AFE SettlementAnalysis 2013 Web

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Geotechnical Engineering Research Laboratory Samuel G. Paikowsky, Sc.D One University Avenue Professor Lowell, Massachusetts 01854Tel: (978) 934-2277 Fax: (978) 934-3046e-mail: [email protected] site: http://www.uml.edu/research_labs/Geotechnical_Engineering/

DEPARTMENT OF CIVIL ANDENVIRONMENTAL ENGINEERING

academic\classes\AdvFound\Class Notes\ AFE_settlement analysis_2010.doc

14.533 Advanced Foundation Engineering

SHORT & LONG TERM SETTLEMENT ANALYSISOF SHALLOW FOUNDATIONS

S. G. Paikowsky


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S. Paikowsky, UMass Lowell Academic\Classes\AdvFnd\Class Notes\AFE_Settlement Analysis_2010.doc

PAGE i

TABLE OF CONTENTS

PAGE

SETTLEMENT CRITERIA & CONCEPT OF ANALYSIS 1

1. Tolerance Criteria of Settlement and Differential Settlement ................................ 12. Types of Settlement and Methods of Analysis ...................................................... 53. General Concepts of Settlement Analysis ............................................................ 6

VERTICAL STRESS INCREASE IN SOIL DUE TO A FOUNDATION LOAD 7 1. Principle ................................................................................................................ 72. Stress Due to Concentrated Load ........................................................................ 83. Stress Due to a Circularly Loaded Area ............................................................... 84. Stress Below a Rectangular Area ......................................................................... 95. General Charts of Stress Distribution Beneath a Rectangular and Strip

Footings .............................................................................................................. 10

6. Stress Under Embankment ................................................................................ 127. Average Vertical stress Increase Due to a Rectangularly Loaded Area ............. 138. Influence Chart Newmarks Solution ................................................................ 159. Using Charts Describing Increase in Pressure ................................................... 1710. Simplified Relationship ....................................................................................... 18

IMMEDIATE SETTLEMENT ANALYSIS 201. General Elastic Relations ................................................................................... 202. Finding E s , : the Modulus of Elasticity and Poissons Ratio .............................. 213. Improved Equation for Elastic Settlement (Mayne and Poulos, 1999) ................ 224. Immediate (Elastic) Settlement of Sandy Soil The strain Influence Factor

(Schmertmann and Hartman, 1978) ................................................................... 245. The Preferable I z Distribution for the Strain Influence Factor .............................. 266. Immediate Settlement in Sandy Soils using Burland and Burbridges (1985)

Method ............................................................................................................... 277. Case History Immediate Settlement in Sand ................................................... 27

a-1The Strain Influence Factor (as in the text) .............................................. 27a-2 The Strain Influence Factor (Schmertmann et al., 1978) ......................... 29b. Elastic Settlement Analysis Section 5.7 ................................................ 30c. Elastic Settlement Analysis Section 5.8 ................................................ 32d. Elastic Settlement Analysis Section 5.10 .............................................. 33e. Summary & Conclusions .......................................................................... 35

8. Immediate (Elastic) Settlement of Foundations on Saturated Clays: (Junbuet al., 1956) Das section 5.9, p.243 .................................................................... 36

CONSOLIDATION SETTLEMENT - LONG TERM SETTLEMENT 381. Principal and Analogy ......................................................................................... 382. Final Settlement Analysis ................................................................................... 39

a. Principal of Analysis ................................................................................. 39b. Consolidation Test (1-D Test) .................................................................. 41


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PAGE ii

c. Obtaining Parameters from Test Results ................................................. 42d. Final Settlement Analysis ......................................................................... 44e. Example Final Consolidation Settlement .............................................. 47f. Terzaghis 1-D Consolidation Equation .................................................... 51

3. Time Rate Consolidation (Das Sects. 1.15 & 1.16, pp. 38-47) ........................... 56

a. Outline of Analysis ................................................................................... 56b. Obtaining Parameters from the Analysis of e-log t Consolidation TestResults (Bowles p. 62) ............................................................................. 60

4. Consolidation Example ....................................................................................... 645. Secondary Consolidation (Compression) Settlement (Bowles p.87) .................. 99


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PAGE 1

SETTLEMENT OF SHALLOW FOUNDATIONS(Das Sections 5.1 through 5.20, pp. 223 - 290)

(Bowles Ch.5, pp.284-340)

SETTLEMENT CRITERIA AND CONCEPT OF ANALYSIS

1. Tolerance Criteria of Settlement and Differential Settlement

Settlement most often governs the design as allowable settlement isexceeded before B.C. becomes critical.

Concerns of foundation settlement are subdivided into 3 levels ofassociated damage:

- Architectural damage - cracks in walls, partitions, etc.- Structural damage - reduced strength in structural members- Functional damage - impairment of the structure functionalityThe last two refer to stress and serviceability limit states,respectively.

In principle, two approaches exist to determine the allowabledisplacements.

(a) Rational Approach to Design

Design Determine Design found. CheckBuilding allowable accordingly cost

Deformation& displacements

not acceptable

OKProblems: - expensive analysis

- limited accuracy in all predictions especiallysettlement & differential settlement


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PAGE 2

1. Empirical Approach (see text section 5.20, TolerableSettlement of Buildings, pp. 283-285)

based on performance of many structures, provide a

guideline for maximum settlement and maximumrotation

S max = maximum settlement = s = differential settlement (between any two points) ( )max = maximum rotation

Angular distortion = tan = ( ) maxs = = S S A B

( )max 1300

architectural damage

( )max 1250

tilting of high structures become visible

( )max 1150

structural damage likely

l

S A

A B

S B

=s


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PAGE 3

maximum settlement (S max ) leading to differential settlement

Masonry wall structure 1 - 2 Framed structures 2 - 4 Silos, mats 3 - 12 Lambe and Whitman Soil Mechanics provides in Table

14.1 and Figure 14.8 (see next page) the allowablemaximum total settlement, tilting and differentialmovements as well as limiting angular distortions.

Correlation Between Maximum Settlement to Angular Distortion

Grant, Christian & Van marke (ASCE - 1974)correlation between angular settlement to maximum settlement,based on 95 buildings of which 56 were damaged.

Type ofFound Type of Soil

s max (in)( )max

all (in)( )max = 1300

Isol. FootingsClay 1200 4Sand 600 2

Mat Clay 138 ft 0.044 B (ft)

Sand no relationship

Limiting values of serviceability are typically s max = 1 for isolatedfooting and s max = 2 for a raft which is more conservative than theabove limit based on architectural damage. Practicallyserviceability needs to be connected to the functionality of the

building and the tolerable limit.


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PAGE 4

(Lambe & Whitman, Soil Mechanics )


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PAGE 5

2. Types of Settlement and Methods of Analysis

Si = Granular Soils S c, S c(s) - Cohesive Soils

Elastic Theory Consolidation Theory Empirical Correlations

In principle, both types of settlement; the immediate and the longterm, utilize the compressibility of the soil, one however, is timedependent (consolidation and secondary compression).

S i (immediate)

S c (consolidation)

S c(S)

(secondarycompression = creep)


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PAGE 6

3. General Concept of Settlement Analysis

Two controlling factors influencing settlements:

Net applied stress - q

Compressibility of soil - c = ( settlement load )

when dealing with clay c = f (t) as it changes with time

s = q x c x f (B)

wheres = settlement [L]

q = net load [F/L 2]c = compressibility [L/(F/L 2)]

f (B) = size effect [dimensionless]

obtain c by lab tests, plate L.T., SPT, CPT

c will be influenced by:

- width of footing = B- depth of footing = D B - location of G.W. Table = d Bw - type of loading static or repeated- soil type & quality affecting the modulus


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PAGE 7

VERTICAL STRESS INCREASE IN THE SOIL DUE TO AFOUNDATION LOAD

(Das 7 th ed., Sect. 5.2-5.8, pp.224-243)(Bowles Sections 5.2 to 5.5, pp.286-302)

1. Principle(a) Required: Vertical stress (pressure) increase under the footing in

order to asses settlement.

(b) Solution: Theoretical solution based on theory of elasticityassuming load on , homogeneous, isotropic, elastic half space. Homogeneous Uniform throughout at every point

we have the same qualities.

Isotropic Identical in all directions, invariantwith respect to direction

Orthotropic (tend to grow or form along a verticalaxis) different qualities in two planes

Elastic capable of recovering shape

(c) Why can we use the elastic solutions for that problem?

Is the soil elastic? no, but

i. We are practically interested in the service loads which are

approximately the dead load. The ultimate load = design load x F.S. Design load = (DL x F.S.) + (LL x F.S.) Service load DL within the elastic zone

ii. The only simple straight forward method we know


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PAGE 8

2. Stress due to Concentrated Load (Bowles p.287)Boussinesq, 1885

P

Xr

RY

v(x,y,z)

Z

p = v = 3P r = 22 y x + (Das eq. 5.1)2z2 [ 1 + ( r z )

2 ]5/2 (Bowles eq. 5.3)

3. Stress due to a Circularly Loaded Area

referring to flexible areas as we assume uniform stress over the area.Uniform stress will develop only under a flexible footing. integration of the above load from a point to an area.

- see Das Eqs. 5.2, 5.3 (text p.225) (Bowles Eq. 5.4, 5.5)

p = v = q o 1 11 2

2 3 2

+

[ ( ) ] / B z

vertical stress under the center

See Das Table 5.1 (p.226) for ( ) ( )

= 2&2

0 B

z B

r f q

v

B

Z


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PAGE 9

4. Stress below a Rectangular Area

p = v = q o x I

below the corner of aflexible rectangular loaded area

m = B z n = L z

Bowles Table 5.1 (p.294) Das Table 5.2 (p.228-229) I = f (m,n)

Stress at a point under different locations

Figure 5.4 Stress below any point of aloaded flexible rectangular area (Das p.230)

use B 1 x L 1 m 1,n 1 I2B1 x L 2 m 1,n 2 I1B2 x L 1 m 2,n 1 I3

p = v = q o (I1 + I 2 + I 3 + I 4) B 2 x L 2 m 2,n 2 I4

Stress at a point under the center of the foundation

p = v = q c x Ic

Ic = f(m 1, n 1) m 1 = L/B n 1 = z/(B/2)

Bowles Table 5.1 (p.294), Das Table 5.3 (p.230) providesvalues of m 1 and n 1.

