Soil Mechanics II - Ege Üniversitesiinsaat.ege.edu.tr/uploads/310_Topic_2.pdf · Soil Mechanics II...

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Ege UniversityDepartment of Civil Engineering

Soil Mechanics II Topic II: Bearing Capacity of Soils

Selim Altun, Ph.D.Associate Professor

Foundation Design The ultimate support for any structure is provided

by the underlying earth or soil material and, therefore, the stability of the structure depends on it Since soil is usually much weaker than other it. Since soil is usually much weaker than other common materials of construction, such as steel and concrete, a greater area or volume of soil is necessarily involved in order to satisfactorily carry a given loading.

Thus, in order to impart the loads carried by structural members of steel or concrete to soil a structural members of steel or concrete to soil, a load transfer device is necessary.

The structural foundation serves the purpose of such a device.

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Foundation Design A foundation is that part of a structure which

transmits loads directly to the underlying soil. This chapter is concerned with the bearing capacity

f il hi h f d ti t d lli d of soils on which foundations are supported, allied to the general philosophy of foundation design.

If a soil stratum near the surface is capable of adequately supporting the structural loads it is possible to use either footings or a raft, these being referred to in general as shallow foundations.

If the soil near the surface is incapable of adequately supporting the structural loads, piles, or other forms of deep foundations such as piers or caissons, are used to transmit the loads to suitablesoil (or rock) at greater depth.

DefinitionsA number of definitions are relevant in this context:

Foundation: The lowest part of a structure which is in contact with soil and transmits loads to it.

Foundation soil or bed: The soil or bed to which loads are transmitted from the base of the structure.

Footing: The portion of the foundation of the structure, which transmits loads directly to the , yfoundation soil.

Bearing capacity: The load-carrying capacity of foundation soil or rock which enables it to bear and transmit loads from a structure.

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Definitions Ultimate bearing capacity: Maximum pressure which a

foundation can withstand without the occurrence of shear failure of the foundation.

Net bearing capacity: Gross bearing capacity minus Net bearing capacity: Gross bearing capacity minus the original overburden pressure or surcharge pressure at the foundation level; obviously, this will be the same as the gross capacity when the depth of foundation is zero, i.e., the structure is founded at ground level.

Safe bearing capacity: Ultimate bearing capacity di id d b th f t f f t Th f t f f t i divided by the factor of safety. The factor of safety in foundation may range from 2 to 5, depending upon the importance of the structure, and the soil profile at the site. The factor of safety should be applied to the net ultimate bearing capacity and the surcharge pressure due to depth of the foundation should then be added to get the safe bearing capacity.

Definitions Allowable bearing pressure: The maximum

allowable net loading intensity on the soil atwhich the soil neither fails in shear nor undergoes excessive or intolerable settlement detrimentalexcessive or intolerable settlement, detrimentalto the structure.

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GENERAL TYPES OF FOUNDATIONS

a. Shallow Foundations

GENERAL TYPES OF FOUNDATIONS

b. Deep Foundations

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GENERAL TYPES OF FOUNDATIONSSpread Footings Spread footing foundation is basically a pad used

to ‘‘spread out’’ loads from walls or columns over a sufficiently large area of foundation soil.

These are constructed as close to the groundsurface as possible consistent with the design requirements, and with factors such as frostpenetration depth and possibility of soil erosion.

Footings for permanent structures are rarelyg p ylocated directly on the ground surface. A spread footing need not necessarily be at small depths; it may be located deep in the ground if the soil conditions or design criteria require.

FOUNDATION DESIGN

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GENERAL TYPES OF FOUNDATIONSStrap Footings –Combined footings A ‘strap footing’ comprises two or more footings

connected by a beam called ‘strap’. This is alsocalled a ‘cantilever footing’ or ‘pump-handle foundation’. This may be required when the footing of an exterior column cannot extend into an adjoining private property.

A combined footing supports two or more columns in a row when the areas required for individual footings are such that they come very near each other. They are also preferred in situations of limited space on one side owing to the existence of the boundary line of private property.

