jcuprd_049640

1. INTRODUCTION

Shallow foundations are generally designed to satisfy bearingcapacity and settlement criteria. The bearing capacity crite-rion stipulates that there is adequate safety against bearingcapacity failure beneath the foundation, and a factor of safetyof three is generally used on the computed ultimate bearingcapacity. Settlement criterion is to ensure that the settlementis within tolerable limits.

It is commonly believed that the settlement criterion ismore critical than the bearing capacity one in the designs ofshallow foundations, especially for foundation width greaterthan 1.5 m, which is often the case. By limiting the total set-tlements, differential settlements and any subsequent dis-tresses to the structure are limited. Generally the settlementsof shallow foundations such as pad or strip footings are lim-ited to 25 mm (Terzaghi et al. 1996).

Douglas (1986) reported the existence of more than 40different methods for estimating settlements in granular soils.All these methods recognize that the applied pressure, soilstiffness and the foundation width are the three most impor-tant variables affecting the settlements in granular soils. Soilstiffness is often quantified indirectly through penetration

resistance such as blow count from standard penetration testor tip resistance from cone penetration test. The objective ofthis paper is to present the current state-of-the-art for com-puting settlements of shallow foundations on granular soils,discuss some of the popular methods and review the empiri-cal correlations for estimating the soil stiffness.

2. CURRENT STATE-OF-THE-ART

The most popular methods for settlement predictions, dis-cussed commonly in text books, are the ones proposed byTerzaghi and Peck (1948), Schmertmann (1970),Schmertmann et al. (1978) and Burland and Burbidge(1985). Meyerhof (1956) and Peck and Bazaraa (1969) meth-ods are similar to the one proposed by Terzaghi and Peck(1948). Two of the more recent methods are after Berardi andLancellotta (1991) and Mayne and Poulos (1999). Sivakuganand Johnson (2004) proposed a probabilistic approach quan-tifying the uncertainties associated with the settlement pre-diction methods.

Computed and measured settlements of full-scale foot-ings have been compared by Jeyapalan and Boehm (1986),Papadopoulos (1992) and Sivakugan et al. (1998). The mes-sage is loud and clear that the predictions are generally signif-icantly greater than the measured values. Based on 79 casehistories of shallow foundations, Sivakugan et al. (1998)showed that Terzaghi and Peck (1948) method overestimatesthe settlements by 218% and Schmertmann (1970) methodoverestimates the settlements by 339%.

19

Braja M. Das*1 and Nagaratnam Sivakugan2

Settlements of shallow foundations ongranular soil — an overview

ABSTRACT: The main objective of this paper is to review the current state-of-the-art for predicting settlements of shallowfoundations in granular soils. The traditional settlement prediction methods are critically reviewed. The Settlement ’94 predic-tion session held in Texas clearly showed the deficiencies in the present settlement prediction methods, which generally over-estimate the settlements and underestimate the allowable pressures, making the foundation designs very conservative. Somerecent developments, including two deterministic methods and a probabilistic approach, are discussed as they have significantpotential to improve the current state-of-the-art. Several empirical correlations relating the modulus of elasticity of soil andpenetration resistances and standard penetration and cone penetration tests are summarized.

KEYWORDS: Shallow foundations, granular soils, settlements, empirical correlations, Settlement ’94

*Corresponding Author

1Geotechnical Engineer, Henderson, Nevada 89044 USA, e-mail: [email protected]

2Associate Professor and Head of Civil and Environmental Engineering,James Cook University, Townsville, Queensland 4811, AUSTRALIA,[email protected]

International Journal of Geotechnical Engineering (2007) 1: (19–29)

DOI 10.3328/IJGE.2007.01.01.19-29J. Ross Publishing, Inc. © 2007

2.1 Accuracy and Reliability of the DifferentMethodsTan and Duncan (1991) defined two parameters for compar-ing settlement prediction methods: accuracy and reliability.Accuracy is how close the predictions by a specific methodare to the measured values, and is defined as the average valueof the ratio of the calculated to measured settlements.Reliability is the probability that the actual settlements wouldbe less than those computed by a specific method. It is ameasure of conservativeness of a settlement predictionmethod. The probabilistic representation of these two terms,accuracy and reliability, is shown in Figure 1. Here, settlementratio (x) is defined as the ratio of calculated to measured set-tlements. A good method should have accuracy closer to 1and reliability closer to 100%. Tan and Duncan (1991) foundthat there is generally a trade-off between accuracy and relia-

bility among all methods. Terzaghi and Peck (1948) andSchmertmann (1970) methods appear to have high reliabilityand poor accuracy, reflecting their conservativeness. On theother hand, Burland and Burbidge (1985) and Berardi andLancellotta (1991) methods have good accuracy, with valuesclose to unity, but low reliability.