See next page for a chart p/q 0 vs. z/B, f(L/B)

Z

L

B

qo


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PAGE 10

5. General Charts of Stress Distribution Beneath a Rectangularand Strip Footings

(a) P qo vs. z B under the center of a rectangular footingwith L B = 1 (square) to L B = (strip)

Stress Increase in a Soil Mass Caused by Foundation Load

Figure 3.41 Increase of stress under the center of a flexible loadedrectangular area

Das Principle of Foundation Engineering, 3 rd Edition


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PAGE 11

(b) Stress Contours (laterally and vertically) of a strip andsquare footings. Soil Mechanics, DM 7.1 p. 167


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PAGE 12

Example: size 8 x 8m, depth z = 4m

Find the additional stress under the center ofthe footing loaded with q 0

1. Generic relationship 4 x 4 x 4 m = 1n = 1

p = (4 x 0.17522)q o = 0.7q o2. Specific to center, m1 = 1, n1 = 1 Table 5.3, Ic = 0.7013. Use Figure 3 of the Navy Square Footing z = B/2, z 0.7p4. Use figure 3.41 (class notes p.12) L/B = 1, Z/B = 0.5 p / qo 0.7

6. Stress Under Embankment (Bowles Sect. 5.4 & Das Sect. 5.6)

Das Fig. 5.10 Embankmentloading (text p.236)

p = = q oI (Das eq.5.23)

I = f ( B z

1 , B z

2 ) Das Fig. 5.11 (p.237)

Example: = 20 kN/m 3 H = 3 m q o = H = 60 kPa

B1 = 4 m B z

1

=45 = 0.80

B2 = 4 m B z

2 = 45

= 0.80

z = 5 m

Fig. 5.11 (p.237) I 0.43 p = 0.43 x 60 = 25.8kPa

4m

4m

4m 4m

Bowles Table 5.1 and DasTable 5.2, I = 0.17522


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PAGE 13

7. Average Vertical Stress Increase due to a RectangularlyLoaded Area

Average increase of stress over a depth H under the corner of arectangular foundation:

B

A

H L

Ia = f(m,n)m = B/Hn = L/Huse Das Fig. 5.7, p. 234

For the average depth between H 1 and H 2q o

H1 H2

Use the following:

p avg = avg = qo [H 2Ia(H2) - H 1Ia(H1) ]/(H2 - H 1)

(eq. 5.19, p.233 in Das)


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PAGE 14

Example: 8x8m footingH = 4m (H 1=0, H 2=4m)

Use 4x4x4 squares m = 1, n = 1

Das Fig. 5.7 (p.234) I a 0.225p avg = 4 x 0.225 x q o = 0.9 q o

0.9 q o is compared to 0.7q o (see previous example) which is thestress at depth of 4m (0.5B). The 0.9 q o reflects the averagestress between the bottom of the footing (q o) to the depth of 0.5B.

Figure 5.7 Griffiths Influence factor I a (Das p.234)


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PAGE 15

8. Influence Chart - Newmarks Solution (Bowles Figure 5.3)

Perform numerical integration of equation 5.1

Influence value = 1200

(# of segments)

each segment contributes the sameamount:

1. Draw the footing shape to a scalewhere z = length AB (2 cm = 20 mm)

2. The point under which we look forv, is placed at the center of thechart.

3. Count the units and partial unitscovered by the foundation

4. v = p = q o x m x I

where m = # of counted unitsq o = contact stress

I = influence factor = 1

200

= 0.005


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PAGE 16

Fig. 3.50 Influence chart for vertical stress z (Newmark, 1942)(All values of ) (Poulos and Davis, 1991)

z = 0.001N p where N = no. of blocks


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PAGE 17

Example

What is the additional vertical stress at a depth of 10 m underpoint A ?

1. z = 10 m scale 20 mm = 10 m

2. Draw building in scale with point A at the center

No. of elements - is (say) 76

v = p = 100 x 76 x 1200

= 38 kPa

9. Using Charts Describing Increase in Pressure

See figures from the Navy Design Manual, Bowles p.292 and Das 3 rd edition Fig 3.41 (notes pp. 12 & 13)Many charts exist for different specific cases like Das Fig. 5.11 (p.237)describing the load of an embankment (for extensive review see ElasticSolutions for Soil and Rock Mechanics by Poulus and Davis)

Most important to note:

1. What and where is the chart good for?e.g. under center or corner of footing?

2. When dealing with lateral stresses, what are the parameters used(mostly ) to find the lateral stress from the vertical stress

10m

5m

20m

AZ = 10m

qcontact = 100kPa

A

20mm

40mm

10mm


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PAGE 18

10. Simplified Relationship

Back of an envelope calculations

2 : 1 Method (text p.231) Bowles Figure 5.1,(p.286)

Das Fig. 5.5, (p.231)

v = P = Q B z L z( )( )+ +

Example:

What is the existing, additional, and total stress at the center ofthe loose sand under the center of the foundation ?

B=3mL=4m

t=19kN/m3

Loose Sand

t=17kN/m3

1m

1m

1m

1MN


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PAGE 19

v = (2 x 19) + (0.5 x 17) = 46.5 kPaUsing 2:1 method:v = 1000

3 15 4 15kN

( . )( . )+ + = 40 kPa q contact = 83.3 kPa

50.0

0qq

Total average stress at the middle of the loose sand t = 86.5 kPaUsing Fig. 3.41 of these notes (p.12):

z B

= 153. = 0.5

L B

= 43

= 1.33 pqo

0.75

p = 0.75 x 83.3 = 62.5 kPaThe difference between the two values is due to the fact that thestress calculated by the 2:1 method is the average stress at thedepth of 1.5m while the chart provides the stress at a point,under the center of the foundation.

This can be checked by examining the stresses under the cornerof the foundation.

m = 315.

= 2 n = 415.

= 2.67

Bowles Table 5.1 (p.294), Das Table 5.2 (p.228-229)I 0.23671 interpolated between

0.23614 0.23782n = 2.5 n = 3

p = 0.23671 x 83.3 = 19.71

Checking the average stress between the center and the corner:

= p pcorner center +2

= 62 5 19 712

. .+ = 41.1 kPa

the obtained value is very close to the stress calculated by the 2:1method that provided the average stress at the depth of 1.5m.(40kPa)


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PAGE 20

IMMEDIATE SETTLEMENT ANALYSIS(Bowles Sections 5.6-5.11, pp. 303-329)

(Das Sections 5.9-5.14, pp. 243-273)

1. General Elastic Relations

Different equations follow the principle of the analysis presentedon p. 8.For a uniform load (flexible foundation) on a surface of a deepelastic layer, the text presents the following detailed analysis:

( ) f ss

se I I E

BqS 2

0

1

= (Das eq. 5.33)

(Bowles eq. 5.16 & 5.16a)

qo = contact stressB = B =B for settlement under the corner

= B =B/2 for settlement under the centerE s , = soils modulus of elasticity and Poissons ratio

within zone of influence = factor depending on the settlement location

for settlement under the center;=4, m =L/B, n =H/(B/2)

for settlement under the corner;=1, m =L/B, n =H/B

Is = shape factor, I s=F 1+

121 F2

F1 & F 2 f(n & m ) use Tables 5.8 and 5.9,pp.248-251

If = depth factor, I f =f(D f /B, s , L/B), use Table 5.10(pp.252); I f =1 for D f =0

For a rigid footing, S e 0.93 S e (flexible footing)


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PAGE 21

2. Finding E s , : the Modulus of Elasticity and Poissons Ratio

For E s : direct evaluation from laboratory tests (triaxial) or usegeneral values and/or empirical correlation. For general values,use Table 5.8 from Das (6 th ed., 2007) and see Bowles section 5.8and Table 5.6.

For (Poissons Ratio): Cohesive SoilsSaturated Clays V = 0, = = 0.5Other Soils, usually = 0.3 to 0.4

Empirical Relations of Modulus of Elasticity

60 N p

E

a

s = = 5 to 15 (Das eq. 2.29)

(5sands with fine s, 10Clean N.C. sand, 15clean O.C. sand)

Navy Design Manual (Use field values): E s /N(E in tsf)

Silts, sandy silts, slightly cohesive silt-sand mixtures 4 Clean, fine to medium, sands & slightly silty sands 7 Coarse sands & sands with little gravel 10 Sandy gravels with gravel 12E s = 2 to 3.5q c (cone resistance) CPT General Value

Table 5.8


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PAGE 22

(Some correlation suggest 2.5 for equidimensional foundationsand 3.5 for a strip foundation.)

General range for clays:N.C. Clays Es = 250c u to 500c u O.C. Clays Es = 750c u to 1000c u

See Das Table 5.7 for E s = C u and = f(PI, OCR)

3. Improved Equation for Elastic Settlement (Mayne and Poulos,1999)

Considering: foundation rigidity, embedment depth, increase

of E s with depth, location of rigid layers withinthe zone of influence.

The settlement below the center of the foundation:

( )20

0 1 s E F Ge

e

E

I I I BqS = (Das eq. 5.46)

B e = BL4 or for a circular foundation B e = B

E s = E 0 + kz being considered through I G IG = f(B, H/B e), = E 0/kBe


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PAGE 23

Das Figure 5.18 (p.255)Variation of I G with

Effect of foundation rigidity is being considered through I F

IF = f(k f ) flexibility factor3

0

2

2

+=

ee

f F B

t

k B

E

E k

k needs to be estimated

Das Figure 5.19 (p.256)Variation of rigiditycorrection factor I F withflexibility factor k F [Eq.(5.47)]

E f = modulus of foundation material

t = thickness of foundation


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PAGE 24

Effect of embedment is being considered through I E;

IE=f(s , D f , B e)

Das Fig. 5.20 (p.256)Variation of embedmentcorrection factor I E with D f /Be [Eq.(5.48)]Note: Figure in the text shows I F

instead of I E.