GENERAL TYPES OF FOUNDATIONSStrap Footings

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GENERAL TYPES OF FOUNDATIONSCombined footings

GENERAL TYPES OF FOUNDATIONSRaft FoundationsA raft or mat foundation is a large footing, usually

ti ll ll supporting walls as well as several columns in two or more rows. This is adopted when individual column footings would tend to be too close or tend to overlap; further tend to overlap; further, this is considered suitable when differential settlements arising out of footings on weak soils are to be minimised.

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GENERAL TYPES OF FOUNDATIONSDeep Foundations According to Terzaghi, if the depth of a footing is

more than the width, it may be considered a deepfoundation.

GENERAL TYPES OF FOUNDATIONSPile Foundations Pile foundations are intended to transmit

structural loads through zones of poor soil to a depth where the soil has the desired capacity to transmit the loads.

They are somewhat similar to columns in that loads developed at one level are transmitted to a lower level; but piles obtain lateral support from the soil in which they are embedded so that there is no concern with regard to buckling and, it is in this respect that they differ from columns.

Piles are slender foundation units which are usually driven into place. They may also be cast-in-place.

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GENERAL TYPES OF FOUNDATIONSPile Foundations

Structural RequirementsStructural Requirements1.1. Factor of Safety against General Shear Failure of Factor of Safety against General Shear Failure of

supporting soil is normally required to be in the supporting soil is normally required to be in the 2 52 5 3 03 0range 2.5 range 2.5 –– 3.03.0

2.2. Tolerable amount of settlement; in particular, Tolerable amount of settlement; in particular, differential settlement should not cause differential settlement should not cause significant damage to structure nor interfere with significant damage to structure nor interfere with functionfunction

3.3. Secondary to these, during construction, there Secondary to these, during construction, there should be no adverse affect on adjacent should be no adverse affect on adjacent structures or servicesstructures or services

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CHOICE OF FOUNDATION TYPE AND PRELIMINARY SELECTION

The type of foundation most appropriate for a given structure depends upon several factors: (i) the function of the structure and the loads it must carry, (ii) the subsurface conditions, (iii) the cost of the foundation in comparison with the cost of the superstructure. These are the principal factors, although several These are the principal factors, although several other considerations may also enter into the picture.

CHOICE OF FOUNDATION TYPE AND PRELIMINARY SELECTIONThe following are the essential steps involved in the final choice of the type of foundation:1. Information regarding the nature of the superstructure and h b bl l d d l lthe probable loading is required, at least in a general way.

2. The approximate subsurface conditions or soil profile is to be ascertained.3. Each of the customary types of foundation is considered briefly to judge whether it is suitable under the existing conditions from the point of view of the criteria for stability—bearing capacity and settlement. The obviously unsuitable types

bmay beeliminated, thus narrowing down the choice.4. More detailed studies, including tentative designs, of the more promising types are made in the next phase.5. Final selection of the type of foundation is made based on the cost—the most acceptable compromise between cost and performance.

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BEARING CAPACITYCriteria for the Determination of Bearing Capacity

The criteria for the determination of bearing capacity of a foundation are based on the requirementsfor the stability of the foundation. These are stated as follows:(i) Shear failure of the foundation or bearing capacity failure, as it is sometimes called,shall not occur. (This is associated with plastic flow of the soil material underneath the foundation, and lateral expulsion of the soil from underneath the footing of the foundation); (ii) The probable settlements, differential as well as total, of the foundation must be limited to safe, tolerable or acceptable magnitudes. In other words, the anticipated settlement under the applied pressure on the foundation should not be detrimental to the stability of the structure.

These two criteria are known as the shear strength criterion, and settlement criterion, respectively. These are independent criteria and hence require independent investigation.

The design value of the safe bearing capacity, obviously, would be the smaller of the two values, obtained from these two criteria. This has already been defined as the allowable bearing pressure.

BEARING CAPACITYFactors Affecting Bearing Capacity

Bearing capacity is governed by a number of factors. The following are some of the moreimportant ones which affect bearing capacity:(i) Nature of soil and its physical and engineering properites;(ii) Nature of the foundation and other details such as the size, shape, depth below the ground surface and rigidity of the structure;(iii) Total and differential settlements that the ( )structure can withstand without functional failure;(iv) Location of the ground water table relative to the level of the foundation; and(v) Initial stresses, if any.

