Elastic Settlement of Shallow Foundations on Granular Soil—A Critical Review

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ELASTIC SETTLEMENT OF SHALLOW FOUNDATIONS ON GRANULAR SOIL— A CRITICAL REVIEW BRAJA M. DAS

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___________________________________ Settlement, S

___________________________________ • Elastic settlement, Se

• Consolidation settlement

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• Primary, Sp • Secondary, Ss S = Se + Sp + Ss

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In his landmark paper in 1927 entitled The Science of Foundations, Karl Terzaghi wrote: “Foundation problems, throughout, are of such character that a strictly theoretical mathematical treatment will always be impossible. The only way to handle them efficiently consists of finding out, first, what has happened on preceding jobs of a similar character; next, the kind of soil on which the operations were performed; and, finally, why the operations have led to certain results. By systematically accumulating such knowledge, the empirical data being well defined by the results of adequate soil investigations, foundation engineering could be developed into a semi-empirical science. . . .”

“The bulk of the work—the systematic accumulation of empirical data—remains to be done.”

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___________________________________ To evaluate the current state of the art for settlement predictions of shallow foundations in sand, in an attempt to promote the use of shallow foundations.  A FHWA initiative 1.

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Federal Highway Administration (FHWA) Texas A & M University Geotest Engineering American Society of Civil Engineers (ASCE)

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___________________________________ Texas A&M University National Geotech Experiment Site Approximately 12m  28m

5 Square Footings:

1m  1m 1.5m  1.5 m 2.5m  2.5m 3m  3m (North) 3m  3m (South)

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PROBLEM:  Predict the load at 25 mm settlement In Situ Test Summary Bore hole shear test  3 Cross hole test  4 Cone penetration test  7 Dilatometer test  4 Pressuremeter test  4 Step blade test  1 Standard penetration test  6

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___________________________________ Number of participants:  31 15 consultants 16 academics  Israel – 1

 Brazil – 1

 Japan – 1

 France – 1

 Canada – 2

 Italy – 1

 Hong Kong – 1

 Australia – 2

 USA – 21

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Methods Used for Settlement Prediction

22 different methods Schmertmann (1970, 1978), Burland and Burbidge (1985) and FEM being popular Alpan (3 times) Bowles (4) Buisman, DeBeer (3) Burland & Burbidge (9) Canada Found. Manual (1) D’Appolonia (4) DeBeer (1) Decourt (1) FEM (1) Hanson (1) Leonard & Frost (4)

Menard/Briaud (5) Meyerhof (4) NAVFAC (4) Oweis (4) Parry (1) Peck (2) Robertson & Campanella (1) Schmertmann (18) Schulze & Sherif (3) Terzaghi & Peck (5) Vesic (6)

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___________________________________ Predicted vs. Measured Values of Q25

___________________________________ Footing (m) Item

11

1.51.5

2.52.5

33

33

Prediction range (kN)

591100

1162950

2954271

4075600

4156400

Measured

850

1500

3600

4500

5200

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___________________________________ Elastic Settlement, Se Existing methods for predicting settlement may be grouped into three categories: A — Methods in which observed settlement of structures are linked to in situ test results (standard penetration test, cone penetration test, Pressuremeter tests) B — Semi-empirical method C — Use of theory of elasticity and modulus of elasticity, Es

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___________________________________ CATEGORY A

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  



Terzaghi and Peck (1948, 1967) Meyerhof (1956, 1965) DeBeer and Martens (1957) Hough (1969) Peck and Bazaraa (1969) Burland and Burbidge (1985)

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___________________________________ Terzaghi and Peck (1948, 1967) Se 4  Se(1)   B1  2 1   B  Se = settlement of prototype foundation measuring BB

Se(1) = settlement of a test plate measuring B1B1 

B1 is usually of the order of 0.3m to 1m 

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Terzaghi and Peck (1948, 1967)

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___________________________________ 2

3q  B  Se  CW CD   N60  B  0.3 

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where q is in kN/m²; B is in m; S is in mm CW = ground water table correction = 1 if depth of water table is greater than 2B below foundation = 2 if depth of water table is less than or equal to B CD = correction for depth of embedment = 1 – (Df /4B )

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___________________________________ Sivakugan, Eckersley and Li (1998) analyzed 79 settlement records of foundations provided by Jeypalan and Boehm (1986) and Papadopoulos (1992).