4. Immediate (elastic) Settlement of Sandy Soil The StrainInfluence Factor (Schmertmann and Hartman, 1978)(Das Section 5.12, pp. 258-263)

The surface settlement

(i) s i = z z

dz=

0

From the theory of elasticity, the distribution of vertical strain z under a linear elastic half space subjected to a uniform distributedload over an area:

(ii) z =q E Iz

q = the contact loadE = modulus of elasticity - the elastic mediumIz = strain influence factor = f ( , point of interest)


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PAGE 25

From stress distribution (see Figure 3.41, p.12 of notes):influence of a square footing 2Binfluence of a strip footing 4B

(both forq

qcontact 10%)

From FEM and test results. Theinfluence factor I z:

q = q q 0

q q 0

vp

0 0.1 0.2 0.3 0.4 0.5

Iz0

0.5B

B

1.5B

2B

2.5B

3B

3.5B

4B

4.5B

ZBelow Footing

equidimensionalfooting

(square, circle)

Izp

strip footing(L/B 10)

B


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PAGE 26

substituting the above into Eq. (i).

For square s i = q I E dz z B

0

2

Approximating the integral by summation and using the abovesimplified vs. D/B relations we get to equation 5.49 of Das.

S e = C 1C 2q I E

z zsi

ni

=

1

q = contact stress (net stress = stress at found q 0)

c1 = 1 - 0.5 v oq'

vo is calculated at the foundation depthIz = strain influence factor from the distribution

E s = modulus in the middle of the layer

C 2 - (use 1.0) or C 2 = 1 + 0.2 log (10t)

Creep correction factor t = elapsed time in yearse.g. t = 5 years, C 2 = 1.34

5. The Preferable Iz Distribution for the Strain Influence Factor

The distribution of I z provided in p.27 of the notes is actually asimplified version proposed by Das (Figure 5.21, p.259). Themore complete version of I z distribution recommended by

Schmertmann et al. (1978) is

vp zp

q I

+= 1.05.0

Where vp is the effective vertical stress at the depth of I zp (i.e.0.5B and 1B below the foundation for axisymmetric and stripfootings, respectively).


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PAGE 27

6. Immediate Settlement in Sandy Soils Using Burland andBurbridges (1985) Method(Das Section 5.13, pp.265-267)

( )( )

20.7

1 2 31.25

0.25e

R R a

LS B q B L B B p

B

= +

(Das eq.5.70)

1. Determine N SPT with depth (Das eq. 5.67, 5.68)2. Determine the depth of stress influence - z (Das eq. 5.69)3. Determine 1, 2, 3 for NC or OC sand (Das p.266)

7. Case History - Immediate Settlement in Sand A rectangular foundation for a bridge pier is of the dimensionsL=23m and B=2.6m, supported by a granular soil deposit. Forsimplicity it can be assumed that L/B 10 and, hence, it is astrip footing. Provided q c with depth (next page) Loading q = 178.54kPa, q = 31.39kPa (at D f =2m)

Find the settlement of the foundation(a-1) The Strain Influence Factor (as in the text)

C 1 = 1 0.5qq

q

= 1 0.5

39.3154.17839.31

= 0.893

C 2 = 0.2 log

1.0t t = 5years C 2 = 1.34

t = 10years C 2 = 1.40

Using the attached Table for the calculation of z (see next page)S e = C 1C 2 ( q -q)

Es Iz z = 0.893 1.34 (178.54 31.39) 18.95 10 -5m

S e = 0.03336m 33mm

For t = 10years S e = 34.5mm


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PAGE 28

For the calculation of the strain in the individual layer and itsintegration over the entire zone of influence, follow the influencechart (notes p.27) and the figure and calculation table below.

Example:z = 0 Iz = 0.2z = 1B = 2.6m Iz = 0.5z1= 0.5m Iz = 0.2 +

2.60.2-0.5 x 0.5 = 0.2577

note: sublayer 1 has a thickness of 1mand we calculate the influence factor atthe center of the layer.

Variation of I z and q c below the foundation

z=0.0mz 1=0.5m

1m

z=2.6m

Iz=0.2Iz=0.2577

Iz=0.5

Layer I


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PAGE 29

(a-2) The Strain Influence Factor (Schmertmann et al., 1978)

vp

zp

q I

+= 1.05.0

q = 31.39kPa t = 15.70kN/m 3 q = 178.54 31.39 = 147.15

vp @ 1B below the foundation = 31.39 + 2.6 (15.70) = 72.20kPa

64.014.050.02.7215.147

1.05.0 =+=+= zp I

This change will affect the table on p. 30 in the following way:

Layer I z (Iz/E z) z[(m 2/kN)x10 -5]1 0.285 3.312 0.505 6.723 0.624 2.084 0.587 1.225 0.525 5.08

6 0.464 0.797 0.382 1.178 0.279 1.329 0.197 0.56

10 0.078 1.06 23.31x10 -5

( )

= z E

I qqC C S

s

ze 21

Using the I zp S e = 40.6mmfor t = 10 years, S e = 42.4mm

Z=10.4m

Z=2.6m

Z=0.0m Iz=0.2

Iz=0.2+0.169xZ

Izp =0.64

Iz=0.082 x (10.4 Z)


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PAGE 30

Using the previously presented elastic solutions for comparison:

(b) The elastic settlement analysis presented in Das sect. 5.10

( ) f sss

e I I E BqS

2

0

1

= (Das eq.5.33)

B = 2.6/2 = 1.3m for centerB = 2.6m for cornerq0 = 178.54kPa (stress applied to the foundation)

Strip footing, zone of influence 4B = 10.4mFrom the problem figure q c 4000kPa. Note the upper

area is most important and the high resistance zonebetween depths 5 to 6.3m is deeper than 2B, so choosing4,000kPa is on the safe side. Can also use weightedaverage (Das Eq. 5.34)

qc 4,000kPa, general, use notes p.23-24:E s = 2.5q c = 104,000kPa, matching the recommendation

for a square footings 0.3 (the material dense)

For settlement under the center:

=4, m =L/B=23/2.6 = 8.85, n =H/(B/2)= (>30m)/(2.6/2) > 23

Das Table 5.8m = 9 n = 12 F 1 = 0.828 F 2 = 0.095m = 9 n = 100 F 1 = 1.182 F 2 = 0.014

the difference between the values of m =8 or m =9 isnegligible so using m =9 is ok. For n one can interpolate.For accurate values one can follow Das Eqs. 5.34 to 5.39.

interpolated values for n =23 F 1=0.872, F 2=0.085


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PAGE 31

for exact calculations:

( )( ) 921.0085.03.01

3.021

872.01

2121

+=

+= F F I s

s

s

As the sand layer extends deep below the footing H/B >>and F 2 is quite negligible.

For settlement under corner:

=1, m =L/B= 8.85, n =H/(B)= (>30m)/2.6 > 11.5

Das Tables 5.8 & 5.9m = 9 n = 12 F 1 = 0.828 F 2 = 0.095

( )( ) 882.0095.03.013.021

828.0 +=s I

Df /B = 2/2.6 = 0.70, L/B = 23/2.6 = 8.85

Das Table 5.10 s = 0.3, B/L = 0.2, D f /B = 0.6 If = 0.85,

Settlement under the center (B = B/2, = 4)

( )( ) ( ) ( )( )2

1 0.3178.54 4 1.15 0.921 0.85 0.0585 58mm10,000e

S m= = =


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PAGE 32

Settlement under the corner (B = B, = 1)

( )( ) ( ) ( )( )2

1 0.3178.54 1 2.3 0.882 0.85 0.0280 28mm

10,000eS m

= = =

Average Settlement = 43mm

Using Das eq. 5.41 settlement for flexible footing =(0.93)(43)

= 40mm

(c) The elastic settlement analysis presented in Das sect. 5.11:

( )20

0 1 s E F Ge

e E

I I I BqS = (Das eq. 5.46)

( )( )m

BL Be 73.8

236.244 ===

ekB

E 0=

Using the given figure of q c with depth, an approximationof q c with depth can be made such that q c=q 0+z(q/z)where q 0 2200kPa, q/z 6000/8 = 750kPa/m

Using the ratio of E s /q c = 2.5 used before, this relationshiptranslates to E 0 = 5500kPa and k = E/z = 1875kPa/m

( )( ) 336.073.818755500

==

H/B e = >10/8.73 > 1.15 no indication for a rigid layerand actually a less dense layer starts at 9m (q c 4000kPa)


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PAGE 33

Das Figure 5.18, 0.34 IG 0.35 (note; H/B e hasalmost no effect in that zone when greater than 1.0)

3

0 2

+=

ee

f

F B

zt

k B E

E k

Using E f = 15x10 6kPa, t = 0.5m

65.173.8

5.02

1875273.8

5500

101536

=

+= x xk F

80.065.1106.4

14106.4

14

=+=+= x xk x

I F

F

( )( )6.15.31

1 4.022.1 +=

f e E

D Be I

s

( )( )95.0

18.201

16.1273.85.3

11 4.03.022.1 ==+

= x E e I

( ) 69mm=== mxxxxS e 0686.03.015500

95.080.035.073.854.178 2

(d) Burland and Burbridges Method presented in Das section5.13, p.265

1. Using q c 4,000kPa = 41.8tsf and as E s 7N and E s 2q c we can also say that: N q c(tsf)/3.5 N 12

2. The variation of q c with depth suggests increase of q c toa depth of 6.5m (2.5B) and then decrease. We can


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PAGE 34

assume that equation 5.69 is valid as the distance tothe soft layer (z ) is beyond 2B.

