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 Terms Foundation: Structure transmits loads to the underlying ground (soil). Footing: Slab element that transmit load from superstructure to ground Embedment depth, Df : The depth below 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 Terms Ultimate bearing capacity q ult

/qf /qu : The maximum bearing pressure that the soil can sustain (i.e it fails). Ultimate net bearing capacity (qunet /qnf /qnu): G Ground Theq maximum bearing pressure = q − γ D nf f that the soil can sustain above or qcurrent D its pressure f = qnf + γoverburden

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.

qnf qs = qns + γD = + γD F Net safe bearing capacity: It is the net ultimate bearing capacity divided by factor of safety, F.

qnf qns = F

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

Df /B ≤ 1 D Terzaghi

Df /B≤ 2-2.5 Others

Df /B > 4

Design Requirements 1. The foundation must not collapse or become unstable under any conceivable load 2. Deformation (settlement) of the structure must be within tolerable limits

Stages in loadsettlement of shallow foundations

Relatively elastic vertical compression The load-settlement curve is almost straight. Local yielding starts to affect Upward and outward movement of the soil with a possible surface heave. General shear failure Large settlements are produced as plastic yielding is fully developed within the soil. In dense sands: softening can occur after collapse.

Collapse and Failure Loads

(a) General shear failure

(b) Local shear failure

(c) Punching 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 probably governed 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-φ 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 φ > 36o ,general shear failure and φ < 28o local shear failure. (iii) Penetration test: N ≥ 30 : G.S.F N ≤ 5 : L.S.F

Contd…

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).

– – – – –

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 penetration iii. Organic matter; peat and muck. iv. Abandoned garbage dumps or loosed fill areas. v. Scouring depth

BEARING CAPACITY ANALYSES IN SOILGENERAL 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 loading them 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.

qult = N c su + σ zD

• 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 σ zD D = γ 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: M A = ( qult Bb)( B / 2) − ( suπBb)( B ) − σ zD Bb( B / 2) 

qult = 2π su + σ zD

It is convenient to define a new parameter, called a bearing capacity factor, Nc and rewrite Equation as: q = N s +σ ult

c u

zD

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 = 2π = 6.28. This simplified formula has only limited applicability in practice because it considers

Contd

Contd… only continuous footings and undrained soil conditions (φ = 0), and it assumes the foundation rotates as the bearing capacity failure occurs. However, this simple derivation illustrates the general methodology required to develop more comprehensive bearing capacity formulas.

 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 and professional 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' + σ ' tan φ '.

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 serves only 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

P

D

B φ

φ

Wedge Zone B

Surcharge Pressure = σ ′

45-φ ′ /2

zD

45-φ /2 Passive Zone

Lowest Shear Surface Radial Shear Zone

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 shear zone 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 σ 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 twodimensional 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:

′ N q + 0.4 γ ′ B N γ qult = 1.3 c′N c + σ zD For continuous foundations: q = c′N + σ ′ N + 0.5γ ′ BN ult

c

zD

q

γ

For ′ ′ qult =circular 1.3 c′ N c + σfoundations zD N q + 0.3γ BNγ

Because of the shape of the failure surface, the values of c′ and φ ′ 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 φ T and σ D for c', φ ', and σ D ′ If saturated undrained conditions exist, we may conduct a total stress analysis with the shear strength defined as cT= Su and φ T= O. In this case, Nc = 5.7, Nq = 1.0, and Nγ = 0.0. The Terzaghi bearing capacity factors are:

