Bearing Capacity

3/7/2015 Bearing capacity

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Bearing capacityFailure mechanisms and derivation of equationsBearing capacity of shallow foundationsPresumed bearing valuesBearing capacity of piles

The ultimate load which a foundation can support may be calculated using bearing capacity theory.For preliminary design, presumed bearing values can be used to indicate the pressures which wouldnormally result in an adequate factor of safety. Alternatively, there is a range of empirical methodsbased on in situ test results.

The ultimate bearing capacity (qf) is the value of bearing stress which causes a sudden catastrophicsettlement of the foundation (due to shear failure).

The allowable bearing capacity (qa) is the maximum bearing stress that can be applied to thefoundation such that it is safe against instability due to shear failure and the maximum tolerablesettlement is not exceeded. The allowable bearing capacity is normally calculated from the ultimatebearing capacity using a factor of safety (Fs).

When excavating for a foundation, the stress at founding level is relieved by the removal of the weightof soil. The net bearing pressure (qn) is the increase in stress on the soil. qn = q qo qo = D where D is the founding depth and is the unit weight of the soil removed.

Failure mechanisms and derivation of equations Bearing capacity

Upper and lower bound solutionsSemicircular slip mechanismCircular arc slip mechanism

A relatively undeformed wedge of soil below the foundation forms an active Rankine zone withangles (45º + '/2).The wedge pushes soil outwards, causing passive Rankine zones to form with angles (45º '/2).The transition zones take the form of log spiral fans.



For purely cohesive soils ( = 0) the transition zones become circular for which Prandtl had shown in1920 that the solution is

qf = (2 + ) su = 5.14 su

This equation is based on a weightless soil. Therefore if the soil is noncohesive (c=0) the bearingcapacity depends on the surcharge qo. For a footing founded at depth D below the surface, thesurcharge qo = . Normally for a shallow foundation (D<B), the shear strength of the soil betweenthe surface and the founding depth D is neglected.

radius of the fan r = r0 .exp[.tan']. is the fan angle in radians (between 0 and /2) ' is the angle of friction of the soil ro = B/[2 cos(45+'/2)]

Upper and lower boundsolutions Failure mechanisms and derivation of

equations

The bearing capacity of a soil can be investigated using the limit theorems of ideal rigidperfectlyplastic materials.

The ultimate load capacity of a footing can be estimated by assuming a failure mechanism and thenapplying the laws of statics to that mechanism. As the mechanisms considered in an upper boundsolution are progressively refined, the calculated collapse load decreases.

As more stress regions are considered in a lower bound solution, the calculated collapse loadincreases.

Therefore, by progressive refinement of the upper and lower bound solutions, the exact solution canbe approached. For example, Terzaghi's mechanism gives the exact solution for a strip footing.

Semicircular slip mechanism Failure mechanisms and derivation of equations

Suppose the mechanism is assumed to have a semicircular slipsurface. In this case, failure will cause a rotation about point O.Any surcharge qo will resist rotation, so the net pressure (q qo) isused. Using the equations of statics:

Moment causing rotation= load x lever arm= [(q qo) x B] x [½B]

Moment resisting rotation= shear strength x length of arc x lever arm= [s] x [.B] x [B]

At failure these are equal:



(q qo ) x B x ½B = s x .B x BNet pressure (q qo ) at failure

= 2 x shear strength of the soilThis is an upperbound solution.

Circular arc slip mechanism Failure mechanisms and derivation of equations

Consider a slip surface which is an arc in cross section, centredabove one edge of the base. Failure will cause a rotation aboutpoint O. Any surcharge qo will resist rotation so the net pressure (q qo) is used. Using the equations of statics:

Moment causing rotation= load x lever arm= [ (q qo) x B ] x [B/2]

Moment resisting rotation= shear strength x length of arc x lever arm= [s] x [2R] x [R]

At failure these are equal:(q qo) x B x B/2 = s x 2 R x R

Since R = B / sin :(q qo ) = s x 4 /(sin )²

The worst case is whentan=2 at = 1.1656 rad = 66.8 deg

The net pressure (q qo) at failure= 5.52 x shear strength of soil

Bearing capacity of shallow foundations Bearing capacity

Bearing capacity equation (undrained)Bearing capacity equation (drained)Factor of safety

The ultimate bearing capacity of a foundation is calculated from an equation that incorporatesappropriate soil parameters (e.g. shear strength, unit weight) and details about the size, shape andfounding depth of the footing. Terzaghi (1943) stated the ultimate bearing capacity of a strip footingas a threeterm expression incorporating the bearing capacity factors: Nc, Nq and N, which arerelated to the angle of friction (´).

qf =c.Nc +qo.Nq + ½.B .Ng

For drained loading, calculations are in terms of effective stresses; ´ is > 0 and N c, Nq and N areall > 0. For undrained loading, calculations are in terms of total stresses; the undrained shear strength (su);Nq = 1.0 and N = 0



c = apparent cohesion intercept qo = D (i.e. density x depth) D = founding depth B = breadth of foundation = unit weight of the soil removed.

