/ )
∑
14,545 13,590 Sum of the squares of each replicate value
∑
145,161
135,424
Square of the total∑ . It is not the same as
∑
∑
14,516.1 13,542.4
∑
28.9
47.6 ∑ = ∑ −
∑
3.21 5.29 = ∑/ − 1
=1
1+
2
2
0.85
is the variance of the difference
between the means
0.92
= (the standard deviation of the
difference between the means)
=1− 2
t = 1.4 Not significant
Table 4.3d: Student’s T-Test of Atterberg Limits Test Results Zone: A
ASWSS (PL) %
NS (PL) %
Remark Level of Significance
Replicate 1 35.50 35.09 Replicate 2 37.17 30.95 Replicate 3 25.54 26.97 Replicate 4 36.11 34.31 Replicate 5 25.00 28.17 Replicate 6 36.50 29.00
173
Replicate 7 37.55 28.00 Replicate 8 35.00 28.00 Replicate 9 36.50 33.00 Replicate 10 28.20 27.15
∑
333.07
300.64 Total (=sum of the 4 replicate values)
10 10 33.31 30.06 Mean (=total/ )
∑
11,317.83
9,122.44
Sum of the squares of each replicate value
∑
110,935.62
90,384.41
Square of the total∑ . It is not the same as
∑
∑
11,093.6 9,038.4
∑
224.23 84.04 ∑ = ∑ −
∑
24.91 9.34 = ∑/ − 1
=1
1+
2
2
3.425 is the variance of the difference
between the means
1.85 = (the standard deviation of the
difference between the means)
=1− 2
t =1.76 Significant
Table 4.3e: Student’s T-Test of Atterberg Limits Test Results Zone: B
ASWSS (PL) %
NS (PL) %
Remark Level of Significance
Replicate 1 27.78 26.67 Replicate 2 29.29 32.58 Replicate 3 29.29 31.01 Replicate 4 27.92 28.22 Replicate 5 30.49 25.54 Replicate 6 29.19 27.75 Replicate 7 28.55 29.00 Replicate 8 26.29 25.72 Replicate 9 28.72 27.65 Replicate 10 28.72 27.65 286.24 281.79 Total (=sum of the 4
174
∑ replicate values) 10 10 28.62 28.18 Mean (=total/ )
∑
8,204.70 7,984.65 Sum of the squares of each replicate value
∑
81,933.33 79,405.60 Square of the total∑ . It is not the same as
∑
∑
8,193.33 7,940.56
∑
11.37 44.09 ∑ = ∑ −
∑
1.26 4.90 = ∑/ − 1
=1
1 +2
2 0.62
is the variance of the difference between the means
0.78 = (the standard deviation of the
difference between the means)
=1− 2
t = 0.56 Not significant
Table 4.3f: Student’s T-Test of Atterberg Limits Test Results Zone: C
ASWSS (PL) %
NS (PL) %
Remark Level of Significance
Replicate 1 35.50 35.25 Replicate 2 36.50 34.50 Replicate 3 32.00 32.00 Replicate 4 33.50 30.95 Replicate 5 33.72 32.55 Replicate 6 28.00 29.15 Replicate 7 27.50 28.15 Replicate 8 28.85 27.15 Replicate 9 26.62 30.25 Replicate 10 25.50 26.40
∑
307.69 306.35 Total (=sum of the 4
replicate values)
10 10 30.77 30.64 Mean (=total/ )
∑
9,607.24 9,465.51 Sum of the squares of each replicate value
175
∑
94,673.14 93,850.32 Square of the total∑ . It is not the same as
∑
∑
9,467.31 9,385.03
∑
139.33 88.48 ∑ = ∑ −
∑
15.48 8.94 = ∑/ − 1
=1
1 +2
2 2.44
is the variance of the difference between the means
1.56 = (the standard deviation of the
difference between the means)
=1− 2
t = 0.08 Not significant
Table 4.3g: Student’s T-Test of Atterberg Limits Test Results Zone: A
ASWSS (PI) %
NS (PI) %
Remark Level of Significance
Replicate 1 4.5 13.91 Replicate 2 6.83 1.05 Replicate 3 4.50 6.03 Replicate 4 15.89 0.69 Replicate 5 3.0 0.83 Replicate 6 5.5 10.00 Replicate 7 6.45 8.00 Replicate 8 5.0 6.00 Replicate 9 13.50 5.00 Replicate 10 6.80 8.85
∑ 71.97 60.42 Total (=sum of the 4
replicate values)
10 10 7.20 6.04 Mean (=total/ )
∑
670.20 537.11 Sum of the squares of each replicate value
∑
5,179.68 3,650.58 Square of the total∑ . It is not the same as
∑
176
∑
517.97 365.06
∑
152.23 172.05 ∑ = ∑ −
∑
16.91 19.16 = ∑/ − 1
=1
1 +2
2 3.61
is the variance of the difference between the means
1.9 = (the standard deviation of the
difference between the means)
=1− 2
t = 0.61 Not significant
Table 4.3h: Student’s T-Test of Atterberg Limits Test Results Zone: B
ASWSS (PI) %
NS (PI) %
Remark Level of Significance
Replicate 1 4.22 10.33 Replicate 2 5.71 4.42 Replicate 3 3.71 16.99 Replicate 4 6.08 7.78 Replicate 5 3.51 8.46 Replicate 6 0.81 4.25 Replicate 7 5.45 4.00 Replicate 8 6.71 6.28 Replicate 9 5.28 2.35 Replicate 10 5.28 5.35
∑ 46.76 70.21 Total (=sum of the 4
replicate values)
10 10 4.68 7.02 Mean (=total/ )
∑
244.60 654.65 Sum of the squares of each replicate value
∑
2,186.50 4,929.44 Square of the total∑ . It is not the same as
∑
∑
218.65 492.94
∑
25.95 161.71 ∑ = ∑ −
∑
2.88 17.97 = ∑/ − 1
177
=1
1 +2
2 2.09
is the variance of the difference between the means
1.45 = (the standard deviation of the
difference between the means)
=1− 2
t = 1.61 Not significant
Table 4.3i: Student’s T-Test of Atterberg Limits Test Results Zone: C
ASWSS (PI) %
NS (PI) %
Remark Level of Significance
Replicate 1 4.50 6.75 Replicate 2 3.50 3.50 Replicate 3 6.00 4.00 Replicate 4 5.5 5.03 Replicate 5 5.28 5.45 Replicate 6 12.00 6.85 Replicate 7 9.50 9.55 Replicate 8 10.15 7.85 Replicate 9 10.38 3.75 Replicate 10 8.50 8.60
∑ 75.21 61.33 Total (=sum of the 4
replicate values)
10 10 7.52 6.13 Mean (=total/ )
∑
643.90 416.59 Sum of the squares of each replicate value
∑
5,656.54 3,761.37 Square of the total∑ . It is not the same as
∑
∑
565.65 376.13
∑
78.25 40.46 ∑ = ∑ −
∑
8.69 4.50 = ∑/ − 1
=1
1 +2
2 1.32
is the variance of the difference between the means
1.15 = (the standard deviation of the
difference between the means)
178
=1− 2
t = 1.03 Not significant
Table 4.3j: Student’s T-Test of Atterberg Limits Test Results Zone: A
ASWSS (LS) %
NS (LS) %
Remark Level of Significance
Replicate 1 4.29 10.00 Replicate 2 5.00 10.71 Replicate 3 5.71 10.00 Replicate 4 8.57 10.71 Replicate 5 10.00 10.71 Replicate 6 4.45 10.91 Replicate 7 6.00 10.50 Replicate 8 8.27 10.25 Replicate 9 8.05 10.25 Replicate 10 10.05 10.05
∑ 70.39 104.09 Total (=sum of the 4
replicate values)
10 10 7.04 10.41 Mean (=total/ )
∑
539.45 1,084.52 Sum of the squares of each replicate value
∑
4,954.75 10,834.73 Square of the total∑ . It is not the same as
∑
∑
495.48 1,083.47
∑
43.99 1.05 ∑ = ∑ −
∑
4.89 0.12 = ∑/ − 1
=1
1+
2
2
0.50 is the variance of the difference
between the means
0.71 = (the standard deviation of the
difference between the means)
=1− 2
t = 4.75 Very highly significant
179
Table 4.3k: Student’s T-Test of Atterberg Limits Test Results Zone: B
ASWSS (LS) %
NS (LS) %
Remark Level of Significance
Replicate 1 8.57 7.86 Replicate 2 9.29 8.57 Replicate 3 8.00 9.29 Replicate 4 8.57 8.57 Replicate 5 8.57 8.57 Replicate 6 9.28 8.55 Replicate 7 8.29 8.75 Replicate 8 8.57 8.55 Replicate 9 8.50 8.57 Replicate 10 8.55 8.57
∑ 86.19 86.85 Total (=sum of the 4
replicate values)
10 10 8.62 8.69 Mean (=total/ )
∑
744.28 756.58 Sum of the squares of each replicate value
∑
7,428.72 7,542.92 Square of the total∑ . It is not the same as
∑
∑
742.87 754.29
∑
1.41 2.29 ∑ = ∑ −
∑
0.16 0.25 = ∑/ − 1
=1
1 +2
2 0.04
is the variance of the difference between the means
0.20 = (the standard deviation of the
difference between the means)
=1− 2
t = 0.35 Not significant
Table 4.3l: Student’s T-Test of Atterberg Limits Test Results Zone: C
ASWSS (LS) NS (LS) Remark Level of
180
% % Significance Replicate 1 7.95 9.25 Replicate 2 8.71 8.85 Replicate 3 8.77 8.57 Replicate 4 8.75 8.90 Replicate 5 8.55 8.55 Replicate 6 7.25 8.25 Replicate 7 8.15 7.00 Replicate 8 6.27 9.15 Replicate 9 7.75 6.75 Replicate 10 8.05 7.15
∑ 80.2 82.42 Total (=sum of the 4
replicate values)
10 10 8.02 8.24 Mean (=total/ )
∑
650.43 687.11 Sum of the squares of each replicate value
∑
6,432.04 6,793.06 Square of the total∑ . It is not the same as
∑
∑
643.20 679.31
∑
7.23 7.8 ∑ = ∑ −
∑
0.80 0.87 = ∑/ − 1
=1
1 +2
2 0.17
is the variance of the difference between the means
0.41 = (the standard deviation of the
difference between the means)
=1− 2
t = 0.54 Not significant
Table 4.4a: T – Test of Compaction Test Results Zone: A
ASWSS (OMC) %
NS (OMC) %
Remark Level of Significance
Replicate 1 20.00 22.47 Replicate 2 20.86 18.00 Replicate 3 18.32 20.00 Replicate 4 25.00 26.51
181
Replicate 5 17.00 25.00 Replicate 6 22.00 19.25 Replicate 7 20.00 20.22 Replicate 8 23.00 25.75 Replicate 9 25.00 20.15 Replicate 10 19.00 19.00
∑ 210.18 216.35 Total (=sum of the 4
replicate values)
10 10 21.02 21.64 Mean (=total/ )
∑
4,483.76 4,766.18 Sum of the squares of each replicate value
∑
44,175.63 46,807.32 Square of the total∑ . It is not the same as
∑
∑
4,417.6 4,680.73
∑
66.16 85,45 ∑ = ∑ −
∑
7.35 9.49 = ∑/ − 1
=1
1 +2
2 1.69
is the variance of the difference between the means
1.3 = (the standard deviation of the
difference between the means)
=1− 2
t = 0.48 Not significant
Table 4.4b: T – Test of Compaction Test Results Zone: B
ASWSS (OMC) %
NS (OMC) %
Remark Level of Significance
Replicate 1 18.56 15.05 Replicate 2 18.36 14.46 Replicate 3 19.17 12.79 Replicate 4 17.97 19.54 Replicate 5 15.55 16.38 Replicate 6 20.72 22.56 Replicate 7 20.68 20.17 Replicate 8 18.18 18.27 Replicate 9 19.27 17.70
182
Replicate 10 16.35 16.32
∑ 184.81 173.24 Total (=sum of the 4
replicate values)
10 10 18.48 17.32 Mean (=total/ )
∑
3,439.92 3,078.50 Sum of the squares of each replicate value
∑
34,154.74 30,012.09 Square of the total∑ . It is not the same as
∑
∑
3,415.47 3,001.21
∑
24.45 77.29 ∑ = ∑ −
∑
2.72 8.59 = ∑/ − 1
=1
1 +2
2 1.13
is the variance of the difference between the means
1.06 = (the standard deviation of the
difference between the means)
=1− 2
t = 1.09 Not significant
Table 4.4c: T – Test of Compaction Test Results Zone: C
ASWSS (OMC) %
NS (OMC) %
Remark Level of Significance
Replicate 1 18.33 20.20 Replicate 2 19.27 19.00 Replicate 3 18.38 18.84 Replicate 4 19.20 18.90 Replicate 5 19.00 19.10 Replicate 6 15.50 16.83 Replicate 7 16.20 15.56 Replicate 8 17.22 14.20 Replicate 9 17.00 16.25 Replicate 10 17.00 16.35
∑ 177.10 175.23 Total (=sum of the 4
replicate values)
10 10 17.71 17.52 Mean (=total/ )
183
∑
3,152.00 3,104.39 Sum of the squares of each replicate value
∑
31,364.41 30,705.55 Square of the total∑ . It is not the same as
∑
∑
3,136.44 3,070.56
∑
15.56 33.83 ∑ = ∑ −
∑
1.73 3.76 = ∑/ − 1
=1
1 +2
2 0.55
is the variance of the difference between the means
0.74 = (the standard deviation of the
difference between the means)
=1− 2
t = 0.25 Not significant
Table 4.4d: T – Test of Compaction Test Results Zone: A
ASWSS (MDD) g /cm3
NS (MDD) g /cm3
Remark Level of Significance
Replicate 1 1.56 1.67 Replicate 2 1.48 1.67 Replicate 3 1.57 1.39 Replicate 4 1.71 1.33 Replicate 5 1.51 1.48 Replicate 6 1.67 1.76 Replicate 7 1.55 1.82 Replicate 8 1.60 1.70 Replicate 9 1.50 1.65 Replicate 10 1.58 1.68
