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CE304-GEOTECHNOLOGY

BEARING CAPACITY28 APRIL 2012- UZ Dept. of Civil Eng.Mr S. Shumba

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BEARING CAPACITY A foundation is that part of a structure which

transmits loads directly to the underlying soil. Foundation engineering applies the knowledge

of soil mechanics, rock mechanics, geology, and structural engineering to the design and construction of foundations for buildings and other structures.

The selection of the type of foundation, such as using a shallow or deep foundation, the development of design parameters, such as the bearing capacity of the foundation and actual foundation design eg determining the type and spacing of steel reinforcement in concrete footings.

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y Shallow foundations: derives its support from

soil or rock close to the lowest part of the structure eg footings and rafts.

Deep founadations: transmit all or a portin of the load to the some sufficient depth below the base of the structure eg piles.

A raft supports many columns or wall loads or where the loads are so large that individual footings will occupy more than 50% of projected building area.

Combined footings are provided intermediate between single spread footings and rafts.

Spread or pad footings used to support and distribute an individual load (column load).

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yTYPES OF FOUNDATION

o Shallow Foundation System i) Spread Foundation

ii) Mat / Raft Foundationo Deep Foundation System

i) Pile iii) Diaphragham wallii) Pile walls iv) Caissons

o Advantages of shallow foundationsa) Cost (affordable)b) Construction Procedure (simple)]c) Material (mostly concrete)d) Labour (doesn’t need expertise)

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ySTRIP FOOTINGS

Strip foundations should be 600mm minimum width.

Foundations should be situated centrally below the wall. Minimum thickness of strip foundations should be 150mm.

Steps in foundations must not be of a greater dimension than the thickness of the foundation.

Where foundations are stepped (on elevation) they should overlap by twice the height of the step, by the dimension of the foundation, or 300mm – whichever is the greater.

The depth of all foundations will be determined by specific site conditions.

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ySTRIP FOOTING

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ySPREAD FOUNDATION

o It’s an enlargement at the bottom of a column/ bearing wall that spreads the applied structural loads over a sufficiently large soil area.o Each column & each bearing wall has its own spread footing, so each structure may include dozens of individual footings. The foundation consists of concrete slabs located under each structural column and a continuous slab under load-bearing walls. For the spread foundation system the structural load is literally spread out over a broad area under the building

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yo Spread footings may be built in different shapes & sizes to accommodate individual needs such as the following: a) Square Spread Footings / Square Footings b) Rectangular Spread Footings c) Circular Spread Footings d) Continuous Spread Footings e) Combined Footings f) Ring Spread Footingso Combined Footings - support more than one column - useful when columns are located too close together for each to have its own footing.

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yRAFT FOUNDATIONS

o A foundation system in which essentially the entire building is placed on a large

continuous footing.o It is a flat concrete slab, heavily reinforced with steel, which carries the downward loads of the individual columns or walls.o Raft foundations are used to spread the load from a structure over a large area, normally the entire area of the structure.

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yCAISSONS (FOR CE404)

o It’s a prefabricated hollow box or cylinder. It is sunk into the ground to some desired

depth and then filled with concrete thus forming a foundation.o Most often used in the construction of bridge

piers & other structures that require foundation beneath rivers & other bodies of water, can be floated to the job site and sunk into place.

o A caisson foundation consists of concrete columns constructed in cylindrical shafts excavated under the proposed structural column locations.

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yDESIGN REQUIREMENTS

1.The factor of safety against shear failure of the supporting soil must be adequate (2.5-3.0). Failure could occur due to inadequate bearing capacity, overturning or sliding.

Ensure applied bearing pressure does not exceed the safe bearing capacity.

2.The settlement of the foundation should be tolerable. Differential settlement should not cause any unacceptable damage nor interfere with the function of the structure.

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yBEARING PRESSURES

Ultimate bearing capacity (qf ): the pressure which would cause shear failure of the supporting soil immediately below and adjacent to a foundation.