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2

Se B   4  Se(1)  B  0.3  2  B   1  Se     B  0.3  4  Se(1) 

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3q  B    N60  B  0.3 

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3q 1  Se    Se  N60 4  Se(1)  q N  60 Se(1) 0.75

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Se 

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Meyerhof  2q(kN/m2 ) (B  1.22m) Se (mm)  N60  1956  2 2 3 q (kN/m )  B  (B  1.22m) S (mm)     e N60  B  0.3 

 1.25q(kN/m2 ) (B  1.22m) Se (mm)  N60  1965  2 2 S (mm)  2q(kN/m )  B  (B  1.22m)    e N60  B  0.3 

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Note: q increased by about 50%

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___________________________________ Se (mm)  CW CD and

1.25q (B  1.22m) N60

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2

2q(kN/m2 )  B  Se (mm)  CW CD   (B  1.22m) N60  B  0.3 

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CW  1.0 and

CD  1.0 

Df 4B

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___________________________________ Meyerhof’s Analysis (1965)

Structure T. Edison, Sao Paulo Banco do Brasil, Sao Paulo Iparanga, Sao Paulo C.B.I. Esplanada, Sao Paulo Riscala, Sao Paulo Thyssen, Dusseldorf Ministry, Dusseldorf Chimney, Cologne

B (m)

Average N60

q (kN/m2)

Se(predicted)

18.3 22.9 9.15 14.6 3.96 22.6 15.9 20.4

15 18 9 22 20 25 20 10

229.8 239.4 220.2 383.0 229.8 239.4 220.4 172.4

1.95 0.99 1.29 1.20 1.56 0.77 0.98 3.30

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Se (observed)

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Average ≈ 1.50

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DeBeer and Martens (1957) Se 

     2.3 log10  o H C  o 

‘o = effective overburden pressure at a depth  = increase in pressure due to foundation loading H = thickness of layer considered q C  1.5 c o Sepredicted  1.9 Field Test Results:

Seobserved

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___________________________________ DeBeer (1965)

___________________________________  Method applied to normally consolidated sand  Reduction factor needed for over−consolidated

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sand

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___________________________________ Hough (1969)

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     C Se  c H log10  o  1  eo  o 

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C c  a(eo  b)

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Value of constant Type of soil

a

b

Uniform cohesionless material (uniformity coefficient Cu ≤ 2) Clean gravel Coarse sand Medium sand Fine sand Inorganic silt

0.05 0.06 0.07 0.08 1.00

0.50 0.50 0.50 0.50 0.50

Well-graded cohesionless soil Silty sand and gravel Clean, coarse to fine sand Coarse to fine silty sand Sandy silt (inorganic)

0.09 0.12 0.15 0.18

0.20 0.35 0.25 0.25

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Peck and Bazaraa (1969) Se (mm)  CW CD

2

2q(kN/m2 )  B    (N1 )60  B  0.3 

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where B is in m

(N1)60 = corrected standard penetration number CW = ‘o /o at 0.5B below the bottom of foundation o = total overburden pressure ‘o = effective overburden pressure CD = 1.0 – 0.4(D/q) 0.5  = unit weight of soil

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___________________________________ Peck and Bazaraa (1969)

___________________________________ (N1 )60 

4N60 3.25  0.01o

(N1 )60 

4N60 1  0.04o

(o  75 kN/m2 )

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Peck and Bazaraa’s Method

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(after D’Appolonia et al. 1970)

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GRANULAR SOIL

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Burland and Burbidge (1985) For gravel or sandy gravel  N60(a)  1.25N60 For fine sand or silty sand below the ground water  N60(a)  15  0.6(N60  15) and N60  15

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where N60(a) = adjusted N60 value

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Depth of Stress Influence, z' If N60(a) [or N60(a)] is approximately constant (or increasing) with depth, B z  1.4  BR  BR 

0.75

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where

BR = reference width = 0.3m B = width of the actual foundation (m)

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___________________________________ Depth of Stress Influence, z'

___________________________________ If N60(a) [or N60(a)] is decreasing with depth, calculate z‘ = 2B and z‘ = distance from the bottom of the foundation to the bottom of the soft soil layer (z“ ).