∑ 15.73 16.15 Total (=sum of the 4
replicate values)
10 10 1.57 1.62 Mean (=total/ )
∑
24.79 26.31 Sum of the squares of each replicate value
∑
247.43 260.82 Square of the total∑ . It is not the same as
184
∑ ∑
24.74 26.08
∑
0.05 0.23 ∑ = ∑ −
∑
0.005 0.026 = ∑/ − 1
=1
1 +2
2 0.031
is the variance of the difference between the means
0.18 = (the standard deviation of the
difference between the means)
=1− 2
t = 0.28 Not significant
Table 4.4e: T – Test of Compaction Test Results Zone: B
ASWSS (MDD) g /cm3
NS (MDD) g /cm3
Remark Level of Significance
Replicate 1 1.93 1.85 Replicate 2 1.80 1.96 Replicate 3 1.65 1.93 Replicate 4 1.57 1.81 Replicate 5 1.70 1.88 Replicate 6 1.68 1.71 Replicate 7 1.67 1.79 Replicate 8 1.56 1.48 Replicate 9 1.66 1.70 Replicate 10 1.65 1.65
∑ 16.87 17.76 Total (=sum of the 4
replicate values)
10 10 1.69 1.78 Mean (=total/ )
∑
28.57 31.73 Sum of the squares of each replicate value
∑
284.59 315.42 Square of the total∑ . It is not the same as
∑
∑
28.46 31.54
∑
0.11 0.19 ∑ = ∑ −
∑
185
0.012 0.02 = ∑/ − 1
=1
1 +2
2 0.0034
is the variance of the difference between the means
0.06 = (the standard deviation of the
difference between the means)
=1− 2
t =1.5 Not significant
Table 4.4f: T – Test of Compaction Test Results Zone: C
ASWSS (MDD) g /cm3
NS (MDD) g /cm3
Remark Level of Significance
Replicate 1 1.67 1.80 Replicate 2 1.90 1.84 Replicate 3 1.83 1.79 Replicate 4 1.72 1.67 Replicate 5 1.52 1.54 Replicate 6 1.94 1.80 Replicate 7 1.90 1.92 Replicate 8 1.82 1.90 Replicate 9 1.79 1.88 Replicate 10 1.72 1.76
∑ 17.81 17.90 Total (=sum of the 4
replicate values)
10 10 1.78 1.79 Mean (=total/ )
∑
31.87 32.16 Sum of the squares of each replicate value
∑
317.19 320.41 Square of the total∑ . It is not the same as
∑
∑
31.72 32.04
∑
0.15 0.12 ∑ = ∑ −
∑
0.016 0.013 = ∑/ − 1
=1
1 +2
2 0.0029
is the variance of the difference between the means
0.054 = (the standard deviation of the
difference between the means)
186
=1− 2
t = 0.19 Not significant
Table 4.5a: Student’s T-Test of Specific Gravity (Gs) Test Results Zone: A
ASWSS (Gs)
NS (Gs)
Remark Level of Significance
Replicate 1 1.64 2.21 Replicate 2 2.04 2.36 Replicate 3 2.14 2.47 Replicate 4 2.26 2.54 Replicate 5 2.45 2.66 Replicate 6 1.88 2.56 Replicate 7 2.17 2.60 Replicate 8 2.48 2.64 Replicate 9 2.56 2.66 Replicate 10 2.64 2.65
∑ 22.26 25.35 Total (=sum of the 4
replicate values)
10 10 2.23 2.54 Mean (=total/ )
∑
50.46 64.46 Sum of the squares of each replicate value
∑
495.51 642.62 Square of the total∑ . It is not the same as
∑
∑
49.55 64.26
∑
0.91 0.2 ∑ = ∑ −
∑
0.10 0.02 = ∑/ − 1
=1
1+
2
2
0.01 is the variance of the difference
between the means
0.1 = (the standard deviation of the
difference between the means)
=1− 2
t = 3.1 Highly significant
187
Table 4.5b: Student’s T-Test of Specific Gravity (Gs) Test Results Zone: B
ASWSS (Gs)
NS (Gs)
Remark Level of Significance
Replicate 1 2.52 2.55 Replicate 2 2.54 2.55 Replicate 3 2.56 2.56 Replicate 4 2.56 2.63 Replicate 5 2.58 2.67 Replicate 6 1.78 2.58 Replicate 7 1.92 2.65 Replicate 8 2.20 2.65 Replicate 9 2.58 2.67 Replicate 10 2.60 2.67
∑ 23.84 26.18 Total (=sum of the 4
replicate values)
10 10 2.38 2.62 Mean (=total/ )
∑
57.68 68.56 Sum of the squares of each replicate value
∑
568.35 685.39 Square of the total∑ . It is not the same as
∑
∑
56.84 68.54
∑
0.84 0.02 ∑ = ∑ −
∑
0.09 0.002 = ∑/ − 1
=1
1 +2
2 0.01
is the variance of the difference between the means
0.1 = (the standard deviation of the
difference between the means)
=1− 2
t = 2.4 Significant
Table 4.5c: Student’s T-Test of Specific Gravity (Gs) Test Results Zone: C
ASWSS (Gs) NS (Gs) Remark Level of
188
Significance Replicate 1 2.50 2.58 Replicate 2 2.57 2.65 Replicate 3 2.58 2.67 Replicate 4 2.64 2.67 Replicate 5 2.66 2.69 Replicate 6 2.14 2.57 Replicate 7 2.25 2.60 Replicate 8 2.40 2.67 Replicate 9 2.61 2.67 Replicate 10 2.63 2.69
∑ 24.98 26.46 Total (=sum of the 4
replicate values)
10 10 2.50 2.65 Mean (=total/ )
∑
62.69 70.03 Sum of the squares of each replicate value
∑
624.00 700.13 Square of the total∑ . It is not the same as
∑
∑
62.4 70.01
∑
0.29 0.02 ∑ = ∑ −
∑
0.32 0.002 = ∑/ − 1
=1
1 +2
2 0.032
is the variance of the difference between the means
0.18 = (the standard deviation of the
difference between the means)
=1− 2
t = 0.83 Not significant
Significance levels show how likely a pattern in a data set is due to chance and the
minimum level used to mean a result is good enough to be believed is 95% or 0.05
(Wikepedia, 2015). In the process of comparing the computed and tabulated values of t, a
non – significant difference at P = 0.05 means that if the null hypothesis (no significant
difference between ASWSS and NS properties) were not correct the computed value of t
189
would be expected to be greater than the tabulated t value at that level of probability P.
There is 99% chance (highly significant) of the properties of ASWSS and NS being
significantly different if the computed t value exceeds the tabulated at P = 0.01 and
99.9% chance (very highly significant) of being significantly different if it exceeds the
tabulated at P = 0.001. Higher levels of significance (P = 0.01 or P = 0.001) simply
confirms that the probability of the conclusion is correct.
By mere inspection of the sequence of observed ASWSS and NS properties, one can see
the differences between the two sets of data but there is the need to verify if the
differences are likely due to chance because of site locations or whether the differences
likely reflect actual differences in the parent population represented by data sample. The t
–test carried out on Atterberg Limits test results of ASWSS and NS revealed that only
twenty five percent (25%) of the tested cases tells that the data are good enough to
support significant difference between ASWSS and NS properties to a minimum
confidence level of 95%. The remaining seventy five percent (75%) tells the direct
opposite, that is, no significant difference between ASWSS and NS Atterberg test results
at confidence level of 95%. However, in either case, there is still five percent (5%)
chance of being wrong.
The compaction test results are one hundred percent (100%) in favour of the fact that
there are no significant differences between the Optimum Moisture Content (OMC) and
Maximum Dry Density (MDD) of ASWSS and NS. However, in the t – test of specific
gravity test results, thirty three percent (33%) gives an indication of highly significant
difference, another thirty three percent (33%) indicates significant difference and the last
thirty four percent (34%) shows no significant difference at confidence level of 95%. It
has to be noted that statistical results empower one to draw conclusions with certain
190
degree of confidence but cannot empirically prove or disprove the same. The
mathematics behind the confidence levels does not exactly guarantee the evaluated
probability. Coincidentally too, these statistical results and their significance levels do not
tell exactly what is supposed to be known but only tell how likely the data are, given the
standing null hypothesis. The desirable knowledge in this case is the likelihood of
differences in ASWSS and NS properties, given the available data.
4.7 Evaluation of Design Data Statistical modeling of geotechnical observations is relatively new. However, intuitive
interpretation of observed data in a discipline fraught with approximations can be very
misleading. Most of the errors associated with geotechnical solutions, and arising from
the use of intuition to interpret observation, are not only found to exist independently of
training but bear remarkable similarity from one individual to another (Baecher and
Christian; 2003).
Regular patterns of data scatter are often displayed in observations with large number of
measurements. This exhibited regularity is not only found within data sets but also among
data sets of this order. It is therefore clear that the statistical properties of observed data
exhibit close similarity with those of the parent population as the data sample becomes
larger. This makes it possible to infer the statistics of the parents’ population from those
of its large number of observations. This is strictly in the case of large number of
observations and not typical of the geotechnical measurement in which the observed data
is always small compared with the parent population. As the sample size becomes larger,
the variations in the statistics of many data sets of the same observation become smaller
while it is significantly larger in small size data. The coefficient of variation of observed
soil data can be as large as 100%, though values in the range of 30%-50% are more
191
common (Baecher Christian 2003; Kulhawy and Trautmann 1996; Phoon and
Kulhawy1996). The statistics and spatial patterns of variation of geotechnical
observations will mimic those of the parent population to the extent to which the sample
sizes are large compared to parent source.
Each soil property has its role, directly or indirectly, in the process of foundation design.
Some properties are applied in design calculations while some simply inform vital design
or construction decisions. In this study the properties that are used directly in design
calculations are soil unit weight (γ), cohesion (), angle of internal resistance (φ) and
foundation width (B). However, evaluation of soil properties was extended to depths 4.0
and 4.5 m in other to show the possible trend of variation of soil properties with depth
using the principle of regression analysis. This was done only to examine the variation of
soil properties to those depths while design calculations were however based on the
measured soil parameters, that is, from depth 1.5 to 3.5 m only.
For site 1 of Zone A, soil properties (, φ and γ) at depth 4.0 m and 4.5 m were
evaluated using equations 3.45 and 3.49, that is,
∑
∑
∑ −⁄ ∑
⁄ −
For site 1 of zone A on Table 4.1(d) the values of (cohesion) at depths 4.0 m and 4.5 m
for SWS were evaluated thus:
= ℎ , = (Cohesion)
= 2.5 = 24
− − – − ( − ) − 1 1 4 − 4
192
− 0.5 − 0.25 3 − 1.5 0 0 0 0 0.5 0.25 − 2 − 1 1
. − 5
.