Contd…

Contd…

a 2θ Nq = 2 cos2 ( 45 + φ ′ / 2) aθ = eπ ( 0.75−φ ′ / 360 ) tan φ ′ N c = 5.7

for φ ′ = 0

Nq −1 Nc = tan φ ′

for φ ′ > 0

 tan φ ′  K pγ Nγ = − 1  2 2  cos φ ′ 

Computation of safe bearing capacity For strip footing: qs = For qs = For qs =

1 [ cN c + γD( N q − 1 )Rw1 + 0.5γBN γRw 2 ] + γD F square footing : 1 [1.3cN c + γD( N q − 1 )Rw1 + 0.4γBN γRw 2 ] + γD F circular footing : 1 [1.3cN c + γD( N q − 1 )Rw1 + 0.3γBN γRw 2 ] + γD F

W here F = F actorof safety 2 to 3 D = D epth of footing B= W idth of footingor diam eterof footing N c , N q , N γ = B earingcapacity factors dependingon φ for general shear failure N c′ , N q′ , N γ′ = B earingcapacity factors for local shear failure c = cohesion for g.s.f Rw1 and Rw 2 = W ater table reduction factor c m = 2 / 3 of c and tanφm = 2 / 3 tanφ

Z   Rw1 = 0.5 1 + w 1  D   Z   Rw 2 = 0.5 1 + w 2  B  

1 If Z w 1 = 0 Rw 1 = , 2

If Z w 1 = D , Rw 1 = 1

1 If Z w 2 = 0 Rw 2 = , If Z w 2 = B , Rw 2 = B , Rw 2 = 1 2

φ (degrees )

Nq

Nγ

Nc

Nq and Nc

Nγ

BEARING CAPACITY FACTORS [After Terzaghi and Peck(1948

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´, φ ´, γ dry rather than cu, φ u, γ 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)

Meyerhof Bearing Capacity Equations Vertical load : qult = cN c sc d c + q N q sq d q + 0.5γB′N γ sγ dγ Inclined Load : qult = cN cic d c + q N qiq d q + 0.5γB′N γ iγ dγ N q = eπ tan φ tan 2 ( 45 + φ / 2) N c = ( N q − 1) cot φ N γ = ( N q − 1) tan(1.4φ )

1. Note use of ′effective′ base dimension B′.L′ by Hansen but not by Vesic′. 2. The values above are consistent with either a vertical load or a vertical load accompanying by a horizontal load H B . 3. With a vertical load and a load H L (and either yH B = 0 or H B > 0) you may have to compute two sets of shape si and d i as si . B , si . Land d i . B , d i . L. For i, Lsubscripts of equation (4 - 2), presented in section. 4 - 6, use ratio L′/B or D/L′.

Notes: 1.Use Hi as either HB or HL . Or both if HL >0. 2.Hansen did not give an ic for φ > 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 η and β , 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 See indicated Terzaghi(1943). table 4-2 for typical values and for kpγ values. qult = cN c sc + qN q + 0.5γBN γsγ

a2 Nq = a cos 2 ( 45 + φ/ 2 ) a = e ( 0.75 π− φ/ 2 ) tan φ N c = ( N q − 1 ) cot φ  tan φ K pγ Nγ = − 1  2 2  cos φ 

For strip round square sc 1.0 1.3 1.3 sγ

1.0

0.6

0.8

Factors

Value B sc = 1 + 0.2 K p L

Shape :

B sq = sγ = 1 + 0.1 K p L sq = sγ = 1 D d c = 1 + 0.2 K p B

Depth :

D d q = d γ = 1 + 0.1 K p B d q = dγ = 1 Inclination :

R

θ <φ

V H

For Any φ

Table 4-3

φ> 10 o φ= 0 Any φ φ> 10 o φ= 0

2  θo  ic = iq =  1 − o  Any φ  90  2 o   θ iγ =  1 − o  φ> 0 φ   iγ = 0 for θ > 0 φ= 0

Where Kp = tan2 (45+φ /2) φ = angle of resultant R measured from vertical without a sign: if φ = 0 all iγ = 1.0 B.L.D = previously defined

