CONCRETE COMPONENTS PACKING HANDBOOKonlinepubs.trb.org/Onlinepubs/shrp/SHRP-C-624.pdfcement coarse...

. SHRP-C-624

Concrete ComponentsPacking Handbook

D.M. RoyB.E. ScheetzR.I.A. Malek

D. Shi

Materials Research LaboratoryThe Pennsylvania State University

University Park, Pennsylvania 16802

" V. JohansenP.J. Andersen

O

G.M. Idom Consult A/SBlokken 44 Birkerod

Denmark

r

.rhrp Strategic Highway Research ProgramNational Research Council

Washington, DC 1993

SHRP-C-624D

Contract C-201

Program Manager: Don M. HarriottProject Manager: Inam JawedProduction Editor: Marsha Barrett

Program Area Secretary: Ann Saccomano

April 1993

key words:cement

coarse aggregateconcrete

free aggregatemix proportioning

packing tablespacking densitysize distribution

Strategic Highway Research ProgramNational Academy of Sciences2101 Constitution Avenue N.W.

Washington, DC 20418

(202) 334-3774

The publication of this report does not necessarily indicate approval or endorsement of the findings, opinions,conclusions, or recommendations either inferred or specifically expressed herein by the National Academy of

Sciences, the United States Government, or the American Association of State Highway and TransportationOfficials or its member states.

© 1993 National Academy of Sciences

a

350/NAP/493

• Acknowledgments

The research described herein was supported by the Strategic Highway ResearchProgram (SHRP). SHRP is a unit of the National Research Council that was authorizedby section 128 of the Surface Transportation and Uniform Relocation Assistance Act of1987.

o°°

in

o Contents

Acknowledgments .............................................. iii

List of Figures ............ ..................................... vii

List of Tables ................................................ ix

Abstract ................................................ xi

Executive Summary .............................................. 1

Introduction ................................................. 1

A. Scope of Handbook .......................................... 1B. Theoretical Basis of Packing .................................... 2C. General Applicability ......................................... 5

Part I Graphical Representation of Particle Packing:An Aid to Concrete Design ................................ 7

Approach .......................................... 7Correlation Between Calculated Packing Density

and Standard Concrete Formulation ....................... 7

Correlation Between Packing Density and Variationsin Concrete Component Size Distribution Allowedby Standard Specification ............................. 19

Appendix 1A ................................................ 31

"- Part A. Experimental Determination of Packing Densities forCements and Mineral Admixtures .......................... 31

Part B. Experimental Determination for Packing Densitiesfor Aggregates ........................................ 33

Part II Packing Handbook: Numeric Data ............................. 35Introduction to the Packing Handbook ........................ 35Design of the Concrete Handbook .......................... 35

V

Instructions in the Use of the Packing Handbook ............... 37Example of Use ........................................ 39Restrictions in the Use of the Packing Handbook ............... 42

References .................................................. 46

Appendix IIA Packing Tables ....................................... 47

vi

, List of Figures

1 Schematic drawing illustrating lower packingdensity due to "wall effect". ............................... 4

2 Cement/fine aggregate/coarse aggregate compositional diagram .... 2

3 Plot of isodensity lines connecting points/cement, sand,and #8 limestone coarse aggregate ......................... 9

4 Plot of isodensity lines connecting points/cement, sand,#67 limestone coarse aggregate ........................... 10

5 Plot of isodensity lines connecting points/cement, sand,#57 limestone coarse aggregate ........................... 11

6 Histograms for sieve distributions ......................... 13

7 Plot of isodensity lines connecting points/cement, sand,#8 quartz coarse aggregate .............................. 15

8 Plot of isodensity lines connecting points/cement, sand,#67 quartz coarse aggregate ............................. 16

9 Plot of isodensity lines connecting points/cement, sand,#57 quartz coarse aggregate ............................. 17

10 Plot of the differences between the isodensity linesfor figures 3 and 7 ..................................... 18

11 PADOT specifications 704.1 (B) .......................... 20

12 Histograms of as-received sand and the maximum and minimumallowable distribution ................................... 21

13 Histograms of as-received #67 limestone aggregate andthe maximum and minimum allowable distribution ............. 22

vii

14 Plot of isodensity lines connecting points/cement 30 micrometers, sand,#67 limestone aggregate ................................ 23

15 Plot of isodensity lines connecting points/cement 17 micrometers, sand,#67 limestone aggregate ................................ 24

16 Plot of isodensity lines connecting points/cement 10 micrometers, sand, "_#67 limestone aggregate ................................ 25

17 Plot of isodensity lines connecting points/cement, sand 0.474 mm,#67 limestone aggregate ................................ 27

18 Plot of isodensity lines connecting points/cement, sand 1.918 mm,#67 limestone aggregate ......... ....................... 28

19 Plot of isodensity lines connecting points/cement, sand,#67 limestone aggregate 1.144 cm.......................... 29

20 Plot of isodensity lines connecting points/cement, sand,#67 limestone aggregate 1.817 cm.......................... 30

21 Typical ternary packing diagram of cement .................. 36

22 Example of the packing handbook ......................... 38

23 Concrete composition using the received size of fine and coarseaggregate and specification limits as allowed PADOT .......... 41

24 Ternary diagram showing the packing density/coarse aggregate 2/8 mm, 8/16 mm and 16/32 mm ............ 44

25 Ternary diagram showing the packing density/cement, microsilica, fly ash .............................. 45

ooo

vln

o List of Tables

1 Variations allowed by the PADOT specifications 704.1 (B) ................. 40

2 Rheological properties of air entrained concretes ......................... 43

ix

o Abstract

Data in this handbook are based upon a computer model of dry packed, monosizedparticles adapted from the theories developed by Aims (1967) and Toufar (1967). Themodel has been demonstrated to adequately describe similar dry packing of powders withvarying size distributions in terms of the Rosin-Rammler D' coefficient. The model hasbeen successfully applied to the system cement/fine aggregate/coarse aggregate and hasmodeled Cement and Concrete Association, Portland Cement Association andPennsylvania Department of Transportation recommended concrete formulations. Theresults theoretically support the location of recommended concrete formulations in aregion of ternary particle mixing which possesses the maximum dry packing density.

The handbook consists of graphical representation of selected formulation variables andtables detailing packing densities for mix proportioning.

xi

CONCRETE COMPONENTS PACKING HANDBOOK:

Applicability to Highway Concrete Design

EXECUTIVE SUMMARY

Standardized formulations for concretes are recommended by such organizations as the

" PCA, CCA, ACI and others. The results of research associated with the packing of dry

components of the concrete system established the theoretical basis upon which these

empirical formulations were developed.

The random arrangement of a polydispersed particle system in a container is defined as

the packing density of the powder and represents the volume fraction of the container which is

occupied by the solids. Packing densities are always related to volume percentages of the

components which are related through density to the masses of the solids being considered.

The results of this modeling demonstrate that the recommended concrete formulations

in general occur in the region of maximum dry packing density in the system cement-sand-

coarse aggregate. In this region minor fluctuations in the proportioning of the concrete will

have very little, if any, effect upon the dry packing density. The body of this handbook consists

of two parts: a graphic presentation of the results of the calculations for a large number of

variables in typical concrete formulations. The second part of the handbook consists of tables

of data for the calculation maximum packing densities for concrete mix formulations.

Evaluation of the effects of packing density of mixtures of particle distributions suggested

that the maximum workability without bleed water was achieved when the porosity of the

packed powders was just filled with water. This condition occurs along a join drawn between

the maximum packing in the sand coarse aggregate system of a concrete and the cement

powder.

With the expanding role of mineral admixtures and chemical admixtures available for

concrete formulations, it is clear that the application of this type of modeling can be useful in

the development of modifications to the current concrete designs which will function to be

either more durable, less expensive or both.

INTRODUCTION

_ A. Scope of Handbook

This handbook has been prepared in two parts. The first part of the text is an illustrative

presentation of data intended to graphically present the ranges of maximum dry particle

packing of typical concrete components. The calculated packing densities are references to

PA DOT, PCA and CCA recommended formulations in an attempt to provide the user with an

understanding of concrete component packing as it relates to common recommended practices.

All calculations in this handbook are based upon the Toufar/Aims models (Alines and Le Goff,

1967/68; Toufar et al., 1967). The presentations in Part I illustrate the changes in packing

associated with accepted ranges in the concrete components and therefore illustrate how this ¢

variability will impact a specific concrete formulation. The data contained in these graphs is

presented in relative terms. For this reason no density values are affixed to the isodensity

lines. Detailed values for specific formulations can be retrieved from the numeric tabulations

in Part II.

B. Theoretical Basis of Packing

The random arrangement of a polydisperse particle system in a container is defined as

the packing density of the powder and represents the volume fraction of the container which is

occupied by the solids. Packing densities are always related to volume percentages of the

components which are related through density to the masses of the solids being considered.

With these simple definitions in mind, the packing density O, can be expressed as

= volv

where:

v = actual volume occupied by the solid

Vo = specific volume of the solid (weight divided by specific density).

By defining Vo = 1, the packing density then becomes:

_= llv

Packing density depends upon the particle size distribution, the particlc shape and the

method by which the particles were packed. Consider two components with particle diameters

dl and d2 such that dl<<d2 in a mixture with the volume fractions rl and r2 and the packing

densities _I and _2-

In the case of a large content of small particles, r1>>r2, the mixture will mainly consist of

small particles with the large particles discretely distributed in between; v = Vl + v2, and Vl =

ri/_1. The matrix of the small particles has the packing density _1 and contributes to the

specific volume with rl/_1. Assuming the coarse particles contribute no pore volume, the

contribution to the specific volume by the large particles is 12. The total volume of the mixture

is;

v =vI + v2 = rl/¢i + 12

and the packing density of the mixture is:

¢mlx = I/v = i/(rl/¢l + 12).

When the volume fraction of the coarse particles is large, r1<<r2, the smaU particles are

accommodated in voids between the large particles, and contribute little to the volume, as rl

approaches zero. The specific volume and the packing density of the mixture are therefore:

v =r2/_

and

• _ =%/r2.

These considerations are based on the assumption that the coarse particles are much larger

than the small particles.

When the assumption dl<<d2 is not valid, the ratio dl/d2 will have an additional effect on

the packing density. The small particles may be too large to fit into the voids between the

larger particles. Along the walls of the container, the packing densities will be smaller

compared to that of the bulk. The magnitude of the "wall effect" will depend on the particle

sizes. A similar effect occurs on the surface of large particles in multicomponent systems in

which the departure from the bulk packing density is dependent upon the ratio of the small to

large particles (Cumberland and Crawford, 1988) as schematically represented in Figure 1.

The above discussion was demonstrated (SHRP C201, 1989) to adequately describe the

behavior of polydisperse (multi-slze) powder systems even though the original Toufar and Aim

publications were developed for monodisperse (single size) particles. Further, the

characteristic diameters of the particle size distributions for the components of concrete were

shown to be adequately described by the D' from the Rosin-Rammler equation (See Appendix

IA):

R(D} = exp{-D/Dl) n}

3

Interface Boundary

0

Bulk Densltyi /

DENSITY

Figure 1. Schematic drawing illustrating lower packing density due to "wall e_ect" of thecontainer and equivalent eEect caused by coarse aggregate in concrete.

4

where R(D) is the residue fraction, D = diameter, D; = characteristic diameter, and n = constant,

ranging from 1.04-4, usually between 1 and 2.

Description Qf R0sin-Rammler JR-R) Distribution

R-R distribution is: R(D) = 1 - F(D) = e - (D/D') n where F(D) = P(d<D) is the cumulative

probability that the diameter d is less than D. D and n are two parameters describing R-R

distribution. To determine D' and n, we transform I_D) = e - (D/D') n to"

In (1) = (D/D,) n

In (Inll = nlnD - nlnD'

If we plot

1In_- vs. D

on In-ln paper, then we have: slope n, the intercept = -nlnD'. It follows that

interceptInD'--n

intercept.)D' = exp (- n

C. General Applicability

The results of the implementation of this mathematical model for dry particle packing,

when applied to the PCA, CCA and PADOT recommended concrete formulations, have been

found to be located within the area of optimal packing on a ternary diagram, fine aggregate-

coarse aggregate-cement. Correlation between dry packing and rheology of the concretes have

found that the workability of the concrete at a fixed cement content and a water-to-cement

ratio is controlled principally by the binary packing of the fine and coarse aggregates. The

optimal workability will be found for the concrete mixture at which the sand-to-coarse

4- aggregate ratio is equal to the densest packing of these two components.

Concrete formulations positioned to the coarse aggregate side of the optimal binary

packing will have a tendency to separate, in contrast to formulations with high cement/paste

contents which may have a tendency to bleed and/or separate.

5

6

PART I

Graphical Representation of Particle Packlng:

An Aid to Concrete Design

o APPROACH

Two widely accepted sources of concrete formulations, the Portland Cement Association

(PCA} (Kosmatka and Panarese, 1988) and the Cement and Concrete Association (McIntosh,

1966) recommendations were used as input in order to map out typical concrete formulations

references to a temary mixture of cement/flne aggregate/coarse aggregate. Figure 2 represents

the results of the mapping of these two sets of recommendations onto the ternary diagram. The

PCA recommendations are based on different formulations with varying coarse aggregate and

water-to-cement ratios while the CCA recommendations are based upon cement-to-fine

aggregate vs. cement-to-coarse aggregate ratios. In all cases, the data in this diagram are based

upon volume percentages of components and the sizes used in the calculation represent the

calculated D' for each respective distribution.

The initiaI portion of this Handbook will deal with the correlation of calculated packing

densities to the time tested concrete formulations recommended by the Portland Cement

Association. The materials that were utilized in the report are materials that were procured

specifically for this program and will therefore represent the data that will directly translate

to laboratory practice. These materials are represented by two morphologically distinct coarse

aggregates: a rounded to sub-rounded quartz and an angular, crushed limestone. The effects of

the utilization of these two extremely different aggregate types will also be discussed.

The second portion of this Handbook will deal in detail with the anticipated differences

that are likely to be encountered in the packing densities in highway concretes due to

variations in particle sizes of component concrete materials allowed by accepted

specifications. In this aspect of the study, the specification for the Pennsylvania Department

of Transportation (PADOT, 1987) were used. Experimental packing densities used in those

calculations were determined according to procedures outlined in Appendix B and C.

CORRELATION BETWEEN CALCULATED PACKING DENSITY AND STANDARD CONCRETEFORMULATIONS

Figures 3, 4 and 5 represent the calculated packing densities for the PCA formulations

which utilize #8, #67 and #57 type coarse aggregates (refer to Figure 2) (ASTM C33) utilizing the

angular limestone aggregates. The gradation analyses of the aggregates are presented in Figure

6 and are in compliance with PADOT specification 703.1 for sand (fine aggregate) and 703.2 for

coarse aggregates.

7

8_

.._-"' 'U_\\\\///.I:#£ g _o0.0> "_

oo _ iI °> s_

i j...Jl_ 4 > ,._

6£I

ei

8

Cement D' PACKINGDENSITY

0.0017cm 0.50.1366cm 0.659

o 0.8210cm 0.61820 • 80

Sand 20 40 60 80 AggregateVOLUME

Figure 3. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete formulations constructed from cement, sand and #8 limestone coarse

aggregate.

J


0.0017cm 0.5 _-0.1366cm 0.6591.3415cm 0.55

20 " 80

40 "- 60i

=1

m

60 _ 40

80 " _ 20

Sand 20 40 60 80 AggregateVOLUNE


aggregate.

10


° 0.0017cm 0.50.1366cm 0.6591.4478cm 0.621

8O

' ii

-- 60

6_ , 40

Sand 20 40 60 80 AggregateVOLUHE


aggregate.

11

Figure 3 represents the calculated packing densities for a system cement/fine

aggregate/#8 limestone coarse aggregate. The maximum density is calculated to be 86% of

theoretical and is located at approximately 15 volume % cement admixed 'with about 60

volume % coarse aggregate. In the back Jacket pocket of this report are two transparencies.

The transparency marked # 1 has inscribed on it three lines of varying water-to-cement ratios

for PCA formulations using #8, #67 and #57 aggregates. The scale of these transparencies is

identical to the figure scale and they are designed to be manually overlain onto the figures.

Examination of Figure 3 with the transparency in place shows that the PCA #8 formulations

occur just off of the maximum packing density in a broad shoulder or plateau region in which

very little variation in packing density occurs at approximately 83%.

Figure 4 represents the calculated packing density for the PCA formulations with #67

aggregate using the same distributions for the sand and cement as in the previous figure. The

centroid of maximum density is observed to have shifted slightly toward the fine aggregate at

approximately the same 15 volume percentage of cement. Placing the transparency over this

figure and observing the middle line corresponding to the #67 aggregate, the range of W/C

permitted generates mixtures which fall directly in the centroid of maximum packing density.

Similar procedures for Figure 5 also reveal that for the #57 aggregate, the W/C variation in the

PCA specification procedures mixtures which lie near to the maximum packing densities. The

centroid has shifted to slightly lower cement contents.

Figures 7, 8 and 9 represent the same packing density calculations based upon the use of

the same cement and sand but with rounded quartz aggregates of the three types. Careful

examination of this set of figures suggests that indeed only minor differences can be observed.

The differences that do occur are directly attributable to the variation in packing densities of

the aggregates which are input as experimental variables in the calculation of the system

packing density. For example, the coarse aggregate (CA) having the lowest packing density

causes a shift of the centroid to a higher fine aggregate (FA) content than the other two CA's.

Figure 10 is presented to exemplify the variations in packing density between the quartz and

limestone shapes that are present in Figures 3 and 7; the #8 aggregate. The rounded aggregate

has the greater packing density. As can be seen, there is a difference of about 8% between the

two different types of #8 aggregate and the variations occur through a region where there is

very little change in packing density over the compositional range. In contrast, the #67

aggregate shows a reversed trend with the limestone mixtures (Figure 4) showing denser

packing than the gravel mixtures (Figure 8),

12

_d

13

-_ i r,,_o r-,.

0

_5

14


" 0.0017cm 0.50.1366cm 0.6590.9640cm 0.699

20 " 80

40 --" 60

L

8O " ['----'-- • 20


Figure 7. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete formulations constructed from cement, sand and #8 quartz coarseaggregate.

15


0.0017cm 0.5. 0.1366cm 0.659

1.3550cm 0.48520 " 80

|

Ii ii

40 60

i

II|

60!

|

80 20

Sand 20 40 60 80 AggregateVOLUME96

Figure 8. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete formulations constructed from cement, sand and #67 quartz coarse

aggregate.

e

16


0.0017cm 0.5° 0.1366cm 0.659

1.4257cm 0.743

20 " 80

40 60

60 40,q


Figure 9. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete formulations constructed from cement, sand and #57 quartz coarse

aggregate.

17

CORRELATION BETWEEN PACKING DENSITY AND VARIATIONS IN CONCRETE COMPONENTSIZE DISTRIBUTIONS ALLOWED BY STANDARD SPECIFICATIONS

The model for calculating packing densities has the potential for widespread commercial

use. One such area concerns the potential for variation in packing and hence in theologic

behavior of standard mixture formulations which result from the use of components which,

although meeting acceptable specifications, would tend to represent extremes of the

specifications. To address this circumstance, the PADOT specification 704.1(B), formulation

AA was chosen as a case example (Figure 11). The variation in formulation allows between

6.25 and 8 bags of cement per cubic yard of concrete at a maximum water-to-cement ratio of

0.47 by weight. Concern for the effects of maximum variation of the concrete components in

the specification (703.1 and 703.2 for sand and aggregate) were therefore addressed. Figures 12

and 13 are histograms of the as-received aggregate and the two allowable extremes. The

characteristic diameters for the distributions, D', are marked on each figure. In Figure 12, the

sand that was received from a commercial supplier is shown to meet the PADOT specification

and possessed a characteristic diameter of 1.37 mm. In contrast, the maximum allowable size

under these specifications is 1.92 mm and the minimum size is 0.48 mm, a spread of about

+_50% over the as-received sand in this case. Figure 13 contains the size distribution for the

#67 limestone aggregate with a characteristic diameter of 1.34 cm. The maximum allowable

characteristic s_e in terms of the PADOT specs is 1.83 crn and the minimum size is 1.14 cm; a

variation of between 30 and 35% over the extremes. Finally, although not shown, variations

in the characteristic size of the cement grind were also explored. The as-received material for

this program possessed a D' of 16.5 micrometers and extremes of 30 and 10 micrometers were

assumed based upon variations in surface area data reported by Bye (1983).

With these materials variations in hand, three sets of calculations were prepared. The

first varied the cement; the second varied the sand; and the third set of calculations varied the

coarse aggregate. In the pocket in the rear of the report is a second transparency marked "#2"

that is scaled to the same dimensions as the remainder of the temary figures used in the report.

On this transparency is a rhomboidal area which designates the allowable variations in the

PADOT 704. I(B) specification for the concrete formulations "AA." The upper horizontal line

represents the maximum allowable cement 8 bags/cubic yard and the parallel line below this is

equivalent to 6.25 bags. The left and right bounds of this area represent the minimum and

maximum permissible coarse aggregate content.

Figures 14, 15 and 16 represent effects of maximum variation in the cement that may be

anticipated. By placing the transparency over the Figure 14 (for maximum D'), one finds that

the PADOT formulation resides directly in the field of maximum calculated packing density.

19

Q.)

0

0

o

I l ¢_

_ _-,t _ _ _'

' ' ' & A_ o

• , ° , . , ° , • _

_ o_ _o

__ __ _._ ._ .8.._ .8. - o_ _o _ _o _r _ _ _.

,_ a : _._ _ _,.gqe "_ l,_ .-

I i_ a

g

20

21

t',,{,0

0

o

-i..J

_-_ 8 ..... -,o , _ ._ _ ,_

Ill C _ W _ c_

O0 _ _ o oo

" ° S_,_::ig:/:i::iiiiiiiii!i:: ":1 _ _0"_ .:............ :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::.:.:: :_] "_ :t_ _J

Ill q_ ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: _

gliiiii?ssiii!ili _ _iiiiiiiii

o o o c_ o o o "5 o

c6

22


0.0030cm 0.50.1366cm 0.6591.3415cm 0.55

20 " 80

m

40 60i

80 20


Figure 14. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete formulations constructed from a cement with D' = 30 micrometers,

sand and #67 limestone aggregate.

23


0.00t7cm 0.50.1366cm 0.6591.3415cm 0.55

20 " 80

m

4( 60

60!

i | --

80 _ 20

Sand 20 40 60 80 AggregateVOLUME%

Figure 15. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete formulations constructed from a cement with D' = 17 micrometers,

sand and #67 limestone aggregate.

24


0.0010cm 0.5: 0.1366cm 0.659

1.3415cm 0.55

20 " 80I

1

40 60ii

I

1

60 - 40

II


Figure 16. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete formulations constructed from a cement with D' = 10 micrometers,sand and #67 limestone aggregate.

25

More specifically, the leaner mixtures are calculated to achieve 86% of theoretical density

while the richer mixtures vary only slight from this value. Continued examination of the

as-received and the finest size distribution of the cement, Figures 15 and 16, respectively,

reveals only very subtle differences. Figure 15 represents the calculated packing diagram for

the as-received materials in this program and hence will serve as the reference for the

variations in all of the components.

Figures 17, 15 and 18 represent the variations that are resultant from the allowable

variation in the fine aggregate component of the formulation, PADOT AA. Here substantially

more change is observed. As in the previous figures, the PADOT formulations fall within the

area of maximum packing densities of about 86%. However, in Figure 17, a larger area of the

compositional range of the formulation, particularly the lean mixes with larger percentages of

coarse aggregate are approaching an area of the diagram in which minor changes will

experience rapid change in packing density. As the average size of the free aggregate increases,

Figures 15 and 18, the region of maximum density is drawn into the compositional region of

the AA foimulation.

Finally, variations in the allowable size of the coarse aggregate were examined and are

presented in Figures 19. 15 and 20. In these simulations, the effects of the variation are much

more apparent simply because the coarse aggregate comprises an increased proportion of the

formulation. In general, all of the materials achieve between 86 and 88% of theoretical density

with the AA formulation lying in the midst of the plateau of maximum density. There appears

to be a wide range of flexibility in selection of the concrete components for the majority of An

formulation possibilities, with the exception of the extreme design with the maximum use of

coarse aggregate; and even then the maximum variations observed are relatively small.

26


0.0017cm 0.50.0474cm 0.7631.3415cm 0.55

20 " 80

m

40 60

80 ' " 20=

-

sand 20 40 60 80 AggregateVOLUME

Figure 17. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete formulations constructed from cement, a sand with D' = 0.474 mm and#67 limestone aggregate.

27


0.0017cm 0.50.1918cm 0.730t.3415cm 0.55

20 " 80

40 60i

60 '. 40

i u ii

l

i

80 _ 20


Figure 18. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete formulations constructed from cement, sand with D' = 1.918 mm and

#67 limestone aggregate.

28


0.0017cm 0.50.1366cm 0.6591.1446cm 0.697

20 " 80

N

40 60

J

60 40/ •

• n • --

80 _ _ 20


Figure 19. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete formulations constructed from cement, sand and #67 limestone

aggregate with D' = 1.144 cm.

29


0.0017cm 0.50.1366cm 0.6591.8174cm 0.684

20 • 80III

40 "-" 6oi

m

6040

i i

II i I

80 9" _ _ ' 20


Figure 20. Plot of isodensity lines connecting points of the same packing density calculatedfor concrete foL',_mlations constructed from cement, sand and #67 limestone

aggregate with D' = 1.817 _n

3O

APPENDIX IA

Part A. Experimental Deter_h_-tion of Packing Densitiesfor Cements and Mlneral Admixtm'_

I. Zero the Mitutoyo Digmatic Analyzer which is mounted on a MSC granite surface stand(Model #0651903) by using the height of the assembled die as the zero point.

2. Prepare 50 grams of material in its desired ratio of components.

3. Put material through riffler three times to ensure an even distribution of your material.

4. Put material in a glass beaker and poke several holes in material to allow for even drying.

5. Dry material in drying oven at 100"C for at least two hours.

6. Weight out 10-k_.05 grams of material, record this height.

7. Pour the 10 grams through a funnel into the I" (2.54 cm) diameter Tungsten Carbidebushing with the bottom plate already in place. Make sure that the surface of the materialis as level as possible. If the material completely fills the dle, remove an of the materialand begin again using only 5 grams of material.

8. Insert the 220 gram Tungsten Carbide piston into the top of the bushing. Be careful not toforce the piston down onto the surface of the material but allow It to rest on the surface.

9. Turn on the vibrating table to speed 4.

10. Place die on the table for 4 minutes and then measure the height of the die again with theDigmatic Indicator. (Measurement should be in ram.) Increase the speed of the table to 5and put the die back onto the table.

11. Vibrate at speed 5 for 2 minutes, take height measurement and increase speed to 6.

12. Vibrate at speed 6 for 2 minutes, take height measurement and increase speed to 7.

13. Vibrate at speed 7 for one half minute, take measurement and decrease speed to 4.

14. Vibrate at speed 4 for one minute and take final measurement.

15. Repeat steps 6-14 for two more s_mples.

16. Calculate density in grams per cubic centlmeter using:

m mass of sample [in grams)Density = v - (3.14)(1.21 cm) 2 (final height of die in cm.)

_r2h = vol.

31

Part B. Ezperlmental Determination for _ Densities far _ntes

Packing densities of the aggregates were determlned using an adaptation to ASTM C-29-87

"STANDARD TEST METHOD FOR UNIT WEIGHT AND VOIDS IN AGGREGATE."

__ A five gallon container was carefully calibrated and titled to approximately 75%capacity. The aggregates were rodded according to the ASTM procedure. Water was added tocompletely cover the aggregate and the container placed on vibrating table at setting 4 forapproximately I-2 minutes; setting 5 through 7 for similar _rnes.