= ∑ (1 − )1 −
∑ 1 − 2
= =
− 11.52.5 = − 4.6
= − 4.6
=
−
= − = 35.5
The fitted model (for cohesion of site 1 zone A in Table C.4) then is = + + = = 35.5 + (− 4.6) + = 35.5 − 4.6 + At depth 1.5m = 35.5 − (4.6 × 1.5) + = 35.5 − 6.9 + = 28.6 + 28 = 28.6 + = 28.0 − 28.6 = − 0.6 At depth 2.0 = 35.5 − (4.6 × 2.0) + = 35.5 − 9.2 + 27 = 26.3 + = 27 − 26.3 = 0.7 At depth 2.5 = 35.5 − (4.6 × 2.5) + = 35.5 − 11.5 + = 24 + 24 = 24 + = 0 At depth 3.0 = 35.5 − (4.6 × 3) + = 35.5 − 13.8 + 22 = 21.7 + = 0.3 At depth 3.5 = 35.5 − (4.6 × 3.5) + = 35.5 − 16.1 + 19 = 19.4 + = − 0.4 Mean value of = 0
193
∴ at depth 4.0 m = = 35.5 − 4.6 × 4+ 0 35.5 − 18.4 = 17.1 at depth 4.5 m = = 35.5 − 4.6 × 4.5+ 0 = 14.8 Similarly, , ϕ and values at depths 4.0 m and 4.5 m for both ASWSS and NS were
evaluated as shown in Table 4.6
Table 4.6 Triaxial Test Results (including estimated values at 4.0 and 4.5 m)
Property Zone Site Depth of Stratum
(m)
Mean Value
ASWSS NS
(kN/m2) ∅ (º) (kN/m3) (kN/m2) ∅ (º) (kN/m3) Triaxial Test Result
A 1 1.5 2.0 2.5 3.0 3.5 4.0 4.5
10 16 10 15 12 16 16
11 9 7 10 9 8 8
15.78 13.97 14.19 15.21 16.01 15.72 15.54
28 27 24 22 19 17 17
13 10 15 8 9 8 7
15.90 16.80 16.80 15.67 16.24 16.27 16.10
2 1.5 2.0 2.5 3.0 3.5 4.0 4.5
10 14 15 14 13 16 16
10 10 9 8 9 18 17
15.96 14.42 14.72 15.98 16.32 16.43 16.23
24 25 19 25 22 19 18
14 12 13 15 16 15 16
17.14 16.24 15.90 16.58 16.12 16.12 16.31
194
B 1
1.5 2.0 2.5 3.0 3.5 4.0 4.5
9 18 19 12 13 19 18
12 13 13 13 15 15 16
16.58 13.98 14.87 16.35 16.35 16.12 16.31
25 17 18 22 28 21 20
16 13 14 16 15 15 15
15.80 16.40 16.60 16.60 16.68 17.00 17.20
2 1.5 2.0 2.5 3.0 3.5 4.0 4.5
9 10 11 12 14 19 18
12 9 10 12 13 14 16
15.98 15.50 14.98 16.10 16.30 16.44 16.58
20 24 19 22 22 21 22
11 13 13 14 16 15 16
15.89 16.22 16.22 16.24 16.40 16.61 16.51
C 1 1.5 2.0 2.5 3.0 3.5 4.0 4.5
10 9 11 10 12 17 18
13 13 13 13 14 12 14
16.20 14.98 15.80 16.24 16.24 14.44 13.62
28 26 25 20 19 16 14
13 13 14 15 16 9 12
15.90 16.82 16.80 16.84 16.84 16.11 15.82
2 1.5 2.0 2.5 3.0 3.5 4.0 4.5
11 13 11 12 10 19 20
9 11 10 12 11 8 8
13.89 14.22 12.92 13.90 14.28 17.22 16.58
23 18 22 19 23 21 21
12 14 13 15 16 8 7
15.51 16.01 16.20 16.24 16.30 16.94 17.02
4.7.1 Trimmed upper and extended lower mean (ASWSS)
Data scatter is the most prominent feature of ASWSS that gives it its character of
inconsistency. The reinforced earth scenario in waste properties determination often gives
high spots of strength character that are too localized to represent the general behavior of
the waste. These values, when applied affect the deduced mean strength of the field and
hence must be trimmed off the observed character of the waste in order to forestall their
possible misleading influence. These values called outliers may, where clearly
conspicuous, be spotted by mere inspection because of their inconsistency with the
observed data distribution. Beside ‘reinforce earth scenario’ the presence of outliers in
data distribution may be caused by measurement/observation or recording errors. Often
195
times, their inclusion in data distribution is detrimental to the very purpose of
investigation. The simplest thing to do is to expunge them from the list.
Researchers (e.g Kottegoda and Rosso 1997) have recommended five percent (5%) upper
trim of data in a normal site investigation to exclude outliers from data distribution. No
doubt, this value need be raised in the investigation exercise of a difficult field like
ASWSS. In this study 15% upper trim of data was applied because of the difficult nature
of ASWSS.
In a randomly heterogeneous field, the chances of capturing data from all possible weak
zones are slim. There is the possibility of excluding some lower values of soil data and
experience and analyses have shown that the existence of weaker zones can change the
shape of slip surfaces crossing the zones It is therefore imperative that an ‘Extended
Lower Mean’ be applied in defining the mean value of soil data. The percentage to be
applied in this respect depends on the site conditions and is largely a matter of judgment
based on prior probability and experience of the project site. An extended lower value of
15% was included in the data distribution of this project to make up for the weak zones of
data source not captured during investigation. The observed values of C from site 1 of
zone A in Table C. 4 of Appendix C (ASWSS) may be tabulated in its descending order
as in Table 4.7
Table 4.7: Descending order of data in Table C. 4 Site A/1 (ASWSS) Zone Site C (kN/m) Mean (kN/m) A 1 16
15 12 10 10
12.6
196
The 15% of upper value of the data was computed by finding the 15% of the total number
of data. For instance in sample A1 there are five listed data and hence 15% of 5 =
×
5 = 0.75. This is not upto single data but closer to it than otherwise and thus may be
approximated to single data which of course is the highest data in value. This
automatically corresponds to 16 / in Table 4.14.This data is therefore trimmed off
or expunged from the list.
The extension of 15% lower value was carried out by the inclusion of new data whose
value is 15% less than the lowest data in the data list. Working with the data in
Table4.14, the lowest value of C is 10 / . A new data whose value is 15% less than
10 would be 8.5 and this is reflected in Table4.7. The corresponding 15% trimmed and
extended lower values are shown in Table 4.8
Table4.8: Trimmed-upper and Extended lower values of data in Table 4.15
Zone Site C (kN/m) Mean Value A 1 15
12 10 10 8.5
11.1
Similarly the observed values of C from site 2 of zone A in Table C.4 (ASWSS) may be
tabulated in its descending order as shown in Table 4.9 while its corresponding 15%
trimmed upper and extended lower values shown in Table 4.10
Table 4.9: Descending order of Data in Table C.4.site A/2 (ASWSS) Zone Site C (kN/m) Mean (kN/m) A 2 15
14 14 13 10
13.2
197
Table 4.10: Trimmed upper and extended lower values of data in Table 4.9
Zone Site C (kN/m) Mean (kN/m) A 2 14
14 13 10 8.5
11.9
In the same way, the statistical properties of the trimmed upper and extended lower mean
values of the ASWSS data and the mean values of its corresponding NS data in Table C.4
were evaluated and shown in Table 4.11.
198
Table4.11: Sample mean (µ), standard deviation () and coefficient of variation (Cov) of soil data Zone Site
ASWSS NS
(kN/m2)
∅ (º) (kN/m3) (kN/m2)
∅ (º) (kN/m3)
Mean (µ)
Cov (%)
Mean (µ)
∅ Cov (%)
Mean (µ)
Cov (%)
Mean (µ)
Cov (%)
Mean (µ)
∅ Cov (%)
Mean (µ)
Cov (%)
A 1 2
11.1 2.86 20 7 1.63 16 13.7 1.4 6 27 1.25 14 10 1.25 16 15.97 1.53 3 11.9 2.27 20 8 1.24 16 14.25 1.4 5 23 1.24 10 13 0.94 11 16.08 1.56 3
B 1 2
11.9 4.23 26 12 1.25 8 13.46 1.88 7 26 2.49 19 14 0.82 9 16.18 0.37 2 9.9 1.76 15 9 1.63 15 14.14 1.41 3 21 2.05 9 12 1.25 14 16.05 0.23 1
C 1 2
9.5 1.35 12 12 0.94 3 14.21 1.47 4 26 2.49 15 13 1.25 14 16.17 0.89 2 10.5 1.43 11 9 1.25 11 12.92 1.39 4 21 2.05 10 12 2.05 11 16.62 0.67 2
199
4.7.2 Design values of soil properties and load effects The 95% fractile specified for the definition of characteristic values by EN 1990 has been
expressed in equations 2.6 and 2.8 for characteristic load effects and characteristic soil
material property respectively. Taking the factor Ψ to be unity, the design value of load
effects equals its characteristic value. The design values of soil data were the
characteristic values computed form the values obtained from equation 2.11, that is,
= [ ]
This computed value for is used to obtain the characteristic value of soil property from
equation 2.8. The characteristic values () were cautiously estimated using equations
2.8 and 2.11. Equation 2.11 provided the standard deviations from the best and worst
estimates of soil data while equation 2.8 provided the characteristic values ( ) based on
the computed standard deviations. These values are shown in Table 4.13.
The population mean of soil data for each zone may be computed using equation 3.1
That is =
∑
Where is the zonal population mean, is the number of strata, is the observed data
size of the stratum and the corresponding mean. The computed mean values are shown
in Table 4.12
Table 4.12: Population mean for zones Property Zone Site Mean Value
ASWSS NS
(kN/m2)
∅ (º) (kN/m3) (kN/m2)
∅ (º) (kN/m3)
C,∅& A 11.5 7.5 13.98 25 11.5 16.03
200
B 10.90 10.5 13.8 23.5 13 16.27 C 10 10.5 13.57 23.5 12.5 15.90
201
Table 4.13: Characteristic values of soil data Zone Site
ASWS Natural Soil
(kN/m2)
∅ (º) (kN/m3) (kN/m2) ∅ (º) (kN/m3)
μ μ μ μ μ μ A 1
2 15 11.1 8.5 9 7 5 14.74 13.7 11.37 28 27 25 12 10 9 16.49 15.97 13.01 14 11.9 8.5 9 8 6 15.54 14.25 12.14 25 23 22 13 13 11 16.8 16.08 13.18
B 1 2
18 11.9 7.7 13 12 10 15.12 13.46 10.57 28 26 22 15 14 13 16.44 16.18 15.56 12 9.9 7.7 11 9 7 15.18 14.14 11.81 24 21 19 13 12 10 16.26 16.05 15.73
C 1 2
11 9.5 7.7 12 12 10 15.28 14.21 11.77 28 26 22 15 13 12 16.37 16.17 14.4 12 10.5 8.5 10 9 7 13.33 12.92 10.09 23 21 18 15 12 10 15.87 15.62 14.3
Where , , are the characteristic values for maximum soil data, , , the characteristic values for
minimum soil data and μc, μ, μ the characteristic values for mean soil data.
202
4.8 Determination of Foundation Width The foundation width is that width of foundation required to support the design load with
the settlement value not exceeding the allowable limit of 25 mm. foundation widths are
computed using ULS design and by equating the design action effects to the design
soil resistance , that is = . The design load effect and design soil resistance are
the factored characteristic load effects and factored characteristic resistance respectively.
These factors were obtained from DA 1.C1 of Eurocode 7 partial factors as 1.35 for
permanent load and 1.5 for variable load respectively. For permanent load of 66.67 kN
and variable load of 40 kN, design action effects = 66.7 × 1.35+ 40 × 1.5=
150
Applying Meyerhof’s (1963) general formula for soil bearing capacity ,
= + + 0.5 4.1
Where , and are coefficients that depends on soil’s angle of shearing resistance,
and = shape factors,
, and = Depth factors. Z = depth and B = foundation width
The design resistance = =
4.2 Where = ultimate bearing capacity of soil
= bearing capacity factor obtained from Eurocode 7 partial factors as 1.4
Using the data of Natural soil of site 1 in zone A, on Table C.4 of Appendix C and based
on vesic’s (1973) bearing capacity coefficients; C=24 = 15.97, Z = 1.5 and ϕ = 10
= 8.39, = 2.47 and = 0.52
Shape factors by DeBeer (1970) proposal:
=1 +
.
= 1.296
=1 +
tanϕ = 1.176
203
=1 − 0.4
= 0.6
Depth factors by Meyerhof (1963)
= 1 + 0.2√
= 1 + .
= = 1 + 0.1√
for ϕ 710o
= tan2 (45+2 )
=259.407 + .
+ 69.583 + 2.491
=
= 1.4 = (185.29 + .
+ 49.702 + 1.779)
For characteristic permanent load of 66.67 kN and characteristic variable load of 40 kN
=66.67 × 1.35+ 40 × 1.5= 150 Limit state equation states that the design load effects equals the design soil
resistance . For the square pad foundation in consideration = 4.3
That is = 185.29 + .
+ 49.702 + 1.779
= 185.29 + 66.241 + 49.702 + 1.779, that is 1.779+234.992 +
66.241= . This and other widths for various Action Effects ( ) were evaluated using
Matlab as shown in Appendix B and the values tabulated in Tables 4.14.
Table 4.14: Evaluated foundation widths using soil data of site 1 in zone A on Table C.4
Depth Action Effects Foundation width (1.5 m) (kN) (m)
50 0.34 100 0.53 150 0.67 200 0.79 250 0.90 300 0.99 350 1.08
204
400 1.17 450 1.25 500 1.32 550 1.39 600 1.46
Similarly, foundation widths were evaluated for zone A site 2, zone B sites 1&2 and zone
C sites 1&2 as shown in Tables 4.15, 4.16, 4.17, 4.18 and 4.19 respectively.
Table 4.15 Evaluated Foundation Widths using soil data of site 2 in zone A
Depth Action Effects Foundation width (1.50 m) (kN) (m)
50 0.28 100 0.44 150 0.57 200 0.68 250 0.77 300 0.86 350 0.94 400 1.02 450 1.08 500 1.15 550 1.21 600 1.27
Table 4.16 Evaluated foundation width using soil data of site 1 of zone B Depth Action Effects Foundation width (1.50 m) (kN) (m)
100 0.43
205
150 0.56 200 0.66 250 0.76 300 0.84 350 0.92 400 0.99 450 1.06 500 1.12 Table 4.17 Evaluated foundation widths using soil data of site 2 in zone B
Depth Action Effects Foundation width (1.5 m) (kN) (m)
100 0.49 150 0.63 200 0.75 250 0.85 300 0.94 350 1.03 400 1.11 450 1.18 500 1.25 Table 4.18 Evaluated foundation widths using soil data of site 1 in zone C
Depth Action Effects Foundation width (1.5 m) (kN) (m)
100 0.44 150 0.56 200 0.67 250 0.76 300 0.85 350 0.93 400 1.00 450 1.07 500 1.14 Table 4.19 Evaluated foundation widths using soil data of site 2 in zone C
Depth Action Effects Foundation width (1.5 m) (kN) (m)
100 0.42 150 0.55 200 0.65 250 0.74 300 0.83
206
350 0.90 400 0.98 450 1.04 500 1.11 4.9 Estimation of Settlement Value
Two most important properties of soil that are desirably measured for use in structural
foundation design involving ASWSS are strength and compressibility. Strength is
expressed in terms of bearing capacity while total settlement value expresses the level of
soil compressibility. Settlement in particular can be a problem in many difficult soils and
as such the knowledge of its value is essential in the preliminary stage of the use of
ASWSS for developments.