• Meyerhof(1963) see Table 4-3 for shape, depth and inclination factors. Vertical Load : qult = cN c sc d c + q N q sq d q + 0.5γB′sγd γ Inclined Load : qult = cN c d c ic + q N q d q iq + 0.5γB′d γiγ N q = e πtan φ tan 2 ( 45 + φ/ 2) N c = ( N q − 1) cot φ

N γ = ( N q − 1) tan( 1.4φ)

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

qult = cN c sc d c ic g c bc + qN q sq d q iq g q bq + 0.5γBN γsγd γiγg γbγ

When

φ= 0

use

qult = 5.14 su ( 1 + sc′ + d c′ − ic′ − bc′ − g c′ ) + q N q = same as Meyerhof above N c = same as Meyerhof above N γ = 1.5( N q − 1) tan φ

Shapeanddepthfactorsfor usein theHansen or Vesic′ bearingcapacityequations Shapefactors Depthfactors B′ s′ =0.2 (φ =0o) d′ =0.4k (φ =0o) c c(H) L′ N q B′ s =1.0+ . k = DBforD/B ≤1 c(H) N L′ c N q B s =1.0+ . k = tan−1(D/B) forD/B >1 c(V) N L c s =1.0forstrip kinradians c _________________________________________________________ B′ s =1.0+ sinφ d =1+2tanφ′(1 −sinφi 2k q q(H) L′ B s =1.0+ tanφ kdefinedabove q(V) L for allφ ______________________________________________________ B′ s =1.0−0.4 ≥0.6 d =1.0 for allφ γ γ(H) L′ B s =1.0−0.4 ≥0.6 γ(V) L

ABLE 4-5(a)

___________________________________________________ Inclination factors Ground factors( base on slope ) ___________________________________________________ H o β i ic′ = 0.5 − 1 − gc′ = A ca 147 o f 1 − iq βo ic = iq − gc = 1.0 − Nq − 1 147 o α   1 0.5 H i  iq = 1 − gq = gγ = ( 1 − 0.5 tan β)5  V + A c cot φ f a  

TABLE 4-5(b)

2≤α ≤5 1

Base factors( tilted base )

α

  1 0.7 H i  iγ = 1 −  V + A c cot φ f a  

(

)

ηo ′ bc = ( φ= 0 ) 147 o α

 0.7 − ηo / 450o H  2 i iγ = 1 −  V + A ca cot φ  f  

2≤α ≤5 2

ηo bc = 1 − ( φ> 0 ) 147 o bq = exp( −2ηtan φ) bγ = exp( −2.7ηtan φ) η in radians

• Vesic′ (1973, 1975).* See Table 4-5 for shape, depth, and other factors. use Hansen' s equations above. N q = same as Meyerhof above N c = same as Meyerhof above N γ = 2( N q + 1) tan φ

_________________________________________ *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.

Table of inclinatio n, ground, and base factors for the Vesi c ′( 1973,1975b ) bearing − capacity equations. See not es below and refer to sketch for identifica tion of terms. __________ __________ __________ __________ __________ ______ Inclinatio nfactors Ground factors (base on slope) __________ __________ __________ __________ __________ ______

Table 4-5(c)

β 5.14

ic′ = 1 −

mH i A f ca N c

( φ= 0 )

g c′ =

ic = iq −

1 − iq Nq −1

( φ> 0 )

g c = iq −

iq , and m defined below   Hi iq = 1.0 − V + A f c a cot φ 

β in radians

1 − iq φ> 0 5.14 tan φ

iq defined with ic

m

g q = g γ = ( 1.0 − tan β)

2

Base factors (tilted base) __________ __________   Hi iγ = 1.0 − 1.0 − V + A f c a cot φ  2+B / L m = mB = 1+ B / L 2+L/ B m = mL = 1+ L / B

m +1

bc′ = g c′ bc = 1 −

( φ= 0 ) 2β 5.14 tan φ

bq = bγ = ( 1.0 − ηtan φ)

2

• Notes:

1. When φ = 0 (and β ≠ 0) use Nγ = -2 sin(±β ) in Nγ 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 +m2L Note use of B and L, not B', L′ 3. Refer to Table sketch and Tables 4-5a,b for term identification. 4. Terms Nc,Nq, and Nγ are identified in Table 4-1. 5. Vesic′ always uses the bearing-capacity equation given in Table 4-1 (uses B‘ in the Nγ term even when Hi = HL). 6. Hi term < 1.0 for computing iq, iγ (always).