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Use z‘ = 2B or z‘ = z“, whichever is smaller.

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___________________________________ Depth of Influence

Correction factor,  

H H 2    1 z  z 

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H = thickness of compressible layer

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For Normally Consolidated Soil Se 1.71    0.14  1.4   BR [N 60 or N 60(a) ] 

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2

 1.25 L       B 0.7  q   B      L   0.25      BR   pa   B   where L = length of the foundation pa = atmospheric pressure (= 100 kN/m2)

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For Overconsolidated Soil

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(q  c ; c  overconsol idation pressure)

___________________________________ Se 0.57    0.447   1.4  BR [N 60 or N 60(a) ]  2

 1.25 L       B  0.7  q   B      L   0.25      BR   pa   B  

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For Overconsolidated Soil (q  c ) : Se 0.57    0.14  1.4   BR [N 60 or N 60(a) ]   1.25 L       B  L   0.25      B  

2 0.7

 B   q  0.67c      pa  BR   

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Probability of Exceeding 25-mm Settlement in the Field (After Sivakugan and Johnson 2004) Predicted methods

Predicted settlement (mm)

Terzaghi & Peck (1948)

Schmertmann (1970)

1 5 10 15 20 25 30 35 40

0.00 0.00 0.00 0.09 0.20 0.26 0.31 0.35 0.387

0.00 0.00 0.02 0.13 0.20 0.27 0.32 0.37 0.42

Burland & Burbidge (1985) 0.00 0.03 0.15 0.25 0.34 0.42 0.49 0.44 0.51

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___________________________________ CATEGORY B 

Schmertmann (1970), Schmertmann et al. (1978)

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Briaud (2007)

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Terzaghi, Peck and Mesri (1996)

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Akbas and Kulhawy (2009)

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___________________________________ Schmertmann (1970)

z 

q(1   s ) [(1  2 s )A  B] Es

E Iz  z s  (1   s )[(1  2 s )A  B] q

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___________________________________ I Se  C1C2 q  z  z Es

q = net stress at the level of the foundation C 1 = correction factor for the depth of the foundation = 1 – 0.5(qo /q) qo = effective overburden pressure at the level of the foundation C 2 = correction factor to account for creep in soil = 1+0.2 log(t/0.1)

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Es = 2qc

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___________________________________ The same 79 foundations records given by Jeypalan and Boehm (1986) and Papadopoulos (1992) were analyzed by Sivakugan et al. (1998).

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Schmertmann et al. (1978)  q  Iz(peak)  0.5  0.1   o 

0.5

Item Iz at z = 0 zp /B

L/B = 1 0.1 0.5

L/B  10 0.2 1.0

zo /B Es

2.0 2.5qc

4.0 3.5qc

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___________________________________ Salgado (2008)

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L Iz (at z 0)  0.1  0.0111   2 B zp L  0.5  0.0555  1   1 B B  zo L  2  0.222  1   4 B B 

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Lee et al. (2008) FEM Analysis Iz (peak )  0.5

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zp L  0.5  0.11   1  1 B  B  

L with a maximum of 1 at  6 B

zo   L   0.95 cos   1     3  4 B  5  B   with a maximum of 4 at

L 6 B

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___________________________________ Terzaghi et al.