2.2 Settlement ’94 Prediction SessionBriaud and Gibbens (1994) documented the class A settle-ment prediction session held at Texas A&M University,College Station, Texas in 1994, where 16 academics and 15consultants participated. An extensive site investigationinvolving 7 cone penetration tests, 6 standard penetrationtests, 4 dilatometer tests, 4 pressuremeter tests, 4 cross holetests, 3 bore hole shear tests and a step blade test was carriedout at a 12 m � 18 m site, where five different square padfootings were to be load tested to failure at a future date.Laboratory test data including maximum/minimum densi-ties, specific gravity of the grains, natural water content, voidratio, densities and friction angles were also available for sandsamples taken from 0.6 m and 3.0 m depths. The soil profileconsisted predominantly of sands. The soil data were avail-able to all participants, who were asked to predict the loads,Q25 and Q150, which would make the five footings settle by 25mm and 150 mm, respectively. Q25 is the allowable footingload satisfying the settlement criterion, and Q150 is more orless the failure load corresponding to ultimate bearing capac-ity. The predicted and measured Q25 and Q150 values aresummarized in Table 1. Also shown in the table are the valuesof measured Q150 divided by the safety factors of 2.5 and 3,which are the allowable footing loads that satisfy the bearingcapacity criterion. It is interesting to note that in all five foot-ings, these allowable loads satisfying bearing capacity crite-rion are reached before the loads corresponding to settlementcriterion. In other words, bearing capacity considerations

20 International Journal of Geotechnical Engineering

Reliability

Accuracy

Settlement ratio (x) =Calculated settlement

Measured settlementfx(x)

XX1—

Figure 1. Accuracy and reliability in settlement predictions.

Table 1. Predicted and measured values of Q25 and Q150

Footing dimensions (m) 1.0 × 1.0 1.5 × 1.5 2.5 × 2.5 3.0 × 3.0 3.0 × 3.0

Q25: Measured (kN): 850 1500 3600 5200 4500

Predicted/Measured: Range 0.07-1.29 0.08-1.73 0.08-1.19 0.08-1.23 0.09-1.24

Mean 0.71 0.84 0.68 0.69 0.70

Std.dev. 0.30 0.60 0.29 0.28 0.35

Q150: Measured (kN): 1740 3400 7100 10250 9000

Predicted/Measured: Range 0.12-2.28 0.12-3.34 0.15-2.32 0.15-2.51 0.15-3.11

Mean 0.65 0.81 0.99 1.08 1.12

Std.dev. 0.45 0.64 0.55 0.59 0.69

Q150/2.5 (Allowable load with FS = 2.5) 696 1360 2840 4100 3600

Q150/3.0 (Allowable load with FS = 3.0) 580 1133 2367 3417 3000

govern the failure of all footings, as opposed to the commonbelief that the settlement considerations are more critical.This is probably due to the overestimations in the settlementprediction methods that result in underestimation of theallowable pressures.

A total of 22 different methods were used by the partici-pants, with Schmertmann (1970, 1978), Burland andBurbidge (1985) and finite element analysis being more pop-ular. Table 1 shows that the quality of predictions were betterfor Q150 than Q25, emphasizing the poor state-of-the-art forsettlement predictions of shallow foundations in sands.

3. TRADITIONAL SETTLEMENT PREDICTIONMETHODS

The traditional settlement prediction methods that werewidely used over the past two decades or more are discussedin this section. These methods are discussed in great detail inseveral foundation engineering text books.

3.1 Terzaghi and Peck (1948) and RelatedMethodsTerzaghi and Peck (1948) proposed the first rational methodfor estimating the settlement of a square footing on granularsoils. They carried out plate load tests using a 300 mm squareplate on sands with N60 = 10, 30 and 50 respectively and thepressure-settlement plots are shown in Figure 2. Here, N60 isthe blow count from standard penetration test, not correctedfor overburden stress. They related the settlement of a Bmeter wide square footing (δfooting) to that of a 300 mm plate(δplate) by the following equation:

(1)

The last term in Eq. 1 accounts for the depth of embedment.Presence of water table in the vicinity of the footing isreflected in the blow count and therefore a separate correc-tion for water table is not warranted. Nevertheless, rise ofwater table, while in service, can reduce the stiffness and pro-duce additional settlements.