At the termination of this procedure, the water in excess of the top surface of the aggregatewas removed. The resulting voidage in the container was determined by measuring the amountof water that remained in the container. Note: prewetted aggregate should be used for thisprocedure to insure that surfaces are at saturation.

33

PART II

Packing -,dbook:N_meric Data

INTRODUCTION TO THE PACKING HANDBOOK

-" Considering the packing model, a typical ternary packing diagram of concrete will

appear as shown in Figure 21. In the figure is seen the area ofma_rnllrn packing and a vertical

line of constant sand to coarse aggregate volume ratio equal to the ratio of maxlmum binary

packing of the two components.

The vertical line indicates the concrete compositions with the optlm_] workability at a

fixed cement content and water-to-cement ratio. Because of the improved workability along

this line, mixtures also have the capacity to be cast with the lowest water-to-cement ratio, and

the line therefore represents the optimal mixtures for the msterials used.

The strength of the concrete therefore should be optlrnlzed along the vertical line,

decreasing or increasing the cement content with Just enough water added for the desired

workability.

For some concrete mixtures with low mortar cohesion, separation may occur to the right

of the vertical line and bleeding may occur at higher cement contents. This may, however, be

avoided by designing a mortar of high internal cohesion, in which case it will be found that the

optimal mixture composition will be found along the vertical llne.

On this background it is apparent that the design of the optlma] highway concrete may be

reduced to the problem of first finding the optimal volume ratio of the sand to the coarse

aggregate and then to find the lowest possible cement content, that with the necessary water

content for the desired workability will give the desired strength.

For that purpose it has been decided to prepare a series of tables presented in a "Packing

Handbook," that for a large variety of sand and coarse aggregates may be used to find the

optimal volume ratio of sand to coarse aggregate.

The following discussion will describe how the handbook is designed and illustrative

examples are given to proportion concrete using the handbook

DESIGN OF THE CONCRETE HANDBOOK

Considering normal sand and coarse aggregate materials these may be found to present

variations of D' within the following size intervals:

Sand 0-4 mm

Coarse aggregate 7-30 mm

35

10 20 .30 /-0 50 60 70 80 90

•VOL._COARSE

Figure 2 I. Typical ternary packing diagram of cement, sand and eoarse aggregate. Within thediagram is drawn the vertical line along which the optimal workabitity may befound.

36

with packing densities, _0, within the following intervals:

Sand 0.5-0.7

Coarse aggregate 0.5-0.7

These intervals cover very large variations but may be found to represent all existing highway

materials.

_" Based on the above variations, the packing handbook has been designed considering all

binary combinations of sand and coarse aggregate, which have been calclJ_ted by the use of the

packing model.

For the calculations, the diameter of the sand was varied in intervals of 0.5 mm and the

diameter of the coarse aggregate in intervals of 1.0 ram, while the packing densities of both

components were varied in intervals of 0.05. The total number of combinations then is 4,800.

For each combination the binary packing density was calculated by increasing the vo]1_me %

of the coarse aggregate in steps of 2%, thereby estimating the volume % of coarse aggregate for

the maximum binary packing from a total number of calculations of 91,200.

The calculations have been summarized in tabular form in Appendix II.A of this report

and typically appear as illustrated from Figure 22. As can be seen from the figure, the data are

sorted into 6 columns: four columns of possible experimental input data and two col1_mr_ of

corresponding output data. As input data are used, the characteristic d4ameter, d', and the

packing density, PHI,0, of both the sand and the coarse aggregate.

Because the input data are presented in relatively coarse intervals, the actual data for the

materials should be rounded off to the nearest possible interval.

The tables give the optimal volume % (precision +_5%)of coarse aggregate to be used in the

binary mixture of sand and coarse aggregate. As a help in choosing between different types of

aggregates, the corresponding binary packing density is also shown as output.

INSTRUCTIONS IN THE USE OF THE PACKING HANDIK)OK

To find the optimal proportion of sand and coarse aggregate for a given type of concrete,

the following procedures should be followed:

I. Determine d' from Rosin-Ramrnler plottings of the grading curves of the sand and

coarse aggregate.

2. Determine the packing density of the sand and coarse aggregate.

3. Choose the d' of the sand and move to the field in the table for the correct d'-interval.

4. Choose the d' of the coarse aggregate and move to the field in the table for the correct

d'-intervals of both the sand and the coarse aggregate.

37

SAND COARSE AGGREGATE VOLUME % MAXIMUM

d ' PHI, 0 d ' PHI, 0 COARSE AGGREGATE DENSITY -

1.5 0.50 13.0 0.55 74.0 0.701.5 0.55 13.0 0.55 72.0 0.711.5 0.60 13.0 0.55 70.0 0.731.5 0.65 13.0 0.55 68.0 0.741.5 0.70 13.0 0.55 66.0 0.76

Figure 22. Example of the packing handbook.

38

5. Find the packing density of the coarse aggregate and move to the field in the table

containing the correct d'-intervals for both materials, and the packing den_ty of the

coarse aggregate.

6. Considering the packhng density of the sand, fiv__]|y move to the line containing the

correct 4 input parameters.

, 7. From this line, read the corresponding volume % of the coarse aggregate to be used in

the binary mixture of sand and coarse aggregate.

EXAMPLE OFUSE

Consider the concrete specifications according to PADOT specification 704.1(b),

illustrated m Table 1. For the type AA concrete to be used for paving will be used sand and

coarse aggregate as specified by PADOT 703.2 and 703.2, with the typical input parameters:

Sand (mm) Coarse Aggregate

d' 1.37 13.4

PHI,0 0.66 0.55

The packing diagram and the compositional area recommended by PADOT are shown in Figure

23.

Following the above procedures, the experimental values first are rounded off:

Sand (ram) Coarse Aggregate

d' 1.5 13.0

PHI,0 0.65 0.55

Using the packing tables for the four input parameters, it is found that the binary mixture

of sand and coarse aggregate has to consist of 68.0 volume % of the coarse aggregate. This result

4 is seen to correlate well with the results of Figure 22, from which it can be seen that the vertical

llne representing the optimal binary packing of sand and coarse aggregate will pass through

the area of maximum ternary packing.

39

Table 1. Variations allowed by the PADOT specification704.1 (b).

CLASS USE CEMENT Y_XI._._ SL_

OF FACTCR _ATER KA_:GE

CONCRETE (Bags/C.¥) CEMENT (I_CHES)

Min. Max. RATIO

(ibs/ibs)

AAA BRIDGE DECK 6.75 8.00 0.43 1-3

AA PAVING 6.25 8.00 0.47 1-3

AA 6.25 8.00 0.47 1-3

A Structures 6.00 8.00 0.50 1-3

C and 4.20 7.00 0.66 2-6

M.E.S. Misc. 8.00 9.00 0.40 1-3

CO_SEcLAsS MIX P OPORTIONSOF DESIGN COMPRESSIVE AGGREGATE SOLID

CONCRETE STRENGTH (PSI) VOLSqJ_E

da_s (Cu. Ft/Cu. ¥d)1 7 28

_ ..... 3600 4500

_ 3000 3750 9.93-13.10

_ 3000 3750 9.93-13.10

A ..... 2750 3300 10.18-13.43

C 1500 2000 11.45-15.10

H.E.S. 3000 3750 9.10-12.00

40

10 90

30 o._ - 70

/ 40 - 60 Z"O(._,_,_.. 50 o.G4 50

._(_' 0.66 --40

60 o.r_

0.7 . 3070 0.72

-- _ 0.74 " --20

80 ,..........-_-- c P_OOTAA.

90 _t

_0 20 30 40 50 60 70 80 90

VOL._ COARSE

Figure 23. Concrete composition using the received size of fine and coarse aggregate andspecification limits as allowed by PADOT.

41

RESTRICTIONS IN THE USE OF THE PAC_ HANDBOOK

The packing handbook was designed to address the proper selection of dry concrete

components and as such does not directly address the behavior of the concrete system.

However, indirectly we have presented the general behavior of formulations that occur to the

extremes, both left and right, of the optimum workabfllty with fixed cement content and W/C.

If concrete formulations are desired which utllJ_,_ the technique of replacement of sand by the

equivalent volume of entrained air, minor effects upon the loci of optlmum workability at

fixed cement content and W/C can be addressed. The loci are displaced toward the sand apex of

the ternary diagram into a region of the packing diagrams which is typically less prone to

changes in packing densities even with fairly significant compositional changes (of the dry

components). As has been stated, within this region formulations are prone to segregation and

bleeding. Data presented in Table 2 suggests that a reference formulation with a sand to coarse

aggregate ratio of 0.6 and a W/C of 0.45 with no entrained air possesses unusable theological

properties exhibiting a very high (unmeasurable) plastic viscosity and a zero slump. These

data support the long-held observation that entrained air, from two rllfl'erent agents in this

case, has a comparable effect as a plasticizer. Here, even with a sand to coarse aggregate ratio of

0.48 and a constant W/C of 0.45 and constant cement content, acceptable plastic viscosities are

achieved as well as comparable slump values. Further, in the practice of air compensating

sand/aggregate foHxaulations, maximizing of the densities of the formulations is achieved and

thus represents areas of future optimization of this handbook.

The packing tables cover all combinations of sand and coarse aggregate within broad

intervals. The tables may be used for estimation of the optimal volume ratio of sand and

coarse aggregate using one type of sand and one type of coarse aggregate, which win be adequate

in the design of concrete for most highways. For some types of high quality concrete, it may be

important to combine cement, slag, fly ash and silica fume into one binder and several size

fractions of sand and coarse aggregate into one type of sand or aggregate. As an tUustration,

the ternary packing of three types of coarse aggregate can be seen from Figure 24 and the

pa_ of cement, silica fume and fly ash can be seen from Figure 25.

42

Table 2. Rheological properties of air entrained concretes.

SAMPLE I FORHULATION$ (VOLYo)I AIR _ SLUNP I UNIT _ I Y STRESSI PL VISCOSITY

I I I I I I[ cement { sand J egg l _Ic [ s'pLastJ Z J (in) [(tb/cuft)J (Nm) ] (Nm.s)

S89-1 15.79 30.76 53.44 0.47 .... 1.5 3.25 148.35 2.87 0.77

S89-1A 15.79 30.76 53.44 0.45 .... 6.7 2.25 138.91 3.10 0.61

ref. w/o

entrainment 15.53 31.90 52.96 0.45 .... 0.0 0.00 --- very high very high

ref. w/o

entrainment 15.53 31.90 52.96 0.45 0.5_ 1.0 2.00 151.10 3.53 0.99

ref. w/

AIR 16.66 26.96 56.38 0.45 .... 6.0 2.38 143.70 3.16 1.18

ref. w/MICROAIR 16.66 26.96 56.38 0.45 .... 6.1 2.25 143.70 3.36 1.65

43

_0 9O

20 _0

30 70

/ 40 50 C_

5O 5O _-

60 _ _0

_°¢_...._.,,o¢1. ." 3070

_e

80 _ 20

10 20 30 _0 50 SO 70 80 _0

VOL_ COARSE

Figure 24. Ternary diagram showing the packing density for all possible combinations of thethree types of aggregate: coarse aggregate 2/8 ram, 8/16 mLu and 16/32 ,,-,,

44

MIGRO _UCA

10 9o

20 80

30 70I

o_z 60 •

._, 50 ,.4o 50 ._.__(:)_' 0.400.44

60 o.4z 40O.4

0.38

70 o.._s 30

80 _ 20

90. 10

crueFJer !0 20 30 40 50 60 70 80 90 pLYASN

VOLJSCOARSE

Figure 25. Ternary diagram showing the packing density for all possible combinations of thethree types of binder:, cement, microsilica and fly ash.

45

REFERENCES

R.B. Aims and P. Le Goff, Powder Technology 1, 281-290 (1967/68).

W. Toufar, M. Born and E. Klose, Freiberger Forschungsheft A 559, VEB Deutscher Verlag Fuer

Grundstoffindustrie (1967).

W. Toufar, E. K1ose and M. Born, Aufbereit_-technik 11,603-608 (1977).

D.J. Cumberland and R.J. Crawford, Handbook of Powder Technology, Elsevier, New York, pp

90-92 (1988).

S.H. Kosmatka and W.C. Panavese, Design and Control of Concrete Mixtures, 13th Ed.,

Portland Cement Association, pp. 90-91 (1988).

J.D. Mclntosh, Concrete Mix Design (2nd Ed., 1966), Cement and Concrete Association (UK), 52

Grosvenor Gardens, London SWI (Table I, p. 12).

Commonwealth of Pennsylvania, Department of Transportation, Specification, Harrisburg,

PA, Publ. 408 (1987).

G.C. Bye, Portland Cement: Composition, Production and Properties, Pergamon Press, New

York (1983).

SHRP 201, Third Quarterly Report (1989).

46

Appendix IIA

Packing Tables

47


d ' PHI, 0 d ' PHI, 0 COARSE AGGREGATE DENSITY

0.5 0.50 7.0 0.50 68.0 0.69

0.5 0.55 7.0 0.50 66.0 0.71

0.5 0.60 7.0 0.50 64.0 0.72

" 0.5 0.65 7.0 0.50 62.0 0.74

0.5 0.70 7.0 0.50 60.0 0.76

0.5 0.50 7.0 0.55 72.0 0.71

0.5 0.55 7.0 0.55 70.0 0.72

0.5 0.60 7.0 0.55 68.0 0.74

0.5 0.65 7.0 0.55 66.0 0.75

0.5 0.70 7.0 0.55 64.0 0.76

0.5 0.50 7.0 0.60 76.0 0.72

0.5 0.55 7.0 0.60 74.0 0.73

0.5 0.60 7.0 0.60 72.0 0.75

0.5 0.65 7.0 0.60 72.0 0.76

0.5 0.70 7.0 0.60 70.0 0.78

0.5 0.50 7.0 0.65 80.0 0.74

0.5 0.55 7.0 0.65 78.0 0.75

0.5 0.60 7.0 0.65 78.0 0.76

0.5 0.65 7.0 0.65 76.0 0.77

0.5 0.70 7.0 0.65 74.0 0.78

0.5 0.50 7.0 0.70 84.0 0.76

0.5 0.55 7.0 0.70 82.0 0.76

0.5 0.60 7.0 0.70 82.0 0.78

0.5 0.65 7.0 0.70 80.0 0.78

0.5 0.70 7.0 0.70 80.0 0.79

0.5 0.50 8.0 0.50 68.0 0.69

0.5 0.55 8.0 0.50 66.0 0.71

0.5 0.60 8.0 0.50 64.0 0.72

0.5 0.65 8.0 0.50 62.0 0.74

0.5 0.70 8.0 0.50 60.0 0.76

0.5 0.50 8.0 0.55 72.0 0.71

0.5 0.55 8.0 0.55 70.0 0.72

0.5 0.60 8.0 0.55 68.0 0.74

0.5 0.65 8.0 0.55 66.0 0.75

0.5 0.70 8.0 0.55 64.0 0.77

o 0.5 0.50 8.0 0.60 76.0 0.72

0.5 0.55 8.0 0.60 74.0 0.74

0.5 0.60 8.0 0.60 72.0 0.75

0.5 0.65 8.0 0.60 72.0 0.76

0.5 0.70 8.0 0.60 70.0 0.78

49



0.5 0.50 8.0 0.65 80.0 0.74

0.5 0.55 8.0 0.65 78.0 0.75

0.5 0.60 8.0 0.65 78.0 0.76

0.5 0.65 8.0 0.65 76.0 0.78

0.5 0.70 8.0 0.65 74.0 0.79

0.5 0.50 8.0 0.70 84.0 0.76

0.5 0.55 8.0 0.70 82.0 0.77

0.5 0.60 8.0 0.70 82.0 0.78

0.5 0.65 8.0 0.70 80.0 0.79

0.5 0.70 8.0 0.70 78.0 0.80

0.5 0.50 9.0 0.50 68.0 0.69

0.5 0.55 9.0 0.50 66.0 0.71

0.5 0.60 9.0 0.50 64.0 0.72

0.5 0.65 9.0 0.50 62.0 0.74

0.5 0.70 9.0 0.50 60.0 0.76

0.5 0.50 9.0 0.55 72.0 0.71

0.5 0.55 9.0 0.55 70.0 0.72

0.5 0.60 9.0 0.55 68.0 0.74

0.5 0.65 9.0 0.55 66.0 0.75

0.5 0.70 9.0 0.55 64.0 0.77

0.5 0.50 9.0 0.60 76.0 0.73

0.5 0.55 9.0 0.60 74.0 0.74

0.5 0.60 9.0 0.60 72.0 0.75

0.5 0.65 9.0 0.60 70.0 0.76

0.5 0.70 9.0 0.60 70.0 0.78

0.5 0.50 9.0 0.65 80.0 0.74

0.5 0.55 9.0 0.65 78.0 0.75

0.5 0.60 9.0 0.65 76.0 0.76

0.5 0.65 9.0 0.65 76.0 0.78

0.5 0.70 9.0 0.65 74.0 0.79

0.5 0.50 9.0 0.70 84.0 0.76

0.5 0.55 9.0 0.70 82.0 0.77

0.5 0.60 9.0 0.70 82.0 0.78

0.5 0.65 9.0 0.70 80.0 0.79

0.5 0.70 9.0 0.70 78.0 0.80

0.5 0.50 i0.0 0.50 68.0 0.69

0.5 0.55 I0.0 0.50 66.0 0.71

0.5 0.60 i0.0 0.50 64.0 0.72

0.5 0.65 i0.0 0.50 62.0 0.74

0.5 0.70 I0.0 0.50 60.0 0.76

5O



0.5 0.50 i0.0 0.55 72.0 0.71

0.5 0.55 i0.0 0.55 70.0 0.73

0.5 0.60 i0.0 0.55 68.0 0.74

0.5 0.65 i0.0 0.55 66.0 0.76

0.5 0.70 i0.0 0.55 64.0 0.77

0.5 0.50 I0.0 0.60 76.0 0.73

0.5 0.55 i0.0 0.60 74.0 0.74

0.5 0.60 i0.0 0.60 72.0 0.75

0.5 0.65 10.0 0.60 70.0 0.77

0.5 0.70 i0.0 0.60 70.0 0.78

0.5 0.50 i0.0 0.65 80.0 0.74

0.5 0.55 I0.0 0.65 78.0 0.76

0.5 0.60 i0.0 0.65 76.0 0.77

0.5 0.65 I0.0 0.65 76.0 0.78

0.5 0.70 I0.0 0.65 74.0 0.79

0.5 0.50 I0.0 0.70 84.0 0.76

0.5 0.55 i0.0 0.70 82.0 0.77

0.5 0.60 i0.0 0.70 80.0 0.78

0.5 0.65 i0.0 0.70 80.0 0.79

0.5 0.70 i0.0 0.70 78.0 0.80

0.5 0.50 ii.0 0.50 68.0 0.69

0.5 0.55 Ii.0 0.50 66.0 0.71

0.5 0.60 Ii.0 0.50 62.0 0.73

0.5 0.65 II.0 0.50 60.0 0.74

0.5 0.70 Ii.0 0.50 60.0 0.76

0.5 0.50 ii.0 0.55 72.0 0.71

0.5 0.55 II.0 0.55 70.0 0.73

0.5 0.60 ii.0 0.55 68.0 0.74

0.5 0.65 ii.0 0.55 66.0 0.76

0.5 0.70 Ii.0 0.55 64.0 0.77

0.5 0.50 ii.0 0.60 76.0 0.73

0.5 0.55 ii.0 0.60 74.0 0.74

0.5 0.60 Ii.0 0.60 72.0 0.75

, 0.5 0.65 II. 0 O. 60 70.0 0.770.5 0.70 II.0 0.60 68.0 0.78

. 0.5 0.50 II.0 0.65 80.0 0.75

0.5 0.55 Ii.0 0.65 78.0 0.76

0.5 0.60 II.0 0.65 76.0 0.77

0.5 0.65 ii.0 0.65 76.0 0.78

0.5 0.70 ii.0 0.65 74.0 0.79

51



0.5 0.50 ii.0 0.70 84.0 0.76

0.5 0.55 ii.0 0.70 82.0 0.77

0.5 0.60 ii.0 0.70 80.0 0.78

0.5 0.65 Ii.0 0.70 80.0 0.79

0.5 0.70 ii.0 0.70 78.0 0.80

0.5 0.50 12.0 0.50 68.0 0.69

0.5 0.55 12.0 0.50 64.0 0.71

0.5 0.60 12.0 0.50 62.0 0.73

0.5 0.65 12.0 0.50 60.0 0.74

0.5 0.70 12.0 0.50 60.0 0.76

0.5 0.50 12.0 0.55 72.0 0.71

0.5 0.55 12.0 0.55 70.0 0.73

0.5 0.60 12.0 0.55 68.0 0.74

0.5 0.65 12.0 0.55 66.0 0.76

0.5 0.70 12.0 0.55 64.0 0.77

0.5 0.50 12.0 0.60 76.0 0.73

0.5 0.55 12.0 0.60 74.0 0.74

0.5 0.60 12.0 0.60 72.0 0.76

0.5 0.65 12.0 0.60 70.0 0.77

0.5 0.70 12.0 0.60 68.0 0.78

0.5 0.50 12.0 0.65 80.0 0.75

0.5 0.55 12.0 0.65 78.0 0.76

0.5 0.60 12.0 0.65 76.0 0.77

0.5 0.65 12.0 0.65 74.0 0.78

0.5 0.70 12.0 0.65 74.0 0.79

0.5 0.50 12.0 0.70 84.0 0.76

0.5 0.55 12.0 0.70 82.0 0.77

0.5 0.60 12.0 0.70 80.0 0.78

0.5 0.65 12.0 0.70 80.0 0.79

0.5 0.70 12.0 0.70 78.0 0.80

0.5 0.50 13.0 0.50 68.0 0.69

0.5 0.55 13.0 0.50 64.0 0.71

0.5 0.60 13.0 0.50 62.0 0.73

0.5 0.65 13.0 0.50 60.0 0.74

0.5 0.70 13.0 0.50 60.0 0.76

0.5 0.50 13.0 0.55 72.0 0.71

0.5 0.55 13.0 0.55 70.0 0.73

0.5 0.60 13.0 0.55 68.0 0.74

0.5 0.65 13.0 0.55 66.0 0.76

0.5 0.70 13.0 0.55 64.0 0.77

52



0.5 0.50 13.0 0.60 76.0 0.73

0.5 0.55 13.0 0.60 74.0 0.74

- 0.5 0.60 13.0 0.60 72.0 0.76

0.5 0.65 13.0 0.60 70.0 0.77

0.5 0.70 13.0 0.60 68.0 0.78

0.5 0.50 13.0 0.65 80.0 0.75

0.5 0.55 13.0 0.65 78.0 0.76

0.5 0.60 13.0 0.65 76.0 0.77

0.5 0.65 13.0 0.65 74.0 0.78

0.5 0.70 13.0 0.65 74.0 0.80

0.5 0.50 13.0 0.70 84.0 0.76

0.5 0.55 13.0 0.70 82.0 0.77

0.5 0.60 13.0 0.70 80.0 0.78

0.5 0.65 13.0 0.70 80.0 0.79

0.5 0.70 13.0 0.70 78.0 0.80

0.5 0.50 14.0 0.50 68.0 0.69

0.5 0.55 14.0 0.50 64.0 0.71

0 •5 0 •60 i4 •0 0 •50 62.0 0 •73

0.5 0.65 14.0 0.50 60.0 0.75

0.5 0.70 14.0 0.50 58.0 0.76

0.5 0.50 14.0 0.55 72.0 0.71

0.5 0.55 14.0 0.55 70.0 0.73

0.5 0.60 14.0 0.55 68.0 0.74

0.5 0.65 14.0 0.55 66.0 0.76

0.5 0.70 14.0 0.55 64.0 0.78

0.5 0.50 14.0 0.60 76.0 0.73

0.5 0.55 14.0 0.60 74.0 0.74

0.5 0.60 14.0 0.60 72.0 0.76

0.5 0.65 14.0 0.60 70.0 0.77

0.5 0.70 14.0 0.60 68.0 0.78

0.5 0.50 14.0 0.65 80.0 0.75

0.5 0.55 14.0 0.65 78.0 0.76

0.5 0.60 14.0 0.65 76.0 0.77

0.5 0.65 14.0 0.65 74.0 0.78

0.5 0.70 14.0 0.65 74.0 0.80

• 0.5 0.50 14.0 0.70 84.0 0.76

0.5 0.55 14.0 0.70 82.0 0.78

0.5 0.60 14.0 0.70 80.0 0.78

0.5 0.65 14.0 0.70 80.0 0.79

0.5 0.70 14.0 0.70 78.0 0.81

53



0.5 0.50 15.0 0.50 66.0 0.69

0.5 0.55 15.0 0.50 64.0 0.71

0.5 0.60 15.0 0.50 62.0 0.73 .