The consolidation tests conducted in this study for both ASWSS and NS gave total
settlement values (Pc) at different foundation depths. These results are shown in Table
C.3 of Appendix C. Pc for ASWSS ranged from 0.0002 – 0.0005, 0.0002 – 0.0004 and
0.0002 – 0.0005 m for zones A, B and C respectively. The corresponding records for NS
showed ranges of 0.0002 – 0.0003, 0.0002 – 0.0005 and 0.0002 – 0.0003 m for zones A,
B and C respectively. Nothing significantly different is noticed between the two sets of
records and none of the test results violated the allowable maximum value of 25 mm.
However, where consolidation test results are not available, theoretical evaluation of total
settlement from the proposed contact pressure and soil parameters may check for the
minimum foundation depth that would satisfy the settlement criterion.
4.10 Reliability of Foundation Design by Monte Carlo Simulation Using the minimum soil properties of zone A site 1 (Natural soil) for a spread foundation: F = 150 kN, B = 0.7 m, Z = 1.5 m C = 25 / , = 9 , Ɣ = 13.01 / N = 7.97 N = 2.29 NƔ = 0.436 S = 1.287 S = 1.158 SƔ = 0.6 D = 1.502 D = 1 DƔ = 1 q = CNSD + ƔZNSD + 0.5ƔBNƔSƔDƔ R = 385.16 + 51.75 + 1.19 = 438.1 kN/m
207
E = FkArea =
. = 306.122 kN/m M = R − E = 131.978 kN/m
Using the mean soil properties of zone A site 1 (Natural soil):
C = 27 kN/m = 10, Ɣ = 15.97 kN/m, B = 0.70 m, Z = 1.5 m N = 8.34 N = 2.47 NƔ = 0.52 S = 1.296 S = 1.176 SƔ = 0.6 D = 1.511 D = 1 DƔ = 1 R = 440.96 + 69.583 + 1.74 = 512.28 kN/m M = 512.28 − 306.122 = 206.158 kN/m
Using the maximum soil properties of zone A site 1 (Natural Soil): C = 28 kN/m = 12 , Ɣ = 16.49 kN/m, B = 0.7 m, Z = 1.5 m N = 9.40 N = 3.06 NƔ = 0.944 S = 1.33 S = 1.213 SƔ = 0.6 D = 1.529 D = 1.26 DƔ = 1.26 R = 535.24 + 115.68 + 4.119 = 655.039 kN/m F = 150 kN E = F
Area where A = Area of foundation base = . = 306.122 kN/m
M = 655.039 − 306.122 = 348.917 kN/m M = 131.978 , Difference between M and M = 216.939 M = 206.158, Simulated numbers = 10,000, M = 348.917 , Interval = 0.007418, μ = 229.024657, σ = 90.027718 β =
= 2.54
Similarly the reliability indices β and probability of failure P for selected loads F , foundation
depth Z and foundation width B were evaluated for all the sites as shown in Tables
4.20a – f.
208
Table 4.20a - f: Reliability indices and probability of failures for selected loads, Foundation
Depths, and Foundation widths by Monte Carlo Simulation.
a Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P A
1
100 0.70 1.5 3.67 0.164E-3 0.0836 0.468 150 0.70 1.5 2.54 0.582E-2 0.0 0.5 150 0.70 2.0 2.58 0.543E-2 0.068 0.474 150 0.70 2.5 2.61 0.514E-2 0.342 0.369 150 0.70 3.0 2.63 0.495E-2 0.615 0.274 150 0.70 3.5 2.67 0.465E-2 1.041 0.151 150 0.75 1.5 2.98 0.154E-2 0.392 0.35 150 0.80 1.5 3.34 0.590E-3 1.031 0.153 150 0.85 1.5 3.63 0.180E-3 1.262 0.111 150 0.90 1.5 3.88 0.799E-4 1.386 0.877E-1 150 1.2 1.5 4.76 0.178E-5 1.50 0.681E-1 150 1.4 1.5 5.04 0.265E-6 1.91 0.316E-1 150 1.6 1.5 5.23 0.165E-6 2.18 0.163E-1 150 2.0 1.5 5.44 0.534E-7 2.69 0.427E-2
b Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P A
2
100 0.70 1.5 4.51 0.339E-5 0.1567 0.44 150 0.70 1.5 3.25 0.791E-3 0.0 0.5 150 0.70 2.0 3.30 0.689E-3 0.0 0.5 150 0.70 2.5 3.35 0.568E-3 0.262 0.4 150 0.70 3.0 3.38 0.501E-3 0.595 0.28 150 0.70 3.5 3.41 0.434E-3 0.952 0.17 150 0.75 1.5 3.74 0.136E-3 0.235 0.41 150 0.80 1.5 4.20 0.204E-4 0.995 0.16 150 0.85 1.5 4.46 0.566E-5 1.078 0.144 150 0.90 1.5 4.73 0.197E-5 1.528 0.64E-1 150 1.2 1.5 5.70 0.153E-7 2.02 0.221E-1 150 1.4 1.5 6.03 0.501E-8 2.51 0.611E-2 150 1.6 1.5 6.23 0.3369E-8 2.88 0.369E-2 150 2.0 1.5 6.45 0.907E-9 3.59 0.196-3
209
c Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P B
1
100 0.70 1.5 5.08 0.242E-6 1.357 0.093 150 0.70 1.5 4.06 0.2828E-4 0.198 0.424 150 0.70 2.0 4.30 0.1471E-4 0.467 0.321 150 0.70 2.5 4.54 0.3149E-5 0.595 0.280 150 0.70 3.0 4.77 0.1718E-5 0.789 0.222 150 0.70 3.5 4.96 0.5356E-6 0.952 0.173 150 0.75 1.5 4.44 0.679E-5 0.534 0.295 150 0.80 1.5 4.66 0.2402E-5 0.895 0.190 150 0.85 1.5 4.94 0.660E-6 1.132 0.91E-1 150 0.90 1.5 5.27 0.1349E-6 1.838 0.37E-1 150 1.2 1.5 6.10 0.344E-8 1.88 0.333E-1 150 1.4 1.5 6.38 0.169E-8 1.998 0.229E-1 150 1.6 1.5 6.56 0.307E-9 2.175 0.1696E-1 150 2.0 1.5 6.70 0.213E-9 2.54 0.582E-2
d Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P B
2
100 0.70 1.5 3.05 0.1238E-2 0.339 0.37 150 0.70 1.5 2.02 0.221E-1 0.052 0.48 150 0.70 2.0 2.19 0.165E-1 0.287 0.39 150 0.70 2.5 2.35 0.112E-1 0.595 0.28 150 0.70 3.0 2.47 0.720E-2 0.995 0.16 150 0.70 3.5 2.63 0.495E-2 1.428 0.08 150 0.75 1.5 2.42 0.856E-2 0.728 0.24 150 0.80 1.5 2.74 0.388E-2 1.30 0.103 150 0.85 1.5 3.01 0.133E-2 1.313 0.101 150 0.90 1.5 3.31 0.657E-3 1.728 0.0576E-1 150 1.2 1.5 4.02 0.305E-4 1.91 0.483E-1 150 1.4 1.5 4.20 0.204E-4 2.06 0.21E-1 150 1.6 1.5 4.47 0.509E-5 2.37 0.105E-1 150 2.0 1.5 4.64 0.253E-5 2.96 0.173E-2
210
e Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P C
1
100 0.70 1.5 4.89 0.971E-6 1.34 0.097 150 0.70 1.5 4.02 0.305E-4 0.13 0.45 150 0.70 2.0 4.22 0.192E-4 0.31 0.38 150 0.70 2.5 4.35 0.119E-4 0.528 0.30 150 0.70 3.0 4.46 0.566E-5 0.728 0.24 150 0.70 3.5 4.60 0.278E-5 0.929 0.18 150 0.75 1.5 4.41 0.849E-5 0.562 0.29 150 0.80 1.5 4.63 0.259E-5 0.895 0.19 150 0.85 1.5 4.89 0.971E-6 1.37 0.9E-1 150 0.90 1.5 5.19 0.186E-6 1.80 0.4E-1 150 1.2 1.5 6.01 0.583E-8 1.89 0.32E-1 150 1.4 1.5 6.33 0.225E-8 1.96 0.26E-1 150 1.6 1.5 6.50 0.347E-9 2.12 0.188E-1 150 2.0 1.5 6.67 0.233E-9 2.52 0.60E-2
f Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P C
2
100 0.70 1.5 2.56 0.56E-2 0.0 0.50 150 0.70 1.5 1.93 0.29E-1 0.0 0.5 150 0.70 2.0 2.05 0.21E-1 0.0 0.5 150 0.70 2.5 2.22 0.155E-1 0.0 0.5 150 0.70 3.0 2.31 0.125E-1 0.157 0.44 150 0.70 3.5 2.48 0.687E-2 0.528 0.3 150 0.75 1.5 2.33 0.118E-1 0.0 0.5 150 0.80 1.5 2.51 0.52E-2 0.25 0.404 150 0.85 1.5 2.84 0.29E-2 0.305 0.383 150 0.90 1.5 3.06 0.12E-2 0.418 0.34 150 1.2 1.5 3.91 0.678E-4 1.5 0.668E-1 150 1.4 1.5 4.00 0.317E-4 2.0 0.228E-1 150 1.6 1.5 4.19 0.21E-4 2.33 0.118E-1 150 2.0 1.5 4.23 0.187E-4 2.84 0.29E-2
4.11 Reliability of Foundation Design by First Order Reliability Method (FORM)
211
As a requirement for FORM analysis the mean values of soil properties with their respective
standard deviations σ were evaluated as shown in Tables 4.29a and b. The use of FORM 5
requires the equation that relates the design load effects and design resistance of soil with their
dependent and independent variables at Limit State which in this case is equation 4.3 that is
= =
1.4 4.4
= /1.4 4.5
Where 1.4 is Eurocode 7 soil resistance factor
= + + 0.5/1.4 4.6
Applying Meyerhof bearing capacity factors, that is
= 1 + 0.2 45 + ∅2
= = 1 for ∅ < 10
= = 1 for ∅ < 10
= 1 + 0.2 45 + ∅2
= 1.4 1 + 0.2 45 + ∅
2 1 + 0.1 45 + ∅
2 +
× 1 × 1+ 0.5 × 1 × 1 = ∗ 4.7
Where ∗ is the factored design resistance of soil.
At Limit state,
= ∗ 4.8
The margin of safety M is expressed as
212
= ∗ − 4.9
FORM 5 program obtains the partial derivatives of equation 4.9 with respect to the dependent
variables (c, ∅ and ). The statistical distribution of is required for the evaluation of β and
and Normal distribution was applied being the most conservative. The reliability indices and
probability of failure of foundation designs on ASWSS and NS were evaluated using FORM 5
software (Appendix A) and data in Table 4.21 as shown in Table 4.22.
