Bearing Capacity of Shallow Foundation

Bearing Capacity of Shallow Foundation

BEARING CAPACITY If a footing is subjected to too great a load, some of the soil supporting it will reach a failure state and the footing may experience a bearing capacity failure. The bearing capacity is the limiting pressure that the footing can support.

Supporting soil

Definitions and Key TermsFoundation: Structure transmits loads to the underlying ground (soil). Footing: Slab element that transmit load from superstructure to ground Embedment depth, Df : The depth below the ground surface where the base of the footing rests. Bearing pressure(q): The normal stress impose

by the footing on the supporting ground.(weight of superstructure +

self weight of footing + weight of earthfill if any.)

Definitions and Key TermsUltimate bearing capacity qult /qf /qu : The maximum bearing pressure that the soil can sustain (i.e it fails).

Ultimate net bearing capacity (qunet /qnf /qnu):

The maximum bearing pressure that the soil can sustain above its current overburden pressure

Dqqor

Dqq

nff

fnf

GGround

Safe bearing capacity: it is the maximum pressure which the soil can carry without shear failure or ultimate bearing capacity, qf , divided by Factor of safety ,F.

Net safe bearing capacity: It is the net ultimate bearing capacity divided by factor of safety, F.

DF

qDqq nf

nss γγ

F

qq nf

ns

Definitions and Key Terms (Cont.)

Allowable bearing capacity: (qall /qa): The working pressure that would ensure an acceptable margin of safety against bearing capacity failure, or It is the net loading intensity at which neither soil fails in shear nor there is excessive settlement detrimental to the structure.

Factor of safety: The ratio between (qunet) and (qall). (F.S. = qunet/qall )

Definitions and Key Terms (Cont.)

Ultimate limit state: A state that defines a limiting shear stress that should not be exceeded by any conceivable or anticipated loading during the life span of a foundation or any geotechnical system.

Serviceability limit state: A state that defines a

limiting deformation or settlement of a foundation, which, if exceeded will impair the function of the supported structure.

Basics

Basics

DDf /B 1Terzaghi

Df /B > 4Df /B 2-2.5Others

Design Requirements

1. The foundation must not collapse

or become unstable under any

conceivable load2. Deformation

(settlement) of the structure must be

within tolerablelimits

Stages in load-settlement of shallow foundations

Relatively elastic verticalcompressionThe load-settlement curve is almoststraight.Local yielding starts to affectUpward and outward movement ofthe soil with a possible surfaceheave.General shear failureLarge settlements are produced asplastic yielding is fully developedwithin the soil. In dense sands: softening can

occur after collapse.

Collapse and Failure Loads

(c) Punching shear failure

(a) General shear failure

(b) Local shear failure

Shallow foundations in rock and undrained clays are governed by the general shear case.

Shallow foundations in dense sands are governed by the general shear case. In this

context, a dense sand is one with a relative density, Dr , greater than about 67%.

Shallow foundations on loose to medium dense sands (30% < Dr< 67%) are

probablygoverned by local shear.

Shallow foundations on very loose sand (Dr < 30%) are probably governed by

punching shear.

Characteristics of Each Failure Mode

General shear (Dense sand):– well defined failure mechanism– continuous slip surface from footing to surface– sudden catastrophic failure

Local shear (Loose sand):– failure mechanism well defined only beneath the footing– slip surfaces do not extend to the soil surface– considerable vertical displacement– lower ultimate capacity

Guide lines to know whether failure is local or general

(i) Stress-strain test: (c- soil) general shear failure occurs at low strain, say <5 % while for local shear failure stress-strain curve continues to rise at strain of 10 to 20 %.

(ii) Angle of shear resistance: For > 36o ,general shear failure and < 28o local shear failure.

(iii) Penetration test: N 30 : G.S.F N 5 : L.S.F

Contd…

(iv) Plate Load Test: Shape of the load settlement curve decides whether it is G.S.F or L.S.F

(v) Density Index : ID > 70 G.S.F

ID < 20 L.S.F

For purely cohesive soil, local shear failure may be assumed to occur when the soil is soft to medium, with an unconfined compressive strength qu 10 t/m2 (or cu 5 t/m2).