0.5 0.65 15.0 0.50 60.0 0.75

0.5 0.70 15.0 0.50 58.0 0.76

0.5 0.50 15.0 0.55 72.0 0.71

0.5 0.55 15.0 0.55 70.0 0.73

0.5 0.60 15.0 0.55 68.0 0.74

0.5 0.65 15.0 0.55 66.0 0.76

0.5 0.70 15.0 0.55 64.0 0.78

0.5 0.50 15.0 0.60 76.0 0.73

0.5 0.55 15.0 0.60 74.0 0.75

0.5 0.60 15.0 0.60 72.0 0.76

O. 5 0.65 15.0 0.60 70.0 0.77

0.5 0.70 15.0 0.60 68.0 0.78

0.5 0.50 15.0 0.65 80.0 0.75

0.5 0.55 15.0 0.65 78.0 0.76

0.5 0.60 15.0 0.65 76.0 0.77

0.5 0.65 15.0 0.65 74.0 0.78

0.5 0.70 15.0 0.65 74.0 0.80

0.5 0.50 15.0 0.70 84.0 0.76

0.5 0.55 15.0 0.70 82.0 0.78

0.5 0.60 15.0 0.70 80.0 0.78

0.5 0.65 15.0 0.70 78.0 0.79

J 0.5 0.70 15.0 0.70 78.0 0.81

0.5 0.50 16.0 0.50 66.0 0.69

0.5 0.55 16.0 0.50 64.0 0.71

0.5 0.60 16.0 0.50 62.0 0.73

0.5 0.65 16.0 0.50 60.0 0.75

0.5 0.70 16.0 0.50 58.0 0.76

0.5 0.50 16.0 0.55 72.0 0.71

0.5 0.55 16.0 0.55 70.0 0.73

0.5 0.60 16.0 0.55 68.0 0.74

0.5 0.65 16.0 0.55 66.0 0.76

0.5 0.70 16.0 0.55 64.0 0.78

0.5 0.50 16.0 0.60 76.0 0.73 •

0.5 0.55 16.0 0.60 74.0 0.75

0.5 0.60 16.0 0.60 72.0 0.76

0.5 0.65 16.0 0.60 70.0 0.77

0.5 0.70 16.0 0.60 68.0 0.79

54


d ' PHI, 0 d ' PHI, 0 COARSE AGGREGATE DENS ITY

0.5 0.50 16.0 0.65 80.0 0.75

0.5 0.55 16.0 0.65 78.0 0.76

. 0.5 0.60 16.0 0.65 76.0 0.77

0.5 0.65 16.0 0.65 74.0 0.78

0.5 0.70 16.0 0.65 74.0 0.80

0.5 0.50 16.0 0.70 84.0 0.76

0.5 0.55 16.0 0.70 82.0 0.78

0.5 0.60 16.0 0.70 80.0 0.79

0.5 0.65 16.0 0.70 78.0 0.79

0.5 0.70 16.0 0.70 78.0 0.81

0.5 0.50 17.0 0.50 66.0 0.69

0.5 0.55 17.0 0.50 64.0 0.71

0.5 0.60 17.0 0.50 62.0 0.73

0.5 0.65 17.0 0.50 60.0 0.75

0.5 0.70 17.0 0.50 58.0 0.76

0.5 0.50 17.0 0.55 72.0 0.71

0.5 0.55 17.0 0.55 70.0 0.73

0.5 0.60 17.0 0.55 68.0 0.74

0.5 0.65 17.0 0.55 66.0 0.76

0.5 0.70 17.0 0.55 64.0 0.78

0.5 0.50 17.0 0.60 76.0 0.73

0.5 0.55 17.0 0.60 74.0 0.75

0.5 0.60 17.0 0.60 72.0 0.76

0.5 0.65 17.0 0.60 70.0 0.77

0.5 0.70 17.0 0.60 68.0 0.79

0.5 0.50 17.0 0.65 80.0 0.75

0.5 0.55 17.0 0.65 78.0 0.76

0.5 0.60 17.0 0.65 76.0 0.77

0.5 0.65 17.0 0.65 74.0 0.78

0.5 0.70 17.0 0.65 74.0 0.80

0.5 0.50 17.0 0.70 84.0 0.76

0.5 0.55 17.0 0.70 82.0 0.78

0.5 0.60 17.0 0.70 80.0 0.79

0.5 0.65 17.0 0.70 78.0 0.79

0.5 0.70 17.0 0.70 78.0 0.81

' 0.5 0.50 18.0 0.50 66.0 0.69

0.5 0.55 18.0 0.50 64.0 0.71

0.5 0.60 18.0 0.50 62.0 0.73

0.5 0.65 18.0 0.50 60.0 0.75

0.5 0.70 18.0 0.50 58.0 0.77

55



0.5 0.50 18.0 0.55 72.0 0.71

0.5 0.55 18.0 0.55 70.0 0.73

0.5 0.60 18.0 0.55 68.0 0.74

0.5 0.65 18.0 0.55 66.0 0.76

0.5 0.70 18.0 0.55 64.0 0.78

0.5 0.50 18.0 0.60 76.0 0.73

0.5 0.55 18.0 0.60 74.0 0.75

0.5 0.60 18.0 0.60 72.0 0.76

0.5 0.65 18.0 0.60 70.0 0.77

0.5 0.70 18.0 0.60 68.0 0.79

0.5 0.50 18.0 0.65 80.0 0.75

0.5 0.55 18.0 0.65 78.0 0.76

0.5 0.60 18.0 0.65 76.0 0.77

0.5 0.65 18.0 0.65 74.0 0.78

0.5 0.70 18.0 0.65 72_0 0.80

0.5 0.50 18.0 0.70 84.0 0.76

0.5 0.55 18.0 0.70 82.0 0.78

0.5 0.60 18.0 0.70 80.0 0.79

0.5 0.65 18.0 0.70 78.0 0.80

0.5 0.70 18.0 0.70 78.0 0.81

0.5 0.50 19.0 0.50 66.0 0.69

0.5 0.55 19.0 0.50 64.0 0.71

0.5 0.60 19.0 0.50 62.0 0.73

0.5 0.65 19.0 0.50 60.0 0.75

0.5 0.70 19.0 0.50 58.0 0.77

0.5 0.50 19.0 0.55 72.0 0.71

0.5 0.55 19.0 0.55 70.0 0.73

0.5 0.60 19.0 0.55 68.0 0.74

0.5 0.65 19.0 0.55 66.0 0.76

0.5 0.70 19.0 0.55 64.0 0.78

0.5 0.50 19.0 0.60 76.0 0.73

0.5 0.55 19.0 0.60 74.0 0.75

0.5 0.60 19.0 0.60 72.0 0.76

0.5 0.65 19.0 0.60 70.0 0.77 .0.5 0.70 19.0 0.60 68.0 0.79

0.5 0.50 19.0 0.65 80.0 0.75

0.5 0.55 19.0 0.65 78.0 0.76

0.5 0.60 19.0 0.65 76.0 0.77

0.5 0.65 19.0 0.65 74.0 0.78

0.5 0.70 19.0 0.65 72.0 0.80

56



0.5 0.50 19.0 0.70 82.0 0.76

0.5 0.55 19.0 0.70 82.0 0.78

0.5 0.60 19.0 0.70 80.0 0.790.5 0.65 19.0 0.70 78.0 0.80

0.5 0.70 19.0 0.70 78.0 0.81

0.5 0.50 20.0 0.50 66.0 0.69

0.5 0.55 20.0 0.50 64.0 0.71

0.5 0.60 20.0 0.50 62.0 0.73

0.5 0.65 20.0 0.50 60.0 0.75

0.5 0.70 20.0 0.50 58.0 0.77

0.5 0.50 20.0 0.55 72.0 0.71

0.5 0.55 20.0 0.55 70.0 0.73

0.5 0.60 20.0 0.55 68.0 0.74

0.5 0.65 20.0 0.55 66.0 0.76

0.5 0.70 20.0 0.55 64.0 0.78

0.5 0.50 20.0 0.60 76.0 0.73

0.5 0.55 20.0 0.60 74.0 0.75

0.5 0.60 20.0 0.60 72.0 0.76

0.5 0.65 20.0 0.60 70.0 0.77

0.5 0.70 20.0 0.60 68.0 0.79

0.5 0.50 20.0 0.65 80.0 0.75

0.5 0.55 20.0 0.65 78.0 0.76

0.5 0.60 20.0 0.65 76.0 0.77

0.5 0.65 20.0 0.65 74.0 0.79

0.5 0.70 20.0 0.65 72.0 0.80

0.5 0.50 20.0 0.70 82.0 0.76

0.5 0.55 20.0 0.70 82.0 0.78

0.5 0.60 20.0 0.70 80.0 0.79

0.5 O. 65 20.0 0_.70 78.0 0.80

0.5 0.70 20.0 0.70 78.0 0.81

0.5 0.50 21.0 0.50 66.0 0.69

0.5 0.55 21.0 0.50 64.0 0.71

0.5 0.60 21.0 0.50 62.0 0.73

" 0.5 0.65 21.0 0.50 60.0 0.75

0.5 0.70 21.0 0.50 58.0 0.77

" 0.5 0.50 21.0 0.55 72.0 0.71

0.5 0.55 21.0 0.55 70.0 0.73

0.5 0.60 21.0 0.55 68.0 0.74

0.5 0.65 21.0 0.55 66.0 0.760.5 0.70 21.0 0.55 64.0 0.78

57



0.5 0.50 21.0 0.60 76.0 0.73

0.5 0.55 21.0 0.60 74.0 0.75

0.5 0.60 21.0 0.60 72.0 0.76

0.5 0.65 21.0 0.60 70.0 0.77

0.5 0.70 21.0 0.60 68.0 0.79

0.5 0.50 21.0 0.65 80.0 0.75

0.5 0.55 21.0 0.65 78.0 0.76

0.5 0.60 21.0 0.65 76.0 0.77

0.5 0.65 21.0 0.65 74.0 0.79

0.5 0.70 21.0 0.65 72.0 0.80

0.5 0.50 21.0 0.70 82.0 0.76

0.5 0.55 21.0 0.70 82.0 0.78

0.5 0.60 21.0 0.70 80.0 0.79

0.5 0.65 21.0 0.70 78.0 0.80

0.5 0.70 21.0 0.70 78.0 0.81

0.5 0.50 22.0 0.50 66.0 0.69

0.5 0.55 22.0 0.50 64.0 0.71

0.5 0.60 22.0 0.50 62.0 0.73

0.5 0.65 22.0 0.50 60.0 0.75

0.5 0.70 22.0 0.50 58.0 0.77

0.5 0.50 22.0 0.55 72.0 0.71

0.5 0.55 22.0 0.55 70.0 0.73

0.5 0.60 22.0 0.55 68.0 0.74

0.5 0.65 22.0 0.55 66.0 0.76

0.5 0.70 22.0 0.55 64.0 0.78

0.5 0.50 22.0 0.60 76.0 0.73

0.5 0.55 22.0 0.60 74.0 0.75

0.5 0.60 22.0 0.60 72.0 0.76

0.5 0.65 22.0 0.60 70.0 0.77

0.5 0.70 22.0 0.60 68.0 0.79

0.5 0.50 22.0 0.65 80.0 0.75

0.5 0.55 22.0 0.65 78.0 0.76

0.5 0.60 22.0 0.65 76.0 0.78

0.5 0.65 22.0 0.65 74.0 0.79 .

0.5 0.70 22.0 0.65 72.0 0.80

0.5 0.50 22.0 0.70 82.0 0.76

0.5 0.55 22.0 0.70 82.0 0.78

0.5 0.60 22.0 0.70 80.0 0.79

0.5 0.65 22.0 0.70 78.0 0.80

0.5 0.70 22.0 0.70 78.0 0.81

58



0.5 0.50 23.0 0.50 66.0 0.69

0.5 0.55 23.0 0.50 64.0 0.71

0.5 0.60 23.0 0.50 62.0 0.73

0.5 0.65 23.0 0.50 60.0 0.75

0.5 0.70 23.0 0.50 58.0 0.77

0.5 0.50 23.0 0.55 72.0 0.71

0.5 0.55 23.0 0.55 70.0 0.73

0.5 0.60 23.0 0.55 68.0 0.74

0.5 0.65 23.0 0.55 66.0 0.76

0.5 0.70 23.0 0.55 64.0 0.78

0.5 0.50 23.0 0.60 76.0 0.73

0.5 0.55 23.0 0.60 74.0 0.75

0.5 0.60 23.0 0.60 72.0 0.76

0.5 0.65 23.0 0.60 70.0 0.78

0.5 0.70 23.0 0.60 68.0 0.79

0.5 0.50 23.0 0.65 80.0 0.75

0.5 0.55 23.0 0.65 78.0 0.76

0.5 0.60 23.0 0.65 76.0 0.78

0.5 0.65 23.0 0.65 74.0 0.79

0.5 0.70 23.0 0.65 72.0 0.80

0.5 0.50 23.0 0.70 .... 82.0 0.76

0.5 0.55 23.0 0.70 82.0 0.78

0.5 0.60 23.0 0.70 80.0 0.79

0.5 0.65 23.0 0.70 78.0 0.80

0.5 0.70 23.0 0.70 78.0 0.81

0.5 0.50 24.0 0.50 66.0 0.69

0.5 0.55 24.0 0.50 64.0 0.71

0.5 0.60 24.0 0.50 62.0 0.73

0.5 0.65 24.0 0.50 60.0 0.75

0.5 0.70 24.0 0.50 58.0 0.77

0.5 0.50 24.0 0.55 72.0 0.71

0.5 0.55 24.0 0.55 70.0 0.73

0.5 0.60 24.0 0.55 68.0 0.74

0.5 0.65 24.0 0.55 66.0 0.76

" 0.5 0.70 24.0 0.55 64.0 0.78

0.5 0.50 24.0 0.60 76.0 0.73

0.5 0.55 24.0 0.60 74.0 0.75

0.5 0.60 24.0 0.60 72.0 0.76

0.5 0.65 24.0 0.60 70.0 0.78

0.5 0.70 24.0 0.60 68.0 0.79

59



0.5 0.50 24.0 0.65 80.0 0.75

0.5 0.55 24.0 0.65 78.0 0.76

0.5 0.60 24.0 0.65 76.0 0.78

0.5 0.65 24.0 0.65 74.0 0.79

0.5 0.70 24.0 0.65 72.0 0.80

0.5 0.50 24.0 0.70 82.0 0.76

0.5 0.55 24.0 0.70 82.0 0.78

0.5 0.60 24.0 0.70 80.0 0.79

0.5 0.65 24.0 0.70 78.0 0.80

0.5 0.70 24.0 0.70 78.0 0.81

0.5 0.50 25.0 0.50 66.0 0.69

0.5 0.55 25.0 0.50 64.0 0.71

0.5 0.60 25.0 0.50 62.0 0.73

0.5 0.65 25.0 0.50 60.0 0.75

0.5 0.70 25.0 0.50 58.0 0.77

0.5 0.50 25.0 0.55 72.0 0.71

0.5 0.55 25.0 0.55 70.0 0.73

0.5 0.60 25.0 0.55 68.0 0.74

0.5 0.65 25.0 0.55 66.0 0.76

0.5 0.70 25.0 0.55 64.0 0.78

0.5 0.50 25.0 0.60 76.0 0.73

0.5 0.55 25.0 0.60 74.0 0.75

0.5 0.60 25.0 0.60 72.0 0.76

0.5 0.65 25.0 0.60 70.0 0.78

0.5 0.70 25.0 0.60 68.0 0.79

0.5 0.50 25.0 0.65 80.0 0.75

0.5 0.55 25.0 0.65 78.0 0.76

0.5 0.60 25.0 0.65 76.0 0.78

0.5 0.65 25.0 0.65 74.0 0.79

0.5 0.70 25.0 0.65 72.0 0.80

0.5 0.50 25.0 0.70 82.0 0.77

0.5 0.55 25.0 0.70 82.0 0.78

0.5 0.60 25.0 0.70 80.0 0.79

0.5 0.65 25.0 0.70 78.0 0.80 :

0.5 0.70 25.0 0.70 78.0 0.81

0.5 0.50 26.0 0.50 66.0 0.69

0.5 0.55 26.0 0.50 64.0 0.71

0.5 0.60 26.0 0.50 62.0 0.73

0.5 0.65 26.0 0.50 60.0 0.75

0.5 0.70 26.0 0.50 58.0 0.77

6O



0.5 0.50 26.0 0.55 72.0 0.71

0.5 0.55 26.0 0.55 70.0 0.73

0.5 0.60 26.0 0.55 68.0 0.74

0.5 0.65 26.0 0.55 66.0 0.76

0.5 0.70 26.0 0.55 64.0 0.78

0.5 0.50 26.0 0.60 76.0 0.73

0.5 0.55 26.0 0.60 74.0 0.75

0.5 0.60 26.0 0.60 72.0 0.76

0.5 0.65 26.0 0.60 70.0 0.78

0.5 0.70 26.0 0.60 68.0 0.79

0.5 0.50 26.0 0.65 80.0 0.75

0.5 0.55 26.0 0.65 78.0 0.76

0.5 0.60 26.0 0.65 76.0 0.78

0.5 0.65 26.0 0.65 74.0 0.79

0.5 0.70 26.0 0.65 72.0 0.80

0.5 0.50 26.0 0.70 82.0 0.77

0.5 0.55 26.0 0.70 82.0 0.78

0.5 0.60 26.0 0.70 80.0 0.79

0.5 0.65 26.0 0.70 78.0 0.80

0.5 0.70 26.0 0.70 78.0 0.81

0.5 0.50 27.0 0.50 66.0 0.70

0.5 0.55 27.0 0.50 64.0 0.71

0.5 0.60 27.0 0.50 62.0 0.73

0.5 0.65 27.0 0.50 60.0 0.75

0.5 0.70 27.0 0.50 58.0 0.77

0.5 0.50 27.0 0.55 72.0 0.71

0.5 0.55 27.0 0.55 70.0 0.73

0.5 0.60 27.0 0.55 68.0 0.74

0.5 0.65 27.0 0.55 66.0 0.76

0.5 0.70 27.0 0.55 64.0 0.78

0.5 0.50 27.0 0.60 76.0 0.73

0.5 0.55 27.0 0.60 74.0 0.75

0.5 0.60 27.0 0.60 72.0 0.76

" 0.5 0.65 27.0 0.60 70.0 0.78

0.5 0.70 27.0 0.60 68.0 0.79

0.5 0.50 27.0 0.65 80.0 0.75

0.5 0.55 27.0 0.65 78.0 0.76

0.5 0.60 27.0 0.65 76.0 0.78

0.5 0.65 27.0 0.65 74.0 0.79

0.5 0.70 27.0 0.65 72.0 0.80

61



0.5 0.50 27.0 0.70 82.0 0.770.5 0.55 27.0 0.70 82.0 0.780.5 0.60 27.0 0.70 80.0 0.790.5 0.65 27.0 0.70 78.0 0.800.5 0.70 27.0 0.70 78.0 0.81

0.5 0.50 28.0 0.50 66.0 0.700.5 0.55 28.0 0.50 64.0 0.710.5 0.60 28.0 0.50 62.0 0.730.5 0.65 28.0 0.50 60.0 0.750.5 0.70 28.0 0.50 58.0 0.77

0.5 0.50 28.0 0.55 72.0 0.710.5 0.55 28.0 0.55 70.0 0.730.5 0.60 28.0 0.55 68.0 0.740.5 0.65 28.0 0.55 66.0 0.760.5 0.70 28.0 0.55 64.0 0.78

0.5 0.50 28.0 0.60 76.0 0.730.5 0.55 28.0 0.60 74.0 0.750.5 0.60 28.0 0.60 72.0 0.760.5 0.65 28.0 0.60 70.0 0.780.5 0.70 28.0 0.60 68.0 0.79

0.5 0.50 28.0 0.65 80.0 0.750.5 0.55 28.0 0.65 78.0 0.760.5 0.60 28.0 0.65 76.0 0.780.5 0.65 28.0 0.65 74.0 0.790.5 0.70 28.0 0.65 72.0 0.80

0.5 0.50 28.0 0.70 82.0 0.770.5 0.55 28.0 0.70 82.0 0.780.5 0.60 28.0 0.70 80.0 0.790.5 0.65 28.0 0.70 78.0 0.800.5 0.70 28.0 0.70 78.0 0.81

0.5 0.50 29.0 0.50 66.0 0.700.5 0.55 29.0 0.50 64.0 0.710.5 0.60 29.0 0.50 62.0 0.730.5 0.65 29.0 0.50 60.0 0.750.5 0.70 29.0 0.50 58.0 0.77

0.5 0.50 29.0 0.55 72.0 0.710.5 0.55 29.0 0.55 68.0 0.730.5 0.60 29.0 0.55 68.0 0.740.5 0.65 29.0 0.55 66.0 0.760.5 0.70 29.0 0.55 64.0 0.78

62

SAND COARSE AGGREGATE VOLUME % MAXIMUMd ' PHI, 0 d ' PHI, 0 COARSE AGGREGATE DENSITY

0.5 0.50 29.0 0.60 76.0 0.730.5 0.55 29.0 0.60 74.0 0.750.5 0.60 29.0 0.60 72.0 0.760.5 0.65 29.0 0.60 70.0 0.780.5 0.70 29.0 0.60 68.0 0.79

0.5 0.50 29.0 0.65 80.0 0.750.5 0.55 29.0 0.65 78.0 0.760.5 0.60 29.0 0.65 76.0 0.780.5 0.65 29.0 0.65 74.0 0.790.5 0.70 29.0 0.65 72.0 0.80

0.5 0.50 29.0 0.70 82.0 0.770.5 0.55 29.0 0.70 82.0 0.780.5 0.60 29.0 0.70 80.0 0.790.5 0.65 29.0 0.70 78.0 0.800.5 0.70 29.0 0.70 78.0 0.81

0.5 0.50 30.0 0.50 66.0 0.700.5 0.55 30.0 0.50 64.0 0.710.5 0.60 30.0 0.50 62.0 0.730.5 0.65 30.0 0.50 60.0 0.750.5 0.70 30.0 0.50 58.0 0.77

0.5 0.50 30.0 0.55 72.0 0.710.5 0.55 30.0 0.55 68.0 0.730.5 0.60 30.0 0.55 68.0 0.740.5 0.65 30.0 0.55 66.0 0.760.5 0.70 30.0 0.55 64.0 0.78

0.5 0.50 30.0 0.60 76.0 0.730.5 0.55 30.0 0.60 74.0 0.750.5 0.60 30.0 0.60 72.0 0.760.5 0.65 30.0 0.60 70.0 0.780.5 0.70 30.0 0.60 68.0 0.79

0.5 0.50 30.0 0.65 80.0 0.750.5 0.55 30.0 0.65 78.0 0.760.5 0.60 30.0 0.65 76.0 0.780.5 0.65 30.0 0.65 74.0 0.790.5 0.70 30.0 0.65 72.0 0.80

0.5 0.50 30.0 0.70 82.0 0.770.5 0.55 30.0 0.70 82.0 0.780.5 0.60 30.0 0.70 80.0 0.790.5 0.65 30.0 0.70 78.0 0.800.5 0.70 30.0 0.70 76.0 0.81

63



1.0 0.50 7.0 0.50 70.0 0.68

1.0 0.55 7.0 0.50 68.0 0.69

1.0 0.60 7.0 0.50 66.0 0.71

1.0 0.65 7.0 0.50 64.0 0.72 "

1.0 0.70 7.0 0.50 62.0 0.74

1.0 0.50 7.0 0.55 74.0 0.69 _

1.0 0.55 7.0 0.55 72.0 0.71

1.0 0.60 7.0 0.55 70.0 0.72

1.0 0.65 7.0 0.55 68.0 0.73

1.0 0.70 7.0 0.55 66.0 0.75

1.0 0.50 7.0 0.60 78.0 0.71

1.0 0.55 7.0 0.60 76.0 0.72

1.0 0.60 7.0 0.60 76.0 0.73

1.0 0.65 7.0 0.60 74.0 0.75

1.0 0.70 7.0 0.60 72.0 0.76

1.0 0.50 7.0 0.65 82.0 0.72

1.0 0.55 7.0 0.65 82.0 0.73

1.0 0.60 7.0 0.65 80.0 0.74

1.0 0.65 7.0 0.65 78.0 0.75

1.0 0.70 7.0 0.65 78.0 0.76

1.0 0.50 7.0 0.70 86.0 0.74

1.0 0.55 7.0 0.70 86.0 0.75

i. 0 O. 60 7 •0 0.70 84 •0 O. 76

1.0 0.65 7.0 0.70 84.0 0.76

1.0 0.70 7.0 0.70 82.0 0.77

1.0 0.50 8.0 0.50 68.0 0.68

1.0 0.55 8.0 0.50 66.0 0.69

1.0 0.60 8.0 0.50 64.0 0.71

1.0 0.65 8.0 0.50 62.0 0.73

1.0 0.70 8.0 0.50 60.0 0.74

1.0 0.50 8.0 0.55 74.0 0.70

1.0 0.55 8.0 0.55 72.0 0.71

1.0 0.60 8.0 0.55 70.0 0.73

1.0 0.65 8.0 0.55 68.0 0.74

1.0 0.70 8.0 0.55 66.0 0.75

1.0 0.50 8.0 0.60 78.0 0.71

1.0 0.55 8.0 0.60 76.0 0.72

1.0 0.60 8.0 0.60 74.0 0.74

1.0 0.65 8.0 0.60 72.0 0.75

1.0 0.70 8.0 0.60 72.0 0.76

64



1.0 0.50 8.0 0.65 82.0 0.73

1.0 0.55 8.0 0.65 80.0 0.74

1.0 0.60 8.0 0.65 80.0 0.75

1.0 0.65 8.0 0.65 78.0 0.76

1.0 0.70 8.0 0.65 76.0 0.77

1.0 0.50 8.0 0.70 86.0 0.74

1.0 0.55 8.0 0.70 84.0 0.75

1.0 0.60 8.0 0.70 84.0 0.76

1.0 0.65 8.0 0.70 82.0 0.77

1.0 0.70 8.0 0.70 82.0 0.78

1.0 0.50 9.0 0.50 68.0 0.68

1.0 0.55 9.0 0.50 66.0 0.70

1.0 0.60 9.0 0.50 64.0 0.71

1.0 0.65 9.0 0.50 62.0 0.73

1.0 0.70 9.0 0.50 60.0 0.75

1.0 0.50 9.0 0.55 74.0 0.70

1.0 0.55 9.0 0.55 72.0 0.71

1.0 0.60 9.0 0.55 70.0 0.73

1.0 0.65 9.0 0.55 68.0 0.74

1.0 0.70 9.0 0.55 66.0 0.76

1.0 0.50 9.0 0.60 78.0 0.72

1.0 0.55 9.0 0.60 76.0 0.73

1.0 0.60 9.0 0.60 74.0 0.74

1.0 0.65 9.0 0.60 72.0 0.75

1.0 0.70 9.0 0.60 70.0 0.76

1.0 0.50 9.0 0.65 82.0 0.73

1.0 0.55 9.0 0.65 80.0 0.74

1.0 0.60 9.0 0.65 78.0 0.75

1.0 0.65 9.0 0.65 78.0 0.76

1.0 0.70 9.0 0.65 76.0 0.77

1.0 0.50 9.0 0.70 86.0 0.75

1.0 0.55 9.0 0.70 84.0 0.76

1.0 0.60 9.0 0.70 84.0 0.76

. 1.0 0.65 9.0 0.70 82.0 0.77

1.0 0.70 9.0 0.70 80.0 0.78

1.0 0.50 i0.0 0.50 68.0 0.68

1.0 0.55 i0.0 0.50 66.0 0.70

1.0 0.60 I0.0 0.50 64.0 0.72

1.0 0.65 i0.0 0.50 62.0 0.73

1.0 0.70 i0.0 0.50 60.0 0.75

65

SAND COARSE AGGREGATE VOLUME % MAXIMUMd ' PHI, 0 d ' PHI, 0 COARSE AGGREGATE DENS ITY

1.0 0.50 I0.0 0.55 72.0 0.701.0 0.55 i0.0 0.55 70.0 0.711.0 0.60 10.0 0.55 70.0 0.731.0 0.65 10.0 0.55 68.0 0.741.0 0.70 10.0 0.55 66.0 0.76

1.0 0.50 i0.0 0.60 78.0 0.72 _1.0 0.55 I0.0 0.60 76.0 0.731.0 0.60 I0.0 0.60 74.0 0.741.0 0.65 i0.0 " 0.60 72.0 0.751.0 0.70 i0.0 0.60 70.0 0.77

1.0 0.50 I0.0 0.65 82.0 0.731.0 0.55 I0.0 0.65 80.0 0.751.0 0.60 i0.0 0.65 78.0 0.75I. 0 0.65 i0.0 0.65 76.0 0.761.0 0.70 i0.0 0.65 76.0 0.78

1.0 0.50 I0.0 0.70 86.0 0.751.0 0.55 10.0 0.70 84.0 0.761.0 0.60 i0.0 0.70 82.0 0.771.0 0.65 i0.0 0.70 82.0 0.781.0 0.70 i0.0 0.70 80.0 0.78

1.0 0.50 II.0 0.50 68.0 0.69I. 0 0.55 ii. 0 0.50 66.0 0.70I. 0 0.60 II. 0 0.50 64.0 0.721.0 0.65 II.0 0.50 62.0 0.741.0 0.70 II.0 0.50 60.0 0.75

1.0 0.50 II.0 0..55 72.0 0.70i. 0 0.55 ii. 0 0.55 70.0 0.71I. 0 0.60 Ii. 0 0.55 68.0 0.731.0 0.65 ii.0 0.55 68.0 0.741.0 0.70 ii.0 0.55 66.0 0.76

1.0 0.50 11.0 0.60 78.0 0.721.0 0.55 II.0 0.60 76.0 0.731.0 0.60 ii.0 0.60 74.0 0.751.0 0.65 II.0 0.60 72.0 0.761.0 0.70 II.0 0.60 70.0 0.77

I. 0 0.50 ii. 0 0.65 82.0 0.731.0 0.55 11.0 0.65 80.0 0.751.0 0.60 ii.0 0.65 78.0 0.761.0 0.65 ii.0 0.65 76.0 0.771.0 0.70 ii.0 0.65 76.0 0.78

66


d' PHI, 0 d' PHI, 0 COARSE AGGREGATE DENSITY

1.0 0.50 ii.0 0.70 86.0 0.75

1.0 0.55 ii.0 0.70 84.0 0.76

1.0 0.60 Ii.0 0.70 82.0 0.77

1.0 0.65 ii.0 0.70 82.0 0.78

1.0 0.70 ii.0 0.70 80.0 0.79

5

1.0 0.50 12.0 0.50 68.0 0.69

1.0 0.55 12.0 0.50 66.0 0.70

1.0 0.60 12.0 0.50 64.0 0.72

1.0 0.65 12.0 0.50 62.0 0.74

1.0 0.70 12.0 0.50 60.0 0.75

1.0 0.50 12.0 0.55 72.0 0.70

1.0 0.55 12.0 0.55 70.0 0.72

1.0 0.60 12.0 0.55 68.0 0.73

1.0 0.65 12.0 0.55 66.0 0.75

1.0 0.70 12.0 0.55 66.0 0.76

1.0 0.50 12.0 0.60 76.0 0.72

1.0 0.55 12.0 0.60 76.0 0.73

1.0 0.60 12.0 0.60 74.0 0.75

1.0 0.65 12.0 0.60 72.0 0.76

I. 0 O. 70 12 •0 O. 60 70.0 O. 77

1.0 0.50 12.0 0.65 80.0 0.73

1.0 0.55 12.0 0.65 80.0 0.75

i. 0 0.60 12.0 0.65 78.0 0.76

I. 0 0.65 12.0 0.65 76.0 0.77

1.0 0.70 12.0 0.65 74.0 0.78

1.0 0.50 12.0 0.70 84.0 0.75

1.0 0.55 12.0 0.70 84.0 0.76

1.0 0.60 12.0 0.70 82.0 0.77

1.0 0.65 12.0 0.70 80.0 0.78

1.0 0.70 12.0 0.70 80.0 0.79

1.0 0.50 13.0 0.50 68.0 0.69

1.0 0.55 13.0 0.50 66.0 0.71

1.0 0.60 13.0 0.50 64.0 0.72

• 1.0 0.65 13.0 0.50 62.0 0.74

1.0 0.70 13.0 0.50 60.0 0.76

" 1.0 0.50 13.0 0.55 72.0 0.70

1.0 0.55 13.0 0.55 70.0 0.72

1.0 0.60 13.0 0.55 68.0 0.73

1.0 0.65 13.0 0.55 66.0 0.75

1.0 0.70 13.0 0.55 64.0 0.76

67



1.0 0.50 13.0 0.60 76.0 0.72

1.0 0.55 13.0 0.60 74.0 0.73

1.0 0.60 13.0 0.60 74.0 0.75

I. 0 0.65 13 •0 0.60 72.0 0.76

1.0 0.70 13.0 0.60 70.0 0.77

1.0 0.50 13.0 0.65 80.0 0.74

1.0 0.55 13.0 0.65 80.0 0.75

1.0 0.60 13.0 0.65 78.0 0.76

1.0 0.65 13.0 0.65 76.0 0.77

1.0 0.70 13.0 0.65 74.0 0.78

1.0 0.50 13.0 0.70 84.0 0.75

1.0 0.55 13.0 0.70 84.0 0.76

1.0 0.60 13.0 0.70 82.0 0.77

1.0 0.65 13.0 0.70 80.0 0.78

1.0 0.70 13.0 0.70 80.0 0.79

i. 0 0.50 14.0 0.50 68.0 0.69

1.0 0.55 14.0 0.50 66.0 0.71

1.0 0.60 14.0 0.50 64.0 0.72

i. 0 0.65 14.0 0.50 62.0 0.74

1.0 0.70 14.0 0.50 60.0 0.76

1.0 0.50 14.0 0.55 72.0 0.71

1.0 0.55 14.0 0.55 70.0 0.72

I. 0 0.60 14.0 0.55 68.0 0.74

1.0 0.65 14.0 0.55 66.0 0.75

1.0 0.70 14.0 0.55 64.0 0.76

i. 0 O. 50 14.0 O. 60 76.0 0.72

1.0 0.55 14.0 0.60 74.0 0.73

I. 0 0.60 14.0 0.60 72.0 0.75

I. 0 0.65 14.0 0.60 72.0 0.76

1.0 0.70 14.0 0.60 70.0 0.78

1.0 0.50 14.0 0.65 80.0 0.74

1.0 0.55 14.0 0.65 78.0 0.75

1.0 0.60 14.0 0.65 78.0 0.76

1.0 0.65 14.0 0.65 76.0 0.77 .