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 Contd… table from

ground surface is equal to or greater than (Df+ B). In case the water table lies at any intermediate depth less than the depth (Df+ 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 1 For any position of the water table within the depth (Df+ B), we may 1 write Eq. as: qu = cN c + γD f N q Rw1 + γBN γRw 2 Where Rw1

2 = reduction factor for water table above

Rw 2

the base level of the foundation, = reduction factor for water table below

the base level of the foundation. γ= γsat for all practical purposes in both the second and third terms of Eq.

Case 1: When the water table lies above the base level of the foundation or when Dw1/Df < 1 (Fig. 12.10a) the equation for Rw1 may be as Dw1  1  written  Rw1 =  1 + 2 D f  For Dw1 / D f = 0 , we have Rw1 = 0.5 ,

and for Dw1 / D f = 1.0 , we have Rw1 = 1.0.

Case 2: When the water table lies below the base level or when Dw2 /B < 1 (12.10 b) the equation for Rw2 is

Dw 2  1 Rw 2 =  1 +  2 B  For Dw 2 / B = 0 , we have Rw 2 = 0.5 and for Dw 2 / B = 1.0 , we have Rw 2 = 1.0 Method 2: Equivalent effective unit weight method

1 qu = cN c + γe 1 D f N q + γe 2 BN γ 2 Where γe 1 = weighted effective γe 2 = weighted effective unit weight of soil lying above the base level of the foundation γm = moist or saturated unit weight of soil lying above WT

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

Case 1 An equation for γ Dw1 ( γm − γ′) γe 1 = γ′ + Df γe 2 = γ′ Case 2 γe 1 = γm Dw 2 ( γm − γ′) γe 2 = γ′ + B

e1

may be written as

General Observations about Bearing Capacity 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 4m this term could be neglected with little error. 4. No one would place a footing on the ground surface of a cohesionless soil mass. 1.

5. It is 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.

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 for

Terzaghi

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.

Hansen, Meyerhof , Vesic′ Hansen , Vesic′

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(empirical From SPT methods)

• • (Terzaghi & Peck ) • Sandy Soil q = 1.025 N c t / m = 10.25 N c 2

25

n

w

n

w

kPa

where q25 = net pressure for settlement not exceeding 25mm . qa = 0.041 N n c w s t / m 2 N n = average corrected N value for overburden ( and submergence if necessary ) c w = water table correction s = Allowable settlement in mm Correction for overburden ( Peck et al ) N n = Cn × N C n = 0.77 log

200 σo

Cn max. = 2 σ

o

σ

o

in t/m2 (10 Ton/m2 ) For σ 2 ≥ 2.5 t/m

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

σ

o

o

≤ 2.5 t/m2

t/m2 Cn

0

2

0.6 – 1.0

1.8

1.5 – 2.0

1.6

10

1.0

Empirical relationships for CN (Note: σ ′ o is in kN/m2) Source Liao and Whitman (1960) Skempton (1986) Seed et al. (1975) Peck et al. (1974)

CN 1 9.78 σo′

2 1 + 0.01 σo′  σo′  1 − 1.25 log   95 . 6    1912  0.77 log    σo′  for σo′ ≥ 2.5 kN / m 2