Contd…

Punching shear (Very Loose sand):– failure mechanism less well defined– soil beneath footing compresses– large vertical displacements– lowest ultimate capacity– very loose soils or at large

embedment depth

Foundation Requirements

1. Safe against failure (bearing capacity or structural failure)

2. Should not exceed tolerable settlement(probable maximum and differential settlement)

3. Its construction should not make any change to existing structure.

4. Should be adequate depth from consideration of adverse environment influence:

i. Zones of high volume change due to moisture fluctuations.

ii. Depth of frost penetrationiii. Organic matter; peat and muck.iv. Abandoned garbage dumps or loosed fill

areas.v. Scouring depth

BEARING CAPACITY ANALYSES IN SOIL-GENERAL SHEAR CASE

Methods of Analyzing Bearing Capacity To analyze spread footings for bearing capacity failures

and design them in a way to avoid such failures, we must understand the relationship between bearing capacity, load,

footing dimensions, and soil properties. Various researchers have studied these relationships using a variety of techniques, including:

Assessments of the performance of real foundations, including full-scale load

tests. Load tests on model footings. Limit equilibrium analyses. Detailed stress analyses, such as finite

element method (FEM) analyses.

• Full-scale load tests, which consist of constructing real spread footings and loadingthem to failure, are the most precise way to evaluate bearing capacity. However, such tests are expensive, and thus are rarely, if ever, performed as a part of routine design. A few such tests have been performed for research purposes.

• Model footing tests have been used quite extensively, mostly because the cost of these tests is far below that for full-scale tests. Unfortunately, model tests have their limitations, especially when conducted in sands, because of uncertainties in applying the proper scaling factors. However, the advent of centrifuge model tests has partially overcome this problem.

• Limit equilibrium analyses are the dominant way to assess bearing capacity of shallow foundations. These analyses define the shape of the failure surface, as shown in Figure , then evaluate the stresses and strengths along this surface. These methods of analysis have their roots in Prandtl' s studies of the punching resistance of metals (Prandtl,1920). He considered the ability of very thick masses of metal (i.e., not sheet metal) to resist concentrated loads. Limit equilibrium analyses usually include empirical factors developed from model tests.

zDucult sNq

• Occasionally, geotechnical engineers perform more detailed bearing capacity analyses using numerical methods, such as the finite element method (FEM). These analyses are more complex, and are justified only on very critical and unusual projects. We will consider only limit equilibrium methods of bearing capacity analyses, because these methods are used on the overwhelming majority of projects.

Essential Points so far

• Failure mode in sands depends on the density of the soil.

• More settlement is expected in loose soils than in dense soils (for the same load). Alternatively, dense soils can sustain more load.

The limit equilibrium method consider the continuous footing as shown in Figure. Let us assume this footing experiences a bearing capacity failure, and that this failure occurs along a circular shear surface as shown. Assume the soil is an undrained clay with a shear strength su.

Neglect the shear strength between the ground surface and a depth D. Thus, the soil in this zone is considered to be only a surcharge load that produces a vertical total stress of zDD = D at a depth D.

The objective of this derivation is to obtain a formula for the ultimate bearing

capacity,qult ,which is the bearing pressure required to cause a bearing capacity failure.

consider a slice of the foundation of length b and taking moments about Point A, we obtain the following:

zDuult

zDuultA

sq

BBbBBbsBBbqM

2

)2/())(()2/)((

It is convenient to define a new parameter, called a bearing capacity factor, Nc and

rewrite Equation as:

Equation is known as a bearing capacity formula, and could be used to evaluate the

bearing capacity of a proposed foundation. According to this derivation, Nc = 2 = 6.28.

This simplified formula has only limited applicability in practice because it considers

zDucult sNq

Contd…

only continuous footings and undrained soil conditions ( = 0), and it assumes thefoundation rotates as the bearing

capacity failure occurs. However, this simple derivation illustrates the general

methodology required to develop more comprehensive bearing capacity formulas.