1.0 0.70 14.0 0.65 74.0 0.78

1.0 0.50 14.0 0.70 84.0 0.76

1.0 0.55 14.0 0.70 82.0 0.76

1.0 0.60 14.0 0.70 82.0 0.78

1.0 0.65 14.0 0.70 80.0 0.78

1.0 0.70 14.0 0.70 80.0 0.79

68



1.0 0.50 15.0 0.50 68.0 0.69

1.0 0.55 15.0 0.50 66.0 0.71

1.0 0.60 15.0 0.50 64.0 0.72

1.0 0.65 15.0 0.50 62.0 0.74

1.0 0.70 15.0 0.50 60.0 0.76

1.0 0.50 15.0 0.55 72.0 0.71

1.0 0.55 15.0 0.55 70.0 0.72

1.0 0.60 15.0 0.55 68.0 0.74

1.0 0.65 15.0 0.55 66.0 0.75

1.0 0.70 15.0 0.55 64.0 0.77

1.0 0.50 15.0 0.60 76.0 0.72

1.0 0.55 15.0 0.60 74.0 0.74

1.0 0.60 15.0 0.60 72.0 0.75

1.0 0.65 15.0 0.60 72.0 0.76

1.0 0.70 15.0 0.60 70.0 0.78

1.0 0.50 15.0 0.65 80.0 0.74

1.0 0.55 15.0 0.65 78.0 0.75

1.0 0.60 15.0 0.65 78.0 0.76

1.0 0.65 15.0 0.65 76.0 0.78

1.0 0.70 15.0 0.65 74.0 0.79

1.0 0.50 15.0 0.70 84.0 0.76

1.0 0.55 15.0 0.70 82.0 0.76

i. 0 0.60 15.0 0.70 82.0 0.78

1.0 0.65 15.0 0.70 80.0 0.79

1.0 0.70 15.0 0.70 78.0 0.79

1.0 0.50 16.0 0.50 68.0 0.69

1.0 0.55 16.0 0.50 66.0 0.71

1.0 0.60 16.0 0.50 64.0 0.72

1.0 0.65 16.0 0.50 62.0 0.74

1.0 0.70 16.0 0.50 60.0 0.76

1.0 0.50 16.0 0.55 72.0 0.71

i. 0 0.55 16.0 0.55 70.0 0.72

1.0 0.60 16.0 0.55 68.0 0.74

1.0 0.65 16.0 0.55 66.0 0.75

i. 0 0.70 16.0 0.55 64.0 0.77

1.0 0.50 16.0 0.60 76.0 0.72

1.0 0.55 16.0 0.60 74.0 0.74

1.0 0.60 16.0 0.60 72.0 0.75

1.0 0.65 16.0 0.60 72.0 0.76

1.0 0.70 16.0 0.60 70.0 0.78

69



1.0 0.50 16.0 0.65 80.0 0.74

1.0 0.55 16.0 0.65 78.0 0.75

1.0 0.60 16.0 0.65 78.0 0.76

I. 0 0.65 16.0 0.65 76.0 0.78

1.0 0.70 16.0 0.65 74.0 0.79

1.0 0.50 16.0 0.70 84.0 0.76

1.0 0.55 16.0 0.70 82.0 0.77

1.0 0.60 16.0 0.70 82.0 0.78

1.0 0.65 16.0 0.70 80.0 0.79

1.0 0.70 16.0 0.70 78.0 0.80

1.0 0.50 17.0 0.50 68.0 0.69

1.0 0.55 17.0 0.50 66.0 0.71

i. 0 0.60 17.0 0.50 64.0 0.72

I. 0 0.65 17.0 0.50 62.0 0.74

1.0 0.70 17.0 0.50 60.0 0.76

1.0 0.50 17.0 0.55 72.0 0.71

I. 0 O. 55 17.0 0.55 70.0 0.72

i. 0 0.60 17.0 0.55 68.0 0.74

i. 0 0.65 17.0 0.55 66.0 0.75

1.0 0.70 17.0 0.55 64.0 0.77

i. 0 0.50 17.0 0.60 76.0 0.72

1.0 0.55 17.0 0.60 74.0 0.74

i. 0 0.60 17.0 0.60 72.0 0.75

1.0 0.65 17.0 0.60 70.0 0.76

1.0 0.70 17.0 0.60 70.0 0.78

1.0 0.50 17.0 0.65 80.0 0.74

i. 0 0.55 17.0 0.65 78.0 0.75

1.0 0.60 17.0 0.65 78.0 0.76

i. 0 0.65 17.0 0.65 76.0 0.78

I. 0 0.70 17.0 0.65 74.0 0.79

1.0 0.50 17.0 0.70 84.0 0.76

1.0 0.55 17.0 0.70 82.0 0.77

1.0 0.60 17.0 0.70 82.0 0.78

1.0 0.65 17.0 0.70 80.0 0.79 ,

i. 0 0.70 17.0 0.70 78.0 0.80

1.0 0.50 18.0 0.50 68.0 0.69

1.0 0.55 18.0 0.50 66.0 0.71

i. 0 0.60 18.0 0.50 64.0 0.72

1.0 0.65 18.0 0.50 62.0 0.74

1.0 0.70 18.0 0.50 60.0 0.76

7O



1.0 0.50 18.0 0.55 72.0 0.71

1.0 0.55 18.0 0.55 70.0 0.72

1.0 0.60 18.0 0.55 68.0 0.74

1.0 0.65 18.0 0.55 66.0 0.75

1.0 0.70 18.0 0.55 64.0 0.77

• 1.0 0.50 18.0 0.60 76.0 0.73

i. 0 0.55 18.0 0.60 74.0 0.74

1.0 0.60 18.0 0.60 72.0 0.75

1.0 0.65 18.0 0.60 70.0 0.76

1.0 0.70 18.0 0.60 70.0 0.78

1.0 0.50 18.0 0.65 80.0 0.74

1.0 0.55 18.0 0.65 78.0 0.75

1.0 0.60 18.0 0.65 76.0 0.76

1.0 0.65 18.0 0.65 76.0 0.78

1.0 0.70 18.0 0.65 74.0 0.79

1.0 0.50 18.0 0.70 84.0 0.76

1.0 0.55 18.0 0.70 82.0 0.77

I. 0 0.60 18.0 0.70 82.0 0.78

1.0 0.65 18.0 0.70 80.0 0.79

1.0 0.70 18.0 0.70 78.0 0.80

I. 0 0.50 19.0 0.50 68.0 0.69

1.0 0.55 19.0 0.50 66.0 0.71

1.0 0.60 19.0 0.50 64.0 0.72

i. 0 O. 65 19.0 0.50 62.0 0.74

1.0 0.70 19.0 0.50 60.0 0.76

1.0 0.50 19.0 0.55 72.0 0.71

1.0 0.55 19.0 0.55 70.0 0.73

1.0 0.60 19.0 0.55 68.0 0.74

i. 0 0.65 19.0 0.55 66.0 0.76

1.0 0.70 19.0 0.55 64.0 0.77

1.0 0.50 19.0 0.60 76.0 0.73

1.0 0.55 19.0 0.60 74.0 0.74

I. 0 0.60 19.0 0.60 72.0 0.75

I. 0 0.65 19.0 0.60 70.0 0.77

1.0 0.70 19.0 0.60 70.0 0.78

1.0 0.50 19.0 0.65 80.0 0.74

I. 0 0.55 19.0 0.65 78.0 0.75

I. 0 O. 60 19.0 0.65 76.0 0.76

i. 0 0.65 19.0 0.65 76.0 0.78

1.0 0.70 19.0 0.65 74.0 0.79

71



1.0 0.50 19.0 0.70 84.0 0.76

1.0 0.55 19.0 0.70 82.0 0.77

I. 0 0.60 19.0 0.70 80.0 0.78

1.0 0.65 19.0 0.70 80.0 0.79

1.0 0.70 19.0 0.70 78.0 0.80

1.0 0.50 20.0 0.50 68.0 0.69 "

1.0 0.55 20.0 0.50 66.0 0.71

1.0 0.60 20.0 0.50 64.0 0.72

1.0 0.65 20.0 0.50 62.0 0.74

1.0 0.70 20.0 0.50 60.0 0.76

1.0 0.50 20.0 0.55 72.0 0.71

1.0 0.55 20.0 0.55 70.0 0.73

1.0 0.60 20.0 0.55 68.0 0.74

1.0 0.65 20.0 0.55 66.0 0.76

1.0 0.70 20.0 0.55 64.0 0.77

1.0 0.50 20.0 0.60 76.0 0.73

1.0 0.55 20.0 0.60 74.0 0.74

1.0 0.60 20.0 0.60 72.0 0.75

1.0 0.65 20.0 0.60 70.0 0.77

1.0 0.70 20.0 0.60 70.0 0.78

1.0 0.50 20.0 0.65 80.0 0.74

1.0 0.55 20.0 0.65 78.0 0.76

1.0 0.60 20.0 0.65 76.0 0.77

i. 0 0.65 20.0 0.65 76.0 0.78

1.0 0.70 20.0 0.65 74.0 0.79

1.0 0.50 20.0 0.70 84.0 0.76

1.0 0.55 20.0 0.70 82.0 0.77

1.0 0.60 20.0 0.70 80.0 0.78

1.0 0.65 20.0 0.70 80.0 0.79

1.0 0.70 20.0 0.70 78.0 0.80

1.0 0.50 21.0 0.50 68.0 0.69

1.0 0.55 21.0 0.50 66.0 0.71

I. 0 0.60 21.0 0.50 62.0 O. 72

1.0 0.65 21.0 0.50 62.0 0.74 %

1.0 0.70 21.0 0.50 60.0 0.76

1.0 0.50 21.0 0.55 72.0 0.71 .

1.0 0.55 21.0 0.55 70.0 0.73

1.0 0.60 21.0 0.55 68.0 0.74

1.0 0.65 21.0 0.55 66.0 0.76

1.0 0.70 21.0 0.55 64.0 0.77

72



1.0 0.50 21.0 0.60 76.0 0.73

1.0 0.55 21.0 0.60 74.0 0.74

1.0 0.60 21.0 0.60 72.0 0.751.0 0.65 21.0 0.60 70.0 0.77

1.0 0.70 21.0 0.60 68.0 0.78

1.0 0.50 21.0 0.65 80.0 0.75

1.0 0.55 21.0 0.65 78.0 0.76

1.0 0.60 21.0 0.65 76.0 0.77

1.0 0.65 21.0 0.65 76.0 0.78

1.0 0.70 21.0 0.65 74.0 0.79

1.0 0.50 21.0 0.70 84.0 0.76

1.0 0.55 21.0 0.70 82.0 0.77

1.0 0.60 21.0 0.70 80.0 0.78

1.0 0.65 21.0 0.70 80.0 0.79

1.0 0.70 21.0 0.70 78.0 0.80

1.0 0.50 22.0 0.50 68.0 0.69

1.0 0.55 22.0 0.50 66.0 0.71

1.0 0.60 22.0 0.50 62.0 0.73

1.0 0.65 22.0 0.50 60.0 0.74

1.0 0.70 22.0 0.50 60.0 0.76

1.0 0.50 22.0 0.55 72.0 0.71

1.0 0.55 22.0 0.55 70.0 0.73

1.0 0.60 22.0 0.55 68.0 0.74

1.0 0.65 22.0 0.55 66.0 0.76

1.0 0.70 22.0 0.55 64.0 0.77

1.0 0.50 22.0 0.60 76.0 0.73

1.0 0.55 22.0 0.60 74.0 0.74

1.0 0.60 22.0 0.60 72.0 0.75

1.0 0.65 22.0 0.60 70.0 0.77

1.0 0.70 22.0 0.60 68.0 0.78

1.0 0.50 22.0 0.65 80.0 0.75

1.0 0.55 22.0 0.65 78.0 0.76

1.0 0.60 22.0 0.65 76.0 0.77

" 1.0 0.65 22.0 0.65 76.0 0.78

1.0 0.70 22.0 0.65 74.0 0.79

1.0 0.50 22.0 0.70 84.0 0.76

1.0 0.55 22.0 0.70 82.0 0.77

1.0 0.60 22.0 0.70 80.0 0.78

i. 0 0.65 22.0 0.70 80.0 0.791.0 0.70 22.0 0.70 78.0 0.80

73



1.0 0.50 23.0 0.50 68.0 0.69

1.0 0.55 23.0 0.50 64.0 0.71

1.0 0.60 23.0 0.50 62.0 0.73 •

1.0 0.65 23.0 0.50 60.0 0.74

1.0 0.70 23.0 0.50 60.0 0.76

1.0 0.50 23.0 0.55 72.0 0.71

1.0 0.55 23.0 0.55 70.0 0.73

I. 0 O. 60 23.0 0.55 68.0 0.74

1.0 0.65 23.0 0.55 66.0 0.76

1.0 0.70 23.0 0.55 64.0 0.77

1.0 0.50 23.0 0.60 76.0 0.73

1.0 0.55 23.0 0.60 74.0 0.74

1.0 0.60 23.0 0.60 72.0 0.76

1.0 0.65 23.0 0.60 70.0 0.77

1.0 0.70 23.0 0.60 68.0 0.78

1.0 0.50 23.0 0.65 80.0 0.75

1.0 0.55 23.0 0.65 78.0 0.76

i. 0 0.60 23.0 0.65 76.0 0.77

1.0 0.65 23.0 0.65 74.0 0.78

1.0 0.70 23.0 0.65 74.0 0.79

1.0 0.50 23.0 0.70 84.0 0.76

1.0 0.55 23.0 0.70 82.0 0.77

1.0 0.60 23.0 0.70 80.0 0.78

1.0 0.65 23.0 0.70 80.0 0.79

1.0 0.70 23.0 0.70 78.0 0.80

i. 0 0.50 24.0 O. 50 68.0 O. 69

1.0 0.55 24.0 0.50 64.0 0.71

1.0 0.60 24.0 0.50 62.0 0.73

1.0 0.65 24.0 0.50 60.0 0.74

1.0 0.70 24.0 0.50 60.0 0.76

1.0 0.50 24.0 0.55 72.0 0.71

1.0 0.55 24.0 0.55 70.0 0.73

1.0 0.60 24.0 0.55 68.0 0.74

1.0 0.65 24.0 0.55 66.0 0.76

1.0 0.70 24.0 0.55 64.0 0.77

1.0 0.50 24.0 0.60 76.0 0.73 "

1.0 0.55 24.0 0.60 74.0 0.74

1.0 0.60 24.0 0.60 72.0 0.76

1.0 0.65 24.0 0.60 70.0 0.77

1.0 0.70 24.0 0.60 68.0 0.78

74


d' PHI,0 d' PHI,0 COARSE AGGREGATE DENSITY

i. 0 0.50 24.0 0.65 80.0 0.75

1.0 0.55 24.0 0.65 78.0 0.76

1.0 0.60 24.0 0.65 76.0 0.77

" 1.0 0.65 24.0 0.65 74.0 0.78

1.0 0.70 24.0 0.65 74.0 0.79

" 1.0 0.50 24.0 0.70 84.0 0.76

1.0 0.55 24.0 0.70 82.0 0.77

1.0 0.60 24.0 0.70 80.0 0.78

1.0 0.65 24.0 0.70 80.0 0.79

1.0 0.70 24.0 0.70 78.0 0.80

1.0 0.50 25.0 0.50 68.0 0.69

1.0 0.55 25.0 0.50 64.0 0.71

1.0 0.60 25.0 0.50 62.0 0.73

1.0 0.65 25.0 0.50 60.0 0.74

1.0 0.70 25.0 0.50 60.0 0.76

1.0 0.50 25.0 0.55 72.0 0.71

1.0 0.55 25.0 0.55 70.0 0.73

1.0 0.60 25.0 0.55 68.0 0".74

1.0 0.65 25.0 0.55 66.0 0.76

1.0 0.70 25.0 0.55 64.0 0.77

1.0 0.50 25.0 0.60 76.0 0.73

1.0 0.55 25.0 0.60 74.0 0.74

1.0 0.60 25.0 0.60 72.0 0.76

i. 0 0.65 25.0 0.60 70.0 0.77

1.0 0.70 25.0 0.60 68.0 0.78

1.0 0.50 25.0 0.65 80.0 0.75

1.0 0.55 25.0 0.65 78.0 0.76

1.0 0.60 25.0 0.65 76.0 0.77

1.0 0.65 25.0 0.65 74.0 0.78

1.0 0.70 25.0 0.65 74.0 0.80

1.0 0.50 25.0 0.70 84.0 0.76

1.0 0.55 25.0 0.70 82.0 0.77

1.0 0.60 25.0 0.70 80.0 0.78

1.0 0.65 25.0 0.70 80.0 0.79

1.0 0.70 25.0 0.70 78.0 0.80

1.0 0.50 26.0 0.50 68.0 0.69

1.0 0.55 26.0 0.50 64.0 0.71

1.0 0.60 26.0 0.50 62.0 0.73

I. 0 0.65 26.0 0.50 60.0 0.74

1.0 0.70 26.0 0.50 60.0 0.76

75



1.0 0.50 26.0 0.55 72.0 0.71

1.0 0.55 26.0 0.55 70.0 0.73

1.0 0.60 26.0 0.55 68.0 0.74

1.0 0.65 26.0 0.55 66.0 0.76 _

1.0 0.70 26.0 0.55 64.0 0.77

1.0 0.50 26.0 0.60 76.0 0.73

1.0 0.55 26.0 0.60 74.0 0.74

1.0 0.60 26.0 0.60 72.0 0.76

1.0 0.65 26.0 0.60 70.0 0.77

1.0 0.70 26.0 0.60 68.0 0.78

1.0 0.50 26.0 0.65 80.0 0.75

1.0 0.55 26.0 0.65 78.0 0.76

1.0 0.60 26.0 0.65 76.0 0.77

1.0 0.65 26.0 0.65 74.0 0.78

1.0 0.70 26.0 0.65 74.0 0.80

1.0 0.50 26.0 0.70 84.0 0.76

1.0 0.55 26.0 0.70 82.0 0.77

1.0 0.60 26.0 0.70 80.0 0.78

1.0 0.65 26.0 0.70 80.0 0.79

1.0 0.70 26.0 0.70 78.0 0.80

1.0 0.50 27.0 0.50 68.0 0.69

1.0 0.55 27.0 0.50 64.0 0.71

1.0 0.60 27.0 0.50 62.0 0.73

1.0 0.65 27.0 0.50 60.0 0.75

1.0 0.70 27.0 0.50 58.0 0.76

1.0 0.50 27.0 0.55 72.0 0.71

1.0 0.55 27.0 0.55 70.0 0.73

1.0 0.60 27.0 0.55 68.0 0.74

1.0 0.65 27.0 0.55 66.0 0.76

1.0 0.70 27.0 0.55 64.0 0.77

1.0 0.50 27.0 0.60 76.0 0.73

1.0 0.55 27.0 0.60 74.0 0.74

1.0 0.60 27.0 0.60 72.0 0.76

1.0 0.65 27.0 0.60 70.0 0.77

1.0 0.70 27.0 0.60 68.0 0.78

1.0 0.50 27.0 0.65 80.0 0.75

1.0 0.55 27.0 0.65 78.0 0.76

1.0 0.60 27.0 0.65 76.0 0.77

1.0 0.65 27.0 0.65 74.0 0.78

1.0 0.70 27.0 0.65 74.0 0.80

76


1.0 0.50 27.0 0.70 84.0 0.761.0 0.55 27.0 0.70 82.0 0.78

, 1.0 0.60 27.0 0.70 80.0 0.781.0 0.65 27.0 0.70 80.0 0.791.0 0.70 27.0 0.70 78.0 0.81

1.0 0.50 28.0 0.50 68.0 0.69

1.0 0.55 28.0 0.50 64.0 0.711.0 0.60 28.0 0.50 62.0 0.731.0 0.65 28.0 0.50 60.0 0.751.0 0.70 28.0 0.50 58.0 0.76

1.0 0.50 28.0 0.55 72.0 0.711.0 0.55 28.0 0.55 70.0 0.731.0 0.60 28.0 0.55 68.0 0.741.0 0.65 28.0 0.55 66.0 0.761.0 0.70 28.0 0.55 64.0 0.78

1.0 0.50 28.0 0.60 76.0 0.731.0 0.55 28.0 0.60 74.0 0.741.0 0.60 28.0 0.60 72.0 0.761.0 0.65 28.0 0.60 70.0 0.771.0 0.70 28.0 0.60 68.0 0.78

I. 0 0.50 28.0 0.65 80.0 0.751.0 0.55 28.0 0.65 78.0 0.761.0 0.60 28.0 0.65 76.0 0.771.0 0.65 28.0 0.65 74.0 0.78i. 0 0.70 28.0 0.65 74.0 0.80

1.0 0.50 28.0 0.70 84.0 0.761.0 0.55 28.0 0.70 82.0 0.781.0 0.60 28.0 0.70 80.0 0.781.0 0.65 28.0 0.70 80.0 0.791.0 0.70 28.0 0.70 78.0 0.81

1.0 0.50 29.0 0.50 68.0 0.691.0 0.55 29.0 0.50 64.0 0.711.0 0.60 29.0 0.50 62.0 0.73

- 1.0 0.65 29.0 0.50 60.0 0.751.0 0.70 29.0 0.50 58.0 0.76

1.0 0.50 29.0 0.55 72.0 0.711.0 0.55 29.0 0.55 70.0 0.731.0 0.60 29.0 0.55 68.0 0.741.0 0.65 29.0 0.55 66.0 0.761.0 0.70 29.0 0.55 64.0 0.78

77


1.0 0.50 29.0 0.60 76.0 0.731.0 0.55 29.0 0.60 74.0 0.751.0 0.60 29.0 0.60 72.0 0.761.0 0.65 29.0 0.60 70.0 0.771.0 0.70 29.0 0.60 68.0 0.78

1.0 0.50 29.0 0.65 80.0 0.75I. 0 0.55 29.0 0.65 78.0 0.761.0 0.60 29.0 0.65 76.0 0.771.0 0.65 29.0 0.65 74.0 0.781.0 0.70 29.0 0.65 74.0 0.80

1.0 0.50 29.0 0.70 84.0 0.761.0 0.55 29.0 0.70 82.0 0.781.0 0.60 29.0 0.70 80.0 0.781.0 0.65 29.0 0.70 78.0 0.791.0 0.70 29.0 0.70 78.0 0.81

1.0 0.50 30.0 0.50 66.0 0.691.0 0.55 30.0 0.50 64.0 0.711.0 0.60 30.0 0.50 62.0 0.731.0 0.65 30.0 0.50 60.0 0.751.0 0.70 30.0 0.50 58.0 0.76

1.0 0.50 30.0 0.55 72.0 0.711.0 0.55 30.0 0.55 70.0 0.731.0 0.60 30.0 0.55 68.0 0.741.0 0.65 30.0 0.55 66.0 0.761.0 0.70 30.0 0.55 64.0 0.78

1.0 0.50 30.0 0.60 76.0 0.731.0 0.55 30.0 0.60 74.0 0.751.0 0.60 30.0 0.60 72.0 0.761.0 0.65 30.0 0.60 70.0 0.771.0 0.70 30.0 0.60 68.0 0.78

1.0 0.50 30.0 0.65 80.0 0.751.0 0.55 30.0 0.65 78.0 0.761.0 0.60 30.0 0.65 76.0 0.771.0 0.65 30.0 0.65 74.0 0.781.0 0.70 30.0 0.65 74.0 0.80

1.0 0.50 30.0 0.70 84.0 0.761.0 0.55 30.0 0.70 82.0 0.781.0 0.60 30.0 0.70 80.0 0.781.0 0.65 30.0 0.70 78.0 0.791.0 0.70 30.0 0.70 78.0 0.81