Meyerhof (1965) noted the conservativeness in his previ-ous method (Meyerhof, 1956) and the modified expressionfor the settlement is:

(2)

(3)

When correction for depth of embedment is taken intoaccount, Eqs. (2) and (3) would become:

(4)

(5)

Peck and Bazaraa (1969) methods adopt Eq. (3), replacingN60 with (N1)60 blow count from standard penetration testcorrected for overburden stress. The settlement should thenbe multiplied by water table correction and depth correction.Thus,

(6)

where

(7)

σo = total overburden stressσ´o= effective overburden stress

(8)

γ = unit weight of soilThe relationships for (N1)60 are:

(9)

and

( )4

1 4(for 75 kN/m )1 60

60 2NN

oo=

+ ′′ ≤

0 0. σσ

CD

qD

f= −⎛

⎝⎜⎞

⎠⎟1 0 0 4

0 5

. .

.γ

CB

Wo=

σ at 0.5 below the bottom of the foundattion

at 0.5 below the bottom of the fo′σo B uundation

δfooting(mm)kPa 2

0.3=

+⎛⎝⎜

C Cq

N

B

BW D

0 53

1 60

. ( )

( )

⎞⎞⎠⎟

2

δfooting(mm)kPa= −

⎛

⎝⎜⎞

⎠⎟1 33

1460

. ( )q

N

D

Bf

for 1.22 mB ≤

δfooting

2

(mm)kPa 2

0.3=

+⎛⎝⎜

⎞⎠⎟

0 53

60

. ( )q

N

B

Bfor 1.22 mB >

δfooting(mm)kPa

for= ≤1 33

60

. ( )q

NB 1.22

δ δfooting plate= ×+

⎛⎝⎜

⎞⎠⎟

−⎛

⎝⎜⎞

⎠⎟2

0 31

4

2B

B

D

Bf

.

Settlements of shallow foundations on granular soil — an overview 21

Applied pressure (kPa)

Set

tlem

ent

(mm

)

0 100 200 300 400 500 600 700 800 900 10000

10

20

30

40

50

60

Loose

Dense

N60 = 10

Medium

Very dense

N60 = 50

N60 = 30

Figure 2. Pressure-settlement plot of a 300 mm square plate in sandswith N60 = 10, 30 and 50 (load test data from Late Professor G.A.Leonards).

δfooting

2

(mm)kPa 2

0.3=

+⎛⎝⎜

⎞⎠⎟

−0 531

60

. ( )q

N

B

B

Dff

BB

4

⎛

⎝⎜⎞

⎠⎟>for 1.22 m

(10)

While Meyerhof (1965) and Peck and Bazaraa (1969) expres-sions imply that the settlement is proportional to the appliedpressure, the load test data (Figure 2) clearly show that this isnot the case in loose and medium sands. It can also be seenthat δfooting/δplate increases with B, and takes the maximumof 4 at very large B.

These methods were originally developed for squarefootings, but are valid for strip footings too. The higher set-tlement due to deeper influence zone is compensated by theincrease in the soil stiffness due the plane strain situation.

3.2 Schmertmann (1970) and Related MethodsSchmertmann (1970) proposed a simple semi-empiricalexpression, based on elastic analysis and supported by modeltests and finite element analysis, to estimate the settlement ofa footing on granular soil as:

(11)

where C1 and C2 are the depth and time correction factorsgiven by:

(12)

(13)

Here, σ′o = effective overburden stress at the foundationlevel, qnet = net applied pressure at foundation level, and t′ =time since loading in years. The variation of the influence fac-tor Iz with depth is represented by the “2B-0.6 diagram”shown in Figure 3a. The modulus of elasticity (E) is estimatedfrom the cone resistance from a static cone penetration test asE = 2qc.