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= Df + 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 Nn 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 i.e 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 qnet25 =11.98 Nn Fd For B≤ 1.22 and 25 mm settlement, q = kN/m2 qnet25 =7.99 Nn Fd (B + 0.305/B)2 For B > 1.22 B in mm By Bowles (50 % above) qnet25 =19.16 Nn Fd (s/25.4) For B≤ 1.22 m (kN/m2) qnet25 =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 q Theory = 30 N kN/m ult

2

D≤ B

Teng (For continuous or strip footing) qnet(ult) =1/60 { 3 N2 BR′ w + 5(100 + N2) Df Rw} For square and circular: qnet(ult) =1/30 {N2 BR′ w + 3(100 + N2) Df Rw} qnet = ulltimate bearing capacity in t/m2 N = corrected SPT value R′ w , Rw = correction factor for water table B = width of footing Df = depth of footing

SAFE BEARING PRESSURE FROM EMPIRICAL EQUATIONS BASED ON CPT VALUES FOR FOOTINGS ON COHESIONLESS q = 3.6 q R kPa for B ≤ 1.2 m SOIL s

c

w2

2

1  qs = 2.1 qc  1 +  Rw 2 kPa for B ≥ 1.2 m B  An approximate formula for all widths qs = 2.7 qc Rw 2 kPa where qc is the cone point resistence in kg/m 2 and qs in kPa. The above equations have been for a settlement of 25 mm.

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.

qc N 55 ≅ 4

By Meyerhof (1956) qc qall ( net ) = For B ≤ 1.22 m settlement 25 mm 15 2 q 3.28 B + 1  qall ( net ) = c  For B > 1.22 m settlement 25 mm  25 3.28 B  where qc = cone penetration resis tan ce kN / m 2 B =m

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

0.8over N q ≅ the 0.8 Ndepth Where qc is averaged γ ≅ qc 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)

For clay one may use

Strip

qult = 2 + 0.28qc

square qult = 5 + 0.34qc

( kg/cm ) ( kg/cm ) 2

2

Bearing Capacity from Plate This is reliableLoad method toTest obtain bearing  capacity. The cost is very high. 

qult, foundation = qult, load test qult, foundation = M + N

B foundation Bload test

Where M includes the N c and N q terms and N is the N γ term 

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



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

qult 

 B foundation   = q plate   B plate  

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.

Housel's (1929) Method of Determining Safe Bearing Pressure from Settlement Consideration Objective To determine the load Qf and the size Q = Ap m + Pp n of a foundation for a permissible Where Q = load applied on a given plate settlement Sf. A = contact area of plate Housel suggests Pp = perimeter of plate two plate load tests with plates of m = a cons tan t corresponding to different sizes, say B1 x B1 and the bearing pressure B2 x B2 for this n = another cons tan t corresponding purpose.

to perimeter shear .

Procedure 1 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 equations For plate load test 1. Q1 =mAp1 + nPp1 For plate load test 2. Q2 =mAp2 + nPp2 The unknown values of m & n can be found by solving the 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 Soils Case (a): Strong over  If H/B is (su1/su2 >1). relatively weak 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

Bearing Capacity on Layered Soils Case (a): Strong over weak (su1/su2 >1) (cont.)

Bearing Capacity on Layered Soils Case (a): Strong over Where: weak B = width of(su1/su2 >1) (cont.) foundation L = length of foundation Nc = 5.14 (see chart) sa = cohesion along the line a-a' in the previous figure.

Bearing Capacity on Layered Soils Case (b): Weak over strong (su1/su2 <1)

Bearing Capacity on Layered Soils II) Dense or compacted If H is relatively sand above soft clay small, failure would extend into the soft clay layer

If H is relatively large, the failure surface would be fully contained within the sand layer.

Bearing Capacity on Layered Soils II) Dense or compacted sand above soft clay (cont.)

Bearing Capacity on Layered Soils II) Dense or compacted sand above soft clay (cont.)

•

BEARING CAPACITY BASED ON BUILDING CODES (PRESUMPTIVE In many cities the local building code PRESSURE)

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 are primarily 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.