75.0

4.1

=

R R B B B z

3. Elastic Settlement (Das eq.5.70)

2

0.7

1 2 3

1.25

0.25e R

R a

L B q BS B

L B p

B

=

+

Assuming N.C. Sand:

1 = 0.14, ( )049.0

12

71.14.12

== 3 = 1

( )( )( )

+= 10054.178

3.0

6.2

6.22325.0

6.223

25.1

1049.014.03.0

2

eS

( )( ) 60mm==

= mS e 060.07854.167.81.95.12

00206.02

BR = 0.3mB = 2.6m


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PAGE 35

(e) Summary and Conclusions

Method Case Settl ement (mm)Strain InfluenceDas sect. 5.12, 5 years

Iz (Das) 33Iz (Schmertmann et al.) 41

ElasticDas sect. 5.10

Center 58Corner 28

Average 40ElasticDas sect. 5.11 69

B & BDas sect. 5.13 60

The elastic solution (section 5.10), the improved equation(section 5.11) and B&B (section 5.13) resulted with a similarsettlement analysis under the center of the footing (57, 69,and 60mm respectively). This settlement is about twice thatof the strain influence factor method as presented by Das.

Averaging the elastic solution method result for the centerand corner and evaluating flexible foundation resulted witha settlement similar to the strain influence factor as proposed

by Schmertmann (39 vs. 41mm). The improved methodconsiders the foundation stiffness.

The elastic solutions of sections 5.10 and 5.11 are quitecomplex and take into considerations many factorscompared to common past elastic methods.

The major shortcoming of all the settlement analyses is theaccuracy of the soils parameters, in particular the soilsmodulus and its variation with depth. As such, many of the

refined factors (e.g. for the elastic solutions of sections 5.10and 5.11) are of limited contribution in light of the soilparameters accuracy.

What to use?(1) From a study conducted at UML Geotechnical

Engineering Research Lab, the strain influence method


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PAGE 36

using I zp recommended by Schmertmann provided thebest results with the mean ratio of load measured toload calculated for a given settlement being about 1.28 0.77 (1 S.D.) for 231 settlement measurements on 53foundations.

(2) Check as many methods as possible, make sure toexamine the simple elastic method.

(3) Check ranges of solutions based on the possible rangeof the parameters (e.g. E 0).

For example, in choosing q c we could examine the variationbetween 3,500 to 6,000 and then the variation in the relationshipbetween q

c and E

s between 2 to 3.5. The results would be:

E smin = 2 x 3,500 = 7,000kPaE smax = 3.5 x 6,000 = 21,000kPa

As S e of equation 5.33 is directly inverse to E s , this range willresult with:

S emin = 27mm, S emax = 81mm (compared to 57mm)

8. Immediate (Elastic) Settlement of Foundations on SaturatedClays: (Junbu et al., 1956), Das section 5.9, p.243

= s = 0.5 Flexible Footings

Se = A 1 A2 s

0

EBq (Das eq.5.30)

A1 = Shape factor and finite layer - A 1 = f(H/B, L/B) A2 = Depth factor - A 2 = f(D f /B)

Note: H/B >>> deep layer the values become asymptotice.g. for L = B (square) and H/B 10 A 1 0.9


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PAGE 37

Das Figure 5.14 Values of A 1 and A 2 for elastic settlement calculation Eq. (5.30) (after Christian and Carrier, 1978)


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PAGE 38

CONSOLIDATION SETTLEMENT - LONG TERM SETTLEMENTConsolidation General, Bowles Sect. 2.10 (pp.54-66) and Das Sect. 1.13 (pp.32-37)

Consolidation Settlement for Foundations, Das Sects. 5.155.20 (pp.273-285)

1. Principle and Analogy

model t = 0 + t = t 1 t =

P P P

P spring = 0 P spring = 0 P spring = H x K spring P spring = Pu = u 0 = 0 u i = P

A u =

P P

Aspring u = u 0 = 0

We relate only to changes, i.e. the initial condition of the stress inthe soil (force in the spring) and the water are being consideredas zero. The water pressure before the loading and at the finalcondition after the completion of the dissipation process ishydrostatic and is taken as zero, (u 0 = u hydrostatic = 0). The force inthe spring before the loading is equal to the weight of the piston(effective stresses in the soil) and is also considered as zero for

the process, P spring = P o = effective stress before loading= P at rest .The initial condition of the process is full load in the water andzero load in the soil (spring), at the end of the process there iszero load in the water and full load in the soil.

H=H o

H=S 1

Piston

Water

Spring

Cylinder

H=0H=S 1

incompressiblewater

S final


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PAGE 39

Analogy Summary

model soilwater waterspring soil skeleton/effective stressespiston foundationhole size permability force P load on the foundation or at the relevant soil

layer due to the foundation

1

P spring /Load U i / U o

010 - log t 10 +

2. Final Settlement Analysis

(a) Principle of Analysis

e = V V

v

s

= W W w

s

initial soil volume = V o = 1 + e o

final soil volume = V f = 1+e o-e

P spring /PU/U i

weight - volume relationssaturated clay

Vv=e 0 W G s=e w

Vs=1 S G s1w


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PAGE 40

V = V o - V f = e

As area A = Constant:Vo = H o x A and V f = H f x A

V = V o-Vf = A(H o-H f )=A x HH = V

A

for 1-D (note, we do not consider 3-D effects and assume porepressure migration and volume change in one direction only).

v = H H o

=V AV A

o = V

V o, substituting for V, e relations

v = V V o

= eV o

= eeo1 +

H = v x H o = eeo1 +

x H o

Calculating e

We need to know:

(i) Consolidation parameters c c, c r at a representative point(s) ofthe layer, based on odometer tests on undisturbed samples.

(ii) The additional stress at the same point(s) of the layer, basedon elastic analysis.


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PAGE 41

(b) Consolidation Test (1-D Test)

1. Oedometer = Consolidometer

2. Test Results

Das Fig. 1.15a Schematic Diagram ofconsolidation test arrangement (p.33)

a) final settlement with b) settlement with time

load after 24 hours under a certain load

e = V V

v

s e d = W V s (V


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PAGE 42

(c) Obtaining Parameters from Test Results

analysis of e-log p results .

1 st Stage - Casagrandes procedure to find max. past pressure.(see Das Figs. 1.15 to 1.17, pp.33 to 37, respectively)(see Bowles Figs. 2.16a and b, pp.74 and 75, respectively)

1. find the max. curvature.- use a constant distance and look for the max. normal.- draw tangent to the curve at that point.

2. draw horizontal line through that point and divide the angle.

3. extend (if doesnt exist) the e-log p line to e = 0.42eo4. extend the tangent to the curve and find its point of intersectionwith the bisector of stage 2. P c = max. past pressure.

Das Figure 1.15 (b) e-log curve for a soft clay from East St. Louis, Illinois (note: atthe end of consolidation, =


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PAGE 43

2nd Stage - Reconstructing the full e-log p (undisturbed) curve(Schmertmanns Method; See Das Figs. 1.16 & 1.17, pp.35 & 37,and Bowles Figure 2.17, p.76)

OCR = p p

c

o

''

1. find the point e o, p o e o = n x G s p o = z

2. find the avg. recompressioncurve and pass a parallel linethrough point 1.

3. find point p c & e.4. connect the above point to

e = 0.42e o

Compression index (or ratio)

C c = e p

plog2

1

=e e

p pc

1 2

2

log

Recompression index (or ratio)

C r = e p

pc

olog

=e e

p p

o

c

o

1

log

See Das p.35-37 and BowlesTable 2.5 for C s & C c values. natural clay C c 0.09(LL -10)

where LL is in (%) (eq.1.50) B.B.C C c = 0.35 C s = 0.07

e o

e 1

e 2

P o P c P 2

C r

C c

1

1


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PAGE 44

(d) Final Settlement Analysis (Bowles p. 83-84)

e = C c logo

o

+ '

e = 1

''log

e

C o

cs

+

2

''log

e

C c

oc

+

(for o + > c)Solution:1. Subdivide layers according to stratification and stress variation2. In the center of each layer calculate vo(o) and 3. Calculate for each layer e i

H = =n

i 1 oi

iee H +

1

replace p c by vmax and p o by vo The average increase of the pressure on a layer ( = av) can beapproximated using Das eq. 5.84 (p.274)

av = 16

(t + 4 m + b)

top middle bottom

f =o+

o = c

v

o f (case 2) case 2


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PAGE 45

Skempton - Bjerrum Modification for Consolidation SettlementDas Section 5.16 p. 275 - 279

The developed equations are based on 1-D consolidation in which the

increase of pore pressure = increase of stresses due to the applied load.Practically we dont have 1-D loading in most cases and hence differenthorizontal and vertical stresses.

u = c + A[1-c]

A = Skemptons pore pressure parameter1

For example: Triaxial Test N.C. OCR = 1 0.5


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PAGE 46

From Das, Figure 5.31 and Table 5.14

Figure 5.31 Settlement ratios for circular (K cir ) and continuous(Kstr ) foundations

Table 5.14 Variation of K cr(OC) with OCR and B/H c

OCRKcr(OC)

B/H c = 4.0 B/H c = 1.0 B/H c = 0.21 1 1 12 0.986 0.957 0.9293 0.972 0.914 0.8424 0.964 0.871 0.7715 0.950 0.829 0.7076 0.943 0.800 0.6437 0.929 0.757 0.5868 0.914 0.729 0.5299 0.900 0.700 0.493

10 0.886 0.671 0.45711 0.871 0.643 0.42912 0.864 0.629 0.41413 0.857 0.614 0.40014 0.850 0.607 0.38615 0.843 0.600 0.37116 0.843 0.600 0.357


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PAGE 47

(e) EXAMPLE - Final Consol idation Settlement

Calculate the final settlement of the footing shown in the figurebelow. Note, OCR = 2 for all depths. Give the final settlementwith and without Skempton & Bjerrum Modification

P = 1MN

4m x 4m

sat = 20 kN/m 3 C c = 0.20C r = 0.05 3B = 12m

w 10 kN/m 3 OCR = 2G s = 2.65

n = 37.7%(note: assume 1-D consolidation)


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PAGE 48

P=1MN, B=4mx4m, q 0 = 1000/16=62.5kPa

z(m) z/B q/q o q

P o(kPa)

P c(kPa)

P o + q=P f

ee

eo1 + H

Layer I 1 (0.25) + 0.90 56.3 10 20 66.3 0.1188 0.1188---------- 2 ----------Layer II 3 (0.75) + 0.50 31.3 30 60 61.3 0.0165 0.0165---------- 4 ----------

Layer III 6 (1.50) + 0.16 10.0 60 120 70.0 0.003 0.006

---------- 8 ----------

Layer IV 10 (2.5) + 0.07 4.4 100 200 104.4 0.001 0.002

---------- 12 ----------

= 0.1433m

1) From Figure 3.41, Notes p. 12 influence depth {10% 2B, 5% 3B} = 12 m.