78



1.5 0.50 7.0 0.50 60.0 0.591.5 0.55 7.0 0.50 54.0 0.601.5 0.60 7.0 0.50 46.0 0.621.5 0.65 7.0 0.50 38.0 0.651.5 0.70 7.0 0.50 26.0 0.70

1.5 0.50 7.0 0.55 68.0 0.611.5 0.55 7.0 0.55 62.0 0.621.5 0.60 7.0 0.55 56.0 0.641.5 0.65 7.0 0.55 48.0 0.661.5 0.70 7.0 0.55 38.0 0.70

1.5 0.50 7.0 0.60 74.0 0.631.5 0.55 7.0 0.60 70.0 0.651.5 0.60 7.0 0.60 64.0 0.661.5 0.65 7.0 0.60 58.0 0.681.5 0.70 7.0 0.60 50.0 0.70

1.5 0.50 7.0 0.65 80.0 0.66I. 5 0.55 7.0 0.65 76.0 0.671.5 0.60 7.0 0.65 72.0 0.681.5 0.65 7.0 0.65 66.0 0.701.5 0.70 7.0 0.65 60.0 0.71

1.5 0.50 7.0 0.70 84.0 0.701.5 0.55 7.0 0.70 82.0 0.701.5 0.60 7.0 0.70 78.0 0.711.5 0.65 7.0 0.70 74.0 0.721.5 0.70 7.0 0.70 68.0 0.73

1.5 0.50 8.0 0.50 70.0 0.67i. 5 0.55 8.0 0.50 68.0 0.691.5 0.60 8.0 0.50 66.0 0.701.5 0.65 8.0 0.50 64.0 0.721.5 0.70 8.0 0.50 62.0 0.73

1.5 0.50 8.0 0.55 76.0 0.681.5 0.55 8.0 0.55 74.0 0.701.5 0.60 8.0 0.55 72.0 0.71

. 1.5 0.65 8.0 0.55 70.0 0.721.5 0.70 8.0 0.55 68.0 0.74

. 1.5 0.50 8.0 0.60 80.0 0.701.5 0.55 8.0 0.60 78.0 0.711.5 0.60 8.0 0.60 76.0 0.721.5 0.65 8.0 0.60 74.0 0.731.5 0.70 8.0 0.60 74.0 0.74

79



1.5 0.50 8.0 0.65 84.0 0.72

1.5 0.55 8.0 0.65 82.0 0.72

1.5 0.60 8.0 0.65 82.0 0.73

1.5 0.65 8.0 0.65 80.0 0.74 ,

1.5 0.70 8.0 0.65 78.0 0.75

1.5 0.50 8.0 0.70 88.0 0.73 _

1.5 0.55 8.0 0.70 88.0 0.74

1.5 0.60 8.0 0.70 86.0 0.74

1.5 0.65 8.0 0.70 84.0 0.75

1.5 0.70 8.0 0.70 84.0 0.76

1.5 0.50 9.0 0.50 70.0 0.67

1.5 0.55 9.0 0.50 68.0 0.69

1.5 0.60 9.0 0.50 66.0 0.71

1.5 0.65 9.0 0.50 64.0 0.72

1.5 0.70 9.0 0.50 62.0 0.74

1.5 0.50 ' 9.0 0.55 74.0 0.69

1.5 0.55 9.0 0.55 72.0 0.70

1.5 0.60 9.0 0.55 70.0 0.71

1.5 0.65 9.0 0.55 70.0 0.73

1.5 0.70 9.0 0.55 68.0 0.74

1.5 0.50 9.0 0.60 80.0 0.70

1.5 0.55 9.0 0.60 78.0 0.72

1.5 0.60 9.0 0.60 76.0 0.73

1.5 0.65 9.0 0.60 74.0 0.74

1.5 0.70 9.0 0.60 72.0 0.75

1.5 0.50 9.0 0.65 84.0 0.72

1.5 0.55 9.0 0.65 82.0 0.73

1.5 0.60 9.0 0.65 80.0 0.74

1.5 0.65 9.0 0.65 80.0 0.75

1.5 0.70 9.0 0.65 78.0 0.76

1.5 0.50 9.0 0.70 88.0 0.74

1.5 0.55 9.0 0.70 86.0 0.74

1.5 0.60 9.0 0.70 86.0 0.75

1.5 0.65 9.0 0.70 84.0 0.76

1.5 0.70 9.0 0.70 84.0 0.76 _"

1.5 0.50 i0.0 0.50 70.0 0.68

1.5 0.55 i0.0 0.50 68.0 0.69

1.5 0.60 I0.0 0.50 66.0 0.71

1.5 0.65 i0.0 0.50 64.0 0.72

1.5 0.70 i0.0 0.50 62.0 0.74

8O



1.5 0.50 i0.0 0.55 74.0 0.69

1.5 0.55 i0.0 0.55 72.0 0.71

1.5 0.60 i0.0 0.55 70.0 0.72

- 1.5 0.65 I0.0 0.55 68.0 0.73

1.5 0.70 10.0 0.55 66.0 0.75

1.5 0.50 i0.0 0.60 78.0 0.71

1.5 0.55 I0.0 0.60 76.0 0.72

1.5 0.60 i0.0 0.60 76.0 0.73

1.5 0.65 i0.0 0.60 74.0 0.74

1.5 0.70 i0.0 0.60 72.0 0.75

1.5 0.50 i0.0 0.65 82.0 0.72

1.5 0.55 10.0 0.65 82.0 0.73

1.5 0.60 10.0 0.65 80.0 0.74

1.5 0.65 i0.0 0.65 78.0 0.75

1.5 0.70 I0.0 0.65 78.0 0.76

1.5 0.50 i0.0 0.70 86.0 0.74

1.5 0.55 10.0 0.70 86.0 0.75

1.5 0.60 I0.0 0.70 84.0 0.75

1.5 0.65 i0.0 0.70 84.0 0.76

1.5 0.70 I0.0 0.70 82.0 0.77

1.5 0.50 ii.0 0.50 70.0 0.68

1.5 0.55 11.0 0.50 66.0 0.69

1.5 0.60 ii.0 0.50 64.0 0.71

1.5 0.65 Ii.0 0.50 64.0 0.72

1.5 0.70 ii.0 0.50 62.0 0.74

1.5 0.50 ii.0 0.55 74.0 0.70

1.5 0.55 ii.0 0.55 72.0 0.71

1.5 0.60 Ii.0 0.55 70.0 0.72

1.5 0.65 II.0 0.55 68.0 0.74

1.5 0.70 ii.0 0.55 66.0 0.75

1.5 0.50 Ii.0 0.60 78.0 0.71

1.5 0.55 ii.0 0.60 76.0 0.72

1.5 0.60 II.0 0.60 74.0 0.73

i. 5 0.65 ii. 0 0.60 74.0 0.75

" 1.5 0.70 ii.0 0.60 72.0 0.76

1.5 0.50 ii.0 0.65 82.0 0.72

1.5 0.55 ii.0 0.65 82.0 0.73

i. 5 0.60 ii. 0 0.65 80.0 0.75

1.5 0.65 ii.0 0.65 78.0 0.76

1.5 0.70 Ii.0 0.65 76.0 0.76

81



1.5 0.50 ii.0 0.70 86.0 0.74

1.5 0.55 ii.0 0.70 86.0 0.75

1.5 0.60 Ii.0 0.70 84.0 0.76

1.5 0.65 ii.0 0.70 82.0 0.76

1.5 0.70 ii.0 0.70 82.0 0.77

I. 5 0.50 12.0 0.50 68.0 0.68 _

1.5 0.55 12.0 0.50 66.0 0.69

1.5 0.60 12.0 0.50 64.0 0.71

1.5 0.65 12.0 0.50 62.0 0.73

1.5 0.70 12.0 0.50 60.0 0.74

1.5 0.50 12.0 0.55 74.0 0.70

1.5 0.55 12.0 0.55 72.0 0.71

1.5 0.60 12.0 0.55 70.0 0.73

1.5 0.65 12.0 0.55 68.0 0.74

1.5 0.70 12.0 0.55 66.0 0.75

1.5 0.50 12.0 0.60 78.0 0.71

1.5 0.55 12.0 0.60 76.0 0.72

1.5 0.60 12.0 0.60 74.0 0.74

1.5 0.65 12.0 0.60 72.0 0.75

1.5 0.70 12.0 0.60 72.0 0.76

1.5 0.50 12.0 0.65 82.0 0.73

I. 5 0.55 12.0 0.65 80.0 0.74

1.5 0.60 12.0 0.65 80.0 0.75

1.5 0.65 12.0 0.65 78.0 0.76

1.5 0.70 12.0 0.65 76.0 0.77

1.5 0.50 12.0 0.70 86.0 0.74

1.5 0.55 12.0 0.70 84.0 0.75

1.5 0.60 12.0 0.70 84.0 0.76

i. 5 0.65 12.0 0.70 82.0 0.77

1.5 0.70 12.0 0.70 82.0 0.78

1.5 0.50 13.0 0.50 68.0 0.68

1.5 0.55 13.0 0.50 66.0 0.70

1.5 0.60 13.0 0.50 64.0 0.71

1.5 0.65 13.0 0.50 62.0 0.73

1.5 0.70 13.0 0.50 60.0 0.75

1.5 0.50 13.0 0.55 74.0 0.70

1.5 0.55 13.0 0.55 72.0 0.71

1.5 0.60 13.0 0.55 70.0 0.73

1.5 0.65 13.0 0.55 68.0 0.74

1.5 0.70 13.0 0.55 66.0 0.76

82



1.5 0.50 13.0 0.60 78.0 0.72

1.5 0.55 13.0 0.60 76.0 0.73

1.5 0.60 13.0 0.60 74.0 0.74

1.5 0.65 13.0 0.60 72.0 0.75

1.5 0.70 13.0 0.60 72.0 0.76

1.5 0.50 13.0 0.65 82.0 0.73

1.5 0.55 13.0 0.65 80.0 0.74

1.5 0.60 13.0 0.65 78.0 0.75

1.5 0.65 13.0 0.65 78.0 0.76

1.5 0.70 13.0 0.65 76.0 0.77

1.5 0.50 13.0 0.70 86.0 0.75

1.5 0.55 13.0 0.70 84.0 0.75

1.5 0.60 13.0 0.70 84.0 0.76

1.5 0.65 13.0 0.70 82.0 0.77

1.5 0.70 13.0 0.70 80.0 0.78

1.5 0.50 14.0 0.50 68.0 0.68

i. 5 0.55 14.0 0.50 66.0 0.70

1.5 0.60 14.0 0.50 64.0 0.72

1.5 0.65 14.0 0.50 62.0 0.73

1.5 0.70 14.0 0.50 60.0 0.75

1.5 0.50 14.0 0.55 74.0 0.70

1.5 0.55 14.0 0.55 72.0 0.71

1.5 0.60 14.0 0.55 70.0 0.73

1.5 0.65 14.0 0.55 68.0 0.74

1.5 0.70 14.0 0.55 66.0 0.76

1.5 0.50 14.0 0.60 78.0 0.72

1.5 0.55 14.0 0.60 76.0 0.73

1.5 0.60 14.0 0.60 74.0 0.74

i. 5 0.65 14.0 0.60 72.0 0.75

1.5 0.70 14.0 0.60 70.0 0.76

I. 5 0.50 14.0 0.65 82.0 0.73

1.5 0.55 14.0 0.65 80.0 0.74

i. 5 0.60 14.0 0.65 78.0 0.75

. 1.5 0.65 14.0 0.65 78.0 0.76

1.5 0.70 14.0 0.65 76.0 0.77

1.5 0.50 14.0 0.70 86.0 0.75

i. 5 0.55 14.0 0.70 84.0 0.76

I. 5 0.60 14.0 0.70 82.0 0.76

1.5 0.65 14.0 0.70 82.0 0.77

1.5 0.70 14.0 0.70 80.0 0.78

83

SAND COARSE AGGREGATE VOLUME % MAXIMUMd ' PHI, 0 d ' PHI, 0 COARSE AGGREGATE DENS ITY

1.5 0.50 15.0 0.50 68.0 0.681.5 0.55 15.0 0.50 66.0 0.70I. 5 0.60 15.0 0.50 64.0 0.721.5 0.65 15.0 0.50 62.0 0.731.5 0.70 15.0 0.50 60.0 0.75

1.5 0.50 15.0 0.55 72.0 0.701.5 0.55 15.0 0.55 70.0 0.711.5 0.60 15.0 0.55 70.0 0.731.5 0.65 15.0 0.55 68.0 0.741.5 0.70 15.0 0.55 66.0 0.76

1.5 0.50 15.0 0.60 78.0 0.721.5 0.55 15.0 0.60 76.0 0.731.5 0.60 15.0 0.60 74.0 0.74I. 5 0.65 15.0 0.60 72.0 0.751.5 0.70 15.0 0.60 70.0 0.77

1.5 0.50 15.0 0.65 82.0 0.731.5 0.55 15.0 0.65 80.0 0.751.5 0.60 15.0 0.65 78.0 0.751.5 0.65 15.0 0.65 76.0 0.761.5 0.70 15.0 0.65 76.0 0.78

1.5 0.50 15.0 0.70 86.0 0.751.5 0.55 15.0 0.70 84.0 0.761.5 0.60 15.0 0.70 82.0 0.771.5 0.65 15.0 0.70 82.0 0.781.5 0.70 15.0 0.70 80.0 0.78

1.5 0.50 16.0 0.50 68.0 0.681.5 0.55 16.0 0.50 66.0 0.701.5 0.60 16.0 0.50 64.0 0.721.5 0.65 16.0 0.50 62.0 0.741.5 0.70 16.0 0.50 60.0 0.75

1.5 0.50 16.0 0.55 72.0 0.701.5 0.55 16.0 0.55 70.0 0.711.5 0.60 16.0 0.55 68.0 0.731.5 0.65 16.0 0.55 68.0 0.741.5 0.70 16.0 0.55 66.0 0.76

1.5 0.50 16.0 0.60 78.0 0.721.5 0.55 16.0 0.60 76.0 0.731.5 0.60 16.0 0.60 74.0 0.751.5 0.65 16.0 0.60 72.0 0.761.5 0.70 16.0 0.60 70.0 0.77

84



i. 5 0.50 16.0 0.65 82.0 0.73

1.5 0.55 16.0 0.65 80.0 0.75

1.5 0.60 16.0 0.65 78.0 0.76

" 1.5 0.65 16.0 0.65 76.0 0.77

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94



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2.0 0.50 9.0 0.50 60.0 0.592.0 0.55 9.0 0.50 54.0 0.602.0 0.60 9.0 0.50 46.0 0.622.0 0.65 9.0 0.50 36.0 0.652.0 0.70 9.0 0.50 26.0 0.70

2.0 0.50 9.0 0.55 68.0 0.612.0 0.55 9.0 0.55 62.0 0.622.0 0.60 9.0 0.55 56.0 0.642.0 0.65 9.0 0.55 48.0 0.662.0 0.70 9.0 0.55 38.0 0.70

2.0 0.50 9.0 0.60 74.0 0.632.0 0.55 9.0 0.60 70.0 0.642.0 0.60 9.0 0.60 64.0 0.662.0 0.65 9.0 0.60 58.0 0.672.0 0.70 9.0 0.60 50.0 0.70

2.0 0.50 9.0 0.65 80.0 0.662.0 0.55 9.0 0.65 76.0 0.672.0 0.60 9.0 0.65 72.0 0.682.0 0.65 9.0 0.65 66.0 0.692.0 0.70 9.0 0.65 60.0 0.71

2.0 0.50 9.0 - 0.70 86.0 0.702.0 0.55 9.0 0.70 82.0 0.702.0 0.60 9.0 0.70 78.0 0.702.0 0.65 9.0 0.70 74.0 0.722.0 0.70 9.0 0.70 68.0 0.73

2.0 0.50 10.0 0.50 70.0 0.672.0 0.55 i0.0 0.50 68.0 0.682.0 0.60 i0.0 0.50 66.0 0.702.0 0.65 i0.0 0.50 64.0 0.712.0 0.70 10.0 0.50 62.0 0.73

95


2.0 0.50 I0.0 0.55 76.0 0.682.0 0.55 i0.0 0.55 74.0 0.702.0 0.60 I0.0 0.55 72.0 0.712.0 0.65 i0.0 0.55 70.0 0.722.0 0.70 I0.0 0.55 68.0 0.73

2.0 0.50 I0.0 0.60 80.0 0.70 :2.0 0.55 i0.0 0.60 78.0 0.712.0 0.60 i0.0 0.60 76.0 0.722.0 0.65 i0.0 0.60 76.0 0.732.0 0.70 I0.0 0.60 74.0 0.74

2.0 0.50 i0.0 0.65 84.0 0.712.0 0.55 I0.0 0.65 84.0 0.722.0 0.60 i0.0 0.65 82.0 0.732.0 0.65 i0.0 0.65 80.0 0.742.0 0.70 I0.0 0.65 80.0 0.75

2.0 0.50 i0.0 0.70 88.0 0.732.0 _ 0.55 i0.0 0.70 88.0 0.742.0 0.60 I0.0 0.70 86.0 0.742.0 0.65 I0.0 0.70 86.0 0.752.0 0.70 I0.0 0.70 84.0 0.75

2.0 O. 50 ii. 0 0.50 70.0 0.672.0 0.55 II.0 0.50 68.0 0.692.0 O. 60 ii. 0 O. 50 66.0 O. 702.0 0.65 ii.0 0.50 64.0 0.722.0 0.70 II.0 0.50 62.0 0.73

2.0 0.50 II.0 0.55 74.0 0.682.0 0.55 ii.0 0.55 74.0 0.702.0 0.60 ii.0 0.55 72.0 0.712.0 0.65 ii.0 0.55 70.0 0.732.0 0.70 Ii.0 0.55 68.0 0.74

2.0 0.50 Ii.0 0.60 80.0 0.702.0 0.55 ii.0 0.60 78.0 0.712.0 0.60 ii. 0 0.60 76.0 0.722.0 0.65 Ii.0 0.60 74.0 0.732.0 0.70 ii.0 0.60 74.0 0.75

2.0 0.50 II.0 0.65 84.0 0.722.0 0.55 ii.0 0.65 82.0 0.72 "2.0 0.60 II.0 0.65 82.0 0.732.0 0.65 ii. 0 0.65 80.0 0.742.0 0.70 ii. 0 0.65 78.0 0.75

96



2.0 0.50 II.0 0.70 88.0 0.73

2,0 0.55 Ii.0 0.70 86.0 0.74

2.0 0.60 ii.0 0.70 86.0 0.752.0 0.65 ii.0 0.70 84.0 0.75

2.0 0.70 II.0 0.70 84.0 0.76

2.0 0.50 12.0 0.50 70.0 0.67

2.0 0.55 12.0 0.50 68.0 0.69

2.0 0.60 12.0 0.50 66.0 0.71

2.0 0.65 12.0 0.50 64.0 0.72

2.0 0.70 12.0 0.50 62.0 0.74

2.0 0.50 12.0 0.55 74.0 0.69

2.0 0.55 12.0 0.55 72.0 0.70

2.0 0.60 12.0 0.55 70.0 0.71

2.0 0.65 12.0 0.55 70.0 0.73

2.0 0.70 12.0 0.55 68.0 0.74

2.0 0.50 12.0 0.60 80.0 0.70

2.0 0.55 12.0 0.60 78.0 0.72

2.0 0.60 12.0 0.60 76.0 0.73

2.0 0.65 12.0 0.60 74.0 0.74

2.0 0.70 12.0 0.60 72.0 0.75

2.0 0.50 12.0 0.65 84.0 0.72

2.0 0.55 12.0 0.65 82.0 0.73

2.0 0.60 12.0 0.65 80.0 0.74

2.0 0.65 12.0 0.65 80.0 0.75

2.0 0.70 12.0 0.65 78.0 0.76

2.0 0.50 12.0 0.70 88.0 0.74

2.0 0.55 12.0 0.70 86.0 0.74

2.0 0.60 12.0 0.70 86.0 0.75

2.0 0.65 12.0 0.70 84.0 0.76

2.0 0.70 12.0 0.70 84.0 0.76

2.0 0.50 13.0 0.50 70.0 0.68

2.0 0.55 13.0 0.50 68.0 0.69

2.0 0.60 13.0 0.50 66.0 0.71

- 2.0 0.65 13.0 0.50 64.0 0.72

2.0 0.70 13.0 0.50 62.0 0.74

- 2.0 0.50 13.0 0.55 74.0 0.69

2.0 0.55 13.0 0.55 72.0 0.70

2.0 0.60 13.0 0.55 70.0 0.72

2.0 0.65 13.0 0.55 68.0 0.73

2.0 0.70 13.0 0.55 68.0 0.74

97



2.0 0.50 13.0 O. 60 78.0 0.70

2.0 0.55 13.0 0.60 78.0 0.72

2.0 0.60 13.0 0.60 76.0 0.73

2.0 0.65 13.0 0.60 74.0 0.74

2.0 0.70 13.0 0.60 72.0 0.75

2.0 0.50 13.0 0.65 84.0 0.72

2.0 0.55 13.0 0.65 82.0 0.73

2.0 0.60 13.0 0.65 80.0 0.74

2.0 0.65 13.0 0.65 78.0 0.75

2.0 0.70 13.0 0.65 78.0 0.76

2.0 0.50 13.0 0.70 88.0 0.74

2.0 0.55 13.0 0.70 86.0 0.75

2.0 0.60 13.0 0.70 84.0 0.75

2.0 0.65 13.0 0.70 84.0 0.76

2.0 0.70 13.0 0.70 82.0 0.77

2.0 0.50 14.0 0.50 70.0 0.68

2.0 0.55 14.0 0.50 68.0 0.69

2.0 0.60 14.0 0.50 66.0 0.71

2.0 0.65 14.0 0.50 64.0 0.72

2.0 0.70 14.0 0.50 62.0 0.74

2.0 0.50 14.0 0.55 74.0 0.69

2.0 0.55 14.0 O. 55 72.0 O. 71

2.0 O. 60 14.0 O. 55 70.0 O. 72

2.0 0.65 14.0 0.55 68.0 0.73

2.0 0.70 14.0 0.55 66.0 0.75

2.0 0.50 14.0 0.60 78.0 0.71

2.0 0.55 14.0 0.60 76.0 0.72

2.0 0.60 14.0 0.60 76.0 0.73

2.0 0.65 14.0 0.60 74.0 0.75

2.0 0.70 14.0 0.60 72.0 0.76

2.0 0.50 14.0 0.65 82.0 0.72

2.0 0.55 14.0 0.65 82.0 0.73

2.0 0.60 14.0 0.65 80.0 0.74

2.0 0.65 14.0 0.65 78.0 0.75

2.0 0.70 14.0 0.65 78.0 0.76

2.0 0.50 14.0 0.70 86.0 0.74 .

2.0 0.55 14.0 0.70 86.0 0.75

2.0 0.60 14.0 0.70 84.0 0.76

2.0 0.65 14.0 0.70 84.0 0.76

2.0 0.70 14.0 0.70 82.0 0.77

98



2.0 0.50 15.0 0.50 70.0 0.68

2.0 0.55 15.0 0.50 66.0 0.69

2.0 0.60 15.0 0.50 64.0 0.71

2.0 0.65 15.0 0.50 62.0 0.73

2.0 0.70 15.0 0.50 62.0 0.74

2.0 0.50 15.0 0.55 74.0 0.70

2.0 0.55 15.0 0.55 72.0 0.71

2.0 0.60 15.0 0.55 70.0 0.72

2.0 0.65 15.0 0.55 68.0 0.74

2.0 0.70 15.0 0.55 66.0 0.75

2.0 0.50 15.0 0.60 78.0 0.71

2.0 0.55 15.0 0.60 76.0 0.72

2.0 0.60 15.0 0.60 74.0 0.73

2.0 0.65 15.0 0.60 74.0 0.75

2.0 0.70 15.0 0.60 72.0 0.76

2.0 0.50 15.0 0.65 82.0 0.73

2.0 0.55 15.0 0.65 80.0 0.73

2.0 0.60 15.0 0.65 80.0 0.75

2.0 0.65 15.0 0.65 78.0 0.76

2.0 0.70 15.0 0.65 76.0 0.77

2.0 0.50 15.0 0.70 86.0 0.74

2.0 0.55 15.0 0.70 86.0 0.75

2.0 0.60 15.0 0.70 84.0 0.76

2.0 0.65 15.0 0.70 82.0 0.76

2.0 0.70 15.0 0.70 82.0 0.78

2.0 0.50 16.0 0.50 68.0 0.68

2.0 0.55 16.0 0.50 66.0 0.69

2.0 0.60 16.0 0.50 64.0 0.71

2.0 0.65 16.0 Q. 50 62.0 0.73

2.0 0.70 16.0 0.50 60.0 0.74

2.0 0.50 16.0 0.55 74.0 0.70

2.0 0.55 16.0 0.55 72.0 0.71

2.0 0.60 16.0 0.55 70.0 0.73

2.0 0.65 16.0 0.55 68.0 0.74

2.0 0.70 16.0 0.55 66.0 0.75

" 2.0 0.50 16.0 0.60 78.0 0.71

2.0 0.55 16.0 0.60 76.0 0.72

2.0 0.60 16.0 0.60 74.0 0.74

2.0 0.65 16.0 0.60 72.0 0.752.0 0.70 16.0 0.60 72.0 0.76

99



2.0 0.50 16.0 0.65 82.0 0.73

2.0 0.55 16.0 0.65 80.0 0.74

2.0 0.60 16.0 0.65 80.0 0.75

2.0 0.65 16.0 0.65 78.0 0.76 "

2.0 0.70 16.0 0.65 76.0 0.77

2.0 0.50 16.0 0.70 86.0 0.74

2.0 0.55 16.0 0.70 84.0 0.75

2.0 0.60 16.0 0.70 84.0 0.76

2.0 0.65 16.0 0.70 82.0 0.77

2.0 0.70 16.0 0.70 82.0 0.78

2.0 0.50 17.0 0.50 68.0 0.68

2 •0 0.55 17.0 0.50 66.0 0.70

2.0 0.60 17.0 0.50 64.0 0.71

2.0 0.65 17.0 0.50 62.0 0.73

2.0 0.70 17.0 0.50 60.0 0.75

2.0 0.50 17.0 0.55 74.0 0.70

2.0 0.55 17.0 0.55 72.0 0.71

2.0 0.60 17.0 0.55 70.0 0.73

2.0 0.65 17.0 0.55 68.0 0.74

2.0 0.70 17.0 0.55 66.0 0.75

2.0 0.50 17.0 0.60 78.0 0.72

2.0 0.55 17.0 0.60 76.0 0.73

2.0 O. 60 17.0 0.60 74 •0 0.74

2.0 0.65 17.0 0.60 72.0 0.75

2.0 0.70 17.0 0.60 72.0 0.76

2.0 0.50 17.0 0.65 82.0 0.73

2.0 0.55 17.0 0.65 80.0 0.74

2.0 0.60 17.0 0.65 78.0 0.75

2.0 0.65 17.0 0.65 78.0 0.76

2.0 0.70 17.0 0.65 76.0 0.77

2.0 0.50 17.0 0.70 86.0 0.75

2.0 0.55 17.0 0.70 84.0 0.75

2.0 0.60 17.0 0.70 84.0 0.76

2.0 0.65 17.0 0.70 82.0 0.77

2.0 0.70 17.0 0.70 80.0 0.78

2.0 0.50 18.0 0.50 68.0 0.68

2.0 0.55 18.0 0.50 66.0 0.70

2.0 0.60 18.0 0.50 64.0 0.71

2.0 0.65 18.0 0.50 62.0 0.73

2.0 0.70 18.0 0.50 60.0 0.75

i00



2.0 0.50 18.0 0.55 74.0 0.70

2.0 0.55 18.0 0.55 72.0 0.71

2.0 0.60 18.0 0.55 70.0 0.73

• 2.0 0.65 18.0 0.55 68.0 0.74

2.0 0.70 18.0 0.55 66.0 0.76

2.0 0.50 18.0 0.60 78.0 0.72

2.0 0.55 18.0 0.60 76.0 0.73

2.0 0.60 18.0 0.60 74.0 0.74

2.0 0.65 18.0 0.60 72.0 0.75

2.0 0.70 18.0 0.60 70.0 0.76

2.0 0.50 18.0 0.65 82.0 0.73

2.0 0.55 18.0 0.65 80.0 0.74

2.0 0.60 18.0 0.65 78.0 0.75

2.0 0.65 18.0 0.65 78.0 0.76

2.0 0.70 18.0 0.65 76.0 0.77

2.0 0.50 18.0 0.70 86.0 0.75

2.0 0.55 18.0 0.70 84.0 0.76

2.0 0.60 18.0 0.70 84.0 0.76

2.0 0.65 18.0 0.70 82.0 0.77

2.0 0.70 18.0 0.70 80.0 0.78

2.0 0.50 19.0 0.50 68.0 0.68

2.0 0.55 19.0 0.50 66.0 0.70

2.0 0.60 19.0 0.50 64.0 0.72

2.0 0.65 19.0 0.50 62.0 0.73

2.0 0.70 19.0 0.50 60.0 0.75

2.0 0.50 19.0 0.55 74.0 0.70

2.0 0.55 19.0 0.55 72.0 0.71

2.0 0.60 19.0 0.55 70.0 0.73

2.0 0.65 19.0 0.55 68.0 0.74

2.0 0.70 19.0 0.55 66.0 0.76

2.0 0.50 19.0 0.60 78.0 0.72

2.0 0.55 19.0 0.60 76.0 0.73

2.0 0.60 19.0 0.60 74.0 0.74

" 2.0 0.65 19.0 0.60 72.0 0.752.0 0.70 19.0 0.60 70.0 0.77

2.0 0.50 19.0 0.65 82.0 0.732.0 0.55 19.0 0.65 80.0 0.74

2.0 0.60 19.0 0.65 78.0 0.75

2.0 0.65 19.0 0.65 78.0 0.76

2.0 0.70 19.0 0.65 76.0 0.78

i01

l



2.0 0.50 19.0 0.70 86.0 0.75

2.0 0.55 19.0 0.70 84.0 0.76

2.0 0.60 19.0 0.70 82.0 0.76

2.0 0.65 19.0 0.70 82.0 0.78 "