Schmertmann et al. (1978) made some modifications tothe above method, with new influence factors as shown inFigure 3b, separating square and strip footings. The influencefactor peaks at a depth of 0.5B for square footing and B forstrip footing, and the peak values are given by:

(14)

where σ′o is computed at the depth where Iz,peak occurs.Noting that the stiffness is about 40% larger for plane straincompared to axisymmetric loading, they suggested that E =2.5qc for square footings and Es = 3.5qc for strip footings. For

Iq

zo

, . .peaknet= +′

0 5 0 1σ

Ct

2 1 0 20 1

= + ′⎛⎝⎜

⎞⎠⎟

. log.

Cq

o1 1 0 5= −

′≥.

σ

net

0.5

δfooting net==

=

∑C C qI dz

Ez

z

z B

1 20

2

( )4

3.25(for 75 kN/m )1 60

60 2NN

ooo=

+ ′′ >

0 01. σσ


0 0.2 0.4 0.6 lz lz0

0.5B

B

2B

3B

4B

z

(a) Schmertmann (1970)

B

0 0.2 0.4 0.60

0.5B

B

2B

3B

4B

z

(b) Schmertmann et al. (1978)

Q

(see Eq 14)lz peak

B/L

= 0

B/L =

1

lz0 0.2 0.4 0.60

0.5B

B

2B

3B

4B

z

(c) Terzaghi et al. (1996)

B/L

= 0

B/L =

1

0 <

B/L

< 1

Figure 3. Iz – z variation: (a) Schmertmann (1970), (b) Schmertmann et al. (1978), (c) Terzaghi et al. (1996).

rectangular footings, the settlements should be computed forsquare and strip footing of the same width, and interpolatedon the basis of B/L (L = length of footing).

Terzaghi et al. (1996) simplified this further and sug-gested influence factors as shown in Figure 3c. Here, Iz,peak =0.6 for both square and strip. For rectangular footing, thedepth of influence (see Figure 3c) can be computed as:

(15)

3.3 Burland & Burbidge (1985) MethodBurland and Burbidge (1985) proposed a semi-empiricalmethod, using the blow counts from standard penetrationtest, based on the review of an extensive database of settle-ment records of shallow foundations for buildings, tanks andembankments on granular soils. They noted that the influ-ence depth of the footing, zI, is approximately B0.7, where Band zI are in meters.

They recommend increasing N60 by 25% in gravel orsandy gravel. For fine sands and silty sands below water table,where N60 >15, driving of the split spoon sampler can dilatethe sands which can produce negative pore water pressuresthat would increase the effective stresses and hence overesti-mate the blow counts. Here, Terzaghi’s correction givenbelow should be applied:

N60,corrected = 15 + 0.5(N60 – 15) (16)

The compressibility of the soil was represented by a com-pressibility index (Ic), defined as:

(17)

where Ic is in MPa-1, and N–

60 is the average value of N60within the influence depth zI. For overconsolidated granularsoils, Ic is 1/3 of what is given in Eq. (17).

Burland and Burbidge (1985) suggested that the settle-ment can be estimated from:

δfooting = qnetIczI (18)

In normally consolidated granular soils, Eq. (18) becomes:

(19)

In overconsolidated granular soils, with preconsolidationpressure of σ′p, Eq. (19) becomes:

(20)

(21)

The settlements estimated as above apply for square foot-ings. For rectangular or strip footings, the settlements have tobe multiplied by the following factor (fs):

(22)

The settlements estimated above imply that there is gran-ular soil at least to a depth of zI. If the thickness (Hs) of thegranular layer below the footing is less than the influencedepth, the settlements have to be multiplied by the followingreduction factor (fl):

(23)

Burland and Burbidge (1985) noted some time-depend-ent settlements of the footings, and suggested a multiplica-tion factor (ft) given by:

(24)

where R3 takes into consideration the time dependent settle-ment during the first three years of loading, and the last com-ponent accounts for the time-dependent settlement thattakes place after the first three years at a slower rate. Suggestedvalues for R3 and Rt are 0.3-0.7 and 0.2-0.8 respectively. Thelower end of the range is applicable for static loads and theupper end for fluctuating loads such as bridges, silos, and tallchimneys.

4. RECENT DEVELOPMENTS IN SETTLEMENTPREDICTION METHODSTwo recent methods that appear to give better settlement pre-dictions are the ones proposed by Berardi and Lancellotta(1991) and Mayne and Poulos (1999). These two methods arebriefly discussed below. Sivakugan and Johnson’s (2004)probabilistic approach is an effective way of quantifying therisk associated with the settlement prediction methods.