2) Subdivide the influence zone into 4 sublayers 2 of 2m in the upper zone(major stress concentration) and 2 of 4 m below.

3) Calculate for the center of each layer: q, P o, P c, P f

4) e o = nG s = 1.0

5) Calculate e for each layer:

e 1 = c r log 2010 + C c log 2066 = 0.1188

e 2 = c r log 6030 + C c log6160

= 0.0165

e 3 = c r log 6070 = 0.003

e 4 = c r log 100104 = 0.001

e

log p

c r

cc

P o P c


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PAGE 49

For the evaluation of the increased stress, use general Charts ofStress distribution beneath a rectangular and strip footings

(a) Use Figure 3.41 (p.12 of notes)

oqP vs. B z under the center of a rectangular footing(use B L = 1)

Stress Increase in a Soil Mass Caused by Foundation Load

Das Principle of FoundationEngineering, 3 rd Edition

Figure 3.41 Increase ofstress under the center of aflexible loaded rectangulararea


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PAGE 50

6) The final settlement, not using the table:

H = Hi eieo1+ = 2m x 11

1188.0+ +2m x 11

0165.0+ + 4m x 11

003.0+

+4 x 00011 1.+ = 0.14m = 14cm

Skempton - Bjerrum ModificationUse Das Figure 5.31, p. 276

A 0.4 Hc/B >>> 2 Settlement ratio < 0.57

Sc < 0.57 x 14 = 8cm Sc < 8cm

Check so lution when using Das equation 5.84 and the averagestress increase:

av = 16

(t + 4 m + b)

Like before, assume a layer of 3B = 12m

t = q o =16

kN1000 = 62.5 kPa

m ( @6m = 1.5B) 0.16q o

b ( @12m = 3B) 0.04q o

av = 1/6 (1 +4 x 0.16 + 0.04)q o = 1/6 x 1.68 x 62.5= 0.28 x 62.5= 17.5 kPa

av = 17.5 kPa

Z = 6m, Z/B = 1.5,oq q = 0.28 q = 17.5 kPa

note: upper 2m contributes 85%of the total settlement


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PAGE 51

P o ' = 60kPa, P c' = 120kPa P f ' =77.5kPa

e = C r log60

5.77 = 0.05 x 0.111 = 0.0056

oe1e

+

x H =11

0056.0+

x12m = 0.033m = 3.33 cm

Why is there so much difference?

As OCR does not change with depth, the influence of the additionalstresses decrease very rapidly and hence the concept of the "averagepoint" layer does not work well in this case. The additional stresses at

the representative point remain below the maximum past pressureand hence large strains do not develop. The use of equation 5.84 ismore effective with a layer of a final thickness.

(f) Terzaghis 1-D Consol idation Equation

Terzaghi used the known diffusion theory (e.g. heat flow) andapplied it to consolidation.

Assumptions:

6. The soil is homogenous and fully saturated.7. The solid and the water are incompressible.8. Darcys Law governs the flow of water out of the pores.9. Drainage and compression are one dimensional.10. The strains are calculated using the small strain theory,

i.e. load increments produces small strains.


56/134PAGE 52


57/134PAGE 53


58/134PAGE 54


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PAGE 56

3. Time Rate Consol idation (Das Sects. 1.15 & 1.16, pp. 38-47)

(a) Outline of Analysis

The consolidation equation is based on homogeneous completelysaturated clay-water system where the compressibility of the water and soilgrains is negligible and the flow is in one direction only, the direction ofcompression.

Utilizing Darcis Law and a mass conservation equation rate of outflow -rate of inflow = rate of volume change; leads to a second order differentialequation

C u

zv

e

2

2 =

t

ue

-t

v

u e = excess pore pressurev = vertical effective stress

Practically, we use either numerical solution or the following tworelationships related to two types of problems:

Problem 1 : Time and Average Consolidation

Equation 1) t i = T H C v dr

v

2

ti - The time for which we want to find the average consolidationsettlement. See Fig. 1.21 (p.42) in Das, and the tables on p.42-43 in the notes.

Tv = time factor T = f (U avg )(L) H dr = the layer thickness of drainage path.

Lt

C v = coeff. of consolidation =

k mw v

m v = coeff. of volume comp. =a

e

v

o1 +

a v = coeff. of compression =

e p


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PAGE 57

Equation 2) Average Consolidation

Uavg = S t/S = Settlement of the layer at time tFinal settlement due to primary consolidation

For initial constant pore pressure with depth

Problem 2: Time related to a consolidation at a specific point

Equation 3) Degree of consolidation at a point U z,t = 1 -uu

z t

z o

,

,

Pore pressure at a point (distance z, time t) U z,t = w x hw z,tFor initial linear distribution of ui the following distribution of porepressures with depths and time is provided.

dr H

H

Das Fig. 1.20 (c)Plot of u/ u o withTv and H/H c (p.39)


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PAGE 58


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PAGE 59


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PAGE 60

(b) Obtaining Parameters from the Analysis of e-log tConsolidation Test Results

Time, t (log scale)

1. find d o - 0 consolidation time t = 0set time t 1, t 2 = 4t 1, t 3 = 4t 2 find corresponding d 1, d 2, d 3 offset d 1 - d 2 above d 1 and d 2 - d 3 above d 2

2. find d 100 - 100% consolidationreferring to primary consolidation (not secondary).

3. find d 50 and the associated t 50

Coefficient of Consolidation

Cv =t

H T i

i dr 2

T i = time factor (equation 1.75, p.41 of Das)

Hdr = drainage path = sampleti = time for i% consolidation

Using 50% consolidation and case I

C v =0197 2

50

. H t

dr T for Uavg = 50%

And linear initial distribution

do d1 d2

d50

d100

t50 t100 to

I n c r e a s

i n g

d t1 t2

t3

1

12

2

d 3


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PAGE 61


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PAGE 62

For simplicity we can write u(z iH, t j) = u i+1,j

t u

z

uC v

=

2

2

Substitute

t

uu

z

uuuC

ji ji ji ji jiv

=

+ ++ ,1,

2

,1,,1 2

which can easily by solved by a computer. For simplicity we canrewrite the above equation as:

u i+1,j = u i+1,j + (1-2 )u i,j + u i-1,j

for which:

( )5.0

2

=

z

t C v

for = 0.5 we get: ( ) ji ji ji uuu ,1,11, 21

++ +=

this form allows for hand calculationse.g. for i = 2, j = 3 u 2,4 = (u 1,3 + u 3,3 )


67/134

PAGE 63


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PAGE 64

4. Consol idation Example

The construction of a new runway in Logan Airport requires thepre-loading of the runway with approximately 0.3 tsf. Thesimplified geometry of the problem is as outlined below, with therunway length being 1 mile.

B = 50 ft

qo = 600 psf

10 ft granular fill sat =115 pcf 5 ft

sat = 110 pcfN.C. BBC C c=0.35

C s=0.07

A f = 0.8930 ft C v=0.05 cm 2/min

e o=1.1

Granular Glacial Till

10ft

z/B=0.2 z=10

z/B=0.5 z=25

z/B=0.8 z=40


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PAGE 65

1) Calculate the final settlement.

Assuming a strip footing and checking the stress distributionunder the center of the footing using Fig. 3.41 (p. 12 of the notes)

Location z (ft) z/B q /q o q (psf)Top of Clay 10 0.2 0.98 588

Middle of Clay 25 0.5 0.82 492

Bottom of Clay 40 0.8 0.60 360

Using the average methodav = 1

6(t + 4 m + b) = 1/6 (588 + 4x492 + 360) = 486 psf

The average number agrees well with the additional stress foundfor the center of the layer, (492psf).

Assuming that the center of the layer represents the entire layer

for a uniform stress distribution. At 25 ft:po = v = 115 x 5 + (115 62.4) x 5 + (110 62.4) x 15

= 575 + 263 + 714 = 1552psf

p f = p o + q = 1552 + 486 = 2038 psf

e = C c log (p f /po) = 0.35 log (2038/1552) = 0.0414

0 . 0 4 1 43 0 1 2 7 . 1

1 1 1 . 1oe

s H H f t i n c h i n c he

= = = = + +


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PAGE 66

2) Assuming that the excess pore water pressure is uniformwith depth and equal to the pressure at the representativepoint, find:

(a) The consolidation settlement after 1 year

Find the time factor:

v

vi C

T t

2dr H= 2

dr Hvi

v

C t T =

C v = 0.05 cm 2/min = 0.00775 in 2/min

Hdr = H/2 = 30 ft / 2 = 15 ft

Tv = 12 x 30 x 24 x 60 x 0.00775 / (15 x 12) 2 = 0.124

Find the average consolidation for the time factor.

For a uniform distribution you can use Das equation 1.74 (p.41) orthe chart or tables provided in the notes.