2.0 0.70 19.0 0.70 80.0 0.78

2.0 0.50 20.0 0.50 68.0 0.68

2.0 0.55 20.0 0.50 66.0 0.70

2.0 0.60 20.0 0.50 64.0 0.72

2.0 0.65 20.0 0.50 62.0 0.73

2.0 0.70 20.0 0.50 60.0 0.75

2.0 0.50 20.0 0.55 72.0 0.70

2.0 0.55 20.0 0.55 70.0 0.71

2.0 0.60 20.0 0.55 70.0 0.73

2.0 0.65 20.0 0.55 68.0 0.74

2.0 0.70 20.0 0.55 66.0 0.76

2.0 0.50 20.0 0.60 78.0 0.72

2.0 0.55 20.0 0.60 76.0 0.73

2.0 0.60 20.0 0.60 74.0 0.74

2.0 0.65 20.0 0.60 72.0 0.75

2.0 0.70 20.0 0.60 70.0 0.77

2.0 0.50 20.0 0.65 82.0 0.73

2.0 0.55 20.0 0.65 80.0 0.752.0 0.60 20.0 0.65 78.0 0.75

2.0 0.65 20.0 0.65 76.0 0.76

2.0 0.70 20.0 0.65 76.0 0.78

2.0 0.50 20.0 0.70 86.0 0.75

2.0 0.55 20.0 0.70 84.0 0.76

2.0 0.60 20.0 0.70 82.0 0.77

2.0 0.65 20.0 0.70 82.0 0.78

2.0 0.70 20.0 0.70 80.0 0.78

2.0 0.50 21.0 0.50 68.0 0.68

2.0 0.55 21.0 0.50 66.0 0.70

2.0 0.60 21.0 0.50 64.0 0.72

2.0 0.65 21.0 0.50 62.0 0.73

2.0 0.70 21.0 0.50 60.0 0.75

2.0 0.50 21.0 0.55 72.0 0.70

2.0 0.55 21.0 0.55 70.0 0.71

2.0 0.60 21.0 0.55 68.0 0.73

2.0 0.65 21.0 0.55 68.0 0.74

2.0 0.70 21.0 0.55 66.0 0.76

102

sAND COARSE AGGREGATE VOLUME % MAXIMUM


2 .0 0.50 21.0 0.60 78.0 0.72

2.0 0.55 21.0 0.60 76.0 0.73

2.0 0.60 21.0 0.60 74.0 0.74

2.0 0.65 21.0 0.60 72.0 0.76

2.0 0.70 21.0 0.60 70.0 0.77

2.0 0.50 21.0 0.65 82.0 0.73

2.0 0.55 21.0 0.65 80.0 0.75

2.0 0.60 21.0 0.65 78.0 0.76

2.0 0.65 21.0 0.65 76.0 0.77

2.0 0.70 21.0 0.65 76.0 0.78

2.0 0.50 21.0 0.70 86.0 0.75

2.0 0.55 21.0 0.70 84.0 0.76

2.0 0.60 21.0 0.70 82.0 0.77

2.0 0.65 21.0 0.70 82.0 0.78

2.0 0.70 21.0 0.70 80.0 0.79

2.0 0.50 22.0 0.50 68.0 0.69

2.0 0.55 22.0 0.50 66.0 0.70

2.0 0.60 22.0 0.50 64.0 0.72

2.0 0.65 22.0 0.50 62.0 0.74

2.0 0.70 22.0 0.50 60.0 0.75

2.0 0.50 22.0 0.55 72.0 0.70

2.0 0.55 22.0 0.55 70.0 0.71

2.0 0.60 22.0 0.55 68.0 0.73

2.0 0.65 22.0 0.55 68.0 0.74

2.0 0.70 22.0 0.55 66.0 0.76

2.0 0.50 22.0 0.60 78.0 0.72

2.0 0.55 22.0 0.60 76.0 0.73

2.0 0.60 22.0 0.60 74.0 0.75

2.0 0.65 22.0 0.60 72.0 0.76

2.0 0.70 22.0 0.60 70.0 0.77

2.0 0.50 22.0 0.65 82.0 0.73

2.0 0.55 22.0 0.65 80.0 0.75

2.0 0.60 22.0 0.65 78.0 0.76

2.0 0.65 22.0 0.65 76.0 0.77

2.0 0.70 22.0 0.65 76.0 0.78

2.0 0.50 22.0 0.70 86.0 0.75

2.0 0.55 22.0 0.70 84.0 0.76

2.0 0.60 22.0 0.70 82.0 0.77

2.0 0.65 22.0 0.70 82.0 0.78

2.0 0.70 22.0 0.70 80.0 0.79

103



2.0 0.50 23.0 0.50 68.0 0.69

2.0 0.55 23.0 0.50 66.0 0.70

2.0 0.60 23.0 0.50 64.0 0.72 .

2.0 0.65 23.0 0.50 62.0 0.74

2.0 0.70 23.0 0.50 60.0 0.75

2.0 0.50 23.0 0.55 72.0 0.70

2.0 0.55 23.0 0.55 70.0 0.72

2.0 0.60 23.0 0.55 68.0 0.73

2.0 0.65 23.0 0.55 66.0 0.75

2.0 0.70 23.0 0.55 66.0 0.76

2.0 0.50 23.0 0.60 76.0 0.72

2.0 0.55 23.0 0.60 76.0 0.73

2.0 0.60 23.0 0.60 74.0 0.75

2.0 0.65 23.0 0.60 72.0 0.76

2.0 0.70 23.0 0.60 70.0 0.77

2.0 0.50 23.0 0.65 82.0 0.73

2.0 0.55 23.0 0.65 80.0 0.75

2.0 0.60 23.0 0.65 78.0 0.76

2.0 0.65 23.0 0.65 76.0 0.77

2.0 0.70 23.0 0.65 76.0 0.78

2.0 0.50 23.0 0.70 84.0 0.75

2.0 0.55 23.0 0.70 84.0 0.76

2.0 0.60 23.0 0.70 82.0 0.77

2.0 0.65 23.0 0.70 80.0 0.78

2.0 0.70 23.0 0.70 80.0 0.79

2.0 0.50 24.0 0.50 68.0 0.69

2.0 O. 55 24.0 0.50 66.0 0.70

2.0 0.60 24.0 0.50 64.0 0.72

2.0 0.65 24.0 0.50 62.0 0.74

2.0 0.70 24.0 0.50 60.0 0.75

2.0 0.50 24.0 0.55 72.0 0.70

2.0 0.55 24.0 0.55 70.0 0.72

2.0 0.60 24.0 0.55 68.0 0.73

2.0 0.65 24.0 0.55 66.0 O. 75 .

2.0 0.70 24.0 0.55 66.0 0.76

2.0 0.50 24.0 0.60 76.0 0.72

2.0 0.55 24.0 0.60 76.0 0.73

2.0 0.60 24.0 0.60 74.0 0.75

2.0 0.65 24.0 0.60 72.0 0.76

2.0 0.70 24.0 0.60 70.0 0.77

104



2.0 0.50 24.0 0.65 80.0 0.73

2.0 0.55 24.0 0.65 80.0 0.75

2.0 0.60 24.0 0.65 78.0 0.76

2.0 0.65 24.0 0.65 76.0 0.77

2.0 0.70 24.0 0.65 74.0 0.78

2.0 0.50 24.0 0.70 84.0 0.75

2.0 0.55 24.0 0.70 84.0 0.76

2.0 0.60 24.0 0.70 82.0 0.77

2.0 0.65 24.0 0.70 80.0 0.78

2.0 0.70 24.0 0.70 80.0 0.79

2.0 ' 0.50 25.0 0.50 68.0 0.69

2.0 0.55 25.0 0.50 66.0 0.71

2.0 0.60 25.0 0.50 64.0 0.72

2.0 0.65 25.0 0.50 62.0 0.74

2.0 0.70 25.0 0.50 60.0 0.76

2.0 0.50 25.0 0.55 72.0 0.70

2.0 0.55 25.0 0.55 70.0 0.72

2.0 0.60 25.0 0.55 68.0 0.73

2.0 0.65 25.0 0.55 66.0 0.75

2.0 0.70 25.0 0.55 66.0 0.76

2.0 0.50 25.0 0.60 76.0 0.72

2.0 0.55 25.0 0.60 74.0 0.73

2.0 0.60 25.0 0.60 74.0 0.75

2.0 0.65 25.0 0.60 72.0 0.76

2.0 0.70 25.0 0.60 70.0 0.77

2.0 0.50 25.0 0.65 80.0 0.73

2.0 0.55 25.0 0.65 80.0 0.75

2.0 0.60 25.0 0.65 78.0 0.76

2.0 0.65 25.0 0.65 76.0 0.77

2.0 0.70 25.0 0.65 74.0 0.78

2.0 0.50 25.0 0.70 84.0 0.75

2.0 0.55 25.0 0.70 84.0 0.76

2.0 0.60 25.0 0.70 82.0 0.77

2.0 0.65 25.0 0.70 80.0 0.782.0 0.70 25.0 0.70 80.0 0.79

2.0 0.50 26.0 0.50 68.0 0.69

2.0 0.55 26.0 0.50 66.0 0.71

2.0 0.60 26.0 0.50 64.0 0.72

2.0 0.65 26.0 0.50 62.0 0.74

2.0 0.70 26.0 0.50 60.0 0.76

105

sAND COARSE AGGREGATE VOLUME % MAXIMUM


2.0 0.50 26.0 0.55 72.0 0.70

2.0 0.55 26.0 0.55 70.0 0.72

2.0 0.60 26.0 0.55 68.0 0.73

2.0 0.65 26.0 0.55 66.0 0.75

2.0 0.70 26.0 0.55 64.0 0.76

2.0 0.50 26.0 0.60 76.0 0.72

2.0 0.55 26.0 0.60 74.0 0.73

2.0 0.60 26.0 0.60 74.0 0.75

2.0 0.65 26.0 0.60 72.0 0.76

2.0 0.70 26.0 0.60 70.0 0.77

2.0 0.50 26.0 0.65 80.0 0.74

2.0 0.55 26.0 0.65 80.0 0.75

2.0 0.60 26.0 0.65 78.0 0.76

2.0 0.65 26.0 0.65 76.0 0.77

2.0 0.70 26.0 0.65 74.0 0.78

2.0 0.50 26.0 0.70 84.0 0.75

2.0 0.55 26.0 0.70 84.0 0.76

2.0 0.60 26.0 0.70 82.0 0.77

2.0 0.65 26.0 0.70 80.0 0.78

2.0 0.70 26.0 0.70 80.0 0.79

2.0 0.50 27.0 0.50 68.0 0.69

2.0 0.55 27.0 0.50 66.0 0.71

2.0 0.60 27.0 0.50 64.0 0.72

2.0 0.65 27.0 0.50 62.0 0.74

2.0 0.70 27.0 0.50 60.0 0.76

2.0 0.50 27.0 0.55 72.0 0.70

2.0 0.55 27.0 0.55 70.0 0.72

2.0 0.60 27.0 0.55 68.0 0.73

2.0 0.65 27.0 0.55 66.0 0.75

2.0 0.70 27.0 0.55 64.0 0.76

2.0 0.50 27.0 0.60 76.0 0.72

2.0 0.55 27.0 0.60 74.0 0.73

2.0 0.60 27.0 0.60 74.0 0.75

2.0 0.65 27.0 0.60 72.0 0.76 .2.0 0.70 27.0 0.60 70.0 0.78

2.0 0.50 27.0 0.65 80.0 0.74

2.0 0.55 27.0 0.65 80.0 0.75

2.0 0.60 27.0 0.65 78.0 0.76

2.0 0.65 27.0 0.65 76.0 0.77

2.0 0.70 27.0 0.65 74.0 0.78

106


2.0 0.50 27.0 0.70 84.0 0.752.0 0.55 27.0 0.70 84.0 0.762.0 0.60 27.0 0.70 82.0 0.782.0 0.65 27.0 0.70 80.0 0.782.0 0.70 27.0 0.70 80.0 0.79

2.0 0.50 28.0 0.50 68.0 0.692.0 0.55 28.0 0.50 66.0 0.712.0 0.60 28.0 0.50 64.0 0.722.0 0.65 28.0 0.50 62.0 0.742.0 0.70 28.0 0.50 60.0 0.76

2.0 0.50 28.0 0.55 72.0 0.712.0 0.55 28.0 0.55 70.0 0.722.0 0.60 28.0 0.55 68.0 0.742.0 0.65 28.0 0.55 66.0 0.752.0 0.70 28.0 0.55 64.0 0.76

2.0 0.50 28.0 0.60 76.0 0.722.0 0.55 28.0 0.60 74.0 0.732.0 0.60 28.0 0.60 72.0 0.752.0 0.65 28.0 0.60 72.0 0.762.0 0.70 28.0 0.60 70.0 0.78

2.0 0.50 28.0 0.65 80.0 0.742.0 0.55 28.0 0.65 78.0 0.752.0 0.60 28.0 0.65 78.0 0.762.0 0.65 28.0 0.65 76.0 0.772.0 0.70 28.0 0.65 74.0 0.78

2.0 0.50 28.0 0.70 84.0 0.762.0 0.55 28.0 0.70 82.0 0.762.0 0.60 28.0 0.70 82.0 0.782.0 0.65 28.0 0.70 80.0 0.782.0 0.70 28.0 0.70 80.0 0.79

2.0 0.50 29.0 0.50 68.0 0.692.0 0.55 29.0 0.50 66.0 0.712.0 0.60 29.0 0.50 64.0 0.722.0 0.65 29.0 0.50 62.0 0.742.0 0.70 29.0 0.50 60.0 0.76

2.0 0.50 29.0 0.55 72.0 0.712.0 0.55 29.0 0.55 70.0 0.722.0 0.60 29.0 0.55 68.0 0.742.0 0.65 29.0 0.55 66.0 0.752.0 0.70 29.0 0.55 64.0 0.77

107



2.0 0.50 29.0 0.60 7.6.0 0.72

2.0 0.55 29.0 0.60 74.0 0.73

2.0 0.60 29.0 0.60 72.0 0.75

2.0 0.65 29.0 0.60 72.0 0.76

2.0 0.70 29.0 0.60 70.0 0.78

2.0 0.50 29.0 0.65 80.0 0.74

2.0 0.55 29.0 0.65 78.0 0.75

2.0 0.60 29.0 0.65 78.0 0.76

2.0 0.65 29.0 0.65 76.0 0.77

2.0 0.70 29.0 0.65 74.0 0.78

2.0 0.50 29.0 0.70 84.0 0.76

2.0 0.55 29.0 0.70 82.0 0.76

2.0 0.60 29.0 0.70 82.0 0.78

2.0 0.65 29.0 0.70 80.0 0.78

2.0 0.70 29.0 0.70 78.0 0.79

2.0 0.50 30.0 0.50 68.0 0.69

2.0 0.55 30.0 0.50 66.0 0.71

2.0 0.60 30.0 0.50 64.0 0.72

2.0 0.65 30.0 0.50 62.0 0.74

2.0 0.70 30.0 0.50 60.0 0.76

2.0 0.50 30.0 0.55 72.0 0.71

2.0 0.55 30.0 0.55 70.0 0.72

2.0 0.60 30.0 0.55 68.0 0.74

2.0 0.65 30.0 0.55 66.0 0.75

2.0 0.70 30.0 0.55 64.0 0.77

2.0 0.50 30.0 0.60 76.0 0.72

2.0 0.55 30.0 0.60 74.0 0.74

2.0 0.60 30.0 0.60 72.0 0.75

2.0 0.65 30.0 0.60 72.0 0.76

2.0 0.70 30.0 0.60 70.0 0.78

2.0 0.50 30.0 0.65 80.0 0.74

2.0 0.55 30.0 0.65 78.0 0.75

2.0 0.60 30.0 0.65 78.0 0.76

2.0 0.65 30.0 0.65 76.0 0.78

2.0 0.70 30.0 0.65 74.0 O. 79

2.0 0.50 30.0 0.70 84.0 0.76 .

2.0 0.55 30.0 0.70 82.0 0.76

2.0 0.60 30.0 0.70 82.0 0.78

2.0 0.65 30.0 0.70 80.0 0.79

2.0 0.70 30.0 0.70 78.0 0.79

I08


2.5 0.50 7.0 0.50 60.0 0.572.5 0.55 7.0 0.50 50.0 0.582.5 0.60 7.0 0.50 40.0 0.612.5 0.65 7.0 0.50 18.0 0.652.5 0.70 7.0 0.50 0.0 0.70

2.5 0.50 7.0 0.55 70.0 0.592.5 0.55 7.0 0.55 62.0 0.602.5 0.60 7.0 0.55 52.0 0.622.5 0.65 7.0 0.55 42.0 0.652.5 0.70 7.0 0.55 0.0 0.70

2.5 0.50 7.0 0.60 76.0 0.622.5 0.55 7.0 0.60 70.0 0.632.5 0.60 7.0 0.60 64.0 0.642.5 0.65 7.0 0.60 54.0 0.662.5 0.70 7.0 0.60 42.0 0.70

2.5 0.50 7.0 0.65 82.0 0.652.5 0.55 7.0 0.65 78.0 0.65215 0.60 7.0 0.65 72.0 0.66

2.5 0.65 7.0 0.65 66.0 0.682.5 0.70 7.0 0.65 56.0 0.70

2.5 0.50 7.0 0.70 88.0 0.702.5 0.55 7.0 0.70 84.0 0.702.5 0.60 7.0 0.70 80.0 0.702.5 0.65 7.0 0.70 74.0 0.702.5 0.70 7.0 0.70 68.0 0.71

2.5 0.50 8.0 0.50 60.0 0.572.5 0.55 8.0 0.50 52.0 0.592.5 0.60 8.0 0.50 42.0 0.612.5 0.65 8.0 0.50 28.0 0.652.5 0.70 8.0 0.50 0.0 0.70

2.5 0.50 8.0 0.55 68.0 0.602.5 0.55 8.0 0.55 62.0 0.612.5 0.60 8.0 0.55 54.0 0.632.5 0.65 8.0 0.55 44.0 0.652.5 0.70 8.0 0.55 28.0 0.70

2.5 0.50 8.0 0.60 76.0 0.622.5 0.55 8.0 0.60 70.0 0.632.5 0.60 8.0 0.60 64.0 0.652.5 0.65 8.0 0.60 56.0 0.662.5 0.70 8.0 0.60 46.0 0.70

109



2.5 0.50 8.0 0.65 82.0 0.652.5 0.55 8.0 0.65 78.0 0.662.5 0.60 8.0 0.65 72.0 0.672.5 0.65 8.0 0.65 66.0 0.68 •2.5 0.70 8.0 0.65 58.0 0.70

2.5 0.50 8.0 0.70 86.0 0.70 '2.5 0.55 8.0 0.70 84.0 0.702.5 0.60 8.0 0.70 80.0 0.702.5 0.65 8.0 0.70 74.0 0.702.5 0.70 8.0 0.70 68.0 0.72

2.5 0.50 9.0 0.50 60.0 0.582.5 0.55 9.0 0.50 52.0 0.592.5 0.60 9.0 0.50 44.0 0.612.5 0.65 9.0 0.50 32.0 0.652.5 0.70 9.0 0.50 0.0 0.70

2.5 0.50 9.0 0.55 68.0 0.602.5 0.55 9.0 0.55 62.0 0.612.5 0.60 9.0 0.55 54.0 0.632.5 0.65 9.0 0.55 46.0 0.652.5 0.70 9.0 0.55 34.0 0.70

2.5 0.50 9.0 0.60 76.0 0.622.5 0.55 9.0 0.60 70.0 0.642.5 0.60 9.0 0.60 64.0 0.652.5 0.65 9.0 0.60 56.0 0.672.5 0.70 9.0 0.60 48.0 0.70

2.5 0.50 9.0 0.65 82.0 0.652.5 0.55 9.0 0.65 76.0 0.662.5 0.60 9.0 0.65 72.0 0.672.5 0.65 9.0 0.65 66.0 0.692.5 0.70 9.0 0.65 58.0 0.70

2.5 0.50 9.0 0.70 86.0 0.702.5 0.55 9.0 0.70 82.0 0.702.5 0.60 9.0 0.70 78.0 0.702.5 0.65 9.0 0.70 74.0 0.712.5 0.70 9.0 0.70 68.0 0.72

2.5 0.50 i0.0 0.50 60.0 0.582.5 0.55 i0.0 0.50 52.0 0.602.5 0.60 i0.0 0.50 44.0 0.622.5 0.65 i0.0 0.50 34.0 0.652.5 0.70 I0.0 0.50 20.0 0.70

ii0


2.5 0.50 i0.0 0.55 68.0 0.602.5 0.55 i0.0 0.55 62.0 0.622.5 0.60 i0.0 0.55 54.0 0.642.5 0.65 i0.0 0.55 46.0 0.652.5 0.70 i0.0 0.55 36.0 0.70

2.5 0.50 I0.0 0.60 76.0 0.632.5 0.55 i0.0 0.60 70.0 0.642.5 0.60 i0.0 0.60 64.0 0.652.5 0.65 I0.0 0.60 56.0 0.672.5 0.70 i0.0 0.60 48.0 0.70

2.5 0.50 I0.0 0.65 80.0 0.662.5 0.55 i0.0 0.65 76.0 0.672.5 0.60 I0.0 0.65 72.0 0.682.5 0.65 i0.0 0.65 66.0 0.692.5 0.70 I0.0 0.65 58.0 0.70

2.5 0.50 i0.0 0.70 86.0 0.702.5 0.55 i0.0 0.70 82.0 0.702.5 0.60 I0.0 0.70 78.0 0.702.5 0.65 i0.0 0.70 74.0 0.712.5 0.70 i0.0 0.70 68.0 0.72

2.5 0.50 Ii.0 0.50 60.0 0.582.5 0.55 ii.0 0.50 54.0 0.602.5 0.60 II.0 0.50 46.0 0.622.5 0.65 ii.0 0.50 36.0 0.652.5 0.70 ii.0 0.50 24.0 0.70

2.5 0.50 ii.0 0.55 68.0 0.612.5 0.55 Ii. 0 0.55 62.0 0.622.5 0.60 Ii. 0 0.55 56.0 0.642.5 0.65 II.0 0.55 48.0 0.662.5 0.70 Ii.0 0155 38.0 0.70

2.5 0.50 Ii.0 0.60 74.0 0.632.5 0.55 II.0 0.60 70.0 0.642.5 0.60 ii.0 0.60 64.0 0.662.5 0.65 Ii.0 0.60 58.0 0.672.5 0.70 ii.0 0.60 50.0 0.70

2.5 0.50 II.0 0.65 80.0 0.662.5 0.55 ii.0 0.65 76.0 0.672.5 0.60 ii.0 0.65 72.0 0.682.5 0.65 II.0 0.65 66.0 0.692.5 0.70 ii.0 0.65 60.0 0.71

111



2.5 0.50 ii.0 0.70 86.0 0.70

2.5 0.55 ii.0 0.70 82.0 0.70

2.5 0.60 ii.0 0.70 78.0 0.70

2.5 0.65 ii.0 0.70 74.0 0.71

2.5 0.70 ii.0 0.70 68.0 0.73

2.5 0.50 12.0 0.50 60.0 0.59 "