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BEARING CAPACITYMethods of Determining Bearing Capacity

The following methods are available for the determination of bearing capacity of a foundation:( ) bl b ld d(i) Bearing capacity tables in various building codes(ii) Analytical methods(iii) Plate bearing tests(iv) Penetration tests(v) Model tests and prototype tests(vi) Laboratory tests(vi) Laboratory tests

BEARING CAPACITYMethods of Determining Bearing Capacity

Bearing capacity tables have been evolved by certain agencies and incorporated in building codes. They are mostly based on past experience and some investigations.

A number of analytical approaches, based on the work of y pp ,Rankine, Fellenius, Housel, Prandtl, Terzaghi, Meyerhof, Skempton, Hansen and Bella may be used. Some of these would be dealt with in later sections.

Plate bearing tests are load tests conducted in the field on a plate. These involve effort and expense. There are also certain limitations to their use.

Penetration tests are conducted with devices known as ‘Penetrometers’, which measure the resistance of soil to penetration. This is correlated to bearing capacity.

Model and prototype tests are very cumbersome and costly and are not usually practicable. Housel’s approach is based on model tests.

Laboratory tests which are simple, may be useful in arriving at bearing capacity, especially of pure clays.

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BEARING CAPACITYAnalytical Methods of Determining Bearing Capacity

The following analytical approaches are available:

1 The theory of elasticity Schleicher’s method1. The theory of elasticity—Schleicher s method.2. The classifical earth pressure theory—Rankine’s method, Pauker’s method and Bell’s method.3. The theory of plasticity—Fellenius’ method, Prandtl’s method, Terzaghi’s method, Meyerhof’s method, Skempton’s method, Hansen’s method and B ll ’ th dBalla’s method.

BEARING CAPACITYTerzaghi’s MethodTerzaghi’s method is, in fact, an extension and improved modification of Pandtl’s (Terzaghi, 1943). Terzaghi considered the base of the footing to be rough which is nearer facts and that it is located at rough, which is nearer facts, and that it is located at a depth Df below the ground surface (Df ≤ b, where b is the width of the footing).

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BEARING CAPACITYTerzaghi’s Method

The soil above the base of the footing is replaced by an equilvalent surcharge, q(= Df). This substitution simplifies the computations very considerably, the error being unimportant and on the safe side. This, in effect, being unimportant and on the safe side. This, in effect, means that the shearing resistance of the soil locatedabove the base is neglected. (For deep foundations, where Df > b, this aspect becomes important and cannot be ignored).

The zone of plastic equilibrium, CDEFG, can be subdivided into I a wedge-shaped zone located beneath the loaded strip in which the major principal stresses are vertical II strip, in which the major principal stresses are vertical, II two zones of radial shear, BCD and ACG, emanating from the outer edges of the loaded strip, with their boundaries making angles (45° – φ/2) and φ with the horizontal, and III two passive Rankine zones, AGF and BDE, with their boundaries making angles (45° – φ/2) with the horizontal.


The soil located in zone I is in a state of elastic equilibrium and behaves as if it were a part of the sinking footing, since its tendency to spread laterally is resisted by the friction and adhesion between the soil and the by the friction and adhesion between the soil and the base of the footing.

This leads one to the logical conclusion that the tangent to the surface of sliding at C will be vertical. Also AC and BC are surfaces of sliding and hence, they must intersect at an angle of (90° – ); therefore, the boundaries AC and BC must rise at an angle to the horizontal.

The footing cannot sink into the ground until the pressure exerted onto the soil adjoining the inclined boundaries of zone I becomes equal to the passive earth pressure. This pressure Pp, acts at an angle ( = = wall friction angle) to the normal on the contact face; that is, vertically, in this case.

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The adhesion force Ca on the faces AC and BC is given by

where c is a unit cohesion of the soil, with shearing resistance of the soil being defined by Coulomb’s equation = c + σ tan.

Considering a unit length of the footing and the Considering a unit length of the footing and the equilibrium of wedge ABC, the vertical components of all forces must sum up to zero.