Using the table in the class notes (p.53 & p.55)

T = 0.125 Case I - uniform or linear initial excess pore pressuredistribution. U = 39.89 % = 40%

= S S U t

avg S t = U avg x S

S t = 0.40 x 7.1 = 2.84 inch


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PAGE 67

(b) What is the pore pressure 10 ft. above the till 1 year afterthe loading?

From above; t = 12 months, T = 0.124

2 Hd r = 30 ft

z / H dr = 20/15 = 1.33 (z is measured from the top of the claylayer)

Using the isochrones with T = 0.124 andz/H = 1.33

We get u e / u i 0.8

u e = 0.8 x 486 = 389 psf

(c) What will be the height of a water column in a piezometerlocated 10 ft above the till: (i) immediately after loadingand (ii) one year after the loading

(i) u i = 486 psf h i = u/ w = 486/62.4 = 7.79ft.

(ii) u e = 389 psf h = u/ w = 389 / 62.4 = 6.20 ft

The water level will be 2.79 ft. above ground and 1.2 ft above theground level immediately after loading and one year after theloading, respectively.


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PAGE 68


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THE TWEN TY SEVENTH TERZAGHI LECTURE

Presented at the American Society of Civil Engineers

1991 Annual Convention

October 22 1991

Journal of Geotechnical Engineering, ASCE, Vol.119, No.9Sept. 1993


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PAGE 70


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IN T R O D U C T IO N T O TH E T W E N T Y S E V E N T HT E R Z A G H I L E C T U R E

By Clyde N. Baker Jr.

Dr. J ames Michae l Duncan w i l l f e e l r i gh t a t home p re sen t i ng t he 27 thTe rzagh i le c tu r e he re t oday. H e a t t en ded h igh s choo l i n Eus t i s , F lo r idawh ich is app rox im a te ly 40 mi no r th o f Or l and o . O ne o f t he h igh li ght s oM ike 's h igh s choo l c a r ee r was p lay ing foo tba l l , and he was t e am cap t a in ih is sen io r yea r. Un fo r tun a t e ly, t ha t t e a m had t he wor s t r e co rd i n t he h i s t o rof the scho ol , and los t one gam e by a score o f 67 to 6 . M ike d id a l it t lbe t t e r a f t e r h igh s choo l . He a t t ended Georg i a Tech a s a co -op s tuden tgradua t ing in 1959 wi th h i s B .S .C.E . His subsequent spec ia l i za t ion in somechan i c s occu r r ed acc iden t a l l y. He r e s igned f rom h i s j ob a s an eng ineein Ta m pa w hen h e was a sked by a supe r io r t o f a ls ify som e t ime shee t s . T hnex t day, he r ece ived a phone ca l l f r om a f r i end who sa id t he r e was a

research ass i s tan tsh ip ava i lab le in so il m echan ics a t G eo rg ia T ec h i f hwan ted t o go back fo r h i s mas t e r ' s deg ree . Mike r e sponded t ha t he d idn 'rea l ly l ike so il m echanics , b u t s ince he had a wi fe and da ug hte r to supp or tand i t was be t te r than s ta rv ing to dea th , he 'd t ake i t . The res t i s h i s to ry.

M ike go t h is M.S .C .E . a t Geo rg i a Tech i n 1962, and w orke d b r i e f ly i nthe So i l s D iv i s ion o f t he Wa te rways Expe r imen t S t a t i on i n Vicksbu rg onh is way t o t he U n ive r s i t y o f Ca l i fo rn ia a t B e rke l ey , w he re he o b t a ine d h iPh .D . deg ree un de r H a r ry S eed in 1965. H e t augh t a t B e rke l ey un t il 198be fo re mov ing t o Vi rg in i a Po ly t echn i c In s t i t u t e and S t a t e Un ive r s i t y i nB lacksbu rg , Vi rg in i a , whe re he now ho lds t he t i t l e o f Un ive r s i t y D i s t i n

gu i shed P ro fe s so r i n t he Depa r tmen t o f C iv i l Eng inee r ing .Th roug hou t h is 30 yea r ca r ee r, M ike ha s bee n an ou t s t and ing r e sea rche r

t eache r, and w or ldwide l e c tu r e r. H e has r ece ived e igh t awards fo r te ach inexce l lence , s even aw ards fo r p ro fe s s iona l a ch i evem en t , and s ix awards for e sea rch and pub l i ca t i ons , i nc lud ing t he We l l i ng ton P r i ze , t he Wa l t e r HH u b e r R e s e a r c h P r i z e , t h e C o l l i n g w o o d P r i z e , a n d t h e T h o m a s A . M i dd l e b r o o k s a w a r d t w i c e f r o m A S C E . To m o r r o w, h e w i l l b e r e c e i v i n g t h eASCE S ta t e -o f - t he -Ar t C iv i l Eng inee r ing Award fo r 1991 .

Tw o them es a ppe a r cons i s t en t l y i n hi s m ore t han 180 pub l i ca ti ons andresearch repor t s : p rac t ica l app l ica t ions o f numer ica l ana lyses , and inves tga t ion o f soi l p rope r t i e s and behav io r. Th ese two the m es w i ll be ev iden t iM ike 's Te rzagh i l e c tu r e on t he L im i t a t i ons o f Co nven t iona l Ana lys is oCon so l ida ti on Se t t l em en t . T he ba s is fo r t he t a lk com es f rom h i s ana ly s io f ex t ens ive s e t t l emen t r eco rds a t Bay Fa rm I s l and i n San F ranc i s co Bayand a t t he Kansa i I n t e rna t i ona l A i rpo r t p ro j ec t i n J apan .

Mike ' s w i f e , Ann , t he i r ch i l d r en Mary, Susan , and John , and h i s s i s t eSa ll y a r e he r e w i th u s t od ay t o en j oy t he 27 th Te rzag h i l e c tu r e . I t is w i thon o r and g rea t p l ea su re , t ha t I p r e sen t t o you Dr. J ames Michae l Du ncan


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L I M I T A T I O N S O F C O N V E N T I O N A L A N A L Y S I S O F

C O N S O L I D A T I O N S E T T L E M E N T

By J . M ichael Duncan, ~ Fellow, ASC E

The T wenty-Seventh Karl Terzaghi Lecture)

ABSTRACT:Consolidation settlements are often large and potentially damagingto structures. Estimating their m agnitudes, and the rates at w hich they will occur,plays an im portant part in m any civil engineering projects. A t B ay Farm Island inSan Francisco Bay, and Kansai International A irp ort in Japan, settlemen t mag-nitudes and settlement rates were of great importance for design. In these andsimilar case s it is important to understand what factors control the accuracy withwhich settlemen t magnitudes and settlement rates can be estimated. Accurate pre-dictions of settlement mag nitudes require accurate evaluations of clay compressi-bility and preconsolidation pressure. Accurate predictions of settlement rates re-quire imp roved methods o f anticipating whether em bedded sand strata will or willnot provide internal drainage; use o f computer an alyses to take into account im-portant factors such as variations in c, w ithin clay layers, nonlinear stress-strain

behavior, and nonuniform strain profile effects; and research to develop an im-proved m odel of clay com pressibility that includes the effects of strain rate.

I N T R O D U C T I O N

T h e w r i t e r a p p r e c i a t e s v e r y m u c h t h e i n v i t a t i o n t o p r e s e n t t h i s l e c t un a m e d i n h o n o r o f K a r l Te r za g h i . C o n s o l i d a t i o n o f c la y w a s o n e o f tp r in c i p al to p i cs o f Te r z a g h i ' s p i o n e e r i n g b o o k ,Erdbaumechanik, p u b l i s h e din 1 92 5. I t w a s t h e s u b j e c t o f s o m e o f t h e f i rs t l a b o r a t o r y t e s ts Te r z a gp e r f o r m e d a t R o b e r t ' s C o l l e g e in t h e e a r l y 1 92 0s , a n d c o n s o l i d a t i o n s e t tm e n t s w e r e t h e f o c u s o f h i s f ir s t c o n s u l t i n g j o b . C o n s o l i d a t i o n s e t t l e m e no f c l ay t h u s s e e m a n a p p r o p r i a t e s u b j e c t f o r a l e c t u r e p r e s e n t e d i n h i s h o n

O t h e r Te r z a g h i L e c t u r e r s h a v e a d d r e s s e d a s p e c t s o f t h is s u b j e c t, n o t a bR u t l e d g e ( 19 7 0 ), a n d L o w e ( 19 7 4 ). A s i l l u s t r a t e d b y t h e c a s e s d e s c r i bh e r e , c o n s o l i d a t i o n s e t t l e m e n t s a r e s t il l v e r y i m p o r t a n t i n m a n y c iv i l e nn e e ri n g p r o je c t s , a n d t h e r e is s ti ll i m p o r t a n t p r o g r e s s t o b e m a d e t o i m p r oo u r a b i li t y t o a n t i c i p a t e a c c u r a t e l y t h e m a g n i t u d e s a n d r a t e s o f c o n s o l i d a t is e t t l e m e n t s .

P R O B L E M S C A U S E D B Y S E T T L E M E N T S

C o n s o l i d a t io n s e t t l e m e n t s c a n r e s u l t in m a n y d i f fe r e n t t y p e s o f p r o b l e ma s i n d i c at e d in Ta b l e 1 ( S k e m p t o n a n d M a c D o n a l d 1 95 6; B j e r r u m 1 96Wa h l s 1 9 9 0 ) .

W h e r e s e t t l e m e n t s a r e l a r g e , t h e g r o u n d s u r fa c e m a y s u b s i d e b e l o w w a ta n d b e f lo o d e d . F l o o d i n g c a n b e p r e v e n t e d i f t h e i n i t ia l g r o u n d s u r f a c em a d e h i g h e n o u g h s o t h a t i t r e m a i n s s a fe l y a b o v e w a t e r a f t e r a ll s e t t l e m eh a s t a k e n p l a c e . To r e m e d i a t e f l o o d i n g , it i s n e c e s s a r y t o c o n s t r u c t d i k ea n d t o u s e d i t c h e s t o l o w e r t h e w a t e r l e v e l b e l o w g r o u n d l e v e l .