2.5 0.55 12.0 0.50 54.0 0.61

2.5 0.60 12.0 0.50 46.0 0.63

2.5 0.65 12.0 0.50 38.0 0.65

2 •5 0.70 12.0 0.50 28.0 0.70

2.5 0.50 12.0 0.55 68.0 0.61

2.5 0.55 12.0 0.55 62.0 0.63

2.5 0.60 12.0 0.55 56.0 0.64

2.5 0.65 12.0 0.55 48.0 0.66

2.5 0.70 12.0 0.55 40.0 0.70

2.5 0.50 12.0 0.60 74.0 0.63

2.5 0.55 12.0 0.60 70.0 0.65

2.5 0.60 12.0 0.60 64.0 0.66

2.5 0.65 12.0 0.60 58.0 0.68

2.5 0.70 12.0 0.60 50.0 0.70

2.5 0.50 12.0 0.65 80.0 0.66

2.5 0.55 12.0 0.65 76.0 0.67

2.5 0.60 12.0 0.65 72.0 0.68

2.5 0.65 12.0 0.65 66.0 0.70

2.5 0.70 12.0 0.65 60.0 O. 71

2.5 0.50 12.0 0.70 84.0 0.70

2.5 0.55 12.0 0.70 82.0 0.70

2.5 0.60 12.0 0.70 78.0 0.71

2.5 0.65 12.0 0.70 74.0 0.72

2.5 0.70 12.0 0.70 68.0 0.73

2.5 0.50 13.0 0.50 70.0 0.67

2.5 0.55 13.0 0.50 68.0 0.68

2.5 0.60 13.0 0.50 66.0 0.70

2.5 0.65 13.0 0.50 64.0 0.71

2.5 0.70 13.0 0.50 62.0 0.73

2.5 0.50 13.0 0.55 76.0 0.68

2.5 0.55 13.0 0.55 74.0 0.70

2.5 0.60 13.0 0.55 72.0 0.71

2.5 0.65 13.0 0.55 70.0 0.72

2.5 0.70 13.0 0.55 68.0 0.74

112



2.5 0.50 13.0 0.60 80.0 0.70

2.5 0.55 13.0 0.60 78.0 0.71

2.5 0.60 13.0 0.60 76.0 0.72

2.5 0.65 13.0 0.60 76.0 0.73

2.5 0.70 13.0 0.60 74.0 0.74

2.5 0.50 13.0 0.65 84.0 0.71

2.5 0.55 13.0 0.65 82.0 0.72

2.5 0.60 13.0 0.65 82.0 0.73

2.5 0.65 13.0 0.65 80.0 0.74

2.5 0.70 13.0 0.65 78.0 0.75

2.5 0.50 13.0 0.70 88.0 0.73

2.5 0.55 13.0 0.70 88.0 0.74

2.5 0.60 13.0 0.70 86.0 0.74

2.5 0.65 13.0 0.70 86.0 0.75

2.5 0.70 13.0 0.70 84.0 0.76

2.5 0.50 14.0 0.50 70.0 0.67

2.5 0.55 14.0 0.50 68.0 0.69

2.5 0.60 14.0 0.50 66.0 0.70

2.5 0.65 14.0 0.50 64.0 0.72

2.5 0.70 14.0 0.50 62.0 0.73

2.5 0.50 14.0 0.55 74.0 0.68

2.5 0.55 14.0 0.55 72.0 0.70

2.5 0.60 14.0 0.55 72.0 0.71

2.5 0.65 14.0 0.55 70.0 0.73

2.5 0.70 14.0 0.55 68.0 0.74

2.5 0.50 14.0 0.60 80.0 0.70

2.5 0.55 14.0 0.60 78.0 0.71

2.5 0.60 14.0 0.60 76.0 0.72

2.5 0.65 14.0 0.60 74.0 0.73

2.5 0.70 14.0 0.60 74.0 0.75

2.5 0.50 14.0 0.65 84.0 0.72

2.5 0.55 14.0 0.65 82.0 0.73

2.5 0.60 14.0 0.65 82.0 0.73

2.5 0.65 14.0 0.65 80.0 0.74

2.5 0.70 14.0 0.65 78.0 0.75

2.5 0.50 14.0 O. 70 88.0 O. 73

2.5 0.55 14.0 0.70 86.0 0.74

2.5 0.60 14.0 0.70 86.0 0.75

2.5 0.65 14.0 0.70 84.0 0.75

2.5 0.70 14.0 0.70 84.0 0.76

113



2.5 0.50 15.0 0.50 70.0 0.67

2.5 0.55 15.0 0.50 68.0 0.69

2.5 0.60 15.0 0.50 66.0 0.71

2.5 0.65 15.0 0.50 64.0 0.72

2.5 0.70 15.0 0.50 62.0 0.74

2.5 0.50 15.0 0.55 74.0 0.69

2.5 0.55 15.0 0.55 72.0 0.70

2.5 0.60 15.0 0.55 70.0 0.71

2.5 0.65 15.0 0.55 70.0 0.73

2.5 0.70 15.0 0.55 68.0 0.74

2.5 0.50 15.0 0.60 80.0 0.70

2.5 0.55 15.0 0.60 78.0 0.72

2.5 0.60 15.0 0.60 76.0 0.73

2.5 0.65 15.0 0.60 74.0 0.74

2.5 0.70 15.0 0.60 72.0 0.75

2.5 0.50 15.0 0.65 84.0 0.72

2.5 0.55 15.0 0.65 82.0 0.73

2.5 0.60 15.0 0.65 80.0 0.74

2.5 0.65 15.0 0.65 80.0 0.75

2.5 0.70 15.0 0.65 78.0 0.76

2.5 0.50 15.0 0.70 88.0 0.74

2.5 0.55 15.0 0.70 86.0 0.74

2.5 0.60 15.0 0.70 86.0 0.75

2.5 0.65 15.0 0.70 84.0 0.76

2.5 0.70 15.0 0.70 84.0 0.76

2.5 0.50 16.0 0.50 70.0 0.68

2.5 0.55 16.0 0.50 68.0 0.69

2.5 0.60 16.0 0.50 66.0 0.71

2.5 0.65 16.0 0.50 64.0 0.72

2.5 0.70 16.0 0.50 62.0 0.74

2.5 0.50 16.0 0.55 74.0 0.69

2.5 0.55 16.0 0.55 72.0 0.70

2.5 0.60 16.0 0.55 70.0 0.72

2.5 0.65 16.0 0.55 68.0 0.73

2.5 0.70 16.0 0.55 68.0 0.74

2.5 0.50 16.0 0.60 78.0 0.70

2.5 0.55 16.0 0.60 78.0 0.72

2.5 0.60 16.0 0.60 76.0 0.73

2.5 0.65 16.0 0.60 74.0 0.74

2.5 0.70 16.0 0.60 72.0 0.75

114



2.5 0.50 16.0 0.65 84.0 0.722.5 0.55 16.0 0.65 82.0 0.732.5 0.60 16.0 0.65 80.0 0.742.5 0.65 16.0 0.65 78.0 0.752.5 0.70 16.0 0.65 78.0 0.76

_ 2.5 0.50 16.0 0.70 88.0 0.742.5 0.55 16.0 0.70 86.0 0.752.5 0.60 16.0 0.70 84.0 0.752.5 0.65 16.0 0.70 84.0 0.762.5 0.70 16.0 0.70 82.0 0.77

2.5 0.50 17.0 0.50 70.0 0.682.5 0.55 17.0 0.50 68.0 0.692.5 0.60 17.0 0.50 66.0 0.712.5 0.65 17.0 0.50 64.0 0.722.5 0.70 17.0 0.50 62.0 0.74

2.5 0.50 17.0 0.55 74.0 0.6g2.5 0.55 17.0 0.55 72.0 0.712.5 0.60 17.0 0.55 70.0 0.722.5 0.65 17.0 0.55 68.0 0.732.5 0.70 17.0 0.55 66.0 0.75

2.5 0.50 17.0 0.60 78.0 0.712.5 0.55 17.0 0.60 76.0 0.722.5 0.60 17.0 0.60 76.0 0.732.5 0.65 17.0 0.60 74.0 0.742.5 0.70 17.0 0.60 72.0 0.75

2.5 0.50 17.0 0.65 82.0 0.722.5 0.55 17.0 0.65 82.0 0.732.5 0.60 17.0 0.65 80.0 0.742.5 0.65 17.0 0.65 78.0 0.752.5 0.70 17.0 0.65 78.0 0.76

2.5 0.50 17.0 0.70 86.0 0.742.5 0.55 17.0 0.70 86.0 0.752.5 0.60 17.0 0.70 84.0 0.752.5 0.65 17.0 0.70 84.0 0.762.5 0.70 17.0 0.70 82.0 0.77

2.5 0.50 18.0 0.50 70.0 0.684

2.5 0.55 18.0 0.50 68.0 0.692.5 0.60 18.0 0.50 66.0 0.712.5 0.65 18.0 0.50 64.0 0.722.5 0.70 18.0 0.50 62.0 0.74

115


2.5 0.50 18.0 0.55 74.0 0.692.5 0.55 18.0 0.55 72.0 0.712.5 0.60 18.0 0.55 70.0 0.722.5 0.65 18.0 0.55 68.0 0.742.5 0.70 18.0 0.55 66.0 0.75

2.5 0.50 18.0 0.60 78.0 0.712.5 0.55 18.0 0.60 76.0 0.722.5 0.60 18.0 0.60 74.0 0.732.5 0.65 18.0 0.60 74.0 0.752.5 0.70 18.0 0.60 72.0 0.76

2.5 0.50 18.0 0.65 82.0 0.722.5 0.55 18.0 0.65 82.0 0.732.5 0.60 18.0 0.65 80.0 0.752.5 0.65 18.0 0.65 78.0 0.752.5 0.70 18.0 0.65 76.0 0.76

2.5 0.50 18.0 0.70 86.0 0.742.5 0.55 18.0 0.70 86.0 0.752.5 0.60 18.0 0.70 84.0 0.762.5 0.65 18.0 0.70 82.0 0.762.5 0.70 18.0 0.70 82.0 0.77

2.5 0.50 19.0 0.50 70.0 0.682.5 0.55 19.0 0.50 66.0 0.692.5 0.60 19.0 0.50 64.0 0.712.5 0.65 19.0 0.50 62.0 0.732.5 0.70 19.0 0.50 62.0 0.74

2.5 0.50 19.0 0.55 74.0 0.702.5 0.55 19.0 0.55 72.0 0.712.5 0.60 19.0 0.55 70.0 0.722.5 0.65 19.0 0.55 68.0 0.742.5 0.70 19.0 0.55 66.0 0.75

2.5 0.50 19.0 0.60 78.0 0.712.5 0.55 19.0 0.60 76.0 0.722.5 0.60 19.0 0.60 74.0 0.732.5 0.65 19.0 0.60 74.0 0.75 .2.5 0.70 19.0 0.60 72.0 0.76

2.5 0.50 19.0 0.65 82.0 0.73 .2.5 0.55 19.0 0.65 80.0 0.732.5 0.60 19.0 0.65 80.0 0.752.5 0.65 19.0 0.65 78.0 0.762.5 0.70 19.0 0.65 76.0 0.77

116


2.5 0.50 19.0 0.70 86.0 0.742.5 0.55 19.0 0.70 86.0 0.752.5 0.60 19.0 0.70 84.0 0.762.5 0.65 19.0 0.70 82.0 0.772.5 0.70 19.0 0.70 82.0 0.78

2.5 0.50 20.0 0.50 68.0 0.682.5 0.55 20.0 0.50 66.0 0.692.5 0.60 20.0 0.50 64.0 0.712.5 0.65 20.0 0.50 62.0 0.732.5 0.70 20.0 0.50 60.0 0.74

2.5 0.50 20.0 0.55 74.0 0.702.5 0.55 20.0 0.55 72.0 0.712.5 0.60 20.0 0.55 70.0 0.732.5 0.65 20.0 0.55 68.0 0.742.5 0.70 20.0 0.55 66.0 0.75

2.5 0.50 20.0 0.60 78.0 0.712.5 0.55 20.0 0.60 76.0 0.722.5 0.60 20.0 0.60 74.0 0.742.5 0.65 20.0 0.60 72.0 0.752.5 0.70 20.0 0.60 72.0 0.76

2.5 0.50 20.0 0.65 82.0 0.732.5 0.55 20.0 0.65 80.0 0.742.5 0.60 20.0 0.65 80.0 0.752.5 0.65 20.0 0.65 78.0 0.762.5 0.70 20.0 0.65 76.0 0.77

2.5 0.50 20.0 0.70 86.0 0.742.5 0.55 20.0 0.70 84.0 0.752.5 0.60 20.0 0.70 84.0 0.762.5 0.65 20.0 0.70 82.0 0.772.5 0.70 20.0 0.70 82.0 0.78

2.5 0.50 21.0 0.50 68.0 0.682.5 0.55 21.0 0.50 66.0 0.702.5 0.60 21.0 0.50 64.0 0.712.5 0.65 21.0 0.50 62.0 0.732.5 0.70 21.0 0.50 60.0 0.75

. 2.5 0.50 21.0 0.55 74.0 0.702.5 0.55 21.0 0.55 72.0 0.712.5 0.60 21.0 0.55 70.0 0.732.5 0.65 21.0 0.55 68.0 0.742.5 0.70 21.0 0.55 66.0 0.75

117



2.5 0.50 21.0 0.60 78.0 0.71

2.5 0.55 21.0 0.60 76.0 0.73

2.5 0.60 21.0 0.60 74.0 0.74

2.5 0.65 21.0 0.60 72.0 0.75

2.5 0.70 21.0 0.60 72.0 0.76

2.5 0.50 21.0 0.65 82.0 0.73

2.5 0.55 21.0 0.65 80.0 0.74

2.5 0.60 21.0 0.65 78.0 0.75

2.5 0.65 21.0 0.65 78.0 0.76

2.5 0.70 21.0 0.65 76.0 0.77

2.5 0.50 21.0 0.70 86.0 0.75

2.5 0.55 21.0 0.70 84.0 0.75

2.5 0.60 21.0 0.70 84.0 0.76

2.5 0.65 21.0 0.70 82.0 0.77

2.5 0.70 21.0 0.70 82.0 0.78

2.5 0.50 22.0 0.50 68.0 0.68

2.5 0.55 22.0 0.50 66.0 0.70

2.5 0.60 22.0 0.50 64.0 0.71

2.5 0.65 22.0 0.50 62.0 0.73

2.5 0.70 22.0 0.50 60.0 0.75

2.5 0.50 22.0 0.55 74.0 0.70

2.5 0.55 22.0 0.55 72.0 0.71

2.5 0.60 22.0 0.55 70.0 0.73

2.5 0.65 22.0 0.55 68.0 0.74

2.5 0.70 22.0 0.55 66.0 0.76

2.5 0.50 22.0 0.60 78.0 0.72

2.5 0.55 22.0 0.60 76.0 0.73

2.5 0.60 22.0 0.60 74.0 0.74

2.5 0.65 22.0 0.60 72.0 0.75

2.5 0.70 22.0 0.60 72.0 0.76

2.5 0.50 22.0 0.65 82.0 0.73

2.5 0.55 22.0 0.65 80.0 0.74

2.5 0.60 22.0 0.65 78.0 0.75

2.5 0.65 22.0 0.65 78.0 0.76

2.5 0.70 22.0 0.65 76.0 0.77

2.5 0.50 22.0 0.70 86.0 0.75

2.5 0.55 22.0 0.70 84.0 0.75

2.5 0.60 22.0 0.70 84.0 0.76

2.5 0.65 22.0 0.70 82.0 0.77

2.5 0.70 22.0 0.70 80.0 0.78

118



2.5 0.50 23.0 0.50 68.0 0.68

2.5 0.55 23.0 0.50 66.0 0.70

2.5 0.60 23.0 0.50 64.0 0.72

2.5 0.65 23.0 0.50 62.0 0.73

2.5 0.70 23.0 0.50 60.0 0.75

2.5 0.50 23.0 0.55 74.0 0.70

2.5 0.55 23.0 0.55 72.0 0.71

2.5 0.60 23.0 0.55 70.0 0.73

2.5 0.65 23.0 0.55 68.0 0.74

2.5 0.70 23.0 0.55 66.0 0.76

2.5 0.50 23.0 0.60 78.0 0.72

2.5 0.55 23.0 0.60 76.0 0.73

2.5 0.60 23.0 0.60 74.0 0.74

2.5 0.65 23.0 0.60 72.0 0.75

2.5 0.70 23.0 0.60 70.0 0.76

2.5 0.50 23.0 0.65 82.0 0.73

2.5 0.55 23.0 0.65 80.0 0.74

2.5 0.60 23.0 0.65 78.0 0.75

2.5 0.65 23.0 0.65 78.0 0.76

2.5 0.70 23.0 0.65 76.0 0.77

2.5 0.50 23.0 0.70 86.0 0.75

2.5 0.55 23.0 0.70 84.0 0.76

2.5 0.60 23.0 0.70 84.0 0.76

2.5 0.65 23.0 0.70 82.0 0.77

2.5 0.70 23.0 0.70 80.0 0.78

2.5 0.50 24.0 0.50 68.0 0.68

2.5 0.55 24.0 0.50 66.0 0.70

2.5 0.60 24.0 0.50 64.0 0.72

2.5 0.65 24.0 0.50 62.0 0.73

2.5 0.70 24.0 0.50 60.0 0.75

2.5 0.50 24.0 0.55 74.0 0.70

2.5 0.55 24.0 0.55 72.0 0.71

2.5 0.60 24.0 0.55 70.0 0.73

2.5 0.65 24.0 0.55 68.0 0.74

2.5 0.70 24.0 0.55 66.0 0.76

, 2.5 0.50 24.0 0.60 78.0 0.72

2.5 0.55 24.0 0.60 76.0 0.73

2.5 0.60 24.0 0.60 74.0 0.74

2.5 0.65 24.0 0.60 72.0 0.75

2.5 0.70 24.0 0.60 70.0 0.77

119


2.5 0.50 24.0 0.65 82.0 0.732.5 0.55 24.0 0.65 80.0 0.742.5 0.60 24.0 0.65 78.0 0.752.5 0.65 24.0 0.65 78.0 0.762.5 0.70 24.0 0.65 76.0 0.78

2.5 0.50 24.0 0.70 86.0 0.752.5 0.55 24.0 0.70 84.0 0.762.5 0.60 24.0 0.70 82.0 0.762.5 0.65 24.0 0.70 82.0 0.782.5 0.70 24.0 0.70 80.0 0.78

2.5 0.50 25.0 0.50 68.0 0.682.5 0.55 25.0 0.50 66.0 0.702.5 0.60 25.0 0.50 64.0 0.722.5 0.65 25.0 0.50 62.0 0.732.5 0.70 25.0 0.50 60.0 0.75

2.5 0.50 25.0 0.55 72.0 0.702.5 0.55 25.0 0.55 70.0 0.712.5 0.60 25.0 0.55 70.0 0.732.5 0.65 25.0 0.55 68.0 0.742.5 0.70 25.0 0.55 66.0 0.76

2.5 0.50 25.0 0.60 78.0 0.722.5 0.55 25.0 0.60 76.0 0.732.5 0.60 25.0 0.60 74.0 0.742.5 0.65 25.0 0.60 72.0 0.752.5 0.70 25.0 0.60 70.0 0.77

2.5 0.50 25.0 0.65 82.0 0.732.5 0.55 25.0 0.65 80.0 0.752.5 0.60 25.0 0.65 78.0 0.752.5 0.65 25.0 0.65 76.0 0.762.5 0.70 25.0 0.65 76.0 0.78

2.5 0.50 25.0 0.70 86.0 0.752.5 0.55 25.0 0.70 84.0 0.762.5 0.60 25.0 0.70 82.0 0.772.5 0.65 25.0 0.70 82.0 0.782.5 0.70 25.0 0.70 80.0 0.78

2.5 0.50 26.0 0.50 68.0 0.68 ,2.5 0.55 26.0 0.50 66.0 0.702.5 0.60 26.0 0.50 64.0 0.722.5 0.65 26.0 0.50 62.0 0.732.5 0.70 26.0 0.50 60.0 0.75

120



2.5 0.50 26.0 0.55 72.0 0.70

2.5 0.55 26.0 0.55 70.0 0.71

2.5 0.60 26.0 0.55 68.0 0.73

2.5 0.65 26.0 0.55 68.0 0.74

2.5 0.70 26.0 0.55 66.0 0.76

2.5 0.50 26.0 0.60 78.0 0.72

2.5 0.55 26.0 0.60 76.0 0.73

2.5 0.60 26.0 0.60 74.0 0.74

2.5 0.65 26.0 0.60 72.0 0.76

2.5 0.70 26.0 0.60 70.0 0.77

2.5 0.50 26.0 0.65 82.0 0.73

2.5 0.55 26.0 0.65 80.0 0.75

2.5 0.60 26.0 0.65 78.0 0.76

2.5 0.65 26.0 0.65 76.0 0.77

2.5 0.70 26.0 0.65 76.0 0.78

2.5 0.50 26.0 0.70 86.0 0.75

2.5 0.55 26.0 0.70 84.0 0.76

2.5 0.60 26.0 0.70 82.0 0.77

2.5 0.65 26.0 0.70 82.0 0.78

2.5 0.70 26.0 0.70 80.0 0.79

2.5 0.50 27.0 0.50 68.0 0.69

2.5 0.55 27.0 0.50 66.0 0.70

2.5 0.60 27.0 0.50 64.0 0.72

2.5 0.65 27.0 0.50 62.0 0.74

2.5 0.70 27.0 0.50 60.0 0.75

2.5 0.50 27.0 0.55 72.0 0.70

2.5 0.55 27.0 0.55 70.0 0.71

2.5 0.60 27.0 0.55 68.0 0.73

2.5 0.65 27.0 0.55 68.0 0.74

2.5 0.70 27.0 0.55 66.0 0.76

2.5 0.50 27.0 0.60 78.0 0.72

2.5 0.55 27.0 0.60 76.0 0.73

2.5 0.60 27.0 0.60 74.0 0.75

- 2.5 0.65 27.0 0.60 72.0 0.76

2.5 0.70 27.0 0.60 70.0 0.77

2.5 0.50 27.0 0.65 82.0 0.73

2.5 0.55 27.0 0.65 80.0 0.75

2.5 0.60 27.0 0.65 78.0 0.76

2.5 0.65 27.0 0.65 76.0 0.77

2.5 0.70 27.0 0.65 76.0 0.78

121

SAND COARSE AGGREGATE VOLUME % MAXIMUMd' PHI, 0 d' PHI, 0 COARSE AGGREGATE DENSITY

2.5 0.50 27.0 0.70 86.0 0.752.5 0.55 27.0 0.70 84.0 0.762.5 0.60 27.0 0.70 82.0 0.772.5 0.65 27.0 0.70 82.0 0.782.5 0.70 27.0 0.70 80.0 0.79

2.5 0.50 28.0 0.50 68.0 0.692.5 0.55 28.0 0.50 66.0 0.702.5 0.60 28.0 0.50 64.0 0.722.5 0.65 28.0 0.50 62.0 0.742.5 0.70 28.0 0.50 60.0 0.75

2.5 0.50 28.0 0.55 72.0 0.702.5 0.55 28.0 0.55 70.0 0.722.5 0.60 28.0 0.55 68.0 0.732.5 0.65 28.0 0.55 66.0 0.742.5 0.70 28.0 0.55 66.0 0.76

2.5 0.50 28.0 0.60 78.0 0.722.5 0.55 28.0 0.60 76.0 0.732.5 0.60 28.0 0.60 74.0 0.752.5 0.65 28.0 0.60 72.0 0.762.5 0.70 28.0 0.60 70.0 0.77

2.5 0.50 28.0 0.65 82.0 0.732.5 0.55 28.0 0.65 80.0 0.752.5 0.60 28.0 0.65 78.0 0.762.5 0.65 28.0 0.65 76.0 0.772.5 0.70 28.0 0.65 76.0 0.78

2.5 0.50 28.0 0.70 84.0 0.752.5 0.55 28.0 0.70 84.0 0.762.5 0.60 28.0 0.70 82.0 0.772.5 0.65 28.0 0.70 82.0 0.782.5 0.70 28.0 0.70 80.0 0.79

2.5 0.50 29.0 0.50 68.0 0.692.5 0.55 29.0 0.50 66.0 0.702.5 0.60 29.0 0.50 64.0 0.722.5 0.65 29.0 0.50 62.0 0.74 .2.5 0.70 29.0 0.50 60.0 0.75

2.5 0.50 29.0 0.55 72.0 0.702.5 0.55 29.0 0.55 70.0 0.722.5 0.60 29.0 0.55 68.0 0.732.5 0.65 29.0 0.55 66.0 0.752.5 0.70 29.0 0.55 66.0 0.76

122



2.5 0.50 29.0 0.60 76.0 0.72

2.5 0.55 29.0 0.60 76.0 0.73

2.5 0.60 29.0 0.60 74.0 0.75

2.5 0.65 29.0 0.60 72.0 0.76

2.5 0.70 29.0 0.60 70.0 0.77

2.5 0.50 29.0 0.65 82.0 0.73

2.5 0.55 29.0 0.65 80.0 0.75

2.5 0.60 29.0 0.65 78.0 0.76

2.5 0.65 29.0 0.65 76.0 0.77

2.5 0.70 29.0 0.65 74.0 0.78

2.5 0.50 29.0 0.70 84.0 0.75

2.5 0.55 29.0 0.70 84.0 0.76

2.5 0.60 29.0 0.70 82.0 0.77

2.5 0.65 29.0 0.70 80.0 0.78

2.5 0.70 29.0 0.70 80.0 0.79

2.5 0.50 30.0 0.50 68.0 0.69

2.5 0.55 30.0 0.50 66.0 0.70

2.5 0.60 30.0 0.50 64.0 0.72

2.5 0.65 30.0 0.50 62.0 0.74

2.5 0.70 30.0 0.50 60.0 0.75

2.5 0.50 30.0 0.55 72.0 0.70

2.5 0.55 30.0 0.55 70.0 0.72

2.5 0.60 30.0 0.55 68.0 0.73

2.5 0.65 30.0 0.55 66.0 0.75

2.5 0.70 30.0 0.55 66.0 0.76

2.5 0.50 30.0 0.60 76.0 0.72

2.5 0.55 30.0 0.60 76.0 0.73

2.5 0.60 30.0 0.60 74.0 0.75

2.5 0.65 30.0 0.60 72.0 0.76

2.5 0.70 30.0 0.60 70.0 0.77

2.5 0.50 30.0 0.65 80.0 0.73

2.5 0.55 30.0 0.65 80.0 0.75

2.5 0.60 30.0 0.65 78.0 0.76

2.5 0.65 30.0 0.65 76.0 0.77

2.5 0.70 30.0 0.65 74.0 0.78

2.5 0.50 30.0 0.70 84.0 0.752.5 0.55 30.0 0.70 84.0 0.76

2.5 0.60 30.0 0.70 82.0 0.77

2.5 0.65 30.0 0.70 80.0 0.78

2.5 0.70 30.0 0.70 80.0 0.79

123



3.0 0.50 7.0 0.50 60.0 0.563.0 0.55 7.0 0.50 50.0 0.583.0 0.60 7.0 0.50 34.0 0.603.0 0.65 7.0 0.50 0.0 0.653.0 0.70 7.0 0.50 0.0 0.70

3.0 0.50 7.0 0.55 70.0 0.583.0 0.55 7.0 0.55 62.0 0.603.0 0.60 7.0 0.55 52.0 0.613.0 0.65 7.0 0.55 34.0 0.653.0 0.70 7.0 0.55 0.0 0.70

3.0 0.50 7.0 0.60 78.0 0.613.0 0.55 7.0 0.60 72.0 0.623.0 0.60 7.0 0.60 64.0 0.633.0 0.65 7.0 0.60 54.0 0.653.0 0.70 7.0 0.60 34.0 0.70

3.0 _ 0.50 7.0 0.65 84.0 0.653.0 0.55 7.0 0.65 80.0 0.653:0 0.60 7.0 0.65 74.0 0.663.0 0.65 7.0 0.65 66.0 0.673.0 0.70 7.0 0.65 56.0 0.70

3.0 0.50 7.0 0.70 90.0 0.703.0 0.55 7.0 0.70 86.0 0.703.0 0.60 7.0 0.70 80.0 0.703.0 0.65 7.0 0.70 76.0 0.703.0 0.70 7.0 0.70 68.0 0.70

3.0 0.50 8.0 0.50 60.0 0.563.0 0.55 8.0 0.50 50.0 0.583.0 0.60 8.0 0.50 38.0 0.603.0 0.65 8.0 0.50 0.0 0.653.0 0.70 8.0 0.50 0.0 0.70

3.0 0.50 8.0 0.55 70.0 0.593.0 0.55 8.0 0.55 62.0 0.603.0 0.60 8.0 0.55 52.0 0.623.0 0.65 8.0 0.55 40.0 0.653.0 0.70 8.0 0.55 0.0 0.70

3.0 0.50 8.0 0.60 78.0 0.613.0 0.55 8.0 0.60 72.0 0.633.0 0.60 8.0 0.60 64.0 0.643.0 0.65 8.0 0.60 54.0 0.653.0 0.70 8.0 0.60 40.0 0.70

124


3.0 0.50 8.0 0.65 84.0 0.653.0 0.55 8.0 0.65 78.0 0.653.0 0.60 8.0 0.65 72.0 0.663.0 0.65 8.0 0.65 66.0 0.673.0 0.70 8.0 0.65 56.0 0.70

3.0 0.50 8.0 0.70 88.0 0.703.0 0.55 8.0 0.70 84.0 0.703.0 0.60 8.0 0.70 80.0 0.703.0 0.65 8.0 0.70 74.0 0.703.0 0.70 8.0 0.70 68.0 0.71

3.0 0.50 9.0 0.50 60.0 0.573.0 0.55 9.0 0.50 52.0 0.593.0 0.60 9.0 0.50 40.0 0.613.0 0.65 9.0 0.50 24.0 0.653.0 0.70 9.0 0.50 0.0 0.70