Contd…

No exact analytical solution for computing bearing capacity of footings is available at present because the basic system of equations describing the yield problems is nonlinear.

On account of these reasons, Terzaghi (1943) first proposed a semi-empirical equation for computing the ultimate bearing capacity of

strip footings by taking into account cohesion, friction and weight of soil, and replacing the overburden pressure with an equivalent surcharge load at the base level of the foundation.

The ultimate bearing capacity, or the allowable soil pressure, can be calculated either from bearing capacity theories or from some of the in situ tests.

Each theory has its own good and bad points. Some of the theories are of academic interest only. However, it is the purpose of the author to present here only such theories which are of basic interest to students in particular andprofessional engineers in general.

Terzaghi's Bearing Capacity Formulas

Assumptions:

The depth of the foundation is less than or equal to its width (D B). The bottom of the foundation is sufficiently rough that no sliding occurs between the foundation and the soil. The soil beneath the foundation is a homogeneous semi-infinite mass (i.e., the soil extends for a great distance below the foundation and the soil properties are uniform

throughout). The shear strength of the soil is described by the formula s = c' + ' tan '.

The general shear mode of failure governs. No consolidation of the soil occurs (i.e.,

settlement of the foundation is due only to

the shearing and lateral movement of the soil).

The foundation is very rigid in comparison to the soil.

The soil between the ground surface and a depth D has no shear strength, and servesonly as a surcharge load.

The applied load is compressive and applied vertically to the centroid of the foundation and no applied moment loads are present.

Bearing Capacity Failure

Transcosna Grain Elevator Canada (Oct. 18, 1913)

West side of foundation sank 24-ft

P

Surcharge Pressure = zD

45-/245-/2

Passive Zone

Lowest Shear Surface

Radial Shear Zone

Wedge Zone

DB

B

Collapse and Failure Loads

Terzaghi considered three zones in the soil, as shown in Figure, immediately beneath the

foundation is a wedge zone that remains intact and moves downward with the foundation. Next, a radial shear zone extends from each

side of the wedge, where he took the shape of the shear planes to be logarithmic spirals.

Finally, the outer portion is the linear shearzone in which the soil shears along planar

surfaces

Since Terzaghi neglected the shear strength of soils between the ground surface and a depth D, the shear surface stops at this depth and the overlying soil has been replaced with the surcharge pressure zD .This approach is conservative, and is part of the reason for limiting the method to relatively shallow foundations (D < B).

Terzaghi developed his theory for continuous foundations (i.e., those with a very large L/B ratio). This is the simplest case because it is a two-

dimensional problem. He then extended it to square and round

foundations by adding empirical coefficients obtained from model tests and produced

the following bearing capacity formulas:

For square foundations:

For continuous foundations:

For circular foundations

BNNNcq qzDcult 3.03.1

BNNNcq qzDcult 5.0

NBNNcq qzDcult 4.03.1

Because of the shape of the failure surface, the values of c and only need to

represent the soil between the bottom of the footing and a depth B below the bottom. The soils between the ground surface and a depth D are treated simply as overburden.

Terzaghi's formulas are presented in terms of effective stresses. However, they also

may be used in a total stress analyses by substituting cT T and D for c', ', and D If saturated undrained conditions exist, we may conduct a total stress analysis with the shear strength defined as cT= Su and T= O. In this case, Nc = 5.7, Nq = 1.0, and N = 0.0.