~Univers ity Dis t ingu ished Prof . , D ept . o f Ci r. En grg . , V i rg in ia Tec h. , Blaeksb uV A 24061


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TA B L E 1 . S e t t le m e n t P r o b le m s

P r o b l e m s P r e v e n t iv e m e a s u r e s R e m e d i a l m e a s u r e s(1) (2) (3)

Flooding

Loss o f s lope to dra in

Tilt ing of structures ( t i l t o0.004 can be d ist inguishedby unaided eye)

Arc hitectural damag e (cracksin walls or f loors , jamm edwindows or doors , unevenfloors)

Structural dama ge (cracks inc o l u m n , f l o o r b e a m s , o rother s t ructura l e lem ents)

Ra ise g round e leva t ion wi thextra f i ll

Al low a ll o r pa r t o f se t tl ementto occur before const ruc-t ion of dra ins

Design or iginal s lopes wi th a l -lowance for changes

Allow al l or par t of se t t lem entto occur before const ruc-t ion o f s t ructures

Design foundations so they areconcentr ical ly loadedUse f loat ing or deep founda-

t ions to reduce se t t lementsAl low a ll o r pa r t o f seRlement

to occur before const ruc-t ion of structures

Use f loa t ing o r deep founda-t ions to reduce magni tudesof to ta l and di fferent ia l se t-

t l ementsUse s t i ff foundat ions so that

di fferent ia l se t t lement doesnot resul t in d is tor t ion ofstructure

Al low a l l o r pa r t o f se t t l ementto occur before const ruc-t ion of structures

Use f loat ing or deep founda-t ions to reduce magni tudes

of total and differential set-t l ements

K e e p g r o u n d - w a t e r l e v e l sbelow ground surface w ithdikes , d i tches , and pum p-ing

Reg rade sur face d ra insRebui ld , replace , or supple-

ment subsurface dra ins

R ele ve l structures using jacksand shims, or mudjacking

Poss ib ly underp in founda-

t ions to minimize subse-quen t se t t l ement

Repa i r damage to res to reva lue

Possibly re level s t ructurePoss ib ly underp in founda-

t ions to minimize subse-quen t se t t l ement

Repa i r damage to res to restructural integri ty

Poss ib ly underp in founda-t ions to minimize subse-quen t se t t l ement

S e t t l em e n t s a r e n e v e r u n i f o rm . D i f f e r e n t i a l s e t t le m e n t s c a n l e a d to m a nt y p e s o f p r o b l e m s . O n e o f t h e s e i s t h e d i s r u p t i o n o f s u r f a c e o r s u b s u r f ad r a i n a g e w h e r e d i f f e r e n t i a l s e t t l e m e n t s r e s u l t in l o ss o f s l o p e t o d r a i n . T hc a n b e p r e v e n t e d , i f t h e m a g n i t u d e o f d i f f e r en t i a l s e t t l e m e n t c a n b e a n t ii p a t e d , b y d e s i g n i n g t h e i n it ia l s lo p e s w i t h a l l o w a n c e s f o r t h e c h a n g e s t hw i ll o c c u r as s e t t l e m e n t t a k e s p l a c e . I m p a i r e d d r a i n a g e c a n b e r e s t o r e d b

r e g r a d i n g e x i s t in g d r a i n s o r b u i l d i n g n e w o n e s .U n e v e n s e t t le m e n t s c a u s e a v a r i e ty o f p r o b l e m s f o r s tr u c t u re s . W h e n t h

i f d i i i ff h d i i f h


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r educ ing ne t l oad ; excava t ion o f 3 m (10 f t ) o f so i l o ff se t s t he load obui ld ing severa l s tor ies h igh . D ee p f ou nd at io ns (dr ive n p i les , d r i ll ed shaand ca i s sons ) r educe se t t l emen t s by ca r ry ing loads to deepe r, l e s s copressible s t ra ta .

I f s t ruc tu res and the i r fou nda t io ns a re d i s to r t ed by d i f f e ren t ia l se t tm e n t s , t h e y m a y b e c r a c k e d a n d d a m a g e d . A r c h i t e c t u r a l d a m a g e i n c l ua ll those fo rms o f d i st re s s t ha t imp a i r t he loo ks o r fun c t ion o f t he s t ruc tubu t do no t r edu ce i ts s t ruc tu ra l l oad -ca r ry ing capac i ty. Arch i t ec tu ra l damse ldom occur s i f t he angu la r d i s to r t ion r e su l t i ng f rom the se t t l em en t is t han t /500 . S t ruc tu ra l dam age impl i e s l os s o f s t ruc tu ra l capac ity. Se t t l emdamage r a re ly r e su l t s i n s t ruc tu ra l co l l apse , bu t a s t ruc tu re damaged se t t l emen t i s more l i ke ly to co l l apse unde r loads imposed by ea r thquawind, o r l ive load .

Once a s t ruc tu re has been damaged by d i f f e ren t i a l s e t t l emen t s , r emedt ion can t ake two fo rms . One i s r epa i r o f t he a rch i t ec tu ra l o r s t ruc tudamag e to r e s to re the s t ruc tu re to a u se fu l s t a t e . R e leve l ing the s t ruc tum ay be r equ i r ed to r e m ov e t il t o r d i s to rt ion . I f s e t t l em en t i s con t inu ingm a y b e n e c e s s a ry t o m o d i f y t h e f o u n d a t i o n s ( u n d e r p i n t h e s t r u c t u r e )r educe o r e l imina te fu tu re se t t l emen t s .

I t is no t unc om m on fo r s e t t lem en t s a s la rge a s s eve ra l f ee t t o occur are su l t o f conso l ida t ion o f so ft c lays . I t is t he r e fo re easy to u nde r s t and impor t ance o f be ing ab le to e s t ima te th e m agn i tudes and r a t e s o f consda t ion se t t l emen t s i n advance , so tha t appropr i a t e des ign f ea tu res can a d o p t e d t o r e d u c e s e t t le m e n t s o r t o a v o i d s e t tl e m e n t - i n d u c e d d a m a g e . Io f t en des ir ed to d eve lop f ac il it ie s , and to beg in us ing them , w h i l e t hey s t i l l se t t l ing , because t ime i s money. To do th i s i t i s usefu l to be ab le

e s t ima te accu ra t e ly how much se t t l emen t w i l l occu r, and how fa s t i t wO c c u r.

The fo l lowing sec t ions of th i s paper d iscuss : (1) The e ffec ts of consoda t ion se t t lem en t s on the des ign and cons t ruc t ion o f two m od ern p ro jecons t ruc ted on f il ls ove r c lays ; (2) the d i ff icu l t ies involv ed in es t imat ing magn i tudes and the r a t e s o f conso l ida t ion se t t lem en t s ; and (3 ) imp romen t s t ha t a r e ne ed ed in the cu r r en t s t a t e o f t he a r t fo r e s t ima t ing se tmen t s and se t t l emen t r a t e s .

Th e Bay Fa rm I s l and and K ansa i A i rp o r t ca se h i sto r ie s t ha t a r e desc r ibhe re have been t r ea t ed in more de t a i l by o the r s (Duncan e t a l . 1991 ; A

1991; Arai e t a l . 1991; Endo et a l . 1991; Maeda, e t a l . 1990; Oikawa Endo 1990 ; Takeuch i 1990 ; Tohma and Yamamoto , 1990) . The fo l lowsec tions use these cases tO il l u s tr a t e t he im por t an ce o f e s t ima t ing se t t l emra tes accura te ly, and the d i ff icu l t ies in doing so .

B AY FA R M I S L A N D

B a y F a r m I s l a n d i s l o c a t e d s o u t h o f A l e m e d a , o n t h e e a s t s i d e o f SF r a n c i s c o B a y. T h e a r e a w h e r e l a rg e s e t t l e m e n t s o c c u r r e d [ a b o u t 2 6 0 (one squa re mi l e ) ] was o r ig ina l ly a t i da l f l a t unde r l a in by 6 -15 m (20-

f t) o f S a n F r a n ci s c o B a y m u d . T h e a r e a w a s f a r m e d b e g i n n in g i n a b1880, and w as d iked o ff and dra ine d fo r mo re e ff ic ien t fa rm ing in 1930.1945 th d ik f i l d E i d f d i i d f l d i l d t d l


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D eve lo pm en t o f t he s it e fo r com m erc ia l and r e s iden t ia l u se began in 19w i th p la c e m e n t o f 2 . 5 - 6 m ( 8 - 2 0 f t) o f h y d r au l i c s a n d fill o v e r t h e Bmud . A cross sec t ion thro ug h the a rea i s show n in F ig . 1 . T hic ke r f il l wp laced where the un de r ly ing B ay m ud was th i cke r. T he f il l was l e f t i n p lfo r 12 yea r s , so tha t mo s t o f t he se t t l em en t du e to con so l ida t ion o f t he Bmud wou ld occ ur be fo re con s t ruc t ion o f s t r ee t s and bu ild ings . In 1979 f ig rading was done , and d eve lop m en t o f t he in f r a s t ruc tu re in the a rea b egPho tographs o f the a rea be f o re and a f t e r dev e lo pm en t a re shown in F igBay Fa rm I s l and today i s an a t t r ac t ive a rea dense ly popu la t ed wi th r edent ia l and l igh t commerc ia l uses .