The weight of the soil in the wedge is given by

Hence, for ΣV = 0,

This equation represents the solution to the problem if Pp is known.

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For the simpler case of Df = 0 and c = 0, q = 0—that is, if the base of the footing rests on the horizontal surface of a mass of cohesionless sand, we have

In this case, H = b/2 tan, = , Kp = Kp, and = 180 – .

Here Kp is the coefficient of passive earth pressure for c = 0, = 180° – , and = ; that is, it is the value purely due to the weight of the soil.


Substituting last Eq. into previous Eq., and putting c = 0

or

where

The value of K is obtained by means of the spiral or the The value of Kp is obtained by means of the spiral or the friction circle method. Since the angle of well friction and the slope angle α of the contact face are equal to and to (180° – ) respectively, the value of Kp and hence of N depend only on ; thus, the values of N for various values of may be established once for all.

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N is called the ‘‘bearing-capacity factor’’ expressing the effect of the weight of the soil wedge, ABC, of a cohesionless soil.

F th l l ti f th b i it f For the calculation of the bearing capacity of a cohesive soil, the computation of Pp involves a considerable amount of labour. Terzaghi, therefore, advocated a simplified approach, which is based on the equation

where Ppn = normal component of the passive earth pressure on a plane contact face with a height H, = slope angle of the contact face, andKpc, Kpq, and Kpγ = coefficients whose values are indpendent of H and .


In the present case,

Also the total passive earth pressure Pp on the contact face is equal to

he e (cK + qK ) P is the no mal component where (cKpc + qKpq) = Ppn is the normal component of the passive earth pressure comprehending the effect of cohesion and surcharge..

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Combining this equation with previous Eq., we have,

wherein Kpc, Kpq, and Kpγ are pure numbers whose values are independent of b.

If the soil wedge, ABC, is assumed weightless ( = 0) (Prandtl, 1920), last Eq. takes the form

The factors Nc and Nq are pure numbers whose values depend only on the value φ in Coulomb’s equation. The value qult c represents the bearing capacity of the weightless soil, if the surcharge q were equal to zero ( = 0 and q = 0), and qultq is the bearing capacity exclusively due to the surcharge q( = 0 and c = 0).


On the other hand, if c = 0 and q = 0, γ being greater than zero, the bearing capacity is given byprevious Eqs. :

If the values c, Df, and are greater than zero,.

This is called ‘‘Terzaghi’s general bearing capacity formula’’. (The discrepancy arising out of the difference in failure surfaces for the two conditions— = 0 and > 0—is considered inconsequential).

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The coefficients Nc, Nq, and Nγ are called ‘‘bearing capacity factors’’ for shallow continuous footings. Since their values depend only on the angle of shearing resistance φ they can be computed once shearing resistance φ they can be computed once and for all.

The problem of Nc and Nq has been rigorously solved by means of Airy’s stress function (Prandtl 1920, Reissner, 1924), for the condition γ = 0:

Ultimate Bearing Capacity,Ultimate Bearing Capacity, qqff The least pressure that would cause shear failure The least pressure that would cause shear failure

of supporting soil immediately below and adjacent of supporting soil immediately below and adjacent t f d tit f d tito a foundationto a foundation

Craig, 6Craig, 6thth Ed.Ed.

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Modes of Failure of Shallow Foundations

General shear Local shear

Punching shear

Fairly incompressible soil

Soft, very compressible soil

Intermediate soil condition

modes of failure:modes of failure:General Shear FailureGeneral Shear Failure

on low compressibility (dense or stiff) soilson low compressibility (dense or stiff) soils plastic equilibrium throughout support and plastic equilibrium throughout support and p q g ppp q g pp

adjacent soil massesadjacent soil masses heaving on both sides of foundationheaving on both sides of foundation final slip (movement of soil) on one side only final slip (movement of soil) on one side only

causing structure to tiltcausing structure to tilt

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Local Shear FailureLocal Shear Failure

on highly compressible soilson highly compressible soils only partial development of plastic equilibriumonly partial development of plastic equilibriumonly partial development of plastic equilibriumonly partial development of plastic equilibrium only slight heaving on sidesonly slight heaving on sides significant compression of soil under footing but significant compression of soil under footing but