Table 4.21a: Mean values and standard deviation of ASWSS properties
Zone Site ASWSS (/ ) (O) (/ ) Mean
μ
Standard deviation
Mean
μ
Standard deviation
Mean
μ
Standard deviation
A 1 11.1 2.86 7 1.63 13.7 1.4 2 11.9 2.27 8 1.24 14.25 1.4
B 1 11.9 4.23 12 1.25 13.46 1.88 2 9.9 1.76 9 1.63 14.14 1.41
C 1 9.5 1.35 12 0.94 14.21 1.47 2 10.5 1.43 9 1.25 12.92 1.39
Table 4.21b: Mean values and standard deviation of NS properties
Zone Site NS (/ ) (O) (/ )
μ
Mean
Standard deviation μ
Mean
Standard deviation μ
Mean
Standard deviation
A 1 27 1.25 10 1.25 15.97 1.53 2 23 1.24 13 0.94 16.08 1.56
B 1 26 2.49 14 0.82 16.18 0.37 2 21 2.05 12 1.25 16.05 0.23
C 1 26 2.49 13 1.25 16.17 0.89 2 21 2.05 12 2.05 15.62 0.67
213
Table 4.22a - f: Reliability indices and probability of failures for selected loads, Foundation Depths, and Foundation widths by First Order Reliability Method (FORM 5) a Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P A
1
100 0.70 1.5 4.02 0.310E-4 0.365 0.360 150 0.70 1.5 2.62 0.1710E-1 0.027 0.49 150 0.70 2.0 2.63 0.169E-1 0.235 0.41 150 0.70 2.5 2.65 0.148E-1 0.290 0.39 150 0.70 3.0 2.66 0.138E-1 0.366 0.36 150 0.70 3.5 2.72 0.392E-2 0.662 0.26 150 0.75 1.5 3.02 0.128E-2 0.339 0.370 150 0.80 1.5 3.5 0.233E-3 0.962 0.17 150 0.85 1.5 4.00 0.317E-4 0.262 0.4 150 0.90 1.5 4.20 0.204E-4 0.341 0.321 150 1.2 1.5 5.00 0.287E-6 1.70 0.492E-1 150 1.4 1.5 5.25 0.159E-6 2.0 0.228E-1 150 1.6 1.5 5.44 0.757E-7 2.35 0.112E-1 150 2.0 1.5 5.50 0.216E-7 3.0 0.135E-2
b Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P A
2
100 0.70 1.5 4.76 0.173E-5 0.235 0.41 150 0.70 1.5 3.40 0.447E-3 0.08 0.47 150 0.70 2.0 3.30 0.679E-3 0.08 0.47 150 0.70 2.5 3.34 0.679E-3 0.34 0.37 150 0.70 3.0 3.47 0.299E-3 0.79 0.22 150 0.70 3.5 3.50 0.233E-3 1.319 0.100 150 0.75 1.5 4.0 0.3167E-4 0.261 0.40 150 0.80 1.5 4.20 0.204E-4 1.047 0.15 150 0.85 1.5 4.50 0.3398E-5 0.262 0.4 150 0.90 1.5 4.88 0.103E-5 0.562 0.29 150 1.2 1.5 5.85 0.1063E-7 2.45 0.786E-2 150 1.4 1.5 6.10 0.344E-8 2.85 0.28E-2 150 1.6 1.5 6.23 0.337E-8 3.00 0.135E-2 150 2.0 1.5 6.50 0.347E-9 3.75 0.132E-3
214
c Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P B
1
100 0.70 1.5 5.15 0.207E-6 1.500 0.668E-1 150 0.70 1.5 4.23 0.187E-4 0.336 0.378 150 0.70 2.0 4.50 0.339E-5 0.528 0.300 150 0.70 2.5 4.82 0.141E-5 0.795 0.22 150 0.70 3.0 4.89 0.971E-6 0.952 0.170 150 0.70 3.5 5.00 0.287E-6 1.319 0.100 150 0.75 1.5 4.46 0.566E-5 0.695 0.250 150 0.80 1.5 4.70 0.215E-5 1.047 0.150 150 0.85 1.5 5.10 0.272E-6 1.250 0.113 150 0.90 1.5 5.38 0.852E-7 2.00 0.228E-1 150 1.2 1.5 6.27 0.292E-8 2.20 0.161E-1 150 1.4 1.5 6.50 0.246E-9 2.30 0.128E-1 150 1.6 1.5 6.65 0.247E-9 2.67 0.456E-2 150 2.0 1.5 6.75 0.179E-9 2.85 0.280E-2
d Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P B
2
100 0.70 1.5 3.06 0.12E-2 0.342 0.369 150 0.70 1.5 2.00 0.227E-1 0.157 0.44 150 0.70 2.0 2.22 0.155E-1 0.300 0.385 150 0.70 2.5 2.40 0.952E-2 0.625 0.271 150 0.70 3.0 2.50 0.621E-2 1.05 0.149 150 0.70 3.5 2.74 0.388E-2 1.40 0.852E-1 150 0.75 1.5 2.50 0.621E-2 0.815 0.214 150 0.80 1.5 2.88 0.251E-2 1.40 0.852E-1 150 0.85 1.5 3.15 0.10E-2 1.350 0.943E-1 150 0.90 1.5 3.50 0.2326E-3 1.70 0.492E-1 150 1.2 1.5 4.10 0.260E-4 2.05 0.211E-1 150 1.4 1.5 4.40 0.905E-5 2.50 0.621E-2 150 1.6 1.5 4.60 0.277E-5 2.65 0.475E-2 150 2.0 1.5 4.75 0.184E-5 3.00 0.135E-2
215
e Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P C
1
100 0.70 1.5 5.00 0.287E-6 1.75 0.448E-1 150 0.70 1.5 4.19 0.21E-4 0.287 0.390 150 0.70 2.0 4.50 0.340E-5 0.500 0.3085 150 0.70 2.5 4.66 0.240E-5 0.65 0.264 150 0.70 3.0 4.75 0.184E-5 0.82 0.213 150 0.70 3.5 4.80 0.153E-5 1.25 0.448E-1 150 0.75 1.5 4.50 0.340E-5 0.65 0.264 150 0.80 1.5 4.75 0.184E-5 0.95 0.174 150 0.85 1.5 5.00 0.287E-6 1.50 0.668E-1 150 0.90 1.5 5.38 0.852E-7 1.80 0.404E-1 150 1.2 1.5 6.50 0.347E-9 2.0 0.227E-1 150 1.4 1.5 6.75 0.179E-9 2.58 0.543E-2 150 1.6 1.5 6.80 0.146E-9 2.65 0.475E-2 150 2.0 1.5 6.88 0.923E-10 2.77 0.358E-2
f Zone Site Load F
kN Foundation width B
(m) Depth Z
(m) NS
β P ASWSS
β P C
2
100 0.70 1.5 2.69 0.427E-2 0.0 0.5 150 0.70 1.5 2.00 0.227E-1 0.0 0.5 150 0.70 2.0 2.10 0.194E-1 0.05 0.48 150 0.70 2.5 2.25 0.145E-1 0.25 0.404 150 0.70 3.0 2.50 0.621E-2 0.32 0.377 150 0.70 3.5 2.75 0.378E-2 0.500 0.308 150 0.75 1.5 2.45 0.808E-2 0.25 0.404 150 0.80 1.5 2.65 0.475E-2 0.75 0.234 150 0.85 1.5 3.00 0.135E-2 0.82 0.213 150 0.90 1.5 3.25 0.791E-3 1.00 0.1586 150 1.2 1.5 4.00 0.317E-4 2.50 0.621E-2 150 1.4 1.5 4.25 0.175E-4 2.85 0.281E-2 150 1.6 1.5 4.32 0.136E-4 3.40 0.456E-3 150 2.0 1.5 4.50 0.339E-5 3.75 0.132E-3
216
4.12 Influence of Foundation Dimensions on the Reliability of Foundation Design.
The horizontal and vertical dimensions of foundations certainly have effects on its
reliability. How depth and width affect the reliability of foundation design is important
so that where necessary dimensions may be determined and applied to the advantage of
the design. The knowledge of their influences may be used to enhance safety indices or
otherwise achieve economy within the limit of chosen target reliability. The individual
influence of horizontal dimensions and the depth of embedment on the reliability of
foundations are illustrated in Figures 4.10a - f and 4.11a - f.
Z
NS SWS
1.5 2.54 0 2 2.58 0.068
2.5 2.61 0.342 3 2.63 0.615
3.5 2.67 1.041
AA
0
0.5
1
1.5
2
2.5
3
1.5 2 2.5 3 3.5
Relia
bilit
y In
dex
(β)
Foundation Depth (m)
NS
SWS
1
1.5
2
2.5
3
3.5
4
Relia
bilit
y In
dex
(β)
NS
SWS
Figure 4.10a Influence of Foundation depth increase on Reliability index of foundation design (Zone A site 1)
217
Z NS SWS
1.5 3.25 0 2 3.3 0 2.5 3.35 0.262 3 3.38 0.595 3.5 3.41 0.952
Z NS SWS
1.5 4.06 0.198 2 4.3 0.467
2.5 4.54 0.595 3 4.77 0.789
3.5 4.96 0.952
Z NS SWS
1.5 2.02 0.052 2 2.19 0.287
2.5 2.35 0.595 3 2.47 0.995
3.5 2.63 1.428
0
1
2
3
4
5
6
1.5 2 2.5 3 3.5
Relia
bilit
y In
dex
(β)
Foundation Depth (m)
NS
SWS
0
0.5
1
1.5
2
2.5
3
1.5 2 2.5 3 3.5
Relia
bilit
y In
dex
(β)
Foundation Depth (m)
NS
SWS
Figure 4.10b Influence of Foundation depth increase on Reliability index of foundation design (Zone A site 2)
Figure 4.10c Influence of Foundation depth increase on Reliability index of foundation design (Zone B site 1)
218
Z NS SWS
1.5 4.02 0.13 2 4.22 0.31
2.5 4.35 0.528 3 4.46 0.728 3.5 4.6 0.929
Z NS SWS
1.5 1.93 0 2 2.05 0
2.5 2.22 0 3 2.31 0.157
3.5 2.48 0.528
00.5
11.5
22.5
33.5
44.5
5
1.5 2 2.5 3 3.5
Relia
bilit
y In
dex
(β)
F0unation Depth (m)
NS
SWS
0
0.5
1
1.5
2
2.5
3
1.5 2 2.5 3 3.5
Relia
bilit
y In
dex
(β)
Foundation Depth (m)
NS
SWS
Figure 4.10d Influence of Foundation depth increase on Reliability index of foundation design (Zone B site 2)
Figure 4.1 (iv) Influence of Foundation depth increase on Reliability index of foundation design (Zone B site 2)
Figure 4.1 (iv) Influence of Foundation depth increase on Reliability index of foundation design (Zone B site 2)
Figure 4.1 (iv) Influence of Foundation depth increase on Reliability index of foundation design (Zone B site 2) Figure 4.1 (iv) Influence of Foundation depth increase on Reliability index of foundation design (Zone B site 2)
Figure 4.10e Influence of Foundation depth increase on Reliability index of foundation design (Zone C site 1)
219
B NS SWS
0.7 2.54 0 0.75 2.98 0.392 0.8 3.34 1.031
0.85 3.63 1.262 0.9 3.88 1.386 1.2 4.76 1.5
1.4 5.04 1.91 1.6 5.23 2.18 2 5.44 2.69
B NS SWS
0.7 3.25 0 0.75 3.74 0.235
0.8 4.2 0.995 0.85 4.46 1.078
0.9 4.73 1.528 1.2 5.7 2.02 1.4 6.03 2.51
1.6 6.23 2.88 2 6.45 3.59
0
1
2
3
4
5
6
0.7 0.75 0.8 0.85 0.9 1.2 1.4 1.6 2
Relia
bilit
y In
dex
(β)
Foundation Width (m)
NS
SWS
0
1
2
3
4
5
6
7
0.7 0.75 0.8 0.85 0.9 1.2 1.4 1.6 2
Relia
bilit
y In
dex(
β)
Foundation Width (m)
NS
SWS
Figure 4.10f Influence of Foundation depth increase on Reliability index of foundation design (Zone C site 2)
Figure 4.1 (vi) Influence of Foundation depth increase on Reliability index of foundation design (Zone C site 2)
Figure 4.1 (vi) Influence of Foundation depth increase on Reliability index of foundation design (Zone C site 2)
Figure 4.11a Influence of Foundation width increase on Reliability index of foundation design (Zone A site 1)
Figure 4.11b Influence of Foundation width increase on Reliability index of foundation design (Zone A site 2)
220
B NS SWS
0.7 4.06 0.198 0.75 4.44 0.534
0.8 4.66 0.895 0.85 4.94 1.132
0.9 5.27 1.838 1.2 6.1 1.88 1.4 6.38 1.998
1.6 6.56 2.175 2 6.7 2.54
B NS SWS
0.7 2.02 0.052 0.75 2.42 0.728
0.8 2.74 1.3 0.85 3.01 1.313
0.9 3.31 1.728 1.2 4.02 1.91 1.4 4.2 2.06
1.6 4.47 2.37 2 4.64 2.96
0
1
2
3
4
5
6
7
8
0.7 0.75 0.8 0.85 0.9 1.2 1.4 1.6 2
relia
bilit
y In
dex
(β)
Foundation Width (m)
NS
SWS
00.5
11.5
22.5
33.5
44.5
5
0.7 0.75 0.8 0.85 0.9 1.2 1.4 1.6 2
Relia
bilit
y In
dex
(β)
Foundation Width (m)
NS
SWS
Figure 4.2 (ii)index of foundation design (Zone A site 2)
Figure 4.2 (ii) Influence of Foundation width increase on Reliability index of foundation design (Zone A site 2)
Figure 4.11c Influence of Foundation width increase on Reliability index of foundation design (Zone B site 1)
Figure 4.11d Influence of Foundation width increase on Reliability index of foundation design (Zone B site 2)
221
B NS SWS
0.7 4.02 0.13 0.75 4.41 0.562 0.8 4.63 0.895
0.85 4.89 1.37 0.9 5.19 1.8 1.2 6.01 1.89 1.4 6.33 1.96 1.6 6.5 2.12 2 6.67 2.52
B NS SWS
0.7 1.93 0 0.75 2.33 0
0.8 2.51 0.25 0.85 2.84 0.305 0.9 3.06 0.418
1.2 3.91 1.5 1.4 4 2 1.6 4.19 2.33
2 4.23 2.84
4.13 Classification of ‘Expected Performance’ of foundation design
0
1
2
3
4
5
6
7
8
0.7 0.75 0.8 0.85 0.9 1.2 1.4 1.6 2
Relia
bilit
y In
dex
(β)
Foundation Width (m)
NS
SWS
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0.7 0.75 0.8 0.85 0.9 1.2 1.4 1.6 2
Relia
bilit
y In
dex
(β)
Foundation Width (m)
NS
SWS
Figure 4.11e Influence of Foundation width increase on Reliability index of foundation design (Zone C site 1)
Figure 4.11f Influence of Foundation width increase on Reliability index of foundation design (Zone C site 2)
222
The ‘Expected Performance’ of engineering designs are classified according to their
safety levels. A range of classification modes are available for many engineering designs
but geotechnical classification is based on consequences of failure. Probability of failure
of 0.02275 or higher is regarded as poor and hence scarcely used in design except for
minor or unimportant structures. In comparison, a target probability of failure of
0.2326E-3 for bridge foundations is regarded as satisfactory. However, the United State
Army Corps of Engineers (1997) published the classification in Table 4.23.
Table 4.23 Standard Classification of ‘Expected Performance’ of Foundation Design
(Source: US Army Corps of Engineer (1997).