The Terzaghi bearing capacity factors are:

Contd…

1cos2

tan

0tan

1

07.5

)2/45(cos2

2

tan360/75.0

2

2

p

qc

c

q

KN

forN

N

forN

ea

aN

Contd…

For strip footing:

DRBN.R)N(DcN.F

q

DRBN.R)N(DcN.F

q

DRBN.R)N(DcNF

q

wwqcs

wwqcs

wwqcs

γγγ

γγγ

γγγ

γ

γ

γ

21

21

21

301311

:footingcircular For

401311

: footing square For

5011

Computation of safe bearing capacity

φφ

γ

γ

tan/tancof/c

factorreductiontableWaterRandR

g.s.fforcohesionc

failureshear

localforfactorscapacityBearingN,N,N

failuresheargeneralforφondepending

factorscapacityBearingN,N,N

footingof diameter or footing ofWidth B

footingof Depth D

to safety of Factor F

mm

ww

qc

qc

32and32

32 Where

21

121

0150

121

0150

222222

2

11111

1

wwwwww

w

wwwww

w

R,BR,BZIf,RZIfB

Z.R

R,DZIf,RZIfD

Z.R

BEARING CAPACITY FACTORS [After Terzaghi and Peck(1948)]

Nq and NcN

(de

gree

s)

NNq

Nc

Bearing Capacity Factors

Effective Stress Analysis Two situations can be simply analysed. The soil is dry. The total and effective stresses are identical and the analysis is identical to that described above except that the parameters used in the equations are c´, ´, dry rather than cu, u, sat. If the water table is more than a depth of 1.5 B (the footing width) below the base of the footing the water can be assumed to have no effect.

Further Developments

Skempton (1951) Meyerhof (1953) Brinch Hanson (1961) De Beer and Ladanyi (1961) Meyerhof (1963) Brinch Hanson (1970) Vesic (1973, 1975)

)4.1tan()1(

cot)1(

)2/45(tan

5.0 : LoadInclined

5.0 :load Vertical

2tan

q

qc

q

qqqcccult

qqqcccult

NN

NN

eN

diNBdiNqdicNq

dsNBdsNqdscNq

Meyerhof Bearing Capacity Equations

.Lor D//BL ratio use 6,-4 section. in presented 2),-(4

equation ofsubscripts,For and , asand

shape of sets twocompute tohavemay you0)or H

0either yH (and Hloada and load a vertical With.3

. Hload

horizontala by ngaccompanyi load a verticalor load

a verticaleither withconsistent are above valuesThe 2.

.cVesiby not but n Hanse

byL.B dimension baseeeffectiv of use Note.1

..,...

B

BL

B

Liddssd

s

LiBiLiBii

i

Notes: 1. Use Hi as either HB or HL . Or both if HL >0.

2. Hansen did not give an ic for > 0. The value above is from Hansen and also used by Vesic.

3. Variable ca = base adhesion on the order of 0.6 to1.0 x base cohesion.

4. refer to sketch for identification of angles and , footing width D, location of Hi(parallel and at top of base slab; usually also produces eccentricity). Especially note V = force normal to base and is not the resultant R from combining V and Hi .

Bearing –capacity equations by the several authors indicated

Terzaghi(1943). See table 4-2 for typical values and for kp values.

806001

313101

12

1

24550

2

2750

2

2

...s

...s

squareroundstripFor

cos

KtanN

cot)N(N

ea

)/(cosaa

NsBN.NqscNq

c

p

qc

tan)/.(

qqccult

γ

γ

γ

φφπ

γγ

φφ

φ

φγ

000

02

1

2

901:nInclinatio

01

10101

B201:Depth

01

10101

201 :Shape

For e Valu Factors

φθγ

φφ

θγ

φθ

φγ

φγ

φ

φγ

φγ

φ

fori

o

oi

Anyo

o

qici

dqd

oBD

pK.dqd

AnyD

pK.cd

sqs

oLB

pK.sqs

AnyLB

pK.cs

H

RV

<

Where Kp = tan2 (45+/2) = angle of

resultant R measured from vertical without a sign: if = 0 all i =

1.0B.L.D = previously defined

Table 4-3

• Meyerhof(1963) see Table 4-3 for shape, depth and inclination factors.

φ

φ

φ

γ

γ

γ

φπ

γγ

γγ

411

1

245

50:Load Inclined

50 :Load Vertical

2

.tanNN

cotNN

/taneN

idB.idNqidcNq

dsB.dsNqdscNq

q

qc

tan

q

qqqcccult

qqqcccult

Hansen (1970).* See Table 4-5 for shape, depth, and other factors.

