elastic settlement a critical review

8/6/2019 Elastic Settlement a Critical Review

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EELASTICLASTIC SSETTLEMENTETTLEMENT OFOF

SSHALLOWHALLOW FFOUNDATIONSOUNDATIONS ONON

GGRANULARRANULAR SSOILOIL—— BBRAJARAJA M. DM. DASAS



Settlement, S

• , e

•

• Primary, S p

, s

S = Se + S + Ss



In

his

landmark

paper

in

1927

entitled

The Science

of

Foundations, Karl Terzaghi wrote:

“Foundation problems, throughout, are of such character that

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. B s stematicall accumulatin

such knowledge, the empirical data being well defined by the

results of adequate soil investigations, foundation engineering

”‐ . . . .“The bulk of the work—the systematic accumulation of

em irical data—remains to be done.”



To evaluate the current state of the art for

settlement redictions of shallow foundations in

sand, in an attempt to promote the use of shallow

foundations.

A FHWA initiative

. e era g way m n s ra on

2. Texas A & M University

.4. American Society of Civil Engineers (ASCE)



exas n vers yNational Geotech Experiment Site

Approximately

12m

28m

5 Square Footings: 1m 1m.5m .5 m

2.5m 2.5m

3m 3m (South)



Predict the load at 25 mm settlement

In Situ Test Summary

Bore o e s ear test 3

Cross

hole

test

4

Dilatometer test 4Pressuremeter test 4

Step blade test 1Standard penetration test 6



Number of participants: 31

15 consultants

16 academics

Israel – 1 Brazil – 1

Canada – 2 Italy – 1

– – USA – 21



Methods Used for Settlement Prediction

Schmertmann (1970, 1978), Burland and Burbidge (1985)

and FEM being popular

Alpan (3 times) Menard/Briaud (5)

Buisman, DeBeer (3)

Burland & Burbidge (9)

NAVFAC (4)

Oweis (4)Canada Found. Manual (1)

D’Appolonia (4)

DeBeer 1

Parry (1)

Peck (2)

Robertson & Cam anella 1

Decourt (1)

FEM (1)

Schmertmann (18)

Schulze & Sherif (3)

Leonard

&

Frost (4)

Vesic (6)



re cte vs. easure a ues o 25

Footing (m)

Item 11 1.51.5 2.52.5 33 33

Pre ct on

range (kN)591100 1162950 2954271 4075600 4156400



, e

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

s an ar pene ra on es , cone

penetration test, Pressuremeter tests)

— em ‐emp r ca me oC — Use of theory of elasticity and modulus of

e ast c ty, E s



CATEGORY A Terzaghi and Peck (1948, 1967)

Meyerhof (1956, 1965)

DeBeer and Martens (1957) Hough (1969)

Peck and Bazaraa 1969

Burland and Burbidge (1985)



,

21)1(

1 BSe

e

e

BB

Se(1) = sett ement o a test p ate measur ng B1B1

B is usuall of the order of 0.3m to 1m



Terzaghi and Peck (1948, 1967)



2

60 3.0

BN

qC C S DW e

where q is in kN/m²; B is in m; S is in mm

C W = ground water table correction

=

below foundation

= 2 if de th of water table is less than or e ual

to B

C = correction for de th of embedment

= 1 – (D f

/4B )



va ugan, c ers ey an

analyzed 79 settlement records

of foundations provided by

Je alan and Boehm 1986

and Papadopoulos (1992).



2BSe

3.0

2

)1( BSe

43.0 )1(SB e

e

32

Bq

Se

13

.

Sq e

4 )1(60 SN ee

75.0)1(Se



Me erhof

)(kN/m2 2q

)(kN/m3

.

195622

60

BqN

e

.

3.060 BNe

m)22.1(

)(kN m25.1(mm)

196560

BN

qSe

m)22.1(

3.0)(kN/m2(mm)

60

BB

BN

qSe

Note: q increased by about 50%



m)22.1( 25.1

(mm) Bq

C C S DW e

andkN m2

22 Bm.

3.0mm

60

BN

DW e

0.1W C

B

DC

f D

40.1



eyer o s na ys s

StructureB

(m)AverageN60

q(kN/m2) )observed(

)predicted(

e

e

SS

T. Edison, Sao Paulo

Banco do Brasil, Sao Paulo

I aran a Sao Paulo

18.3

22.9

9.15

15

18

9

229.8

239.4

220.2

1.95

0.99

1.29

C.B.I. Esplanada, Sao Paulo

Riscala, Sao Paulo

14.6

3.96

22

20

383.0

229.8

1.20

1.56

,

Ministry, Dusseldorf

Chimney, Cologne

.

15.9

20.4

20

10

.

220.4

172.4

.