A to t a l o f 45 se t t l emen t p l a t e s were used to mon i to r t he se t t l emen t Bay Fa rm I s land f rom 1967 to 1979 ( Jave te 1983). The se t t l emen t s m easua t t he 10 loca t ions where the Bay mud was th i ckes t a r e shown in F ig .Tw o th ings can be s een c lear ly in th i s f igure : F i r s t , the se t t lem ents a re la rAs mu ch a s 2 m (7 f t ) o f s e t t l em en t oc cur re d by 1979. S econd , t he se t t l emis no t un i fo rm. In 1979 the m easu red se t t l emen t s va r i ed f rom a li tt le m

than 1 m (4 f t ) to a l i t t le m or e th an 2 m (7 f t ) .T h e d i f fe r e n c es i n t h e m a g n i t u d e s o f t h e s e t t l e m e n t s f r o m p o i n t t o p oa re no t due to d i f f e ren t t h i cknesses o f Bay m ud . F or the 10 loca t ions whthe se t t l emen t s shown in F ig . 3 were measu red , t he th i ckness o f t he Bm ud var ied only f rom 14 m (45 ft ) to 15 m (50 f t ) . Th e smal les t se t t lem eshown in F ig . 3 w ere m easu red a t a l oca t ion wh ere the B ay mu d w as 14(46 f l ) thick, the largest where i t was 14.6 m (48 f t ) thick.

Th e m agn i tudes o f t he se t t l em en t s be a r som e re l a t ionsh ip to e ff ec t ivedepth . J ave te (1983) def ine d effec t ive f il l dep th as the th ickness of we igh ing 17.3 kN /m 3 (110 lb /cu f t ) t ha t wo u ld p rod uce the same load

the unde r ly ing Ba y mud , co ns ide r ing m oi s t un i t we igh t above the obs e rvave rage wa te r leve l and bu oy an t un i t we igh t be low. Al tho ugh the re i s sore la t ionship be tw een se t t le m ent a nd effec t ive f il l dep th , i t is no t cons is teT he po in t wi th an e ffec t ive f il l de pth of 5 .1 m (16 .6 f t) se t t led less tha n poin t wi th an e ffec t ive f il l de pth of 3 .3 m (10 .9 f t ) . T he poin t wi th an e ffecfill dep th o f 6 .8 m (22 .4 ft ) se t t led less than a poin t wi th an e ffec t ive depth of 6 .2 m (20 .3 f t ) . The sca t te r in the measured va lues i s s ign i f ica

Studies done s ince 1980 (Jave te 1983; Duncan e t a l . 1991) ind ica te tmuch o f t he e r r a t ic va r i a t ion in se t t lem en t f ro m p lace to p l ace a t Ba y Fa

B a y F a r m I s la n d ( a b o u t 1 s q u a r e m i le o r 2 6 0 h e c t a r e s ) )

- 0 : : ; 5 : ; : : ; : . :: ~ . / . . ~ . . ~ ' . ~ . ~ ; ; : : : : ; : : ; ; ; ; : . : ~ : ; ; ; : ; ; ; : ; : ; ; ; : # . ~ . ~ . N ' . ~ : . ~ : : ; ~ ; : : : : : : ; ; : : ; ; ; ; ; : : ; : ; ; : : : : ~ . / . . ~ . ~ . % . . ~ ; : ; ; ; ; ~ ; ;

- l O m-40 f t

F i rm soi ls


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FIG. 2. B ay Farm Island: (a) after Fillin g, be fore De velopm en t of Infrastructure;and (b) after Development

Island was due to random variations in crust thickness from one locationto another, as discussed later in this paper.

In 1979 the se ttlements were still continuing, at rates varying from 50 mm(2 in.) to 75 mm (3 in.) per year. Just before final grading and construction

of streets and buildings was to begin in 1979, the developer asked a geo-technical engineering firm to make an estimate of the maximum amount ofdiff i l l h i h b i d b b ildi d


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l r r -

2 m -

3 m -

F i l l i n g b e g a n

'67 '68 '69 '70o=-_ i,-- , ,

\ I " ~ .

9 , ,I j : . . . .2

3

4

5

6

7

8

9

10

D e v e l o p m e n t b e g a n

D a t e I'71 72 '73 '74 '75 '76 '77 '78 '79 '80 '81

" ' , ~ S "~ ' -- , B a y M u d t h ic k n e ssI K 9 4 " - - 1 , , , 4 , H = 4 6 i t ~

" - . 9 9 "" - 4 . . . (14 .0 m) \ E f f e c t i v e f i ll d e p t h" - , | I I " " .'~ " . . . . . . ~ 1 ~ 1 6 . 6 I t ( 5 .1 m )

"1 1 . L L 11 .0 ff (3 .4m)4 9 i t , ~ '~ -11.3 ff (3.5 m)

" ' ' - . ~ ~ \ " - 1 5 . 1 'i t ( 4 . 6 m )10 s e t t le m e n t p l a t e s ~ ' - - , _ . 9 ~ _ 1 3 . 8 t t (4 .2 m )B a y M u d t h i ck n e s s v a r ie s f r o m " - - , 4 , S , 9 i ~ L 1 0 . 9 f f ( 3. 3m )4 5 I t t o50 ff (13,7 m to 15.2 m) - 4 . . . ~_~ ',-17.9 ff (5.5r n )D a t a fr o m a r e a s w i t h w e l l - d e v e l o p e d H / ' \ \ ~ 2 2 . 4 I t (6 .8 m )c r u s t a n d a r e a s w i t h l it tl e o r n o c r u s t , = 48 ff J \k -18 .5 f t (5 .6 m)

(14.6 m) k- 20.3 ff (6,2 m)

F I G. 3 . M e a s u r e d S e t t l e m e n t s a t B a y F a r m I s l an d

and se t t l emen t r a t e s , and pa r t i c ipa t ed i n eva lua t ing the da t a ob t a ined f romt h e 4 5 s e t tl e m e n t p l a t es a t t h e s i te . T h e y t h u s h a d c o n s i d e r a b l e i n f o r m a t i o n

a n d e x p e r i e n c e o n w h i c h t o b a s e t h e i r e s t i m a t e o f t h e m a x i m u m p o s s i b l ed i f f e r en t i a l s e t t l emen t i n a bu i ld ing . They were a l so we l l aware o f t he pos -s ib le l ega l con seq uen ces o f unde re s t im a t ing the d i f f e r en ti a l s e t t l em en t s . I fd i f f e r en t i a l s e t t l emen t s occu r r ed t ha t we re l a rge r t han they e s t ima ted , t heym i g h t b e d e e m e d l i a b l e f o r a s h a r e o f t h e r e s u l t i n g d a m a g e s .

Cons ide r ing ca re fu l ly a l l o f t he ava i l ab l e i n fo rma t ion , and no t w i sh ing toincu r exp osu re t o und ue l iab i li ty, f i rm A e s t im a ted tha t d i f f e r en ti a l s e t tl e -m en t s a s l a rge as 300 m m 1 .0 f t ) m igh t be p os s ib l e w i th in a s t ruc tu re 23m s q u a r e 7 5 f t s q u a r e ) s u p p o r t e d o n s h a l l o w f o u n d a t i o n s a t t h e s it e.

T h e d e v e l o p e r w a s n o t p l e a s e d w i t h t h i s a n s w e r. D e s i g n i n g s t r u c t u r e s

a n d f o u n d a t i o n s f o r s u c h c o n d i t i o n s w o u l d b e e x c e p t i o n a l l y d i f f i c u l t a n de x p e n si ve . O b t a i ni n g t he r e q u ir e d d e v e l o p m e n t p e r m i t w a s p r ob a b l y o u t o ft h e q u e s t i o n if t h e d e v e l o p e r h a d t o b a s e t h e d e v e l o p m e n t p l a n o n s u c hla rge va lues o f e s t ima ted d i f f e r en t i a l s e t t l emen t .

U n d e r s t a n d a b l y, t h e d e v e l o p e r w h o a l re a d y h a d m a d e a v e r y l arg e i n-v e s t m e n t in t h e s it e ) w a n t e d a s e c o n d o p i n i o n . F o r t hi s h e tu r n e d t o a n o t h e rgeo techn ica l f i rm f i rm B) t ha t had a l so do ne cons ide rab l e wor k a t t he s it e.F ir m B c o n s i d e r e d t h e s a m e i n f o r m a t i o n as f ir m A , b u t w a s m o r e i n f l u e n c e db y h o w t h e ir p r o s p e c ts o f r e c e i v in g f u r t h er w o r k f r o m t h e d e v e l o p e r m i g h tbe i n f luenced by the i r e s t ima te .

Cons ide r ing ca re fu l ly a l l o f t he ava i l ab l e i n fo rma t ion , and no t w i sh ing toj eopa rd i ze t he i r chances fo r fu r the r work wi th t he deve lope r, f i rm B e s t i -

d h d ff l l l h f ) l k l


82/134

s im p l y t o a c c e p t th e m o r e f a v o r a b l e a n s w e r a n d t o i g n o r e t h e l e s s f a v o r a bB o t h h a d t o b e a c c o m m o d a t e d i n t h e p e r m i t a p p l i c a t i o n .

A t t h is s ta g e t h e d e v e l o p e r a s k e d t h e w r i t e r if h e c o u l d w o r k w i th tt w o f i r m s , t o g e t t h e m t o a g r e e o n a c o m m o n e s t i m a t e . T h e w r i t e r , b eop t imi s t ic and p e rh aps a li t tl e na ive , r ep l i ed t h a t t ha t c e r t a in ly w ou ld p o s s i b l e . H e e x p l a i n e d t o t h e d e v e l o p e r, a s h e h a d e x p l a i n e d t o s t u d em a n y t i m e s , t h a t o n c e t h e c o n d i t i o n s t o b e a n a l y z e d h a d b e e n d e c i d e d , a n s w e r w a s d e t e r m i n e d . T h e r e f o r e a ll t h a t w o u l d b e n e c e s s a r y w o u l d b eg e t t h e t w o fi r m s t o a g r e e o n w h a t c o n d i t i o n s s h o u l d b e c o n s i d e r e d , at h e y w o u l d t h e n a r r iv e a t th e s a m e a n s w e r.

I t p r o v e d t o b e n o t s o e a s y t o g e t f i r m A a n d f i r m B t o a g r e e o n tc

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