Bearing CapacityBearing Capacity

�� foundations are designed to transmit foundations are designed to transmit load from the structure they support to load from the structure they support to

the soilthe soil

�� foundations are generally grouped into foundations are generally grouped into �� foundations are generally grouped into foundations are generally grouped into two categories:two categories:

A. Shallow FoundationsA. Shallow Foundations

B. Deep FoundationsB. Deep Foundations

Shallow FoundationsShallow Foundations

�� the most common (and cheapest) type the most common (and cheapest) type of shallow foundations areof shallow foundations areSPREAD FOOTINGSSPREAD FOOTINGS

�� square spread square spread �� square spread square spread footings to support footings to support individual columns individual columns (also circular)(also circular)

McCarthy, 6McCarthy, 6thth Ed.Ed.

�� Strip Footings to support wall loadsStrip Footings to support wall loads

�� Rectangular and Trapezoidal Footings for two Rectangular and Trapezoidal Footings for two

McCarthy, 6McCarthy, 6thth Ed.Ed.

�� Rectangular and Trapezoidal Footings for two Rectangular and Trapezoidal Footings for two columns (combined footing) or machine basecolumns (combined footing) or machine base

McCarthy, 6McCarthy, 6thth Ed.Ed.

RAFT or MAT FoundationsRAFT or MAT Foundations

�� To lower the bearing pressure and reduce To lower the bearing pressure and reduce differential settlement on soils with low bearing differential settlement on soils with low bearing capacity or erratic or variable conditionscapacity or erratic or variable conditions

McCarthy, 6McCarthy, 6thth Ed.Ed.

FLOATING FoundationsFLOATING Foundations

�� where deep deposits of compressible, cohesive where deep deposits of compressible, cohesive

McCarthy, 6McCarthy, 6thth Ed.Ed.

�� where deep deposits of compressible, cohesive where deep deposits of compressible, cohesive soil are present and piles are impracticalsoil are present and piles are impractical

�� building’s substructure is a combination mat building’s substructure is a combination mat and caisson to create a rigid boxand caisson to create a rigid box

�� weight of earth displaced by foundation is weight of earth displaced by foundation is equal to total weight of structure, thereby equal to total weight of structure, thereby minimizing settlement from consolidationminimizing settlement from consolidation

Deep FoundationsDeep Foundations

�� used when soil near surface has poor used when soil near surface has poor loadload--bearing capacitybearing capacity

loose soil

�� they transmit load through weak soil they transmit load through weak soil strata (overburden) to stronger, loadstrata (overburden) to stronger, load--bearing stratum (eg., bedrock, dense bearing stratum (eg., bedrock, dense sand and gravel, etc.)sand and gravel, etc.)

bedrock

Types of Deep FoundationsTypes of Deep Foundations

�� where loadwhere load--bearing stratum bearing stratum no more than 5 m deepno more than 5 m deep

�� not used much any morenot used much any more

PIERSPIERS

McCarthy, 6McCarthy, 6thth Ed.Ed.

CAISSONSCAISSONS

McCarthy, 6McCarthy, 6thth Ed.Ed.

�� where overwhere over--burden no more burden no more than 8 than 8 -- 9 m 9 m thickthick

�� replacing piersreplacing piers

PILESPILES

�� deep overdeep over--burden burden more than 8 more than 8 -- 9 m 9 m thickthick

�� Various types and Various types and placement placement methodsmethodsmethodsmethods

Craig, 6Craig, 6thth Ed.Ed.

Structural RequirementsStructural Requirements

1.1. Factor of Safety against General Shear Failure Factor of Safety against General Shear Failure of supporting soil is normally required to be in of supporting soil is normally required to be in the range 2.5 the 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 differential settlement should not cause differential settlement should not cause significant damage to structure nor interfere significant damage to structure nor interfere with functionwith function

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

Ultimate Bearing Capacity,Ultimate Bearing Capacity, qqff

��The least pressure that would cause shear The least pressure that would cause shear failure of supporting soil immediately below failure of supporting soil immediately below and adjacent to a foundationand adjacent to a foundation

Craig, 6Craig, 6thth Ed.Ed.

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 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

Local Shear FailureLocal Shear Failure

�� on highly compressible soilson highly compressible soils

�� only 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 significant compression of soil under footing but no tiltingbut no tilting

Punching Shear FailurePunching Shear Failure

�� on loose, uncompacted soilson loose, uncompacted soils

�� vertical 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

Terzaghi’s TheoryTerzaghi’s Theory

�� strip footing of infinite length and width Bstrip footing of infinite length and width B

�� 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 (→↑→↑))

Craig, 6Craig, 6thth Ed.Ed.

Craig, 6Craig, 6thth Ed.Ed.

�� transition betweentransition between ↓ ↓ && ↔↑↔↑:: ACD & BCG (zones ACD & BCG (zones 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

�� Neglecting the shear strength of the soil above Neglecting the shear strength of the soil above

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

Craig, 6Craig, 6thth Ed.Ed.

�� Neglecting the shear strength of the soil above Neglecting the shear strength of the soil above depth D implies that this soil is a surcharge: depth D implies that this soil is a surcharge: qq00 == γγDD

�� Terzaghi’s general equation:Terzaghi’s general equation:

qqff = = 0.50.5γγBNBNγγ + + cNcNcc + + γγDNDNqq

Contribution of:Contribution of: Soil Self Soil Self WeightWeight

Shear Shear StrengthStrength

SurchargeSurcharge

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

are derived from various sourcesare derived from various sources

Craig, 6Craig, 6thth Ed.Ed.

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

qccf DNSNcSNγBq γγγ ++= )()(5.0

)45(tan 22)tan( φφπ += eN q

)cot()1( φ−= qc NN

)4.1tan()1( φγ −= qNN

�� theory was developed theory was developed for strip footingsfor strip footings

�� to adapt to square, to adapt to square, circular and circular and rectangular shapes, rectangular shapes, )4.1tan()1( φγ −= qNN

FOOTING TYPE

Sγ Sc

Strip 1.0 1.0

Square 0.8 1.2

Circular 1.6 1.2

Rectangular )(2.01L

B− )(2.01L

B+

rectangular shapes, rectangular shapes, Terzaghi & Peck Terzaghi & Peck developed shape developed shape 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, qthe allowable bearing capacity, qaa is the value is the value used in the design of footing sizeused in the design of footing size

�� in North America, a factor of safety against in North America, a factor of safety against general shear failure, F is applied to the general shear failure, F is applied to the ultimate bearing capacity, qultimate bearing capacity, q ::ultimate bearing capacity, qultimate bearing capacity, qff::

F

qq f

a =

qcc

a DNF

NScNSBq γ

γ γγ ++

=)()(5.0

�� in Britain, F is not applied to the surcharge:in Britain, F is not applied to the surcharge:

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 φφuu = 0, N= 0, Nqq = 1 = 1 �� since since φφuu = 0, N= 0, Nqq = 1 = 1 and:and:

DNcq cuf γ+=�� values of Nvalues of Ncc are are

acquired from acquired from

Skempton’s ChartSkempton’s Chart→→Craig, 6Craig, 6thth Ed.Ed.