(1996) L zo  21  log    4  B  

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Iz z z 0 E s

z  zo

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Se  q 

E s (L / B ) L  1  0.4 log    1.4 E s(L / B1) B E s(L / B1)  3.5qc    t days  Se (creep)   0.1  zo log    1 day   qc  q c  weighted mean value qc (in MN/m2 )

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81 Foundation and 92 Plate Load Tests

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Load-Settlement Curve Based on Pressuremeter Test Briaud (2007)

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Pressuremeter Test

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___________________________________ q   [ f(L / B) , fe , f , fd ]pp(mean) Se R  0.24 B R

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  gamma function

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___________________________________ SHAPE FACTOR f(L / B)  0.8  0.2

B L

ECCENTRICITY FACTOR e fe  1  0.33  Center B 0.5 e fe  1    Edge B

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LOAD INCLINATION FACTOR  (deg)  f  1   Center  90 

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2

 (deg)  f  1   Edge  360  0.5

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SLOPE FACTOR 0.1

f, d

d  0.8 1   3 : 1 slope  B

d f, d  0.7 1    B

0.15

2 : 1 slope

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___________________________________ Long-term settlement, including creep = t Se    t1 

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0.03

t = design life (in hours) t 1 = 1 hour

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___________________________________ Akbas and Kulhawy (2009) L1 - L2 Method 37 Sites

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167 Axial compression field load tests

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___________________________________ ___________________________________ Mean Se(L1) = (0.23%)B Mean Se(L2) = (5.39%)B

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___________________________________ ___________________________________ Se Q B  QL2 0.69  Se   1.68   B

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___________________________________ B>1m QL2 = ultimate bearing capacity Qu (Vesic 1973, 1975)

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B≤1m  Q  QL2   u   Quq  B  Qu  N portion of Vesic' s theory

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Quq  Nq portion of Vesic' s theory

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___________________________________ Note: Vesic’s theory includes compressibility factor. So

Qu  f ( , E s , ,  , B)

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Proper assumption of Es and  is needed.

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CATEGORY C Use of Theory of Elasticity and Modulus of Elasticity 1  2s Se  qo (B) Is If Es Es = average modulus of elasticity (z = 0 to z = 4B) B‘ = B/2 s = Poisson’s ratio

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___________________________________ Steinbrenner (1934)

___________________________________ Is = shape factor = f (m, n) For Se at the center :  = 4 m n

L B

H B   2

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___________________________________ Fox (1948) D L  I f  depth factor  f  f , and  s   B B 

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Se(rigid)  0.93Se(flexible, center)

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Variation of If L /B Df /B

1.0

2.0

5.0

Poisson’s ratio s = 0.30 0.20 0.40 0.60 0.80 1.00 2.00

0.902 0.808 0.738 0.687 0.650 0.562

0.930 0.857 0.796 0.747 0.709 0.603

0.951 0.899 0.852 0.813 0.780 0.675

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Poisson’s ratio s = 0.40 0.20 0.40 0.60 0.80 1.00 2.00

0.932 0.848 0.779 0.727 0.689 0.596

0.955 0.893 0.836 0.788 0.749 0.640

0.970 0.927 0.886 0.849 0.818 0.714

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Bowles (1987)

Weighted average, E s 

 E s(i ) z

z = H or 4B, whichever is smaller Es = 500(N60 + 15) kN/m2

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z

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___________________________________ Mayne and Poulos (1999)

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E s  Eo  kz Se 

q Be IG IR IE (1  2s ) Eo

 E H IG  influence factor  f    o ,  k Be Be   IR  foundation rigidity correction factor

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IE  foundation embedment correction factor 4BL  Be      

0.5

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___________________________________ IR 

IE  1 

  4

1    Ef  2t 3 4.6  10   B e  Eo  k  Be   2 

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1 B  3.5 exp1.22 s  0.4  e  1.6   Df 

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Berardi and Lancellotta (1991) qB Es Is = influence factor for a rigid foundation (μs = 0.15) (Tsytovich, 1951)

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Se  Is

L /B 1 2 3 5 10

0.5 0.35 0.39 0.40 0.41 0.42

H 1 /B 1.0 1.5 0.56 0.63 0.65 0.75 0.67 0.81 0.68 0.84 0.71 0.89

2.0 0.69 0.88 0.96 0.99 1.06

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___________________________________ Berardi and Lancellotta (1991) re-analyzed field performance of 130 structures on predominantly silica sand as reported by Burland and Burbidge    0.5  Es  KE pa  o  pa  