Bearing capacity equation(undrained) Bearing capacity of shallow

foundations

Skempton's equation is widely used for undrained clay soils:qf = su .Ncu + qo

where Ncu = Skempton's bearing capacity factor, which can be obtainedfrom a chart or by using the following expression:

Ncu = Nc.sc.dc

where sc is a shape factor and dc is a depth factor.

Nq = 1, N = 0, Nc = 5.14sc = 1 + 0.2 (B/L) for B<=Ldc = 1+ Ö(0.053 D/B ) for D/B < 4

Bearing capacity equation (drained) Bearing capacity of shallow foundations

Bearing capacity factorsShape factorsDepth factors

Terzaghi (1943) stated the bearing capacity of a foundation as a threeterm expression incorporatingthe bearing capacity factors Nc, Nq and N. He proposed the following equation for the ultimate bearing capacity of a long strip footing:

qf =c.Nc +qo.Nq + ½.B .N

This equation is applicable only for shallow footings carrying vertical noneccentric loading. For rectangular and circular foundations, shape factors are introduced.

qf = c .Nc .sc + qo .Nq .sq + ½ .B .N .sg

Other factors can be used to accommodate depth, inclination of loading, eccentricity of loading,inclination of base and ground. Depth is only significant if it exceeds the breadth.



Bearing capacity factors Bearing capacity equation (drained)

The bearing capacity factors relate to the drained angle of friction ('). The c.Nc term is thecontribution from soil shear strength, the qo.Nq term is the contribution from the surcharge pressureabove the founding level, the ½.B..Ng term is the contribution from the self weight of the soil.Terzaghi's analysis was based on an active wedge with angles ' rather than (45+'/2), and his bearingcapacity factors are in error, particularly for low values of '. Commonly used values for Nq and Ncare derived from the PrandtlReissner expression giving

Exact values for Ng are not directly obtainable; values have been proposed by Brinch Hansen (1968),which are widely used in Europe, and also by Meyerhof (1963), which have been adopted in NorthAmerica.

Brinch Hansen:N = 1.8 (Nq 1) tan'

Meyerhof:N = (Nq 1) tan(1.4 ')

Shape factors Bearing capacity equation (drained)

Terzaghi presented modified versions of his bearing capacity equation for shapes of foundation otherthan a long strip, and these have since been expressed as shape factors. Brinch Hansen and Vesic(1963) have suggested shape factors which depend on '. However, modified versions of the Terzaghifactors are usually considered sufficiently accurate for most purposes.

sc sq ssquare 1.3 1.2 0.8circle 1.3 1.2 0.6rectangle (B<L) 1+ 0.2(B/L) 1+ 0.2(B/L) 1 0.4(B/L)B = breadth, L = length

Depth factors Bearing capacity equation (drained)

It is usual to assume an increase in bearing capacity when the depth (D) of a foundation is greater than



the breadth (B). The general bearing capacity equation can be modified by the inclusion of depthfactors.

qf = c.Nc.dc + qo.Nq.dq + ½ B..dfor D>B:

dc = 1 + 0.4 arctan(D/B)dq = 1 + 2 tan('(1sin')² arctan(B/D)d = 1.0

for D=<B:dc = 1 + 0.4(D/B)dq = 1 + 2 tan('(1sin')² (B/D)d = 1.0

Factor of safety Bearing capacity of shallow foundations

A factor of safety Fs is used to calculate the allowable bearing capacity qa from the ultimate bearingpressure qf. The value of Fs is usually taken to be 2.5 3.0.

The factor of safety should be applied only to the increase in stress, i.e. the net bearing pressure qn.Calculating qa from qf only satisfies the criterion of safety against shear failure. However, a value forFs of 2.5 3.0 is sufficiently high to empirically limit settlement. It is for this reason that the factors ofsafety used in foundation design are higher than in other areas of geotechnical design. (For slopes, thefactor of safety would typically be 1.3 1.4).