0.98

3.30

Average ≈ 1.50



DeBeer and Martens (1957)

3.2

C o

e

10

‘o = effective overburden pressure at a depth

= increase in pressure due to foundation loadingH = thickness of layer considered

cqC 5.1

Field Test Results:o 9.1predicted eS

o servee



DeBeer (1965)

−

sand



Hough (1969)

log

110H

eS

o

o

o

ce

)( beaC oc



Value of

Type of soilconstant

a b

(uniformity coefficient C u ≤ 2)Clean gravel 0.05 0.50

Coarse sand

Medium sand

Fine sand

0.06

0.07

0.08

0.50

0.50

0.50Inorganic silt 1.00 0.50

Well‐graded cohesionless soil

Silty sand and gravelClean, coarse to fine sand

Coarse to fine silt sand

0.090.12

0.15

0.200.35

0.25

Sandy silt (inorganic) 0.18 0.25



Peck and Bazaraa (1969)

)(kN/m2

(mm)22

BqC C S DW e

where B is in m

.601

(N1)60 = corrected standard penetration number

C = ‘ at 0.5B below the bottom of foundation o = total overburden pressure

‘ = effective overburden ressure

C D = 1.0 – 0.4(D/q) 0.5

=



Peck and Bazaraa (1969)

kN m754 260

NN

01.025.3 o

)kN/m75(

04.01

4)( 260

601

o

o

NN



Peck and Bazaraa’s Method

a ter ppo on a et a .



GRANULAR SOILBurland and Burbidge (1985)

60)(60 25.1 ravel sand

or gravel For NN a

)15(6.015 water ground the

below sand silty

60)(60 NN a

an 60

where N60(a) = adjusted N60 value



'

If

N60(a) [or

N60(a)]

is

approximately

constant

(or

increasing) with depth,

75.0

4.1

Bz

where

RR

BR = reference width = 0.3m

B = width of the actual foundation m



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“ ).

‘ = ‘ = “



Depth of Influence

12factor,Correction

zz

H = thickness of compressible layer



S 71.1

aR NNB

4.1

)(6060 ]or[

.

qBB

L7.025.1

aR pB

B

L25.0

where L = length of the foundation

pa = atmospheric pressure (= 100 kN/m2)



For

Overconsolidated

Soilpressure)idationoverconsol ;( ccq

S 57.0

aR NNB 4.1)(6060 ]or[

.

qBB

L7.0

2

25.1

aR pB

BL25.0



For Overconsolidated Soil

:)( cq

eS 57.014.0

aR NNB ]or[

2

.)(6060

cq

B

B

LB 67.0

25.1 7.0

B.



Probability of Exceeding 25‐mm Settlement in the Field

Predicted methods

Predicted

settlement Terzaghi & Peck Schmertmann

Burland &

Burbidge

1

5

0.00

0.00

0.00

0.00

0.00

0.0310

15

0.00

0.09

0.02

0.13

0.15

0.25

2530

.

0.260.31

.

0.270.32

.

0.420.49

35

40

0.35

0.387

0.37

0.42

0.44

0.51



CATEGORY B Schmertmann (1970),

.

Briaud (2007)

Terzaghi, Peck and Mesri (1996)

Akbas and Kulhawy (2009)



Schmertmann (1970)

])21[()1(

B A

E

qs

s

sz

])21)[(1( B AE

I sssz

z

q



zE

qC C Ss

ze 21

q = net stress at the level of the foundation

1 = correc on ac or or e ep o e oun a on

= 1 – 0.5(qo /q)

o

foundation

2

= 1+0.2log(t /0.1)

E s = 2qc



The same 79 foundations records

given by Jeypalan and Boehm (1986)

and Papadopoulos (1992)

were anal zed b

Sivakugan et al. (1998).



Schmertmann et al (1978)



Schmertmann et al. (1978)

5.0

(peak) 1.05.0

o

zI

Item L/B = 1 L/B 10

Iz at z = 0 0.1 0.2

z p /B 0.5 1.0

zo

. .

E s 2.5qc 3.5qc



Salgado (2008)

20111.01.0)0(at LI zz

Lz ..

BB

41222.02 BBzo



Lee et al. (2008)

FEM Analysis

5.0I

Lz p

6at1of maximumawith

..

L

BB

4315cos95.0 L

BB

o

at4o max mumaw t B



Terzaghi et al.

(1996)

L

Bo



zzzIo

0z se E

4.1log4.01)1/(

)/(

BLs

BLs

B

L

E

E

5.3)1/( cBLs qE

dayslog1.0

cree oe

t zS

2

c

cc



81 Foundation and 92 Plate Load Tests



81 Foundation and 92 Plate Load Tests

L d S l C



Load‐Settlement Curve

Based on Pressuremeter TestBriaud (2007)



Pressuremeter Test



],,,[ (mean))/( p f f f f q pd eBL

24.0

R

R

B

Se

functiongamma



SHAPE FACTOR

L

B

f BL 2.08.0)/(

ECCENTRICITY FACTOR

B

e f e Center33.01

eBe f e Edg1

0.5

LOAD INCLINATION FACTOR



LOAD INCLINATION FACTOR

Center90

(deg)1

2

f

Edge(deg)15.0

f

slope1:318.01.0

d f d

15.0

d

,B



ong‐term sett ement, nc u ng creep =

03.0t

1 t Se

t = design life (in hours)

1 =



L1 ‐ L2 Method

167 Axial compression field load tests



e(L1) = .