4.1 Berardi and Lancellotta (1991) MethodBerardi and Lancellotta (1991) proposed a method to esti-mate the elastic settlement which takes into account the vari-ation of the modulus of elasticity of soil with the strain level.This method is also described by Berardi et al. (1991).According to this procedure:

(25)δfooting

net= Iq B

Es

f R Rt

t t= + + ′1

33 log

fH

z

H

zls

I

s

I

= −⎛⎝⎜

⎞⎠⎟

2

fL B

L Bs =+

⎛⎝⎜

⎞⎠⎟

1 25

0 25

2. /

. /

δ σfooting net i= − ′⎛⎝⎜

⎞⎠⎟

qN

Bp

2

3

1 71

601 4

0 7..

. ff q ≥ ′σ p

δ σfooting net if= ≤ ′1

3

1 71

601 4

0 7qN

B q p

..

.

δfooting net= qN

B1 71

601 4

0 7..

.

INc = 1 71

601 4

..

z BL

BI = +⎛⎝⎜

⎞⎠⎟

2 1 log


where Is = influence factor for a rigid footing (Tsytovich,1951) and E = modulus of elasticity of soil. The variation ofIs (Tsytovich, 1951) with Poisson’s ratio v = 0.15 is given inTable 2.

Analytical and numerical evaluations have shown that,for circular and square footings, the depth z25 below the foot-ing beyond which the residual settlement is about 25% of thesurface settlement can be taken as 0.8 to 1.3B. For strip foot-ings (L/B ≥ 10), z25 is about 50 to 70% more as compared tothat for square footings. Thus the depth of influence zI can betaken to be z25. The modulus of elasticity E in Eq. (25) can beevaluated as:

(26)

where pa = atmospheric pressure, σ′o and Δσ′ = effectiveoverburden stress and net effective stress increase due to thefoundation loading, respectively, at a depth B/2 below thefoundation, and KE = nondimensional modulus number.

After reanalyzing the performance of 130 structuresfound on predominantly silica sand as reported by Burlandand Burbidge (1986), Berardi and Lancellotta (1991)obtained the variation of KE with the relative density Drat δ/B = 0.1% and KE at varying strain levels. Figures 4a and4b show the average variation of KE with Dr and[KE(δ/B)/KE(δ/B=0.1%)] with δ/B

In order to estimate the elastic settlement of the footing,an iterative procedure is suggested, which can be described asfollows:

A. Determine the variation of the blow count fromstandard penetration test N60 within the zone ofinfluence, that is z25.

B. Determine the corrected blow count (N1)60 as:

(27)

where σ′o = vertical effective stress

C. Determine the average corrected blow count fromstandard penetration test (N

–1)60 and hence the

average relative density as:

(28)

D. With known Dr, determine KE(δ/B = 0.1%) fromFigure 4a and, hence, E from Eq. (26) for δ/B =0.1%.

E. With the known value of E from Step D, the mag-nitude of elastic settlement δfooting can be calcu-lated from Eq. (25).

F. If the calculated δ/B is not the same as the assumedδ/B, then use the calculated δ/B from Step E anduse Figure 4b to estimate a revised KE(δ/B). Thisvalue can now be used in Eqs. (26) and (25) toobtain a revised δfooting. This iterative procedurecan be continued until the assumed and calculatedδfooting is the same.

DN

r =⎛⎝⎜

⎞⎠⎟

1

0 5

60

.

( )N No

1 60 60

2

1=

+ ′⎛⎝⎜

⎞⎠⎟σ

E K ppE a

o

a

=′ + ′⎛

⎝⎜⎞⎠⎟

σ σ0 50 5

..

Δ


Figure 4. (a) Variation of KE with Dr for δ/B = 0.1%. (b) Variation of[KE(δ/B)/KE(δ/B = 0.1%)] with δ/B (adapted from Berardi and Lancellotta,1991).