Reliability Index () Probability of failure () Performance level 0-1 0.5-0.16 Hazardous 1-1.5 0.16-0.07 Unsatisfactory 1.5-2.0 0.07-0.023 Poor 2.0-2.5 0.023-0.006 Below average 2.5-3.0 0.006-0.001 Above average 3.0-4.0 0.001-0.00003 Good 4.0-5.0 0.00003-0.0000003 High Above 5.0 Above 0.0000003 Very high
Using the above classification, the spread foundation design on ASWSS in Table 4.20 may be
classified as in Table 4.24a - f
Table 4.24 Classification of ‘Expected Performance’ of spread foundation design
a
223
Zone Site Load F kN
Foundation width B
(m)
Depth Z
(m)
(ASWSS) P
Performance level
A
1
100 0.70 1.5 0.468 Hazardous 150 0.70 1.5 0.5 Hazardous 150 0.70 2.0 0.474 Hazardous 150 0.70 2.5 0.369 Hazardous 150 0.70 3.0 0.274 Hazardous 150 0.70 3.5 0.151 Unsatisfactory 150 0.75 1.5 0.35 Hazardous 150 0.80 1.5 0.153 Unsatisfactory 150 0.85 1.5 0.111 Unsatisfactory 150 0.90 1.5 0.877E-1 Unsatisfactory 150 1.2 1.5 0.681E-1 Poor 150 1.4 1.5 0.316E-1 Poor 150 1.6 1.5 0.163E-1 Below average 150 2.0 1.5 0.427E-2 Above average
b Zone Site Load
F kN
Foundation width B
(m)
Depth Z
(m)
(ASWSS) P
Performance level
A
2
100 0.70 1.5 0.44 Hazardous 150 0.70 1.5 0.5 Hazardous 150 0.70 2.0 0.5 Hazardous 150 0.70 2.5 0.4 Hazardous 150 0.70 3.0 0.28 Hazardous 150 0.70 3.5 0.17 Hazardous 150 0.75 1.5 0.41 Hazardous 150 0.80 1.5 0.16 Hazardous 150 0.85 1.5 0.144 Unsatisfactory 150 0.90 1.5 0.64E-1 Poor 150 1.2 1.5 0.221E-1 Below average 150 1.4 1.5 0.611E-2 Below average 150 1.6 1.5 0.369E-2 Above average 150 2.0 1.5 0.196-3 High
c
224
d Zone Site Load F
kN Foundation
width B (m)
Depth Z
(m)
(ASWSS) P
Performance level
B
2
100 0.70 1.5 0.37 Hazardous 150 0.70 1.5 0.48 Hazardous 150 0.70 2.0 0.39 Hazardous 150 0.70 2.5 0.28 Hazardous 150 0.70 3.0 0.16 Unsatisfactory 150 0.70 3.5 0.08 Unsatisfactory 150 0.75 1.5 0.24 Hazardous 150 0.80 1.5 0.103 Unsatisfactory 150 0.85 1.5 0.101 Unsatisfactory 150 0.90 1.5 0. 576E-1 Poor 150 1.2 1.5 0.483E-1 Poor 150 1.4 1.5 0.21E-1 Below average 150 1.6 1.5 0.105E-1 Below average 150 2.0 1.5 0.173E-2 Above average
Zone Site
Load F kN
Foundation width B
(m)
Depth Z
(m)
(ASWSS) P
Performance level
B
1
100 0.70 1.5 0.093 Unsatisfactory 150 0.70 1.5 0.424 Hazardous 150 0.70 2.0 0.321 Hazardous 150 0.70 2.5 0.280 Hazardous 150 0.70 3.0 0.222 Hazardous 150 0.70 3.5 0.173 Hazardous 150 0.75 1.5 0.295 Hazardous 150 0.80 1.5 0.190 Hazardous 150 0.85 1.5 0.91E-1 Unsatisfactory 150 0.90 1.5 0.37E-1 Poor 150 1.2 1.5 0.333E-1 Poor 150 1.4 1.5 0.229E-1 Below average 150 1.6 1.5 0.1696E-1 Above average 150 2.0 1.5 0.582E-2 Above average
225
e Zone Site Load F
kN Foundation
width B (m)
Depth Z
(m)
(ASWSS) P
Performance level
C
1
100 0.70 1.5 0.097 Unsatisfactory 150 0.70 1.5 0.45 Hazardous 150 0.70 2.0 0.38 Hazardous 150 0.70 2.5 0.30 Hazardous 150 0.70 3.0 0.24 Hazardous 150 0.70 3.5 0.18 Hazardous 150 0.75 1.5 0.29 Hazardous 150 0.80 1.5 0.19 Hazardous 150 0.85 1.5 0.9E-1 Unsatisfactory 150 0.90 1.5 0.4E-1 Poor 150 1.2 1.5 0.32E-1 Poor 150 1.4 1.5 0.26E-1 Poor 150 1.6 1.5 0.188E-1 Below average 150 2.0 1.5 0.60E-2 Above average
f Zone Site Load F
kN Foundation
width B (m)
Depth Z
(m)
(ASWSS) P
Performance level
C
2
100 0.70 1.5 0.50 Hazardous 150 0.70 1.5 0.5 Hazardous 150 0.70 2.0 0.5 Hazardous 150 0.70 2.5 0.5 Hazardous 150 0.70 3.0 0.44 Hazardous 150 0.70 3.5 0.3 Hazardous 150 0.75 1.5 0.5 Hazardous 150 0.80 1.5 0.404 Hazardous 150 0.85 1.5 0.383 Hazardous 150 0.90 1.5 0.34 Hazardous 150 1.2 1.5 0.122E-1 Below average 150 1.4 1.5 0.26E-2 Above average 150 1.6 1.5 0.59E-3 Good 150 2.0 1.5 0.108E-3 Good
4.14 Geotechnical Properties of ASWSS and NS
226
The heterogeneous composition of ASWSS makes its raw data to be skewed, resulting in
non-identical extreme values extending out in both directions in a data distribution
function. The standard deviation of its data set is typically inflated by the high data
scatter. Outliers in ASWSS properties, with valid presence in this study, were not
discarded to make the data set fit analytical procedures that generally require normality,
but to eliminate the influence of unusual presence of materials not formed by the regular
geological processes or its environmental modifying factors. While outliers may define
crucial and significant points in a hydrological data set, their presence in geotechnical
observations dangerously inflate design data to the detriment of the design. Expunging
outliers from a data set to suit a pre-conceived analytical process is unwarranted because
transformation procedures capable of achieving symmetry are available (Helsel and
Hirsch, 2002).
A casual inspection of ASWSS properties, side by side with those of its corresponding
NS reveals sharp differences in some data values; however convergence of the two sets of
data begins to be gradually achieved from the depth of 2.5 m below the surface. The
spatial order and geotechnical relationships that tend to exist among observed data of
normal ground was not visible in most of ASWSS data. For instance the high values of
observed c that are associated with high values of observed in cohesive soil of natural
ground was not noticeable in ASWSS data (Table C.4 of Appendix C).
Considerable differences in the geotechnical properties of ASWSS and NS were
observed. The liquid and plastic limits of ASWSS fall in the ranges of 28 – 32% and
25 – 37% respectively. The angles of internal resistance range from 7 - 15º for ASWSS
and 8 - 17º for NS. Clay and silt account for up to 90% of ASWSS in some cases while as
227
low as 9 kN/m2 cohesion was recorded. The composition of organic matters in ASWSS
was found in the range of 2.1 – 5% while that of calcium and magnesium range between
106 mg/kg and 1000 mg/kg. Corrosive agents of sulphate and carbonate in ASWSS were
found in the ranges of 220 –589 mg/kg and 28 – 50 mg/kg respectively.
The main mineral compositions of ASWSS were Quartz (Silicon Oxide), Rutile
(Titanium Oxide) and Stolzite (Lead Tungsten Oxide). There were no traces of expansive
minerals like illite, kaolinite and montmorillonite which are capable of making the use of
such soil for developments a difficult one. However, most of the composition of sulphate,
chloride and magnesium/calcium occurred in proportions higher than the specified limits
of World Health Organisation and Environmental Protection Agency (WHO/EPA). The
silver like colour precipitate signifies the presence of silver which resulted from the
droplets of can materials. Oxidation and reduction reactions of the chlorides of these
heavy metals (silver, magnesium and calcium) with cement attack and slow down the
hardening process of concrete which eventually reduces its strength continuously.
Sulphate, carbonate and PH are all agents of corrosion. Their harsh presence in soil, as it
is in ASWSS of this study, attack foundation reinforcement.
ASWSS, as seen from the results of its site investigation in this study, is usually
characterized by weak zones that are randomly distributed. It is obvious that no amount
of sampling plan can capture all the weak spots of ASWSS so that the major parts of the
weak zones have no account in the evaluated design data, and hence the measured
average strength of soil samples on which design is based differs from and is higher in
value than the actual global average. This is one of the major causes of foundation failure
228
on ASWSS, especially where conventional methods are applied both in design and
evaluation of design data.
The isolated high spots would have had a positive impact on the average properties of
ASWSS except that its scanty distribution makes it too localized to form part of the
average strength. These are the effects of ‘reinforced earth scenario’ which ends up
shooting up the average strength beyond its field reality. The way to circumvent it is by
skilful trimming of data to give it a resemblance to the average field reality. In the
absence of this trim, foundation members are either designed below its safe level or
designers are tempted to apply elusively high traditional factor of safety in a defensible
and uneconomical manner.
4.15 Design Values
The only way to appreciate the peculiarity of ASWSS is to understand that its formation
is such that the properties of the test samples, unlike NS, may not, in many practical
instances mimic the average behavior of its parent population. This calls for a treatment
procedure that would reduce the irregularities to its acceptable minimum. The study
applied 15% for both trimmed upper and extended lower mean to the ASWSS properties
in order to exclude the influence of ‘reinforced earth scenario’ and include
approximately, data from weaker zones which might have escaped the adopted sampling
plan.
Design values are the final deduced values of soil data that are applied directly in design
calculations. The effect of any misrepresentation at this level may be dramatic on design
results. Design values of soil properties must be as representative of the site average as
possible. The trimming of outliers and inclusion of extended lower values were targeted
229
towards achieving this goal. It is rather saver, though less economical, to underestimate
the average strength characteristics of ASWSS at this stage than to overestimate them.
Designs are either carried out above the limit state (safe region) or below it (unsafe
region). . Design values of cohesion, angle of internal resistance and unit weight of soil
were obtained in the ranges of 9.5 – 12 kN/m2, 7 - 20° and 12.9 – 14.3 kN/m3
respectively for ASWSS while those of NS were 21 – 27 kN/m2, 10 - 14° and 15.6 – 16.2
kN/m2 respectively. These ranges show higher values of strength characteristics for NS as
generally expected.
4.16 Safety Indices of ASWSS and NS
A wide range of safety analyses employ simulation and reliability techniques in
evaluating the safety indices of the system under study. Usually, the choice of methods is
informed by and bound to the application discipline, and hence the detail approach and
limit of precision reflect the educated preference of the user. It is important to note that
while the conventional reliability method measures the reliability of the site being
investigated based on the evaluated properties of soil samples, the method adopted in this
study measures the reliability of the entire engineering field in relation to the proposed
loading. The study explored the contrasting responses of NS and ASWSS to loading by
carrying out spread foundation designs on NS and ASWSS using the same loading and
geometric conditions. The difference represents, invariably, the environmental effects
imposed on a geotechnical field by the presence of solid waste and its component
(leachate).
Both Monte Carlo Simulation (MCS) and First Order Reliability Method (FORM) were
used in the evaluation of safety indices of foundation designs. The results of the two
230
reveal that for most of the span of safety index, the use of MCS is more conservative and
that for values of less than 1, the two results are a little divergent. The results suggest,
therefore, that in design and analysis based on geotechnical data, which usually, is
fraught with high approximations and uncertainties, it is reasonable to adopt MCS.
The safety of foundation designs on ASWSS and NS was obtained in terms of reliability
index and probability of failure. Despite the record of small probability of failure of
0.00013, corresponding to reliability index of 3.75, there were few cases of zero
reliability indices corresponding to probability of failure of 0.5 on ASWSS (Table 4.24).
It is clear also from the results that increase in the depth of foundation adds not much to
its reliability and that an increase of 0.05 m in foundation width may raise the reliability
index by up to 0.5. The reliability index obtained by an increase of 0.1 m in foundation
width is equivalent to that obtained when foundation depth is increased by 1.5 m. In
addition, it is outstandingly noticed that up to twice NS foundation width is required in
ASWSS to reduce the probability of failure () to its equivalent value in NS (Tables
4.20 and 4.22).
4.17 Performance Classification of ASWSS
The basis for classifying the expected performance of foundation design is safety. Safety
is examined at different levels depending on the consequences of failure. The safety of
foundation designs on ASWSS and NS was obtained in terms of reliability index and
probability of failure. The record of high probability of failure of as much as 0.5
consequently make the foundation designs on ASWSS ranged from ‘hazardous to high’
safety index in the standard classification format despite the fact that
P of 0.0228( = 2) is seldom used except for unimportant structures like farm houses.
231
A total of forty (40) out of one hundred and sixty eight (168) cases of ASWSS foundation
designs satisfy this minimum reliability index criterion. Out of 84 design cases of
ASWSS in this study, 41 fall in hazardous class, 15 in unsatisfactory, 10 in poor, 8 in
below average, 7 in above average, 2 in good and 1 in high class. It must be noted,
however, that most of the time these facts about ASWSS are not discovered because of
inadequate sampling plan and poor soil data treatment. Improvements on the safety
indices could be made by reducing the values of imposed loads or increasing the
foundation dimensions.