3.0 0.50 9.0 0.55 70.0 0.593.0 0.55 9.0 0.55 62.0 0.613.0 0.60 9.0 0.55 54.0 0.623.0 0.65 9.0 0.55 42.0 0.653.0 0.70 9.0 0.55 24.0 0.70

3.0 0.50 9.0 0.60 76.0 0.623.0 0.55 9.0 0.60 70.0 0.633.0 0.60 9.0 0.60 64.0 0.643.0 0.65 9.0 0.60 56.0 0.663.0 0.70 9.0 0.60 44.0 0.70

3.0 0.50 9.0 0.65 82.0 0.653.0 0.55 9.0 0.65 78.0 0.663.0 0.60 9.0 0.65 72.0 0.673.0 0.65 9.0 0.65 66.0 0.683.0 0.70 9.0 0.65 58.0 0.70

3.0 0.50 9.0 0.70 88.0 0.703.0 0.55 9.0 0.70 84.0 0.703.0 0.60 9.0 0.70 80.0 0.703.0 0.65 9.0 0.70 74.0 0.703.0 0.70 9.0 0.70 68.0 0.71

3.0 0.50 I0.0 0.50 60.0 0.57&

3.0 0.55 10.0 0.50 52.0 0.593.0 0.60 10.0 0.50 42.0 0.613.0 0.65 i0.0 0.50 30.0 0.653.0 0.70 i0.0 0.50 0.0 0.70

125



3.0 0.50 i0.0 0.55 68.0 0.60

3.0 0.55 i0.0 0.55 62.0 0.61

3.0 0.60 i0.0 0.55 54.0 0.63

3.0 0.65 i0.0 0.55 44.0 0.65

3.0 0.70 I0.0 0.55 30.0 0.70

3.0 0.50 I0.0 0.60 76.0 0.62

3.0 0.55 i0.0 0.60 70.0 0.63

3.0 0.60 i0.0 0.60 64.0 0.65

3.0 0.65 i0.0 0.60 56.0 0.66

3.0 0.70 i0.0 0.60 46.0 0.70

3.0 0.50 i0.0 0.65 82.0 0.65

3.0 0.55 i0.0 0.65 78.0 0.66

3.0 0.60 i0.0 0.65 72.0 0.67

3.0 0.65 i0.0 0.65 66.0 0.68

3.0 0.70 I0.0 0.65 58.0 0.70

3.0 0.50 i0.0 0.70 86.0 0.70

3.0 0.55 I0.0 0.70 82.0 0.70

3.0 0.60 I0.0 0.70 78.0 0.70

3.0 0.65 i0.0 0.70 74.0 0.71

3.0 0.70 I0.0 0.70 68.0 0.72

3.0 0.50 ii.0 0.50 60.0 0.58

3.0 0.55 ii.0 0.50 52.0 0.60

3.0 0.60 Ii.0 0.50 44.0 0.62

3.0 0.65 ii.0 0.50 32.0 0.65

3.0 0.70 ii.0 0.50 0.0 0.70

3.0 0.50 ii.0 0.55 68.0 0.60

3.0 0.55 ii.0 0.55 62.0 0.62

3.0 0.60 Ii.0 0.55 54.0 0.63

3.0 0.65 ii.0 0.55 46.0 0.65

3.0 0.70 ii.0 0.55 34.0 0.70

3.0 0.50 ii.0 0.60 76.0 0.63

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4.0 0.50 7.0 0.65 90.0 0.654.0 0.55 7.0 0.65 84.0 0.654.0 0.60 7.0 0.65 76.0 0.654.0 0.65 7.0 0.65 66.0 0.664.0 0.70 7.0 0.65 48.0 0.70

4.0 0.50 7.0 0.70 98.0 0.704.0 0.55 7.0 0.70 90.0 0.704.0 0.60 7.0 0.70 84.0 0.704.0 0.65 7.0 0.70 78.0 0.704.0 0.70 7.0 0.70 68.0 0.70

4.0 0.50 8.0 0.50 60.0 0.554.0 0.55 8.0 0.50 46.0 0.574.0 0.60 8.0 0.50 0.0 0.604.0 0.65 8.0 0.50 0.0 0.654.0 0.70 8.0 0..50 0.0 0.70

4.0 0.50 8.0 0.55 72.0 0.584.0 0.55 8.0 0.55 62.0 0.594.0 0.60 8.0 0.55 48.0 0.614.0 0.65 8.0 0.55 0.0 0.654.0 0.70 8.0 0.55 0.0 0.70

4.0 0.50 8.0 0.60 80.0 0.60° 4.0 0.55 8.0 0.60 72.0 0.61

4.0 0.60 8.0 0.60 64.0 0.634.0 0.65 8.0 0.60 50.0 0.654.0 0.70 8.0 0.60 0.0 0.70

147



4.0 0.50 8.0 0.65 86.0 0.654.0 0.55 8.0 0.65 82.0 0.654.0 0.60 8.0 0.65 74.0 0.654.0 0.65 8.0 0.65 66.0 0.664.0 0.70 8.0 0.65 52.0 0.70

4.0 0.50 8.0 0.70 92.0 0.704.0 0.55 8.0 0.70 88.0 0.704.0 0.60 8.0 0.70 82.0 0.704.0 0.65 8.0 0.70 76.0 0.704.0 0.70 8.0 0.70 68.0 0.70

4.0 0.50 9.0 0.50 60.0 0.564.0 0.55 9.0 0.50 48.0 0.584.0 0.60 9.0 0.50 30.0 0.604.0 0.65 9.0 0.50 0.0 0.654.0 0.70 9.0 0.50 0.0 0.70

4.0 0.50 9.0 0.55 70.0 0.584.0 0.55 9.0 0.55 62.0 0.594.0 0.60 9.0 0.55 50.0 0.614.0 0.65 9.0 0.55 32.0 0.654.0 0.70 9.0 0.55 0.0 0.70

4.0 0.50 9.0 0.60 78.0 0.614.0 0.55 9.0 0.60 72.0 0.624.0 0.60 9.0 0.60 64.0 0.634.0 0.65 9.0 0.60 52.0 0.654.0 0.70 9.0 0.60 30.0 0.70

4.0 0.50 9.0 0.65 84.0 0.654.0 0.55 9.0 0.65 80.0 0.654.0 0.60 9.0 0.65 74.0 0.654.0 0.65 9.0 0.65 66.0 0.674.0 0.70 9.0 0.65 54.0 0.70

4.0 0.50 9.0 0.70 90.0 0.704.0 0.55 9.0 0.70 86.0 0.704.0 0.60 9.0 0.70 82.0 0.704.0 0.65 9.0 0.70 76.0 0.704.0 0.70 9.0 0.70 68.0 0.70

4.0 0.50 I0.0 0.50 60.0 0.564.0 0.55 i0.0 0.50 50.0 0.584.0 0.60 I0.0 0.50 36.0 0.604.0 0.65 I0.0 0.50 0.0 0.654.0 0.70 i0.0 0.50 0.0 0.70

148



4.0 0.50 i0.0 0.55 70.0 0.594.0 0.55 I0.0 0.55 62.0 0.604.0 0.60 i0.0 0.55 52.0 0.624.0 0.65 I0.0 0.55 38.0 0.654.0 0.70 i0.0 0.55 0.0 0.70

4.0 0.50 i0.0 0.60 78.0 0.614.0 0.55 I0.0 0.60 72.0 0.624.0 0.60 i0.0 0.60 64.0 0.644.0 0.65 10.0 0.60 54.0 0.654.0 0.70 10.0 0.60 38.0 0.70

4.0 0.50 I0.0 0.65 84.0 0.654.0 0.55 10.0 0.65 78.0 0.654.0 0.60 i0.0 0.65 74.0 0.664.0 0.65 i0.0 0.65 66.0 0.674.0 0.70 i0.0 0.65 56.0 0.70

4.0 0.50 i0.0 0.70 88.0 0.704.0 0.55 I0.0 0.70 84.0 0.704.0 0.60 i0.0 0.70 80.0 0.704.0 0.65 I0.0 0.70 76.0 0.704.0 0.70 i0.0 0.70 68.0 0.71

4.0 0.50 ii.0 0.50 60.0 0.574.0 0.55 Ii.0 0.50 50.0 0.584.0 0.60 ii.0 0.50 38.0 0.604.0 0.65 II.0 0.50 14.0 0.654.0 0.70 ii.0 0.50 0.0 0.70

4.0 0.50 ii.0 0.55 70.0 0.594.0 0.55 ii.0 0.55 62.0 0.604.0 0.60 ii.0 0.55 52.0 0.624.0 0.65 ii.0 0.55 40.0 0.654.0 0.70 ii.0 0.55 0.0 0.70

i

4.0 0.50 II.0 0.60 78.0 0.624.0 0.55 Ii.0 0.60 70.0 0.634.0 0.60 ii.0 0.60 64.0 0.644.0 0.65 Ii.0 0.60 54.0 0.664.0 0.70 ii.0 0.60 42.0 0.70

J

4.0 0.50 ii.0 0.65 84.0 0.654.0 0.55 Ii.0 0.65 78.0 0.65

" 4.0 0.60 Ii.0 0.65 72.0 0.664.0 0.65 ii.0 0.65 66.0 0.684.0 0.70 II.0 0.65 56.0 0.70

149

i



4.0 0.50 ii.0 0.70 88.0 0.704.0 0.55 ii.0 0.70 84.0 0.704.0 0.60 ii.0 0.70 80.0 0.704.0 0.65 ii.0 0.70 74.0 0.704.0 0.70 Ii.0 0.70 68.0 0.71

4.0 0.50 12.0 0.50 60.0 0.574.0 0.55 12.0 0.50 52.0 0.594.0 0.60 12.0 0.50 40.0 0.614.0 0.65 12.0 0.50 24.0 0.654.0 0.70 12.0 0.50 0.0 0.70

4.0 0.50 12.0 0.55 70.0 0.594.0 0.55 12.0 0.55 62.0 0.614.0 0.60 12.0 0.55 54.0 0.624.0 0.65 12.0 0.55 42.0 0.654.0 0.70 12.0 0.55 24.0 0.70

4.0 0.50 12.0 0.60 76.0 0.624.0 0.55 12.0 0.60 70.0 0.634.0 0.60 12.0 0.60 64.0 0.644.0 0.65 12.0 0.60 56.0 0.664.0 0.70 12.0 0.60 44.0 0.70

4.0 0.50 12.0 0.65 82.0 0.654.0 0.55 12.0 0.65 78.0 0.664.0 0.60 12.0 0.65 72.0 0.674.0 0.65 12.0 0.65 66.0 0.684.0 0.70 12.0 0.65 58.0 0.70

4.0 0.50 12.0 0.70 88.0 0.704.0 0.55 12.0 0.70 84.0 0.704.0 0.60 12.0 0.70 80.0 0.704.0 0.65 12.0 0.70 74.0 0.704.0 0.70 12.0 0.70 68.0 0.71

4.0 0.50 13.0 0.50 60.0 0.574.0 0.55 13.0 0.50 52.0 0.594.0 0.60 13.0 0.50 42.0 0.614.0 0.65 13.0 0.50 28.0 0.654.0 0.70 13.0 0.50 0.0 0.70 _*

4.0 0.50 13.0 0.55 68.0 0.604.0 0.55 13.0 0.55 62.0 0.61 34.0 0.60 13.0 0.55 54.0 0.634.0 0.65 13.0 0.55 44.0 0.654.0 0.70 13.0 0.55 30.0 0.70

J

150


d' PHI,0 d' PHI,0 COARSE AGGREGATE DENSITY

4.0 0.50 13.0 0.60 76.0 0.62

4.0 0.55 13.0 0.60 70.0 0.63

4.0 0.60 13.0 0.60 64.0 0.65

4.0 0.65 13.0 0.60 56.0 0.66

4.0 0.70 13.0 0.60 46.0 0.70

4.0 0.50 13.0 0.65 82.0 0.65

4.0 0.55 13.0 0.65 78.0 0.66

4.0 0.60 13.0 0.65 72.0 0.67

4.0 0.65 13.0 0.65 66.0 0.68

4.0 0.70 13.0 0.65 58.0 0.70

4.0 0.50 13.0 0.70 86.0 0.70

4.0 0.55 13.0 0.70 84.0 0.70

4.0 0.60 13.0 0.70 78.0 0.70

4.0 0.65 13.0 0.70 74.0 0.70

4.0 0.70 13.0 0.70 68.0 0.72

4.0 0.50 14.0 0.50 60.0 0.58

4.0 0.55 14.0 0.50 52.0 0.59

4.0 0.60 14.0 0.50 44.0 0.61

4.0 0.65 14.0 0.50 32.0 0.65

4.0 0.70 14.0 0.50 0.0 0.70

4.0 0.50 14.0 0.55 68.0 0.60

4.0 0.55 14.0 0.55 62.0 0.61

4.0 0.60 14.0 0.55 54.0 0.63

J 4.0 0.65 14.0 0.55 46.0 0.65

4.0 0.70 14.0 0.55 32.0 0.70

4.0 0.50 14.0 0.60 76.0 0.62

4.0 0.55 14.0 0.60 70.0 0.64

4.0 0.60 14.0 0.60 64.0 0.65

4.0 0.65 14.0 0.60 56.0 0.67

4.0 0.70 14.0 0.60 46.0 0.70

4.0 0.50 14.0 0.65 82.0 0.65

4.0 0.55 14.0 0.65 78.0 0.66

4.0 0.60 14.0 0.65 72.0 0.67

4.0 0.65 14.0 0.65 66.0 0.68

• 4.0 0.70 14.0 0.65 58.0 0.70

4.0 0.50 14.0 0.70 86.0 0.70

i 4.0 0.55 14.0 0.70 82.0 0.70

4.0 0.60 14.0 0.70 78.0 0.70

4.0 0.65 14.0 0.70 74.0 0.71

4.0 0.70 14.0 0.70 68.0 0.72

151


4.0 0.50 15.0 0.50 60.0 0.584.0 0.55 15.0 0.50 52.0 0.604.0 0.60 15.0 0.50 44.0 0.624.0 0.65 15.0 0.50 34.0 0.654.0 0.70 15.0 0.50 14.0 0.70

4.0 0.50 15.0 0.55 68.0 0.604.0 0.55 15.0 0.55 62.0 0.624.0 0.60 15.0 0.55 54.0 0.634.0 0.65 15.0 0.55 46.0 0.654.0 0.70 15.0 0.55 34.0 0.70

4.0 0.50 15.0 0.60 76.0 0.634.0 0.55 15.0 0.60 70.0 0.644.0 0.60 15.0 0.60 64.0 0.654.0 0.65 15.0 0.60 56.0 0.674.0 0.70 15.0 0.60 48.0 0.70

4.0 0.50 15.0 0.65 82.0 0.654.0 0.55 15.0 0.65 76.0 0.664.0 0.60 15.0 0.65 72.0 0.674.0 0.65 15.0 0.65 66.0 0.694.0 0.70 15.0 0.65 58.0 0.70

4.0 0.50 15.0 0.70 86.0 0.704.0 0.55 15.0 0.70 82.0 0.704.0 0.60 15.0 0.70 78.0 0.704.0 0.65 15.0 0.70 74.0 0.714.0 0.70 15.0 0.70 68.0 0.72

4.0 0.50 16.0 0.50 60.0 0.584.0 0.55 16.0 0.50 52.0 0.604.0 0.60 16.0 0.50 44.0 0.624.0 0.65 16.0 0.50 34.0 0.654.0 0.70 16.0 0.50 20.0 0.70

4.0 0.50 16.0 0.55 68.0 0.604.0 O. 55 16.0 0.55 62.0 0.624.0 0.60 16.0 0.55 54.0 0.644.0 0.65 16.0 0.55 46.0 0.654.0 0.70 16.0 0.55 36.0 0.70 e

4.0 0.50 16.0 0.60 76.0 0.634.0 0.55 16.0 0.60 70.0 0.64 _"4.0 0.60 16.0 0.60 64.0 0.654.0 0.65 16.0 0.60 56.0 0.674.0 0.70 16.0 0.60 48.0 0.70

152



4.0 0.50 16.0 0.65 80.0 0.664.0 0.55 16.0 0.65 76.0 0.674.0 0.60 16.0 0.65 72.0 0.684.0 0.65 16.0 0.65 66.0 0.694.0 0.70 16.0 0.65 58.0 0.70

4.0 0.50 16.0 0.70 86.0 0.704.0 0.55 16.0 0.70 82.0 0.704.0 0.60 16.0 0.70 78.0 0.704.0 0.65 16.0 0.70 74.0 0.714.0 0.70 16.0 0.70 68.0 0.72

4.0 0.50 17.0 0.50 60.0 0.584.0 0.55 17.0 0.50 54.0 0.604.0 0.60 17.0 0.50 46.0 0.624.0 0.65 17.0 0.50 36.0 0.654.0 0.70 17.0 0.50 24.0 0.70

4.0 0.50 17.0 0.55 68.0 0.614.0 0.55 17.0 0.55 62.0 0.624.0 0.60 17.0 0.55 54.0 0.644.0 0.65 17.0 0.55 48.0 0.664.0 0.70 17.0 0.55 38.0 0.70

4.0 0.50 17.0 0.60 74.0 0.634.0 0.55 17.0 0.60 70.0 0.644.0 0.60 17.0 0.60 64.0 0.664.0 0.65 17.0 0.60 58.0 0.674.0 0.70 17.0 0.60 48.0 0.70

4.0 0.50 17.0 0.65 80.0 0.664.0 0.55 17.0 0.65 76.0 0.67

4.0 0.60 17.0 0.65 72.0 0.684.0 0.65 17.0 0.65 66.0 0.694.0 0.70 17.0 0.65 60.0 0.71

4.0 0.50 17.0 0.70 86.0 0.704.0 0.55 17.0 0.70 82.0 0.704.0 0.60 17.0 0.70 78.0 0.70

4 4.0 0.65 17.0 0.70 74.0 0.714.0 0.70 17.0 0.70 68.0 0.73

4.0 0.50 18.0 0.50 60.0 0.594.0 0.55 18.0 0.50 54.0 0.604.0 0.60 18.0 0.50 46.0 0.624.0 0.65 18.0 0.50 36.0 0.654.0 0.70 18.0 0.50 26.0 0.70

153


4.0 0.50 18.0 0.55 68.0 0.614.0 0.55 18.0 0.55 62.0 0.624.0 0.60 18.0 0.55 56.0 0.644.0 0.65 18.0 0.55 48.0 0.664.0 0.70 18.0 0.55 38.0 0.70

4.0 0.50 18.0 0.60 74.0 0.634.0 0.55 18.0 0.60 70.0 0.644.0 0.60 18.0 0.60 64.0 0.664.0 0.65 18.0 0.60 58.0 0.674.0 0.70 18.0 0.60 50.0 0.70

4.0 0.50 18.0 0.65 80.0 0.664.0 O. 55 18.0 O. 65 76.0 0.674.0 0.60 18.0 0.65 72.0 0.684.0 0.65 18.0 0.65 66.0 0.694.0 0.70 18.0 0.65 60.0 0.71

4.0 0.50 18.0 0.70 86.0 0.704.0 0.55 18.0 0.70 82.0 0.704.0 0.60 18.0 0.70 78.0 0.704.0 0.65 18.0 0.70 74.0 0.724.0 0.70 18.0 0.70 68.0 0.73

4.0 0.50 19.0 0.50 60.0 0.594.0 0.55 19.0 0.50 54.0 0.614.0 0.60 19.0 0.50 46.0 0.634.0 0.65 19.0 0.50 38.0 0.654.0 0.70 19.0 0.50 28.0 0.70

4.0 0.50 19.0 0.55 68.0 0.614.0 0.55 19.0 0.55 62.0 0.624.0 0.60 19.0 0.55 56.0 0.644.0 0.65 19.0 0.55 48.0 0.664.0 0.70 19.0 0.55 40.0 0.70

4.0 O. 50 19.0 0.60 74.0 0.634.0 O. 55 19.0 0.60 70.0 0.654.0 0.60 19.0 0.60 64.0 0.664.0 0.65 19.0 0.60 58.0 0.684.0 0.70 19.0 0.60 50.0 0.70 _

4.0 0.50 19.0 0.65 80.0 0.664.0 0.55 19.0 0.65 76.0 0.67 '_4.0 0.60 19.0 0.65 72.0 0.684.0 0.65 19.0 0.65 66.0 0.704.0 0.70 19.0 0.65 60.0 0.71

154



4.0 0.50 19.0 0.70 84.0 0.704.0 0.55 19.0 0.70 82.0 0.704.0 0.60 19.0 0.70 78.0 0.714.0 0.65 19.0 0.70 74.0 0.724.0 0.70 19.0 0.70 68.0 0.73

4.0 0.50 20.0 0.50 70.0 0.674.0 0.55 20.0 0.50 68.0 0.684.0 0.60 20.0 0.50 66.0 0.704.0 0.65 20.0 0.50 64.0 0.714.0 0.70 20.0 0.50 62.0 0.73

4.0 0.50 20.0 0.55 76.0 0.684.0 0.55 20.0 0.55 74.0 0.704.0 0.60 20.0 0.55 72.0 0.714.0 0.65 20.0 0.55 70.0 0.724.0 0.70 20.0 0.55 68.0 0.73

4.0 0.50 20.0 0.60 80.0 0.704.0 0.55 20.0 0.60 78.0 0.714.0 0.60 20.0 0.60 76.0 0.724.0 0.65 20.0 0.60 76.0 0.734.0 0.70 20.0 0.60 74.0 0.74

4.0 0.50 20.0 0.65 84.0 0.714.0 0.55 20.0 0.65 84.0 0.724.0 0.60 20.0 0.65 82.0 0.734.0 0.65 20.0 0.65 80.0 0.744.0 0.70 20.0 0.65 80.0 0.75

4.0 0.50 20.0 0.70 88.0 0.734.0 0.55 20.0 0.70 88.0 0.744.0 0.60 20.0 0.70 86.0 0.744.0 0.65 20.0 0.70 86.0 0.754.0 0.70 20.0 0.70 84.0 0.75

4.0 0.50 21.0 0.50 70.0 0.674.0 0.55 21.0 0.50 68.0 0.684.0 0.60 21.0 0.50 66.0 0.70

• 4.0 0.65 21.0 0.50 64.0 0.714.0 0.70 21.0 0.50 62.0 0.73

. 4.0 0.50 21.0 0.55 76.0 0.684.0 0.55 21.0 0.55 74.0 0.704.0 0.60 21.0 0.55 72.0 0.714.0 0.65 21.0 0.55 70.0 0.724.0 0.70 21.0 0.55 68.0 0.74

155



4.0 0.50 21.0 0.60 80.0 0.70

4.0 0.55 21.0 0.60 78.0 0.71

4.0 0.60 21.0 0.60 76.0 0.72

4.0 0.65 21.0 0.60 76.0 0.73

4.0 0.70 21.0 0.60 74.0 0.74

4.0 0.50 21.0 0.65 84.0 0.714.0 0.55 21.0 0.65 82.0 0.72

4.0 0.60 21.0 0.65 82.0 0.73

4.0 0.65 21.0 0.65 80.0 0.74

4.0 0.70 21.0 0.65 78.0 0.75

4.0 0.50 21.0 0.70 88.0 0.73

4.0 0.55 21.0 0.70 88.0 0.74

4.0 0.60 21.0 0.70 86.0 0.74

4.0 0.65 21.0 0.70 86.0 0.75

4.0 0.70 21.0 0.70 84.0 0.76

4.0 0.50 22.0 0.50 70.0 0.67

4.0 0.55 22.0 0.50 68.0 0.69

4.0 0.60 22.0 0.50 66.0 0.70

4.0 0.65 22.0 0.50 64.0 0.72

4.0 0.70 22.0 0.50 62.0 0.73m

4.0 0.50 22.0 0.55 74.0 0.68

4.0 0.55 22.0 0.55 74.0 0.70

4.0 0.60 22.0 0.55 72.0 0.71

4.0 0.65 22.0 0.55 70.0 0.73

4.0 0.70 22.0 0.55 68.0 0.74

4.0 0.50 22.0 0.60 80.0 0.70

4.0 0.55 22.0 0.60 78.0 0.71

4.0 0.60 22.0 0.60 76.0 0.72

4.0 0.65 22.0 0.60 74.0 0.73

4.0 0.70 22.0 0.60 74.0 0.75

4.0 0.50 22.0 0.65 84.0 0.72

4.0 0.55 22.0 0.65 82.0 0.72

4.0 0.60 22.0 0.65 82.0 0.73

4.0 0.65 22.0 O. 65 80.0 0.74

4.0 0.70 22.0 0.65 78.0 0.75 _'

4.0 0.50 22.0 0.70 88.0 0.73

4.0 0.55 22.0 0.70 86.0 0.74 :

4.0 0.60 22.0 0.70 86.0 0.75

4.0 0.65 22.0 0.70 84.0 0.75

4.0 0.70 22.0 0.70 84.0 0.76

156



4.0 0.50 23.0 0.50 70.0 0.67

4.0 0.55 23.0 0.50 68.0 0.69

4.0 0.60 23.0 0.50 66.0 0.70

4.0 0.65 23.0 0.50 64.0 0.72

4.0 0.70 23.0 0.50 62.0 0.73

4.0 0.50 23.0 0.55 74.0 0.69

4.0 0.55 23.0 0.55 72.0 0.70

4.0 0.60 23.0 0.55 72.0 0.71

4.0 0.65 23.0 0.55 70.0 0.73

4.0 0.70 23.0 0.55 68.0 0.74

4.0 0.50 23.0 0.60 80.0 0.70

4.0 0.55 23.0 0.60 78.0 0.72

4.0 0.60 23.0 0.60 76.0 0.73

4.0 0.65 23.0 0.60 74.0 0.74

4.0 0.70 23.0 0.60 72.0 0.75

4.0 0.50 23.0 0.65 84.0 0.72

4.0 0.55 23.0 0.65 82.0 0.73

4.0 0.60 23.0 0.65 80.0 0.73

4.0 0.65 23.0 0.65 80.0 0.75

4.0 0.70 23.0 0.65 78.0 0.75

4.0 0.50 23.0 0.70 88.0 0.73

4.0 0.55 23.0 0.70 86.0 0.74

4.0 0.60 23.0 0.70 86.0 0.75

4.0 0.65 23.0 0.70 84.0 0.75

4.0 0.70 23.0 0.70 84.0 0.76

4.0 0.50 24.0 0.50 70.0 0.67

4.0 0.55 24.0 0.50 68.0 0.69

4.0 0.60 24.0 0.50 66.0 0.71

4.0 0.65 24.0 0.50 64.0 0.72

4.0 0.70 24.0 0.50 62.0 0.74

4.0 0.50 24.0 0.55 74.0 0.69

4.0 0.55 24.0 0.55 72.0 0.70

4.0 0.60 24.0 0.55 70.0 0.71

4.0 0.65 24.0 0.55 70.0 0.73

4.0 0.70 24.0 0.55 68.0 0.74

4.0 0.50 24.0 0.60 80.0 0.70

• 4.0 0.55 24.0 0.60 78.0 0.72

4.0 0.60 24.0 0.60 76.0 0.73

4.0 0.65 24.0 0.60 74.0 0.74

4.0 0.70 24.0 0.60 72.0 0.75

157



4.0 0.50 24.0 0.65 84.0 0.724.0 0.55 24.0 0.65 82.0 0.734.0 0.60 24.0 0.65 80.0 0.744.0 0.65 24.0 0.65 80.0 0.754.0 0.70 24.0 0.65 78.0 0.76

4.0 0.50 24.0 0.70 88.0 0.744.0 0.55 24.0 0.70 86.0 0.744.0 0.60 24.0 0.70 86.0 0.754.0 0.65 24.0 0.70 84.0 0.764.0 0.70 24.0 0.70 84.0 0.76

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161

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