Experience has shown that the settlement of a typical foundation on soft clay is likely to be acceptableif a factor of 2.5 is used. Settlements on stiff clay may be quite large even though ultimate bearingcapacity is relatively high, and so it may be appropriate to use a factor nearer 3.0.

Presumed bearing values Bearing capacity

For preliminary design purposes, BS 8004 gives presumed bearing values which are the pressureswhich would normally result in an adequate factor of safety against shear failure for particular soiltypes, but without consideration of settlement.Category Types of rocks and soils Presumed bearing valueNoncohesive soils Dense gravel or dense sand and gravel >600 kN/m²

Medium dense gravel, or medium dense sand and gravel <200 to 600 kN/m²

Loose gravel, or loose sand and gravel <200 kN/m² Compact sand >300 kN/m² Medium dense sand 100 to 300 kN/m²



Loose sand <100 kN/m² depends on degree of looseness

Cohesive soils Very stiff bolder clays & hard clays 300 to 600 kN/m² Stiff clays 150 to 300 kN/m² Firm clay 75 to 150 kN/m² Soft clays and silts < 75 kN/m² Very soft clay Not applicablePeat Not applicableMade ground Not applicable

Presumed bearing values for Keuper Marl

Weathering Zone Description Presumed bearingvalue

Fully weathered IVb Matrix only as cohesive soil

Partiallyweathered

IVa Matrix with occasional pellets less than 3mm 125 to 250 kN/m²III Matrix with lithorelitics up to 25mm 250 to 500 kN/m²

II Angular blocks of unweathered marl with virtuallyno matrix 500 to 750 kN/m²

Unweathered 1 Mudstone (often not fissured) 750 to 1000 kN/m²

Bearing capacity of piles Bearing capacity

Driven piles in noncohesive soilBored piles in noncohesive soilDriven piles in cohesive soilBored piles in cohesive soilCarrying capacity of piles in a layered soilEffects of ground water

The ultimate bearing capacity of a pile used in design may be one three values: the maximum load Qmax, at which further penetration occurs without the load increasing; a calculated value Qf given by the sum of the endbearing and shaft resistances; or the load at which a settlement of 0.1 diameter occurs (when Qmax is not clear).

For largediameter piles, settlement can be large, therefore a safety factor of 22.5 is usually used onthe working load.

A pile loaded axially will carry the load:partly by shear stresses (s) generated along the shaft of the pile andpartly by normal stresses (qb) generated at the base.

The ultimate capacity Qf of a pile is equal to the base capacity Qb plus the shaft capacity Qs.

Qf = Qb + Qs = Ab . qb + (As . s)

where Ab is the area of the base and As is the surface area of the shaft within a soil layer.



Full shaft capacity is mobilised at much smaller displacements thanthose related to full base resistance. This is important whendetermining the settlement response of a pile. The same overallbearing capacity may be achieved with a variety of combinations ofpile diameter and length. However, a long slender pile may be shownto be more efficient than a short stubby pile. Longer piles generate alarger proportion of their full capacity by skin friction and so theirfull capacity can be mobilised at much lower settlements.

The proportions of capacity contributed by skin friction and endbearing do not just depend on the geometry of the pile. The type ofconstruction and the sequence of soil layers are important factors.

Driven piles in noncohesive soil Bearing capacity of piles

Ultimate pile capacityStandard penetration testCone penetration test

Driving a pile has different effects on the soil surrounding it depending on the relative density of thesoil. In loose soils, the soil is compacted, forming a depression in the ground around the pile. In densesoils, any further compaction is small, and the soil is displaced upward causing ground heave. In loosesoils, driving is preferable to boring since compaction increases the endbearing capacity.

In noncohesive soils, skin friction is low because a low friction 'shell' forms around the pile. Taperedpiles overcome this problem since the soil is recompacted on each blow and this gap cannot develop.

Pile capacity can be calculated using soil properties obtained from standard penetration tests orcone penetration tests. The ultimate load must then be divided by a factor of safety to obtain aworking load. This factor of safety depends on the maximum tolerable settlement, which in turndepends on both the pile diameter and soil compressibility. For example, a safety factor of 2.5 willusually ensure a pile of diameter less than 600mm in a noncohesive soil will not settle by more than15mm.

Although the method of installing a pile has a significant effect on failure load, there are no reliablecalculation methods available for quantifying any effect. Judgement is therefore left to the experienceof the engineer.