Table 2. Variation of Is

Depth of influence, zI

B

L/B 0.5 1.0 1.5 2.0

1 0.35 0.56 0.63 0.69

2 0.39 0.65 0.76 0.88

3 0.40 0.67 0.81 0.96

5 0.41 0.68 0.84 0.89

10 0.42 0.71 0.89 1.06

4.2 Mayne and Poulos (1999) MethodMayne and Poulos (1999) provided a general relationship forelastic settlement calculation of footings using displacementinfluence factors derived from elasticity continuum theory.Here, it is assumed that the soil stiffness increases linearlywith depth, from a value of Eo at footing level. According tothis theory (Figure 5a):

(29)

where = equivalent diameter of a rectangularfooting

ν =Poisson’s ratio of soilIG =displacement influence factor (Figure 5b)IE =settlement coefficient factor to account for depth

of embedmentIF =rigidity coefficient factor

The relationships to estimate IE and IF are:

(30)

(31)

where Ef = modulus of elasticity of the footing material(which is, in most cases, reinforced concrete), t = footingthickness, and k = increase in soil stiffness per unit depth (i.e.,E = Eo + kz). The above procedure will give good results pro-vided the modulus of elasticity of soil is predicted reasonablywell.

4.3 Sivakugan and Johnson’s (2004)Probabilistic ApproachNoting the different degrees of scatter associated with the set-tlement prediction methods, a probabilistic approach is moreappropriate than the traditional deterministic methods. Themagnitude of settlement can have different meaning depend-ing on which method was used for the computations.Sivakugan and Johnson (2004) developed a probabilisticframework, based on the settlement records in the literature,to quantify the risk associated with the settlement predictionmethods. They proposed probabilistic design charts, for four

different settlement prediction methods, which enable thedesigner to quantify the probability that the actual settlementwill exceed a specific limiting value. The design chart for lim-iting settlement value of 25 mm is shown in Figure 6.

It can be seen from Figure 6 that when the settlementestimated by Terzaghi and Peck or Schmertmann et al.method is 25 mm, there is only 26% probability that theactual settlement will exceed 25 mm, demonstrating theirconservativeness. The Burland and Burbidge method is aclear improvement on the quality of predictions, and theBerardi and Lancellotta method improves this even further.

I

E

EB

k

t

B

F

f

o

= +

++ ′

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟ ′

⎛⎝⎜

⎞⎠⎟

π4

1

4 6 10

2

23

.

IB

D

E

f

= −

− ′⎛

⎝⎜

⎞

⎠⎟ +

⎡

⎣⎢⎢

⎤

⎦

11

3 5 1 22 0 4 1 6. exp( . . ) .ν ⎥⎥⎥

′ = ⎛⎝⎜

⎞⎠⎟

BBL4

0 5

π

.

δν

footingnet=

′ −q B I I I

EG F E

o

( )1 2


Rigid Layer

Depth, z

Compressiblesoil layer

t

B´

Ev

EfDf

Eo

Hs

qnet

E

E =Eo + kz

(a)

(b)

1.0

0.8

0.6

0.4

0.2

0

Eo lkB´

Hs lB´ = 0.2

G

10.0

5.0

2.0

1.0

0.5

0.01 0.1 1 10 100

>30

Figure 5. Solution of Mayne and Poulos: (a) Footing on a compressiblelayer; (b) Variation of IG with Eo/kB′ and Hs/B′.


Table 3. Correlations between E and N60 for granular soils

Reference Relationship Soil type

Schultze and Melzer (1965)

Webb (1969)

Ferrent (1963)

Begemann (1974)

Trofimenkov (1974)

Kulhawy and Mayne (1990)

E Np

o

a

= −′

+ ±⎛⎝⎜

⎞⎠⎟

′246 2 263 4 375 6 57 660. log . . .

σ σoo

a

o

ap p

⎛⎝⎜

⎞⎠⎟

≤′

≤0 522

0 1 2

.

.forσ

Dry sand

Sand

Clayey sand

Sand

Silt with sand togravel with sand

Sand

Sand

C = 3 for silt with sand and12 for gravel with sand

E

pN

a

= +5 1560( )

E

pN

a

= +3 33 560. ( )

E

pN

a

= −7 5 1 260. ( )ν

E

pC N N

E

pC N

a

a

= + − >

= + +

40 6 15

40 6

60

60

( )

( )

for 60

for 60N <15

E

pN

a

= ( log350 60to 500)

E

pN

a

==

αα

60

5 for sand with fines; 10 for cllean normally

consolidated sands; and 15 forr clean overconsolidated sands

0 5 10 15 20 25 30 35 40 45 50 55 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Predicted settlement (mm)

p (a

ctua

l set

tlem

ent

will

exc

eed

25

mm

)

Berardi & Lancellotta

Burland & Burbidge

Schmertmann et al.