Ultimate bearing capacity solutions are based primarily on the Theory of Plasticity; that is, the soil mass is incompressible (does not deform) prior to shear failure. After failure, deformation (plastic flow) occurs with no increase in shear.

Theoretical predictions can only be applied to soils that are homogeneous and incompressible. However, most soils are neither homogeneous nor incompressible. Consequently, known theoretical solutions are used in bearing capacity analyses but are modified to provide for variations in soil characteristics.

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APPROACHES TO FOUNDATION DESIGN

1. The permissible stress method, as used in BS 8004: 1986 [7], uses a lumped factor of safety to ensure that the pressure applied to a foundation element is significantly less than the value which would cause shear failure in the supporting soil. The applied pressure is due to dead load and maximum imposed load. A relatively high factor of 2–3 (more often the latter) is specified to allow for uncertainties in soil conditions and analytical method, and to ensure that settlement is not excessive.

The allowable bearing capacity (qa) is defined as the maximum pressure which may be applied to the soil such that an adequate factor of safety against shear failure is ensured and that settlement (especially differential settlement) should not cause unacceptable damage nor interfere with the function of the structure.

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y 2. The limit state method, on which Eurocode

7 (EC7) is based, aims at ensuring that all relevant performance requirements are satisfied under all conceivable circumstances.

Ultimate limit states are concerned with the avoidance of collapse or major damage. Serviceability limit states are aimed at the avoidance of unacceptable settlement which could give rise to minor damage or impairment of function.

Design is based on partial safety factors which are applied to characteristic permanent (dead) and variable (imposed) loads.

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yMODES OF FAILURE: (A) GENERAL SHEAR, (B)

LOCAL SHEAR AND (C) PUNCHING SHEAR

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yMODES OF FAILURE

1. General shear failure: involves total rupture of the underlying soil. There is a continuous shear failure of the soil (solid lines) from below the footing to the ground surface.

Continuous failure surfaces develop between the edges of the footing and the ground surface (well defined continuous slip surfaces up to ground level).

Heaving occurs on both sides with final collapse and tilting on one side.

Failure is sudden and catastrophic. As the pressure is increased towards the value qf

the state of plastic equilibrium is reached initially in the soil around the edges of the footing and then gradually spreads downwards and outwards.

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y Ultimately the state of plastic equilibrium is fully

developed throughout the soil above the failure surfaces.

Typical of soils of low compressibility (i.e. dense or stiff soils).

Failure is mobilising the full value of shear strength of the soil accompanied by large and excessive settlements. The mechanism causing failure for shallow foundations depends on the soil type (compressibility) and type of loading.

When the load is plotted versus settlement of the footing, there is a distinct load at which the foundation fails and this is designated qult . The value of Qult divided by the width (B) and length (L) of the footing is considered to be the ‘‘ultimate bearing capacity’’ (qult ) of the footing. The ultimate bearing capacity has been defined as the bearing stress that causes a sudden catastrophic failure of the foundation.

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2. LOCAL SHEAR FAILURE (TRANSITION)

Involves rupture of the soil only immediately below the footing. There is soil bulging on both sides of the footing, but the bulging is not as significant as in general shear. Local shear failure can be considered as a transitional phase between general shear and punching shear.

Significant compression of the soil under the footing and only partial development of the state of plastic equilibrium.

Well defined slip surfaces only below the foundation, discontinuous on either side. Large vertical displacements required before slip surfaces appear at ground level.

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y The failure surfaces do not reach the ground

surface and only slight heaving occurs on both sides with no tilting and no catastrophic failure.

Ultimate bearing capacity not well defined. Occurs on soils of moderate to high

compressibility eg medium sands. 3. Punching Shear Failure: does not develop

the distinct shear surfaces associated with a general shear failure. For punching shear, the soil outside the loaded area remains relatively uninvolved and there is minimal movement of soil on both sides of the footing.

The process of deformation of the footing involves compression of soil directly below the footing as well as the vertical shearing of soil around the footing perimeter.

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y Occurs when there is relatively high

compression of the soil under the footing, accompanied by shearing in the vertical direction around the edges of the footing.