φ

φ

γ

γ

γγγγγγ

tanN.N

N

N

qgbidss.q

bgidsBN.

bgidsNqbgidscNq

q

c

q

cccccuult

qqqqqqccccccult

151

above Meyerhof as same

above Meyerhof as same

1145use

0When

50

:General

0.6LB0.41.0γ(V)sφallfor1.0γd0.6LB0.41.0γ(H)s ______________________________________________________φallfor abovedefinedktanφLB1.0q(V)s

k2sinφi(1φ2tan1qdsinφLB1.0q(H)s _________________________________________________________ radiansinkstripfor1.0cs1D/Bfor(D/B)1tankLB.cNqN1.0c(V)s

1D/BforBDkLB.cNqN1.0c(H)s)o0(φ0.4kcd)o0(φLB0.2c(H)s factors Depth factors Shape equations capacitybearing cVesior Hansen the in usefor factors depth and Shape

TABLE 4-5(a)

radiansin

)tan.exp(b

)tanexp(qb

)(oo

cbcotac

fAV

iHo/o.

i

)(oo

cbcotac

fAV

iH.

i

)basetilted(factorsBase

)tan.(gqgcotac

fAV

iH.

qi

oo

.cgqN

qiqici

oo

cgac

fA

iH

.ci

___________________________________________________)slopeonbase(factorsGroundfactorsnInclinatio___________________________________________________

η

φηγ

φηα

φηα

φ

ηγ

φηα

φγ

α

βγ

α

φ

β

β

72

252

2

0147

1245070

1

0147

1701

51

2

5501150

1

14701

1

1

147150

TABLE 4-5(b)

• Vesic (1973, 1975).* See Table 4-5 for shape, depth, and other factors.

_________________________________________

tanNN

aboveMeyerhofassameN

aboveMeyerhofassameN

q

c

q

φγ 12

above. equations sHansen' use

*These methods require a trial process to obtain design base dimensions since width B and length L are needed to compute shape, depth, and influence factors. †See Sec. 4-6 when ii < 1.

2

1

2

0112

1452

112

00101

base)(tiltedfactorsBase

0101

withdefinedbelowdefinedand

0145

10

1

1

14501

slope)on(basefactorsGroundfactorsnInclinatio

terms.oftionidentificaforsketchtoreferandbelowesnotSee

equations.capacitybearing1973,1975bc Vesithe

for factors base and ground, n,inclinatio of Table

φη

φβ

φφ

βφ

φφ

φ

ββ

φ

γ

γ

γ

tan.bbB/LB/L

mm

tan.b

L/BL/B

mm

)(gbcotcAV

H..i

____________________

tan.ggcotcAV

H.i

iim,i

tan.

iig)(

N

iii

radiansin.

g)(NcA

mHi

________________________________________________________

________________________________________________________

qL

cB

cc

m

af

i

q

m

af

iq

cqq

q

qc

q

q

qc

c

caf

ic

Table 4-5(c)

• Notes:1. When = 0 (and 0) use N = -2 sin(±) in N term.2. Compute m = mB when Hj = HB (H parallel to B) and

m = mLwhen Hi =HL (H parallel to L). If you have both HB and Hi ,use m = mB 2 +m2

L Note use of B and L, not B', L3. Refer to Table sketch and Tables 4-5a,b for term identification.4. Terms Nc,Nq, and N are identified in Table 4-1.

5. Vesic always uses the bearing-capacity equation given in Table 4-1 (uses B‘ in the N term even when Hi = HL).

6. Hi term < 1.0 for computing iq, i (always).

General Observations about Bearing Capacity

• 1. The cohesion term dominates in cohesive soils.• 2. The depth term (γ D Nq) dominates in cohesionless soils. Only a small increase

in D• increases qu substantially.• 3. The base width term (0.5 γ B Nγ) provides some increase in bearing capacity for

both• cohesive and cohesionless soils. In cases where B < 3 to 4 m this term could be• neglected with little error.• 4. No one would place a footing on the ground surface of a cohesionless soil mass.• 5. It's highly unlikely that one would place a footing on a cohesionless soil with a• Dr < 0.5. If the soil is loose, it would be compacted in some manner to a higher• density prior to placing footings on it.• 6. Where the soil beneath the footing is not homogeneous or is stratified, some

judgment• must be applied to determining the bearing capacity.