CHAPTER FIVE
CONCLUSION AND RECOMMENDATIONS A common thing in engineering judgment is that confidence is placed on the likelihood of
the measured material properties while past events which may possibly explain the likely
order of present circumstances are relegated. For instance, if ASWSS investigation
reveals satisfactory sample data for engineering purpose, the tendency is to assume that
the result is similar to that of the parent population, without regard to high base-rate of
failure, if any. In all cases, a balanced posterior probability is influenced by prior
232
probability and likelihood of data. This chapter summarizes the conclusive remarks and
recommendations based on the combined application of these sources of evidence in
analyzing the reliability of ASWSS for structural developments.
5.1 Summary Risk and reliability analysis in engineering entails mathematical approaches that are
closely connected to the principles of probability and statistics. The general advocacy is
that geotechnical reliability should not advance beyond FORM so as to avoid undesirable
complexity in statistics and calculations because geotechnical data does not have
sufficient physical robustness to withstand sophisticated mathematics. Besides, it is
feared that further complexity in treatment would render the field and laboratory efforts
towards predicting and inferring the geotechnical state of geological materials to mere
statistical exercise. This study, therefore from field data acquisition/transcription to
evaluation of safety indices, employed simple and available mathematical and statistical
methods, especially in analysis and evaluation of safety indices of designs. Combined
concepts of the probability of events based on long series of similar occurrence and the
measurement of probability on the strength of empirical knowledge of events have been
applied to assess the properties and uncertainties in the use of ASWSS for developments.
Comprehensive acquisition of soil physical and chemical properties was done using
laboratory analysis. Monte Carlo simulation and Hasofer-Lind Approach (FORM) were
used side by side to evaluate the safety indices of foundation designs both on NS and
ASWSS. As expected the safety indices of designs on NS are far better than those on
ASWSS.
5.2 Conclusion
233
The conventional methods of site investigation and treatment of soil data have proved
inadequate in accessing the exact geotechnical capability of ASWSS. In most cases the
unusual field conditions like the presence of weak zones and ‘reinforced earth scenarios’
neither play appropriate roles nor have account in the evaluated representative value of
the strength characteristics. This is in addition to statistical imprecision resulting from
insufficient statistical data obtained from inadequate characterization of ASWSS.
Occurrence of ‘reinforced earth scenarios’ and unnoticed weak spots on ASWSS hinder
the efforts towards predicting the design values that are truly representative of the global
average. Foundation failures, therefore, were recorded in the past because of over
reliance on the raw data obtained via conventional methods of investigation and lack of
adequate provision for experience – based guidance in the evaluation of average strength
of ASWSS.
Up to seventy percent (70%) of triaxial test results (, ∅ and ) of ASWSS were
significantly lower than those of the corresponding NS, with a scale of about one in two
(1 in 2) in some cases. These are the main strength parameters of soil and large
differences between their ASWSS and NS values indicate large differences between the
strength characteristics of ASWSS and NS respectively. However, with just twenty five
percent (25%) Atterberg Limits test results showing significant difference and one
hundred percent (100%) compaction test results showing no difference at all between
ASWSS and NS, the state of geotechnical properties alone could not have been
responsible for the scale of failures recorded in the use ASWSS for developments.
The long - term effects of over seventy percent (70%) of sulphate, fifty percent (50%) of
chloride and calcium/magnesium contents in excess of EPA/WHO prescribed maximum
234
value certainly impact negatively on the stability and continuous performance of ASWSS
foundation members. The subtle but salient effects of this source of foundation failure
can persist for a long period of time before it finally results into obvious signs of failure.
The levels of degradation of ASWSS that have spent over twenty (20) years of
abandonment no more threaten the ultimate or serviceability performance of foundation
members. The fact that majority of the design cases fall in hazardous class, which is the
worst state of failure tendency, is an indication of the risk involved in the use of ASWSS
for building construction. Low values of safety indices of foundation designs on ASWSS
showed clearly that it is unsuitable for heavy structures. However, light and minor
structures can be sustained with relevant design techniques.
5.3 Recommendations
Based on the findings of this study, the following recommendations are made:
1. Geotechnical characterization of ASWSS should be obtained via a sampling plan that is
generally more detailed than that of natural ground. It should be an attempt to capture the
majority of site irregularities that are associated with ASWSS.
2. It is strongly submitted that the characterization plan of ASWSS and evaluation of design
values should include informed percentages of ‘upper trim’ and ‘lower extended’ mean
respectively.
3. Where ASWSS is adequately investigated, a minimum foundation depth of 2.0 m with its
relevant foundation width is capable of achieving average reliability; otherwise
foundation depth should not be less than 2.5 m.
235
4. It is reasonable also to increase the foundation width, within the acceptable limits of
settlement provision however, so as to enhance the safety index of the design especially
where the target reliability index has not been attained.
5. Foundation members should be strictly protected against the damaging effects of
chemical compounds by using sulphate resistant cement in all cases of ASWSS
foundation constructions.
6. The expected performance of structural foundations proposed to be built on ASWSS
should be assessed via a reliability based risk assessment procedure or geotechnical
solution that truly and tractably shed light on the prospect of foundation functionality.
7. A minimum of ‘Above Average’ classification of structural foundation design of ASWSS
should never be compromised except for minor and unimportant structures.
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APPENDIX B: Determination of Foundation Width using MATLAB clear; syms x; solve ('1.779*x^3+234.992*x^2+66.241*x=150') clear; syms x; solve ('1.779*x^3+234.992*x^2+66.241*x=200') clear ; syms x; solve ('1.779*x^3+234.992*x^2+66.241*x=250') clear;
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syms x; solve ('1.779*x^3+234.992*x^2+66.241*x=300') clear ; syms x; solve ('1.779*x^3+234.992*x^2+66.241*x=350') clear; syms x; solve ('1.779*x^3+234.992*x^2+66.241*x=400') clear; syms x; solve ('1.779*x^3+234.992*x^2+66.241*x=450') clear; syms x; solve ('1.779*x^3+234.992*x^2+66.241*x=500') clear; syms x; solve ('1.779*x^3+234.992*x^2+66.241*x=550') Appendix C: Results of Laboratory Determination of Geotechnical Properties of ASWSS and NS Table C.1 Atterberg Limits Test Results Property Zone Site Depth
of Stratum
(m)
Mean Value
ASWSS (%) NS (%)
LL PL PI LS LL PL PI LS Atterberg Test Results
A 1 1.5 2.0 2.5 3.0 3.5
40.00 44.00 40.00 52.00 28.00
35.50 37.17 25.54 36.11 25.00
4.50 6.83 4.50 15.89 3.00
4.29 5.00 5.71 8.57 10.00
49.00 32.00 33.00 35.00 29.00
35.09 30.95 26.97 34.31 28.17
13.91 1.05 6.03 0.69 0.83
10.00 10.71 10.00 10.71 10.71
2 1.5 42.00 36.50 5.5 4.45 39.00 29.00 10.00 10.91
250
2.0 2.5 3.0 3.5
44.00 40.00 50.00 35.00
37.55 35.0 36.50 28.20
6.45 5.0 13.5 6.80
6.00 8.27 8.05 10.05
36.00 34.00 38.00 36.00
28.00 28.00 33.00 27.15
8.00 6.00 5.00 8.85
1050 10.25 10.25 10.05
B 1
1.5 2.0 2.5 3.0 3.5
32.00 35.00 33.00 34.00 34.00
27.78 29.29 29.29 27.92 30.49
4.22 5.71 3.71 6.08 3.51
8.57 9.29 8.00 8.57 8.57
37.00 37.00 48.00 36.00 34.00
26.67 32.58 31.01 28.22 25.54
10.33 4.42 16.99 7.78 8.46
7.86 8.57 9.29 8.57 8.57
2 1.5 2.0 2.5 3.0 3.5
30.00 34.00 33.00 34.00 34.00
29.19 28.55 26.29 28.72 28.72
0.81 5.45 6.71 5.28 5.28
9.28 8.29 8.57 8.50 8.55
32.00 33.00 32.00 30.00 33.00
27.75 29.00 25.72 27.65 27.65
4.25 4.00 6.28 2.35 5.35
8.55 9.75 8.55 8.57 8.57
C 1 1.5 2.0 2.5 3.0 3.5
38.00 40.00 38.00 39.00 39.00
33.50 36.50 32.00 33.50 33.72
4.50 3.50 6.00 5.5 5.28
7.95 8.71 8.77 8.75 8.55
42.00 38.00 36.00 36.00 38.00
35.25 34.50 32.00 30.95 32.55
6.75 3.50 4.00 5.03 5.45
9.25 8.85 8.57 8.90 8.55
2 1.5 2.0 2.5 3.0 3.5
40.00 37.00 39.00 37.00 34.00
28.00 27.50 28.85 26.62 25.50
12.00 9.50 10.15 10.38 8.50
7.25 8.15 6.27 7.75 8.05
36.00 38.00 35.00 34.00 35.00
29.15 28.45 27.15 30.25 26.40
6.85 9.55 7.85 3.75 8.60
8.25 7.00 9.15 6.75 7.15
Table C.2: Dry Density/Moisture Content Test Results Property Zone Site Depth
of Stratum
(m)
Mean Value
ASWSS NS
MDD (g/cm3)
OMC (%)
MDD (g/cm3)
OMC (%)
Dry Density/Moisture Content
A 1 1.5 2.0 2.5 3.0 3.5
1.56 1.48 1.57 1.71 1.51
20.00 20.86 18.32 25.00 17.00
1.67 1.67 1.39 1.33 1.48
22.47 18.00 20.00 26.51 25.00
2 1.5 2.0 2.5 3.0 3.5
1.67 1.55 1.60 1.50 1.58
22.00 20.00 23.00 25.00 19.00
1.76 1.82 1.70 1.65 1.68
19.25 20.22 25.75 20.15 19.00
251
B 1
1.5 2.0 2.5 3.0 3.5
1.93 1.80 1.65 1.57 1.70
18.56 18.36 19.17 17.97 15.55
1.85 1.96 1.93 1.81 1.88
15.05 14.46 12.79 19.54 16.38
2 1.5 2.0 2.5 3.0 3.5