Ultimate pile capacity Driven piles in noncohesive soil



The ultimate carrying capacity of a pile is:Qf = Qb + Qs

The base resistance, Qb can be found from Terzaghi's equation for bearing capacity,qf = 1.3 c Nc + qo Nq + 0.4 B N

The 0.4 term may be ignored, since the diameter is considerably less than the depth ofthe pile.The 1.3 c Nc term is zero, since the soil is noncohesive.

The net unit base resistance is thereforeqnf = qf qo = qo (Nq 1)

and the net total base resistance isQb = qo (Nq 1) Ab

The ultimate unit skin friction (shaft) resistance can be found from

qs = Ks .'v .tanwhere 'v = average vertical effective stress in a given layer

= angle of wall friction, based on pile material and ´Ks = earth pressure coefficient

Therefore, the total skin friction resistance is given by the sum of the layer resistances:

Qs = (Ks .'v .tan .As)

The selfweight of the pile may be ignored, since the weight of the concrete is almost equal to theweight of the soil displaced.Therefore, the ultimate pile capacity is:

Qf = Ab qo Nq + (Ks .'v .tan .As)

Values of Ks and can be related to the angle of internal friction (´) using the following tableaccording to Broms.

Material Ks

low density high density

steel 20° 0.5 1.0concrete 3/4 ´ 1.0 2.0timber 2/3 ´ 1.5 4.0

It must be noted that, like much of pile design, this is an empirical relationship. Also, from empiricalmethods it is clear that Qs and Qb both reach peak values somewhere at a depth between 10 and 20diameters.

It is usually assumed that skin friction never exceeds 110 kN/m² and base resistance will not exceed11000 kN/m².



Standard penetration test Driven piles in noncohesive soil

The standard penetration test is a simple insitu test in which the Nvalue is the mumber of blows taken to drive a 50mm diameter bar300mm into the base of a bore hole.

Schmertmann (1975) has correlated Nvalues obtained from SPTtests against effective overburden stress as shown in the figure. The effective overburden stress = the weight of material above thebase of the borehole the wight of water e.g. depth of soil = 5m, depth of water = 4m, unit weight of soil =20kN/m³, 'v = 5m x 20kN/m³ 4m x 9.81kN/m³ 60 kN/m²

Once a value for ´ has been estimated, bearing capacity factors can be determined and used in theusual way.

Meyerhof (1976) produced correlations between base and frictional resistances and Nvalues. It isrecommended that Nvalues first be normalised with respect to effective overburden stress:

Normalised N = Nmeasured x 0.77 log(1920/´v)

Pile type Soil typeUltimate base resistance

qb (kPa)Ultimate shaft resistance

qs (kPa)

Driven Gravelly sand Sand

40(L/d) N but < 400 N

2 Navg

Sandy silt Silt

20(L/d) N but < 300 N

Bored Gravel and sands 13(L/d) N but < 300 N

Navg

Sandy silt Silt

13(L/d) N but < 300 N

L = embedded length d = shaft diameter Navg = average value along shaft

Cone penetration test Driven piles in noncohesive soil

Endbearing resistance The endbearing capacity of the pile is assumed to be equal to the unit cone resistance (qc). However,due to normally occurring variations in measured cone resistance, Van der Veen's averaging method isused:



qb = average cone resistance calculated over a depth equal to three pile diameters aboveto one pile diameter below the base level of the pile.

Shaft resistance The skin friction can also be calculated from the cone penetration test from values of local sidefriction or from the cone resistance value using an empirical relationship: At a given depth, qs = Sp. qc where Sp = a coefficient dependent on the type of pile Type of pile SpSolid timber ) Precast concrete ) Solid steel driven ) 0.005 0.012

Openended steel 0.003 0.008

Bored piles in noncohesive soil Bearing capacity of piles

The design process for bored piles in granular soils is essentially the same as that for driven piles. Itmust be assumed that boring loosens the soil and therefore, however dense the soil, the value of theangle of friction used for calculating Nq values for end bearing and values for skin friction must bethose assumed for loose soil. However, if rotary drilling is carried out under a bentonite slurry ' canbe taken as that for the undisturbed soil.

Driven piles in cohesive soil Bearing capacity of piles

Driving piles into clays alters the physical characteristics of the soil. In soft clays, driving piles resultsin an increase in pore water pressure, causing a reduction in effective stress;.a degree of ground heavealso occurs. As the pore water pressure dissipates with time and the ground subsides, the effectivestress in the soil will increase. The increase in 'v leads to an increase in the bearing capacity of thepile with time. In most cases, 75% of the ultimate bearing capacity is achieved within 30 days ofdriving.