EFFECT OF WATER TABLE ON BEARING CAPACITY

• The theoretical equations developed for computing the ultimate bearing capacity qu of soil are

• based on the assumption that the water table lies at a depth below the base of the foundation equal

• to or greater than the width B of the foundation or otherwise the depth of the water table from

• ground surface is equal to or greater than (D,+ B). In case the water table lies at any intermediate

• depth less than the depth (D,+ B), the bearing capacity equations are affected due to the presence of

• the water table.

• Two cases may be considered here.• Case 1. When the water table lies above the

base of the foundation.• Case 2. When the water table lies within depth

B below the base of the foundation.• We will consider the two methods for

determining the effect of the water table on bearing

• capacity as given below.

Method 1For any position of the water table within the depth (Df+ B), we may write Eq. as:

Eq.oftermsthirdandsecond

thebothinpurposespracticalallfor

.foundation the of level base the

below table waterfor factor eduction

,foundation the of level base the

above table waterfor factor reduction21

sat

2

1

21

γγ

γγ γ

rR

RWhere

RBNRNDcNq

w

w

wwqfcu

• Case 1:When the water table lies above the base level of the foundation or when Dwl/Df < 1

• (Fig. 12.10a) the equation for Rwl may be written as

..Rhavewe,.D/Dforand

,.Rhavewe,D/DFor

D

DR

wfw

wfw

f

ww

0101

500

121

11

11

11

• Case 2:When the water table lies below the base level or when Dw2/B < 1 (12.1 Ob) the equation for Rw2 is

• Method 2: Equivalent effective unit weight method

0101

500

121

22

22

22

.Rhavewe,.B/Dforand

.Rhavewe,B/DFor

B

DR

ww

ww

ww

WTabovelyingsoil

ofweightunitsaturatedormoist

foundationtheof

levelbasetheabovelyingsoilof

weightuniteffectiveweighted

effectiveweightedWhere21

2

1

21

m

e

e

eqfecu BNNDcNq

γ

γ

γ

γγ γ

sat =saturated unit weight of soil below the WT (cas1 or case 2) =Submerged unit weight of soil =(sat- w)

Case 1An equation for e1 may be written as

γγγγ

γγ

γγ

γγγγ

mw

e

me

e

mf

we

B

D

D

D

22

1

2

11

2Case

Which Equations to Use There are few full-scale footing tests

reported in the literature (where one usually goes to find substantiating data).

The reason is that, as previously noted, they are very expensive to do and the

cost is difficult to justify except as pure research (using a government grant) or for a precise determination for an important project— usually on the basis of settlement control.

Few clients are willing to underwrite the costs of a full-scale footing load test

when the bearing capacity can be obtained— often using empirical SPT or CPT data directly—to a sufficient precision for most projects.

Use for Best forTerzaghi

Hansen, Meyerhof , Vesic

Hansen , Vesic

Very cohesive soils where D/B 1or for a quick estimate of qult to compare with other methods. Do not use for footings with moments and/or horizontal forces or for tilted bases and/or sloping ground.

Any situation that applies, depending on user’s preference or familiarity with a particular method.