=



Se

68.169.02

SB

Q

Q

eL



=

≤ m

2

qu

uL Q

BQ

theorysVesic'of portionu NQ

theorysVesic'of portionqqu NQ



Note: Vesic’s theory includes compressibility factor. So

),,,,( BE f Q su

s .

CATEGORY C



Use of Theory of Elasticity andModulus of Elasticit

2 f s

s

soe II

E BqS )(

E s = average modulus of elasticity (z = 0 to z = 4B)

B‘ = B/2

s = Poisson’s ratio



Steinbrenner (1934)

Is = shape factor = f (m, n)

For Se at the center : = 4

B

Lm

B

Hn



Fox 1948

and,factordepth s f

f B

L

B

D f I

center)(flexible,(rigid) 93.0 ee SS

Variation of I f



D f /BL /B

1.0 2.0 5.0

’ s = .

0.20

0.40

0.902

0.808

0.930

0.857

0.951

0.899

.

0.80

1.00

.

0.687

0.650

.

0.747

0.709

.

0.813

0.780

. . . .

Poisson’s ratio s = 0.40

0.20 0.932 0.955 0.970

0.40

0.600.80

0.848

0.7790.727

0.893

0.8360.788

0.927

0.8860.849

.

2.00

.

0.596

.

0.640

.

0.714



zE E i ss )( average,Weighted

,

s = 60



Mayne and Poulos (1999)

os zk E E



)1( 2s

E RGee

IIIBqS

o

HE ,ac orn uence

BBk ee

G

factorcorrectionrigidityfoundation

IR

5.04 BL

e



24

3 f

R

t E

I

2

.ee

oBk

BE

1

1E I

6.14.022.1exp5.3

f

e

s D



Berardi and Lancellotta (1991)



s

seE

qBIS

Is = influence factor for a rigid foundation (μs

= 0.15)

(Tsytovich, 1951)

H 1 /B

. . . .

1 0.35 0.56 0.63 0.69

3

.

0.40

.

0.67

.

0.81

.

0.96

10

.

0.42

.

0.71

.

0.89

.

1.06



Berardi and Lancellotta (1991) re‐analyzed field

erformance of 130 structures on redominantl

silica sand as reported by Burland and Burbidge

1963)(Janbu, 5.0

5.0

oaE s

p

pK E

pa = a mosp er c pressure

at a depth B/2 below the foundation ando



npenetratiostandardcorrectedaverage601 Nzonen uencet ennum er

H15 = (1.2 to 2.8)B

25 = . o .

Influence zone for L B ≥ 10:

H15 (1.8 to 2.4)B

. .



Skempton (1986)

2

01.01

2

60601

o

mnso

602601

r D

N



P d f C l l i SE ( d)



Procedure for Calculating SE (continued)

6. Determine

Is..

calculate Se.

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

. , e E .

11. Repeat Steps 5, 7 and 8 until the assumed and

e .

Settlement Prediction in Granular Soils

―



ro a s c pproacSivakugan and Johnson (2004), Geotechnique, Vol. 54,

‐

Predicted Settlement – 25 mm

Probability of

exceeding 25 mm

Method in the field

Terzaghi & Peck (1948) 0.26 (26%)

Schmertmann (1970)

Burland & Burbidge (1985)

0.27 (27%)

0.42 (42%)

erar ance otta .



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.

.

S h t t l (1978) T hi t l (1996)



Schmertmann et al. (1978), Terzaghi et al. (1996),

Sal ado 2008 and Lee et al. 2008 will ive

reasonable results with proper values of E s .5. Su ested E relations:

BLs LE 4.1log4.01

)/(

cBLs

BLs

qE 5.3)1/(

)1/(

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

50 .

7. Pressuremeter method of develo in load‐

settlement relationship is er effecti e b t ma



settlement 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. Relationshi s

for

settlement

develo ed

usin

theory of elasticity will give equally good results

provided a realistic E s is used.

Use of iteration method is suggested.

If not, used Terzaghi et al.’s relationship

(1996).



What we have seen is a systematic

accumu a on o now e ge over years.

The

parameters

for

comparing

settlement

reliability.

Reliability is the probability that the actual

settlement would be less than that computed

by

a

specific

method.

In

choosing

a

method

for

design

it

all

comes



In choosing a method for design, it all comesdown to keeping a critical balance between

,

at times, knowing the non‐homogeneous

nature of soil in eneral. We cannot be over‐

conservative but, at the same time, not be

accurate.

We need to keep in mind what Karl Terzaghi

sa n e ames orres ec ure a e

Institute of Civil Engineers in London: “

‘an act of God’.”

elastic settlement a critical review

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