no tiltingno tilting

Punching Shear FailurePunching Shear Failure

on loose, uncompacted soilson loose, uncompacted soils vertical shearing around edges of footingvertical shearing around edges of footingvertical shearing around edges of footingvertical shearing around edges of footing high compression of soil under footing, hence high compression of soil under footing, hence

large settlementslarge settlements no heaving, no tiltingno heaving, no tilting

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Terzaghi’s TheoryTerzaghi’s Theory

strip footing of infinite length and width Bstrip footing of infinite length and width B uniform surcharge quniform surcharge q on surface of isotropicon surface of isotropic


uniform surcharge, quniform surcharge, q00 on surface of isotropic, on surface of isotropic, homogeneous soilhomogeneous soil

Rankine active wedge, ABC: forces Rankine active wedge, ABC: forces Passive zones, ADE (Passive zones, ADE () & BGF () & BGF ())

transition betweentransition between :: ACD & BCG (zones ACD & BCG (zones or radial shear or slip fans)or radial shear or slip fans)


or radial shear or slip fans)or radial shear or slip fans) above EDCGF: plastic equilibriumabove EDCGF: plastic equilibrium below EDCGF: elastic equilibriumbelow EDCGF: elastic equilibrium

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the more general case is a footing at depth Dthe more general case is a footing at depth D

Neglecting the shear strength of the soil above Neglecting the shear strength of the soil above depth depth D D implies that this soil is a surcharge: implies that this soil is a surcharge: qq00 == DDTerzaghi’sTerzaghi’s general equation:general equation:


Terzaghi’sTerzaghi’s general equation:general equation:

qqultult = = cNcNcc + + DNDNqq + + 0.50.5BNBN

Contribution of:Contribution of: Soil Self Soil Self WeightWeight

SurchargeSurchargeCohesionCohesion

Bearing Capacity FactorsNc, Nq & N are the “b i it f t ”“bearing capacity factors”corresponding to:

1. Cohesion “case”

2. Surcharge or burial “case”

3. Self weight of soil “case”

Nc, Nq and N are all functions of

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Variations in the Bearing Capacity Factors between “methods”

1) Hansen [or Brinch-Hansen] analyses

generally accepted as most accurate

2) Terzaghi, the pioneer, misconstrued Nc

3) Meyerhof the 2nd best of these 3

Effects of Soil Properties

Bearing capacity = fn(, , B, c and qo)

has the greatest influence

Both the 2nd and 3rd terms in the equation depend on

− if water is above the bottom of the footing, “the surcharge weight” is also affected

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Bearing Capacity FactorsBearing Capacity Factors NN, N, Ncc and Nand Nqq are bearing capacity factors and are are bearing capacity factors and are

derived from various sourcesderived from various sources


The Bearing Capacity Factors, Nc, Nq

140

160

or

40

60

80

100

120

ari

ng

Ca

pa

cit

y F

ac

to

0

20

40

0 10 20 30 40 50

Angle of Friction (kPa)

Be

a

Nc

Nq

26

25

30

ac

tor

NC clay, saturated, short term loading

5

10

15

20

Bea

rin

g C

ap

aci

ty F

a

Nc Nq

5.14

0

5

0 5 10 15 20 25 30


B

1.0

The Bearing Capacity Factor, N

200

250

tor,

N

50

100

150

ea

rin

g C

ap

ac

ity

Fac

t

rough

smooth

Hansen

0

0 10 20 30 40 50


Be

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The Bearing Capacity Factors

The Bearing Capacity Factors ( Vesic 1973 )

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THE SURCHARGE TERM- most footings are buried

1

qo = 1D

D

Effect of Footing Size

Last term with N has B or footing breadth

Wider footing, greater bearing capacity

– BUT for = 0 soil, B has little effect

N = 0! for = 0

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Factor of Safety, qu to qsafe?

A Factor of Safety of 3?

oγqoc

safe qSofF

NγB5.01)(NqNcq

= [nett ultimate bearing capacity (FoS)] + surcharge

= [qu nett (FoS)] + qo

The General Bearing Capacity Eqn.