When base is tilted; when footing is on a slope or when D/B > 1

Bearing Pressure from In situ Tests• From Empirical Formulae• SPT• (Terzaghi & Peck )• Sandy Soil

o

n

nn

w

n

wna

wnwn

log.C

NCN

aletPeckoverburdenforCorrection

mminsettlementAllowables

correctiontablewaterc

)necessaryifesubmergencand(

overburdenforvalueNcorrectedaverageN

m/tscN.q

.mmexceedingnotsettlementforpressurenetqwhere

kPacN.m/tcN.q

σ200

770

0410

25

25100251

2

25

2

25

Cn max. = 2

o in t/m2 (10 Ton/m2 )

o 2.5 t/m2

Correction for submergence(very fine silty sand below water table and N > 15)N =15+ ½(Nn – 15)

o t/m2 Cn

0 20.6 – 1.0 1.81.5 – 2.0 1.610 1.0

For o 2.5 t/m2

Bearing Pressure for Rafts and Piers

• q50 =2.05 Nn cw t/m2

• q50 = net pressure for settlement = 50 mm or differential settlement = 20 mm

• cw = 0.5 + 0.5 Dw /D + B 1

• Where Dw = depth of water table below the ground surface

• cw = 0.5 for Dw= 0 and cw= 1 for Dw= D + B• The proximity of water table is likely to reduce

the bearing capacity by 50 % or increase the settlement by 100 % .

• For designing of footings, generally N values are determined at 1 m interval as the test boring is advanced.

• Generally the average corrected values of N over a distance from the base of footing to a depth B – 2B below the footing is calculated. When several borings are made, the lowest average should be used.

• For raft. N is similarly calculated or determined, if Nn is less than 5.

• Sand is too loose and should be compacted or alternative foundation on piles or piers should be considered.

• If the depth of raft D ie less than 2.5 m, the edges of raft settle more than the interior because of lack of confinement of sand.

By Meyerhof’s Theory

• qnet 25 =11.98 Nn Fd For B 1.22m and 25 mm settlement, q = kN/m2

• qnet 25 =7.99 Nn Fd (B + 0.305/B)2 For B > 1.22m• B in mm• By Bowles (50 % above)• qnet 25 =19.16 Nn Fd (s/25.4) For B 1.22 m (kN/m2)

• qnet 25 =11.98 (B + 0.305/B)2 (For B > 1.22m) x Nn Fd (s/25.4)

• Where Fd = Depth factor = 1 + 0.33(Df /B) 1.33• s = tolerable settlement.

Parry’s Theoryqult = 30 N kN/m2 D B

Teng (For continuous or strip footing) qnet (ult) =1/60 { 3 N2 BRw + 5(100 + N2) Df Rw}

For square and circular: qnet (ult) =1/30 {N2 BRw + 3(100 + N2) Df Rw}

qnet = ulltimate bearing capacity in t/m2

N = corrected SPT value Rw , Rw = correction factor for water table

B = width of footing Df = depth of footing

Empirical relationships for CN (Note: o is in kN/m2)

Source CN

Liao and Whitman (1960)

Skempton (1986)

Seed et al. (1975)

Peck et al. (1974)

o

.σ1

789

o. σ 01012

695

2511.

log. oσ

252

1912770

m/kN.for

log.

o

o

σ

σ

SAFE BEARING PRESSURE FROM EMPIRICAL EQUATIONS

BASED ON CPT VALUES FOR FOOTINGS ON COHESIONLESS SOIL

mm.25ofsettlementa

forbeenhaveequationsaboveThe

kPain andkg/m

in resistence point cone the is where

kPa72

widthsall for formula eapproximat An

m21forkPa1

112

m21forkPa63

2

2

2

2

2

.q

q

Rq.q

.BRB

q.q

.BRq.q

s

c

wcs

wcs

wcs

Meyerhof (1956)

• Allowable bearing pressure of sand can be calculted:

• q c is in units kg/cm2. If qc is in other units kg/cm2, you must convert them before using in the equation below.

455cq

N

By Meyerhof (1956)

mB

m/kNcetanresisnpenetratioconeqwhere

mmsettlementm.BForB.

B.qq

mmsettlementm.BForq

q

c

cnetall

cnetall

2

2

25221283

128325

2522115

Terzaghi

• The bearing capacity factors for the use in Terzaghi equations can be estimated as:

• Where qc is avaeraged over the depth interval from about B/2 above to 1.1B below the footing base. This approximation should be applicable for Df / B 1.5. For chesionless soil one may use:

• Strip qult = 28 - 0.0052 (300- qc)1.5 (kg/cm2)

• For square qult = 48 - 0.009 (300- qc)1.5 (kg/cm2)

cq qN.N. γ8080

For clay one may use

2

2

kg/cm3405

kg/cm2802

cult

cult

q.qsquare

q.qStrip

Bearing Capacity from Plate Load Test This is reliable method to obtain bearing capacity. The cost is very high.