1.68 1.67 1.56 1.66 1.65
20.72 20.68 18.18 19.27 16.35
1.71 1.79 1.48 1.70 1.65
22.56 20.17 18.27 17.70 16.32
C 1 1.5 2.0 2.5 3.0 3.5
1.67 1.90 1.83 1.72 1.52
18.33 19.27 18.38 19.20 19.00
1.80 1.84 1.79 1.67 1.54
20.20 19.00 18.84 18.90 19.10
2 1.5 2.0 2.5 3.0 3.5
1.94 1.90 1.82 1.79 1.72
15.50 16.20 17.22 17.00 17.00
1.80 1.92 1.90 1.88 1.76
16.83 15.56 14.20 16.25 16.35
252
Table C.3: Consolidation Test Results Property Zone Site Depth of
Stratum (m)
Mean Value
ASWSS NS
Cv (m2/yr) Mv (m2/kN) Ρ C (m) Cv (m2/yr) Mv (m2/kN) Ρ C (m) Consolidation Test Result
A 1 1.5 2.0 2.5 3.0 3.5
2.242 2.138 1.832 2.813 1.271
0.0106 0.0061 0.0076 0.0092 0.0077
0.0004 0.0002 0.0003 0.0005 0.0002
1.642 1.342 1.382 1.738 2.773
0.0058 0.0095 0.0070 0.0084 0.0055
0.0002 0.0002 0.0002 0.0003 0.0003
2 1.5 2.0 2.5 3.0 3.5
2.042 2.188 1.946 2.902 1.786
0.0091 0.0078 0.0068 0.0070 0.0072
0.0003 0.0005 0.0002 0.0004 0.0003
1.640 1.760 1.566 1.928 2.113
0.0038 0.0056 0.0067 0.0072 0.0071
0.0002 0.0003 0.0002 0.0003 0.0002
B 1
1.5 2.0 2.5 3.0 3.5
2.062 3.264 2.215 1.912 1.708
0.0094 0.0061 0.0073 0.0098 0.0136
0.0004 0.0004 0.0003 0.0003 0.0004
3.624 2.123 1.391 8.687 1.448
0.0076 0.0068 0.0064 0.0132 0.0098
0.0005 0.0003 0.0002 0.0022 0.0003
2 1.5 2.0 2.5 3.0 3.5
2.156 2.007 1.678 1.782 1.660
0.0061 0.0070 0.0056 0.0078 0.0055
0.0003 0.0004 0.0002 0.0003 0.0002
2.969 2.143 2.002 1.896 1.672
0.0088 0.0084 0.0056 0.0067 0.0071
0.0004 0.0003 0.0003 0.0002 0.0002
C 1 1.5 2.0 2.5 3.0 3.5
2.256 2.196 1.652 2.923 1.261
0.0102 0.0072 0.0059 0.0069 0.0058
0.0005 0.0005 0.0003 0.0004 0.0002
1.632 1.772 1.012 1.682 2.549
0.0063 0.0060 0.0049 0.0058 0.0038
0.0002 0.0003 0.0002 0.0003 0.0003
2 1.5 2.0 2.5 3.0 3.5
2.147 2.668 1.932 2.944 1.699
0.0059 0.0049 0.0052 0.0078 0.0134
0.0004 0.0003 0.0003 0.0002 0.0003
1.959 2.012 1.532 1.782 1.324
0.0079 0.0052 0.0058 0.0061 0.0076
0.0002 0.0003 0.0002 0.0003 0.0002
253
Table C.4: Triaxial Test Result Property Zone Site Depth
of Stratum
(m)
Mean Value
ASWSS NS
(kN/m2) ∅ (º) (kN/m3) (kN/m2) ∅ (º) (kN/m3) Triaxial Test Result
A 1 1.5 2.0 2.5 3.0 3.5
10 16 10 15 12
11 9 7 10 9
15.78 13.97 14.19 15.21 16.01
28 27 24 22 19
13 10 15 8 9
15.90 16.80 16.80 15.67 16.24
2 1.5 2.0 2.5 3.0 3.5
10 14 15 14 13
10 10 9 8 9
15.96 14.42 14.72 15.98 16.32
24 25 19 25 22
14 12 13 15 16
17.14 16.24 15.90 16.58 16.12
B 1
1.5 2.0 2.5 3.0 3.5
9 18 19 12 13
12 13 13 13 15
16.58 13.98 14.87 16.35 16.35
25 17 18 22 28
16 13 14 16 15
15.80 16.40 16.60 16.60 16.68
2 1.5 2.0 2.5 3.0 3.5
9 10 11 12 14
12 9 10 12 13
15.98 15.50 14.98 16.10 16.30
20 24 19 22 22
11 13 13 14 16
15.89 16.22 16.22 16.24 16.40
C 1 1.5 2.0 2.5 3.0 3.5
10 9 11 10 12
13 13 13 13 14
16.20 14.98 15.80 16.24 16.24
28 26 25 20 19
13 13 14 15 16
15.90 16.82 16.80 16.84 16.84
2 1.5 2.0 2.5 3.0 3.5
11 13 11 12 10
9 11 10 12 11
13.89 14.22 12.92 13.90 14.28
23 18 22 19 23
12 14 13 15 16
15.51 16.01 16.20 16.24 16.30
254
(a) Table C.5a: Specific Gravity Test Result
Property Zone Site Depth of Stratum
(m)
Mean Value
ASWSS NS
Specific Gravity Test Result
A 1 1.5 2.0 2.5 3.0 3.5
1.64 2.04 2.14 2.26 2.45
2.21 2.36 2.47 2.54 2.66
2 1.5 2.0 2.5 3.0 3.5
1.88 2.17 2.48 2.56 2.64
2.56 2.60 2.64 2.66 2.65
B 1
1.5 2.0 2.5 3.0 3.5
2.52 2.54 2.56 2.56 2.58
2.55 2.55 2.56 2.63 2.67
2 1.5 2.0 2.5 3.0 3.5
1.78 1.92 2.20 2.58 2.60
2.58 2.65 2.65 2.67 2.67
C 1 1.5 2.0 2.5 3.0 3.5
2.50 2.57 2.58 2.64 2.66
2.58 2.65 2.67 2.67 2.69
2 1.5 2.0 2.5 3.0 3.5
2.14 2.25 2.40 2.61 2.63
2.57 2.60 2.67 2.67 2.69
255
Table C. 5b: Natural Moisture Content Test Result Property Zone Site Depth of
Stratum (m)
Mean Value
ASWSS (%) NS (%)
Natural Moisture Content Test Result
A 1 1.5 2.0 2.5 3.0 3.5
19.14 10.71 24.06 39.42 41.44
18.15 22.38 36.10 41.76 23.11
2 1.5 2.0 2.5 3.0 3.5
22.27 19.72 20.11 22.42 30.45
11.17 10.28 14.32 20.37 23.32
B 1
1.5 2.0 2.5 3.0 3.5
13.89 21.71 10.70 19.13 14.53
6.88 8.85 9.96 7.97 18.88
2 1.5 2.0 2.5 3.0 3.5
14.68 20.24 32.44 38.45 30.67
10.11 9.27 12.42 13.16 14.22
C 1 1.5 2.0 2.5 3.0 3.5
16.11 22.92 26.42 28.17 30.45
11.45 12.18 13.66 12.72 13.80
2 1.5 2.0 2.5 3.0 3.5
19.45 22.40 30.48 34.55 36.06
12.99 13.42 14.56 14.58 14.55
256
Table C. 6: Sieve Analysis (Wet/Dry) Property Zone Site Depth of
Stratum (m)
Mean Value
ASWSS (%) NS (%)
Sieve Analysis (Wet/Dry) Percentage clay & silt (%)
A 1 1.5 2.0 2.5 3.0 3.5
43.80 64.70 71.48 89.92 70.86
32.64 53.86 42.00 68.68 63.84
2 1.5 2.0 2.5 3.0 3.5
45.77 48.92 58.12 60.25 56.55
30.74 28.91 42.48 60.40 56.52
B 1
1.5 2.0 2.5 3.0 3.5
48.14 65.90 23.64 55.02 45.70
38.22 20.56 19.64 50.78 35.12
2 1.5 2.0 2.5 3.0 3.5
40.44 62.68 70.04 62.66 68.72
38.00 42.20 30.35 22.50 38.27
C 1 1.5 2.0 2.5 3.0 3.5
52.50 50.68 65.44 58.32 62.62
36.40 32.46 40.47 28.74 30.04
2 1.5 2.0 2.5 3.0 3.5
42.36 28.85 39.48 52.43 56.44
32.35 27.20 28.45 32.31 30.46
257
Table C.7a: Results of Chemical Analysis Season: Wet
Property Zone Site Depth of Stratum
(m)
Mean Value
ASWSS (mg/l) (mg/kg) (mg/l) (mg/kg)
NS
(mg/l) (mg/kg) (mg/l) (mg/kg) pH Sulphate Chloride Carbonate ΣCa+Mg pH Sulphate Chloride Carbonate ΣCa+Mg pH Sulphate Chloride Carbonate ΣCa+Mg
A 1 1.5 2.0 2.5 3.0 3.5
6.3 6.2 6.3 7.2 7.5
473.18 491.81 584.10 686.13 691.82
522.63 568.60 605.32 612.10 620.10
28.80 26.00 20.33 35.20 38.16
899 886 543 297 189
6.8 6.2 6.0 7.0 7.3
264.45 271.81 274.15 282.43 289.50
280.64 376.90 390.55 430.63 472.39
Nil 26.80 29.95 33.10 32.16
233 201 188 165 134
2 1.5 2.0 2.5 3.0 3.5
6.3 6.4 6.5 7.2 7.6
436.44 501.60 578.15 585.42 596.33
643.20 658.32 784.10 786.37 799.10
27.20 28.10 30.67 33.80 40.67
776 654 498 201 188
6.0 6.9 6.3 7.0 7.4
224.41 266.83 241.50 268.42 286.53
320.50 338.77 386.76 440.19 489.10
30.22 36.19 37.55 32.20 40.00
289 233 178 167 150
B 1
1.5 2.0 2.5 3.0 3.5
6.4 6.8 6.9 7.7 7.9
399.25 452.46 477.10 484.70 495.18
499.40 538.45 555.67 620.19 699.42
28.90 36.88 38.70 39.22 40.30
556 322 178 121 199
6.0 6.6 6.8 6.2 6.9
234.12 243.55 265.10 285.60 292.56
299.60 320.15 338.60 415.20 440.88
31.23 30.88 32.60 38.30 39.10
290 207 188 167 143
2 1.5 2.0 2.5 3.0 3.5
6.3 6.4 7.2 7.5 7.6
399.60 468.31 474.10 552.19 560.15
568.32 658.10 740.19 821.22 866.32
28.80 20.13 32.10 36.80 39.50
659 440 308 187 154
6.1 6.4 6.8 7.2 7.4
249.73 256.40 295.66 250.17 259.22
320.32 335.59 430.66 442.72 450.33
27.60 29.89 30.35 33.22 36.48
278 231 178 144 107
C 1 1.5 2.0 2.5 3.0 3.5
6.4 6.6 7.5 7.5 7.6
389.15 499.10 542.10 578.55 588.42
420.67 496.18 542.15 599.30 620.10
27.30 29.30 30.19 23.25 40.00
443 200 176 143 108
6.0 6.1 6.3 7.4 7.5
267.50 284.10 222.10 275.15 246.44
315.22 329.18 330.72 356.84 415.10
27.00 25.23 28.45 32.10 38.73
195 187 144 143 122
2 1.5 2.0 2.5 3.0 3.5
6.3 6.4 6.6 7.2 7.6
235.10 245.20 265.44 269.67 298.30
356.78 422.13 443.17 587.67 595.10
24.60 29.90 29.92 30.35 40.00
389 339 218 155 106
6.3 6.0 6.1 6.5 7.3
220.55 242.20 240.17 256.68 280.99
353.10 388.90 420.95 467.30 488.76
20.22 24.68 29.16 28.15 39.70
180 167 133 121 120
WHO/EPA LIMIT 6-9
≤ 400 ≤ 600
≤ 50 ≤ 200 6-9 ≤ 400 ≤ 600 ≤ 50 ≤ 200
Table C.7b: Results of Chemical Analysis Season: Dry
258
Property Zone Site Depth of Stratum
(m)
Mean Value
ASWSS
(mg/l) (mg/kg) (mg/l) (mg/kg)
NS
(mg/l) (mg/kg) (mg/l) (mg/kg) pH Sulphate Chloride Carbonate ΣCa+Mg pH Sulphate Chloride Carbonate ΣCa+Mg pH Sulphate Chloride Carbonate ΣCa+Mg
A 1 1.5 2.0 2.5 3.0 3.5
8.5 8.3 8.0 7.1 7.0
903.65 789.13 673.16 469.10 336.22
972.30 648.62 459.39 344.86 322.45
50.10 48.90 42.33 33.62 30.19
1000 989 765 337 204
8.2 8.0 8.0 6.9 6.5
400.63 283.13 270.22 254.55 230.22
617.10 454.96 429.60 342.85 320.54
50.00 46.17 42.15 30.62 29.88
233 200 176 108 77
2 1.5 2.0 2.5 3.0 3.5
8.6 8.4 7.5 7.0 6.2
698.30 664.23 555.45 489.10 370.24
768.70 656.12 495.22 348.90 275.66
50.32 47.35 34.77 33.28 28.60
1001 897 822 444 287
8.3 8.2 7.2 6.8 6.0
390.30 362.33 345.45 268.10 386.22
560.76 450.66 324.96 340.45 270.54
49.56 46.35 31.73 31.22 26.49
176 102 87 80 55
B 1
1.5 2.0 2.5 3.0 3.5
9.0 8.6 8.3 7.1 6.0
699.23 615.68 598.45 586.43 488.43
692.23 520.27 463.45 322.10 310.15
48.50 44.92 39.65 35.22 28.57
667 434 219 177 136
8.9 8.5 8.0 7.0 5.8
395.15 300.66 296.53 280.56 288.00
500.31 500.27 446.50 315.11 310.10
43.77 40.09 36.67 30.24 23.00
192 180 171 100 83
2 1.5 2.0 2.5 3.0 3.5
8.9 8.3 7.0 6.2 6.0
494.62 395.33 368.46 295.11 288.62
498.69 344.25 342.30 288.73 276.90
48.97 47.50 33.24 30.76 28.95
545 407 227 188 146
8.3 8.3 6.8 6.0 6.0
382.56 355.34 363.45 294.00 259.35
488.67 342.25 322.06 268.33 254.89
48.65 46.45 30.28 29.66 25.86
189 166 143 98 67
C 1 1.5 2.0 2.5 3.0 3.5
8.7 8.3 7.8 7.6 6.8
676.00 640.12 435.68 398.11 389.42
697.15 532.45 321.67 288.49 266.88
50.44 50.10 48.35 29.63 20.86
877 552 328 200 183
8.5 8.1 7.6 7.5 6.3
346.00 340.10 324.65 296.11 249.66
495.00 320.64 320.17 260.83 239.68
49.88 48.89 45.35 24.09 20.86
170 165 129 109 56
2 1.5 2.0 2.5 3.0 3.5
8.9 8.3 8.0 7.1 7.0
634.22 620.19 577.66 539.13 520.56
599.00 588.99 567.73 423.50 344.12
48.99 47.60 46.77 45.28 34.66
448 278 192 156 115
8.6 8.1 8.0 7.0 6.9
322.10 315.15 223.37 234.00 200.54
589.00 584.67 563.85 420.31 340.12
46.90 46.72 42.33 40.33 32.66
196 192 128 119 87
WHO/EPA LIMIT 6-9
≤ 400 ≤ 600
≤ 50 ≤ 200 6-9 ≤ 400 ≤ 600 ≤ 50 ≤ 200
259
Table C. 8: Results of Organic Matter Content Test (ASWSS) Zone Site Depth(m) Organic Matter Content (%) ASWSS
A 1 1.5 3.72
2.0 3.65 2.5 3.22 3.0 2.89 3.5 2.10
2 1.5 4.06 2.0 3.88 2.5 3.45 3.0 2.78 3.5 2.33
B 1 1.5 5.01 2.0 4.89 2.5 4.51 3.0 3.88 3.5 2.90
2 1.5 3.88 2.0 3,22 2.5 2.80 3.0 2.56
3.5 2.04
C 1 1.5 4.87 2.0 4.66 2.5 4.32 3.0 2.99 3.5 2.36
2 1.5 4.55 2.0 4.05 2.5 3.81 3.0 2.70 3.5 2.09
WHO/ EPA LIMIT ≤ 10
Appendix D : Application of T - table in the Computation of T values Table D. 1: T distribution critical values (Udacity, 2015)
260