Well defined slip surfaces only below the foundation, none on either side.

Large vertical displacements produced by soil compressibility.

No heaving of the ground surface away from the edges and no tilting of the footing or catastrophic failure.

Occur in a soil of low compressibility if the foundation is located at considerable depth.

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y The failure mode to be expected for a given

soil profile cannot be predicted. The statement can be made, however, that the mode of failure depends substantially on the compressibility or incompressibility of the soil mass.

Soil type alone does not determine the failure mode. For example, a shallow footing supported on a very dense sand will usually fail in general shear, but the same footing supported on a very dense sand which is underlain by a soft clay layer may fail in punching shear.

Local shear failure may exhibit both general and punching shear characteristics, soil compression beneath the footing, and possible ground surface bulging.

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Local shear failure

Punching

shear failure

General shear falure

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yFAILURE UNDER A STRIP FOOTING

II II

IIIII

I- ACTIVE RANKINE ZONEII- ZONES OF RADIAL SHEARIII- PASSIVE RANKINE ZONE

Above ADCGF- PLASTIC EQM.; Below ADCGF- ELASTIC EQM.

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y The footing of width B and infinite length, carries a

uniform pressure q on the surface of a homogeneous, isotropic soil mass. The shear strength parameters are c and Ф but the unit weight is assumed zero.

When the pressure becomes equal to the ultimate bearing capacity qf the footing will have been pushed downwards into the soil mass, producing a state of plastic equilibrium, in the form of an active Rankine zone, below the footing, the angles ABC and BAC being 45 = Ф /2.

The downward movement of the wedge ABC forces the adjoining soil sideways, producing outward lateral forces on both sides of the wedge.

Passive Rankine zones ADE and BGF therefore develop on both sides of the wedge ABC, the angles DEA and GFB being 45 - Ф /2.

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FAILURE UNDER A STRIP FOOTING CONT.

The transition between the downward movement of the wedge ABC and the lateral movement of the wedges ADE and BGF takes place through zones of radial shear (also known as slip fans) ACD and BCG, the surfaces CD and CG being logarithmic spirals (or circular arcs if Ф= 0) to which BC and ED, or AC and FG, are tangential.

A state of plastic equilibrium thus exists above the surface EDCGF, the remainder of the soil mass being in a state of elastic equilibrium (Below zones I, II and III).

An expression for the bearing capacity has also been derived for the general shear mode of failure and is based on the superposition of three components.

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y Zones I, II and III are in a state of plastic

equilibrium. Zone I (Active Rankine State) is pushed

downwards and in turn pushes the radial shear zones II sideways and the passive Rankine zones III sideways and upwards.

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yBEARING CAPACITY EQUATIONS

Footing at a depth D below the surface

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y Foundations are not normally located on the

surface of a soil mass, as assumed in the above solutions, but at a depth D below the surface.

It is assumed that the shear strength of the soil between the surface and depth D is neglected, this soil being considered only as a surcharge imposing a uniform pressure qo= ƴD on the horizontal plane at foundation level.

Shallow foundation (interpreted as a foundation for which the depth D is not greater than the breadth B).

The most commonly used bearing capacity equation is the equation developed by Terzaghi:

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y The ultimate bearing capacity of the soil

under a shallow strip footing can be expressed by the following equation:

qf = 0.5γBN + cNc + γDNq

where Nγ , Nq and Nc are bearing capacity factors depending only on Ф.

0.5 γBN represents the contribution to bearing capacity resulting from the self weight of the soil (and friction in the soil).

cNc is the contribution due to the constant component of shear strength (cohesion and friction in the soil).

γDNq is the contribution due to the surcharge pressure (and friction in the soil).