By using several sizes of plates this equation can be solved graphically for qult.

termNthe

isNandtermsNandNtheincludesMWhere

B

BNMq

qq

qc

testload

foundationfoundationult

testloadultfoundationult

γ

,

,,

Practically, for extrapolating plate load tests for sands (which are often in a configuration so that the Nq term is negligible), use the following

It is not recommended unless the Bfoundation/Bplate is not much more than about 3. When the ratio is 6 to 15 or more the extrapolation from a plate- load test is little more than a guess that could be obtained at least as reliably using an SPT or CPT correlation.

plate

foundationplateult B

Bqq

Housel's (1929) Method of Determining Safe Bearing Pressure from Settlement Consideration

ObjectiveTo determine the load Qf and the size of a foundation for a permissible settlement Sf.

Housel suggests two plate load tests with plates of different sizes, say B1 x B1 and

B2 x B2 for this purpose.

.shearperimeterto

ingcorrespondttanconsanothern

pressurebearingthe

toingcorrespondttanconsam

plateofperimeterP

plateofareacontactA

plategivenaonappliedloadQWhere

nPmAQ

p

pp

Procedure1 Two plate load tests are to be conducted at

the foundation level of the prototype as per the procedure explained earlier.

2. Draw the load-settlement curves for each of the plate load tests.

3. Select the permissible settlement Sf. for the foundation.

4. Determine the loads Q1 and Q2 from each of the curves for the given permissible settlement sf

Now we may write the following equationsQ1 =mAp1 + nPp1

For plate load test 1.Q2 =mAp2 + nPp2

For plte load test2.The unknown vaues of m&n can be found by solvingthe above equations.The equation for a prototype foundation may be written as

Qf = mAf + nPf

Where Af area of the foundation, Pf =perimeter of the foundation.

When Af and Pf are known, the size of the foundation can be determined.

Bearing Capacity on Layered SoilsCase (a): Strong over weak

(su1/su2 >1). If H/B is relatively small, failure

would occur as punching in the first layer, followed

by general shear failure in the second (the weak) layer If H/B is relatively

large, the failure surface would be fully contained within the first (upper layer).


(su1/su2 >1) (cont.)


(su1/su2 >1) (cont.)Where:B = width of foundationL = length of foundationNc = 5.14 (see chart)sa = cohesion along the line a-a' in the previous figure.

Bearing Capacity on Layered SoilsCase (b): Weak over strong

(su1/su2 <1)

Bearing Capacity on Layered SoilsII) Dense or compacted sand

above soft clayIf H is relativelysmall, failure wouldextend into the softclay layer

If H is relativelylarge, the failuresurface would befully containedwithin the sandlayer.


above soft clay (cont.)


above soft clay (cont.)

BEARING CAPACITY BASED ON BUILDING CODES

(PRESUMPTIVE PRESSURE)• In many cities the local building code

stipulates values of allowable soil pressure to use when designing foundations. These values are usually based on years of experience, although in some cases they are simply used from the building code of another city.

Values such as these are also found in engineering and building-construction handbooks.

These arbitrary values of soil pressure are often termed presumptive pressures.

Most building codes now stipulate that other soil pressures may be acceptable if

laboratory testing and engineering considerations can justify the use of alternative values.

Presumptive pressures are based on a visual soil classification.

Table 4-8 indicates representative values of building code pressures. These values areprimarily for illustrative purposes, since it is generally conceded that in all but minor construction projects some soil exploration should be undertaken

• Major drawbacks to the use of presumptive soil pressures are that they do not reflect the depth of footing, size of footing, location of water table, or potential settlements.

Documents

Bearing Capacity of Shallow Foundation