For piles driven into stiff clays, a little consolidation takes place, the soil cracks and is heaved up.Lateral vibration of the shaft from each blow of the hammer forms an enlarged hole, which can thenfill with groundwater or extruded porewater. This, and 'strain softening', which occurs due to the largestrains in the clay as the pile is advanced, lead to a considerable reduction in skin friction comparedwith the undisturbed shear strength (su) of the clay. To account for this in design calculations anadhesion factor, , is introduced. Values of can be found from empirical data previously recorded.A maximum value (for stiff clays) of 0.45 is recommended.

The ultimate bearing capacity Qf of a driven pile in cohesive soil can be calculated from: Qf = Qb + Qs



where the skin friction term is a summation of layer resistances Qs = ( .su(avg) .As)

and the end bearing term is Qb = su .Nc .Ab

Nc = 9.0 for clays and silty clays.

Bored piles in cohesive soil Bearing capacity of piles

Following research into bored castinplace piles in London clay, calculation of the ultimate bearingcapacity for bored piles can be done the same way as for driven piles. The adhesion factor should betaken as 0.45. It is thought that only half the undisturbed shear strength is mobilised by the pile due tothe combined effect of swelling, and hence softening, of the clay in the walls of the borehole.Softening results from seepage of water from fissures in the clay and from the unset concrete, andalso from 'work softening' during the boring operation.

The mobilisation of full endbearing capacity by largediameter piles requires much largerdisplacements than are required to mobilise full skinfriction, and therefore safety factors of 2.5 to 3.0may be required to avoid excessive settlement at working load.

Carrying capacity of piles in layered soil Bearing capacity of piles

When a pile extends through a number of different layers of soil with different properties, these haveto be taken into account when calculating the ultimate carrying capacity of the pile. The skin frictioncapacity is calculated by simply summing the amounts of resistance each layer exerts on the pile. Theend bearing capacity is calculated just in the layer where the pile toe terminates. If the pile toeterminates in a layer of dense sand or stiff clay overlying a layer of soft clay or loose sand there is adanger of it punching through to the weaker layer. To account for this, Meyerhof's equation is used.

The base resistance at the pile toe is qp = q2 + (q1 q2)H / 10B but £ q1

where B is the diameter of the pile, H is the thickness between the base of the pile and the top of theweaker layer, q2 is the ultimate base resistance in the weak layer, q1 is the ultimate base resistance inthe strong layer.



Effects of groundwater Bearing capacity of piles

The presence and movement of groundwater affects the carrying capacity of piles, the processes ofconstruction and sometimes the durability of piles in service.

Effect on bearing capacity In cohesive soils, the permeability is so low that any movement of water is very slow. They do notsuffer any reduction in bearing capacity in the presence of groundwater. In granular soils, the position of the water table is important. Effective stresses in saturated sands canbe as much as 50% lower than in dry sand; this affects both the endbearing and skinfriction capacityof the pile.

Effects on construction When a concrete castinplace pile is being installed and the bottom of the borehole is below the watertable, and there is water in the borehole, a 'tremie' is used.

With its lower end lowered to the bottom of the borehole, the tremmie isfilled with concrete and then slowly raised, allowing concrete to flowfrom the bottom. As the tremie is raised during the concreting it must bekept below the surface of the concrete in the pile. Before the tremie iswithdrawn completely sufficient concrete should be placed to displace allthe free water and watery cement. If a tremie is not used and more than afew centimetres of water lie in the bottom of the borehole, separation ofthe concrete can take place within the pile, leading to a significantreduction in capacity.

A problem can also arise when boring takes place through clays. Siteinvestigations may show that a pile should terminate in a layer of clay.However, due to natural variations in bed levels, there is a risk of boringextending into underlying strata. Unlike the clay, the underlying bedsmay be permeable and will probably be under a considerable head of water. The 'tapping' of suchaquifers can be the cause of difficulties during construction.



Effects on piles in service The presence of groundwater may lead to corrosion or deterioration of the pile's fabric. In the case of steel piles, a mixture of water and air in the soil provides conditions in which oxidationcorrosion of steel can occur; the presence of normally occurring salts in groundwater may acceleratethe process. In the case of concrete piles, the presence of salts such as sulphates or chlorides can result incorrosion of reinforcement, with possible consequential bursting of the concrete. Therefore, adequatecover must be provided to the reinforcement, or the reinforcement itself must be protected in someway. Sulphate attack on the cement compounds in concrete may lead to the expansion and subsequentcracking. Corrosion problems are minimised if the concrete has a high cement/aggregate ratio and iswell compacted during placement.

Bearing Capacity

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