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y Values of Nγ are obtained by determining the

total passive resistance and adhesive force on the planes AC and BC. The most widely used values for Nγ are those by Hansen and Meyerhoff:

1. Nγ = 1.8 (Nq -1) tan Ф (Brinch Hansen- widely used)

2. Nγ = (Nq -1) tan (1.4 Ф) (Meyerhoff) In EC7 the following value is proposed: Nγ = 2.0 (Nq -1) tan Фo Terzaghi’s values of Nc and Nγ were obtained

by modifying the Prandtl-Reissner solution. Values attributed to Prandtl and Reissner are:

o Nq =exp (∏ tan Ф) tan2 (45o + Φ/2)o Nc = (Nq -1) cot Ф

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ySHAPE FACTORS

The ultimate bearing capacities of square, rectangular and circular footings are determined by means of semi-empirical shape factors applied to the solution for a strip footing.

The bearing capacity factors Nc, Nq and N should be multiplied by the respective shape factors sc, sq and sƴ .

The original Terzaghi equation was derived for a very long (strip) foundation where shearing in only two dimensions was assumed. However for rectangular foundations shearing of the soil will also occur at the ends, producing an enhanced ‘end effect’.

For circular and square foundations a three dimensional mass of soil will be sheared.

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y These effects are catered for by modifying

Terzaghi’s equation using the shape factors. The shape factors proposed by Terzaghi and

Peck are still widely used. These are sƴ =0.8 for a square footing or 0.6 for

a circular footing. sc = 1.2 and sq = 1.0.

For a square footing: qf =0.4ƴBNƴ + 1.2c Nc + ƴDNq

For a circular footing: qf =0.3ƴBNƴ + 1.2c Nc + ƴDNq

For a rectangular footing of breadth B and length L the shape factors are obtained by linear interpolation between the values for a strip footing (B/L =0) and a square footing (B/L =1).

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yBEARING CAPACITY FACTORS FOR

SHALLOW FOUNDATIONS

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y

SKEMPTON’S VALUES OF NC FOR ΦU

=0

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y In the case of saturated clays under

undrained conditions (Φu =0) the ultimate bearing capacity of a footing is expressed as: qf =cNc + ƴD

Nc is a function of the shape of the footing and the depth to breadth ratio (see figure on previous slide).

The factor for a rectangular footing of dimensions BxL (B<L) is the value for a square footing multiplied by (0.84 + 0.16B/L).

qa (allowable bearing capacity) is the bearing pressure that will cause either undrained or drained settlement or creep equal to a specified tolerable design limit.

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BEARING CAPACITY COEFFICIENTS

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yBEARING CAPACITY FACTORS FOR

GRANULAR SOILS

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yBEARING CAPACITY FACTORS FOR

COHESIVE SOIL

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yFACTOR OF SAFETY

Total foundation pressure (q) is the actual pressure on the soil due to the weight of the structure.

The net foundation pressure (qn) is the increase in pressure at foundation level being the total foundation pressure less the weight of soil per unit area permanently removed, i.e. the difference in pressure on the soil before and after construction.

The unit weight may be either the total stress or the effective stress value, depending on the type of analysis.

qn = q- ƴD

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y According to the permissible stress method, the

factor of safety (F ) with respect to shear failure is defined in terms of net ultimate bearing capacity (qnf ).

If the value of is relatively high, there is no significant difference between the values of F in terms of net and total pressures.

In the limit state method the design bearing resistance (Rd) is calculated using the factored shear strength parameters.

The vertical design load (Vd) is calculated from factored loads without subtracting the weight of overburden soil (because safety is not defined in terms of the ratio Rd/Vd). The bearing resistance limit state is satisfied if the design load is less than or equal to the design bearing resistance.

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This is used to obtain the net safe bearing pressure qs

Net qs = Net qult/ F Gross qs= Net qult/ F + ƴD The net ultimate bearing capacity (qult = qf )

is the maximum additional pressure the soil can support in excess of the stress at foundation level which existed before placing the foundation.

qult = qnf = qf – ƴD

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y Soil mechanics is defined as the application

of the laws and principles of mechanics and hydraulics to engineering problems dealing with soil as an engineering material.

Geotechnical Engineering: the application of civil engineering technology to some aspect of the earth, therefore including soil and rock as engineering materials.

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THANK YOU