Considers soil rigidity, (r) footing shape, (s) depth of embedment, (d) Inclined load, (i) base inclination, (b) Ground inclination, (g)

γB

γqoqqqqqqcccccccu N

2

γBgbidsrNqgbidsrNcgbidsrq

Note: shape factors not used with inclination factors?

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Effect of depth, D (u = 0)D/B Brinch -

Hansen

0 5.14cu + qo

1 7.2cu + qo

8.4cu + qo

Effect of depth, D (u = 0)

D = 0qu surface

D = B1.4qu surface

D >> B

1.63qu surface

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The Influence of a WT

If ithi 1 5D t d id

zw1

If zw within 1.5D, assume at underside

of footing and use in self weight term

Buoyancy if too high?

Footing Shape – shape factors B=L

L/B 1 2 5sc 1.19 1.10 1.04

= 0 s 1 00 1 00 1 00 = 0 sq 1.00 1.00 1.00

s 0.6 0.8 0.92

sc 1.61 1.31 1.12 = 30 sq 1.58 1.29 1.12

s 0.6 0.8 0.92

sc 2.01 1.50 1.20 = 45 sq 2.00 1.50 1.20

s 0.6 0.8 0.92

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General Shear Failure of Footings (Ultimate General Shear Failure of Footings (Ultimate Bearing Capacity)Bearing Capacity)

)(5.0)( SNγBDNSNcq qccult

)45(tan 2)tan( eN

theory was developed theory was developed for strip footingsfor strip footings

)45(tan 2)( eNq

)cot()1( qc NN

)4.1tan()1( qNNFOOTING

TYPE Sγ Sc

Strip 1.0 1.0

to adapt to square, to adapt to square, circular and circular and rectangular shapes, rectangular shapes, TerzaghiTerzaghi & Peck & Peck developed shape developed shape f t h hi hf t h hi h

Strip 1.0 1.0

Square 0.8 1.2

Circular 0.6 1.2

Rectangular )(2.01L

B )(2.01

L

B

factors here which factors here which are still widely used are still widely used today:today:

Allowable Bearing CapacityAllowable Bearing Capacity the allowable bearing capacity, the allowable bearing capacity, qqaa is the value is the value

used in the design of footing sizeused in the design of footing size F F is applied to the ultimate bearing capacity, is applied to the ultimate bearing capacity, qqff::

F

qq fa

FF t bt b li d t th hli d t th h

qcc

a DNF

NScNSBq

)()(5.0

F F can not becan not be applied to the surcharge:applied to the surcharge:

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Skempton’s NSkempton’s Ncc ValuesValues if undrained shear if undrained shear

strength parameters strength parameters are used for the are used for the design then a special design then a special case arises:case arises:

since since uu = 0, N= 0, Nqq = 1 = 1 and:and:

DNcqf DNcq cuf values of Nvalues of Ncc are are

acquired from acquired from Skempton’s ChartSkempton’s Chart


Non-Homogeneous Soil- soil profiles

Approximations can apply SO LONG Approximations can apply, SO LONG AS the general mechanism of instability remains• NOT THE CASE for very soft clay, in

thin layer, over hard soily ,

─ Toothpaste tube?

• NOR strong thin layer over weak layer

─ Punching shear

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Non-Homogeneous Soil?

Load spreading technique

Stronger layer

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Weaker Layer

Load, Q

Footing, B x L

Depth to layer, DL

Ignore lower layer and check surface qa

New “footing” area (B+DL)(L+DL)

Pressure, qL = Q/area

Check qa2

Ensure lower layer not overstressed by qL

- reduce qa as required

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Alternative treatment if u = 0 soils

Centre of rotation?

Layer 1, cu1

rotation?

B

Radius, B?

Layer 2 , cu2

Other Factorsa) Adjacent footings suitably

spaced to reduce interaction spaced to reduce interaction (refer to failure mechanisms)

b) Rate of loading appropriate strength

t ?parameters?

c) Inclined slopes adjacent to footings influence on slope stability?

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BEARING CAPACITY OF SOILS Tables of safety bearing capacity

This tabels can be used for the first design. The bearing capacity of soil can be estimated roughly from safety bearing capacity tabels depending on the soil type and its conditions.