Terzaghi & Peck

Figure 6. Probabilistic design chart.

5. EMPIRICAL CORRELATIONS FOR MODULUSOF ELASTICITY, E

One of the main factors that contribute to the uncertainty insettlement predictions is our inability to quantify the soilstiffness correctly. Soil stiffness, measured by the modulus ofelasticity, is generally quantified indirectly through the pene-tration resistances from standard penetration or cone pene-tration tests. The various empirical correlations relating N60and qc to E are summarized in Tables 3 and 4 respectively.

6. SUMMARY AND CONCLUSIONS

The current state-of-the-art for predictions of the settlementsof shallow foundations in granular soils is discussed. TheSettlement ′94 prediction session held in Texas clearly showedthe deficiencies in the current state-of-the-art, where the pre-dictions from the 31 international experts varied in a widerange. In spite of having access to the full data from a rigor-

ous site investigation program, their predictions of Q25, theload required to produce 25 mm settlement, were signifi-cantly less than what was measured, implying that the settle-ments were overestimated in general. In reality, thegeotechnical engineer has access to very limited data from thefield, and the quality of predictions can only be worse.

The load test data for the five footings at the above pre-diction sessions showed that, provided the factor of safety isgreater than 2.5, bearing capacity considerations are morecritical than the settlement criterion. It is the poor state-of-the-art for settlement predictions, which results in overesti-mation of the settlements and underestimations of theallowable pressures, which leads one to believe that the settle-ment criterion generally governs the design of shallow foun-dations in granular soils.

The traditional settlement prediction methods, includingTerzaghi and Peck (1948), Schmertmann (1970) and Burlandand Burbidge (1985) are discussed. Two of the most recentmethods, proposed by Berardi and Lancellotta (1991) andMayne and Poulos (1999) appear to give better and more


Table 4. Correlations between E and qc for granular soils

Reference Relationship Soil type

Schultze and Melzer (1965)

Webb (1969)

Buisman (1940) E = 1.5qc Sand

Schmertmann (1970) E = 2qc Sand

Schmertmann et al. (1978) E = 2qc (axisymmetric loading) Normally consolidated sandE = 3.5qc (axisymmetric loading)

Vesic (1970) E = 2(1 + D2r )qc Sand

Bachelier and Parez (1965) E = αqc All soils

DeBeer (1965) E = 1.5qc Sand

E = 1.5qc (for qc> 3 MN/m2)

DeBeer (1974) E = 3qc (for qc < 3 MN/m2) Sand (Greek practice)

E = αqc (1.5 < α < 2) Sand (U.K. practice)

Trofimenkov (1964) E = 2.5qc Sand (lower limit)

Trofimenkov (1974) E = 3qc SandE = 7qc Clay

Thomas (1968) E = αqc (α = 3 to 12) Sand

Bogdanovi (1973) E = 1.5qc (for qc > 4 MN/m2) Sand and sandy gravel

E = 1.5 to 1.8qc (for 2 MN/m2 < qc < 4 MN/m2) Silty saturated sand

E = 1.8 to 2.5qc(for 1 MN/m2 < qc < 2 MN/m2)

E = 2.5 to 3.0qc(for 0.5 MN/m2 < qc < 1 MN/m2)

E ca

=′⎛

⎝⎜⎞⎠⎟

′301.1log o oq

p p– 382.3 +60.3±50.3

σ σ

aa a

⎛⎝⎜

⎞⎠⎟

′0.522

ofor 0 0.8σp

Dry sand

Sand below water tableClayey sand below water table

E/qc = 2.5(qc + 30)

E/qc = 1.67(qc + 15)

α = 0.8 to 0.9 for pure sand; 1.3 to 1.9 for silty sand;3.8 to 5.7 for clayey sand; and 7.7 for soft clay

Clayey silt with silty sand, andsilty saturated sand with silt

(USSR practice)

realistic settlement predictions. The probabilistic design chartpresented by Sivakugan and Johnson (2004) can be used toestimate the probability that the actual settlement will exceed25 mm in the field, based on the settlements estimated fromthe traditional methods.

Several empirical correlations relating the modulus ofelasticity of soil to blow count from a standard penetrationtest and cone resistance from a cone penetration test are dis-cussed. These correlations are quite useful in assessing the soilstiffness, which is required in the settlement computations.

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