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0.5

(Janbu, 1963)

pa = atmospheric pressure o and  at a depth B/2 below the foundation

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KE  f N1 60

N1 60  average corrected standard penetratio n number in the influence zone

Influence zone for square foundation: H15 = (1.2 to 2.8)B H25 = (0.8 to 1.3)B Influence zone for L/B ≥ 10: H15  (1.8 to 2.4)B H25  (1.2 to 2.0)B

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___________________________________ Skempton (1986)

___________________________________   2 N1 60  N60    1  0.01o  o is in kN/m2

N1 60 Dr2

 60

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Procedure for Calculating SE

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Berardi and Lancellotta (1991)

1. Obtain the variation of N60 within the influence zone (i.e., H25).

2. Obtain (N1)60 within the influence zone.

3. Obtain N 1 60 .

4. Obtain KE at Se /B = 0.1%.

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0.5

   0.5   .

5. Calculate E s  KE pa  o pa  

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___________________________________ Procedure for Calculating SE (continued) 6. Determine Is. 7. Use an equation from theory of elasticity to calculate Se. 8. Calculate Se /B. Is it equal to assumed Se /B ?

9. If so, the calculated Se in Step 7 is the answer.

10. If not, use Se /B from Step 8 to obtain the new KE. 11. Repeat Steps 5, 7 and 8 until the assumed and calculated Se /B are equal.

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Settlement Prediction in Granular Soils ― A Probabilistic Approach Sivakugan and Johnson (2004), Geotechnique, Vol. 54, No. 7, 449-502.

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Predicted Settlement – 25 mm

Method Terzaghi & Peck (1948) Schmertmann (1970) Burland & Burbidge (1985) Berardi & Lancellotta (1991)

Probability of exceeding 25 mm in the field 0.26 (26%) 0.27 (27%) 0.42 (42%) 0.52 (52%)

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___________________________________ COMMENTS AND CONCLUSIONS 1. Meyerhof’s relations (1965) simple to use. On the average, will give Se(predicted)/Se(observed)  1.5 to 2.0.

2. Peck & Bazaraa method (1969) is not superior to that of Meyerhof (1965).

3. Burland & Burbidge (1965) is an improved method over that of Meyerhof (1965) and Peck & Bazaraa (1969).

Difficult to estimate overconsolidation pressure from field exploration.

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___________________________________ 4. Modified strain influence factor methods of Schmertmann et al. (1978), Terzaghi et al. (1996), Salgado (2008) and Lee et al. (2008) will give reasonable results with proper values of Es .

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5. Suggested Es relations: E s (L / B ) L  1  0.4 log    1.4 E s(L / B1) B

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E s(L / B1)  3.5qc

6. The Es (L/B = 1) relationship can be related to N60 via D50 .

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___________________________________ 7. Pressuremeter method of developing loadsettlement relationship is very effective, but may not be cost effective.

8.

L1 – L2 (Akbas and Kulhawy) is a good method.

However proper assumption of E and  needed to estimate QL2.

9. Relationships for settlement developed using theory of elasticity will give equally good results provided a realistic Es is used.  Use of iteration method is suggested.  If not, used Terzaghi et al.’s relationship

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(1996).

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___________________________________  What we have seen is a systematic

accumulation of knowledge over 60 years.

The parameters for comparing settlement prediction methods are accuracy and reliability.

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 Reliability is the probability that the actual

settlement would be less than that computed by a specific method.

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___________________________________  In choosing a method for design, it all comes down to keeping a critical balance between reliability and accuracy, which can be difficult at times, knowing the non-homogeneous nature of soil in general. We cannot be overconservative but, at the same time, not be accurate.  We need to keep in mind what Karl Terzaghi said in the 45th James Forrest Lecture at the Institute of Civil Engineers in London: “Foundation failures that occur are no longer ‘an act of God’.”

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