TypeType of of SoilSoil qqaa(t/m(t/m22))

BedrockBedrock >100>100

Dense Dense GravelGravel, Dense , Dense GravelGravel + + sandsand >60>60

Medium dense Gravel, Medium dense Gravel + kum Medium dense Gravel, Medium dense Gravel + kum 2020--6060

Dense Dense SandSand >30>30

MediumMedium dense dense SandSand 1010--3030

LooseLoose SandSand <10 <10 ??

VeryVery hard hard ClayClay 3030--6060

Hard Hard ClayClay 1515--3030

MediumMedium hard hard ClayClay 7.57.5--1515

SoftSoft ClayClay <7.5 <7.5 ??

BEARING CAPACITY OF SOILS Eccentric Loaded Footings

Footings can be under the influence of vertical bending moment, as well as under axial loading. In this case, both the central normal force, as well as the influence of bending moment, the footing can be converted to a single download as the eccentric loaded situation.

NMy N ex

My

y

My

Nx x

y

L

Bex

N

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BEARING CAPACITY OF SOILS Eccentric Loaded Footings

In this case, Eccentricity occurs:

e=My/N

Footings under eccentric load carry the load less than the Footings under eccentric load carry the load less than the centrally loaded one under the same conditions. Centrally loaded footing fails on both sides, while the foundation is loaded only on one side of the eccentric failure takes place

NeNm

e mN N

BEARING CAPACITY OF SOILS Evaluation methods used to determine the bearing capacity

of foundations : Conventional method (Centrally loaded footings):

In this method, the pressure distribution under the base is determined using considering some assumptions. The actual pressure distribution under the footing downloaded centrally varies depending on the soil type. The average uniform pressure distribution is accepted in the calculation for simplicity.

q

N

q

N

qav

actualaccepted

Sand

qav

Clay

A

N

Area

Loadqav

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In Clayey soil

In Clayey soil

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In Clayey soil

In Sandy soil

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In Sandy soil

In Sandy soil

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BEARING CAPACITY OF SOILS Conventional method (Eccentrically loaded footings):

Eccentric loaded rigid foundations are made under the following assumptions to determine the pressure distributions The base pressure distribution is linear. Resultant distribution is equal to the load acting on the eccentric ( y=0) Eccentric load and the combination of vertical distribution is in the same

direction ( M=0). The tensile stress does not occur between soil and base.

N Ne e

B B

actualaccepted

Small Eccentricity Large Eccentricity

actualaccepted

N N


There are three case for the pressure distribution under footing downloaded eccentrically in one direction:

Load inside the core (eLoad inside the core (exx<L/6)<L/6)

y x xmaks ,min 2

y

M N e 6 eN N N1

B LA W BL BL L6

LoadLoad on on thethe corecore lineline ((eexx=L/6)=L/6)

maks

2 N

BL

maks

x

2 N 2 NLs B L 3 e2

LoadLoad outsideoutside thethe corecore ((eexx>L/6)>L/6)

xLL s L 3 e2

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There are three case for the unit pressure distribution under strip footing downloaded eccentrically in one direction:

Load inside the core (eLoad inside the core (exx<L/6)<L/6)

xmaks ,min

6 eN1

B B

LoadLoad on on thethe corecore lineline ((eexx=L/6)=L/6)

maks

2 N

B

LoadLoad outsideoutside thethe corecore ((eexx>L/6)>L/6)

maks

x

2 N 2 NBs 3 e2


In the case of loading inside the core, the pressure distributioncan be calculated using following equation for the rectengular footing downloaded eccentrically in two direction:

y y yx x xmaks,min 2 2

x y

M N e 6 eM N e 6 eN N N1

A W W B L L B 6 B L 6 B L B L

As a result, the calculated maximum pressure As a result, the calculated maximum pressure underunder thethe basebase should not should not exceed the safe exceed the safe bearingbearing capacitycapacity of of soilsoil..

m aks e m inq

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Reduced width method (Meyerhof) Reduction coefficient method

BEARING CAPACITY OF SOILS

Plan

Eccentricity of Loading

e2BBBeffective

l

Q

e

Breduced = B'

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