Footings Soil Pressure

16Footings

16-1 INTRODUCTION

Footings and other foundation units transfer the loads from the structure to the sO'~supporting the structure. Because the soil is genera1ly much weaker than the ~

columns and walls that must be supported, the contact area between the soil and ;;;...ing is much larger than that betWeen the supported member and the footing.

The more common types of footings are illustrated in Fig. 16-1. Strip footingfootings display essentially one-dimensional action, cantilevering out on each si&:wall. Spread footings are pads that distribute the column load to an area of soil 3P"... _column. These distribute the load in two directions. Sometimes spread footm;pedestals, are stepped, or are tapered to save materia1s. A pi/e cap transmits the coi::..c-to a series of pi/es, which, in tum, transmit the load to a strong soil layer at sorn=below the surface. Combined footings transmit the loads from two or more colurm:soil. Such a footing is often used when one column is c10se to a property line. A m...~fOlmdation transfers the loads from all the columns in a building to the underlyingfoundations are used when vel)' weak soils are encountered. Caissons 2 to 5 ft in ~ .

are sometimes used instead of piles to transmit heav)' column loads to deep foun~ers. Frequently, these are enlarged at the bonom (bel/elf) to apply load to a larger~

The choice of foundation type is selected in consultation with the geotechrn........neer. Factors to be considered are the soil strength, the soil type, the variabilityc~type over the area and with increasing depth. and the susceptibility of the soi: "" .

building to deflections.Strip, spread, and combined footings are considered in this chapter since ~

the most basic and most common t)'pes.

16-2 SOIL PRESSUREUNDER FOOTINGS

786

The distribution of soil pressure under a footing is a function of the type of soil an~ative rigidit)' of the soil and the foundation pad. A concrete footing on sand \\~pressure distribution similar to Fig. 16-2a.The sand near the edges of the footing

~0n 45-= 5::- :: ~_= _-cer I=ootings . 787

/

(b) Spread 'OO;,"g

(d) Tapered 'oo'-~

---

(f) Cambined 'OC' .~

(g) Mat ar ra'; 'x ~

/'

--

b

788 · Chapter 16 Footings

Fig. 16-2Pressure distribution underfootings. (a) Footing on sand. (b) Footing on clay.

displace laterally when the footing is loaded, causing a decrease in soil pressure ::-edges. On the other hand, the pressure distribution under a footing on clay is s~Fig. 16-2b.As the footing is loaded, the soil under the footing detlects in a bO\\hdepression, relieving the pressure under the middle of the footing. For design pu~is customary to assume that the soil pressures are linearly distributed in such a wa: ~~resultant vertical soil force is collinear with the resultant downward force.

Design Methods

Allowable StressDesign

There are two differentphilosophies for the design of footings [16-1], [16-2].The 5:---lowable stress design. Almost exclusively,footing design is based on the allowable.acting on the soil at unfactored or service loads. For a concentrically loaded spread - ,

'i,Ps ::5 %A

where

Ps is the specified (unfactored) load acting on the footing. Section 2.4.1 of "-.:.gives an updated set of load combinations for allowable stress design [16-.?Comrnittee 318 has not considered these for footing design as yet.

qa is the allowable stress for the soil given by (16-3), presented in the next suh ~

A is the area of the footing in contact with the soil.

Limit-States Design

The second design philosophy is a limit-states design based on factored loads and ;....resistances [16-1], [16-2], given by

where

cf>is a resistance factor to account for the variability of the load-resisting ~-of the soil under the footing.

RII is the engineer's best estimate of the resistance of the soil under the foon:-;CI'is a load factor.

Ps is the specified load acting on the soil at the base of the footing.

The load factors, CI',in (16-2) are those used in building design. Two sets of loa:! -and load combinations are available for design, those in ACI 318-02, Sections 9.2 .L~-or thoseinACI318-02,AppendixC. Resistancefactorsfor limit-statesdesignof -

are still being developed. Current estimates of cf>values for shallow footings areas-

Section 16-2 Soil Pressure Under Footings · 789

for vertical resistance, 4> = 0.5

for sliding resistancedependenton friction, with cohesion equal to zero, 4> = 0.8

for sliding resistancedependenton cohesion, with friction equal to zero, 4> = 0.6

Serviceability limit states should also be checked [16-1], [16-2], [16-3].

At the time of writing, virtually all building footings in North America are designed

by using allowable-stress design applied to failures of the concrete foundation element or

the soil itself (16-1). The rest of this chapter will apply allowable-stress design to the soil

and then use ultimate-load design for the reinforced concrete foundation structure.

Limit States for the Design of Foundations

Limit States Governed by the SoU

Three primary ultimate limit states of the soil supporting an isolated foundation are [16-1],[16-3].

1. a bearing failure of the soil under the footing (Fig. 16-3),2. a serviceability failure in which excessive differential settlement between adja-

cent footings causes architectural or structural damage to the structure, or3. excessive total settlement.

Settlement occurs in two stages: immediate settlement as the loads are applied, and a long-term settlement known as consolidation.

Procedures for minimizing differential settlements involve a degree of geotechnicalengineering theory outside the realm of this book.

Bearing failures are controlled by limiting the service-load stress under the footingto less than an allowable stress, qa' as in (16-1).

Limit States Governed by the Structure

Similarly,there are three primary structurallimit states for the foundations themselves[16-1], [16-2]:

4. flexural failure of the portions of the footing that project from the column or wall,5. shear failure of the footing, and6. inadequateanchorageof the flexural reinforcement in the footing.

As stated earlier, bearing failures of the soil supporting the foundation are prevented bylimiting the service-load stress under the footing to less than an allowable stress

= qult ( 16-3)qa FS

where qult is the stress corresponding to the failure of the soj) under the footing and FS is afactor of safety in the range of 2.5 to 3. Values of qa are obtained from the principles of

footing.

geotechnical engineering and depend on the shape of the footing, the depth of ~the overburdenor surchargeon top of the footing,the positionof the watertable ~ .

type of soil. When using a value of qaprovided by a geotechnical engineer, it is ~. .to know what strengths were measured and in what kind of tests, and what asSl.':"-have been made in arriving at this allowable soil pressure, particularly with res~burden and depth to the base of the footing.

It should be noted that qa in (16-3) is a service-load stress, whereas the restructure has been designed by using factored loads corresponding to the ultim...states. The method of accounting for this difference in philosophy is explained I~


Fig. 16-4Soil pressure under a footing:loads within kem.

Elastic Distribution of Soil Pressure under a Footing

The soil pressure under a footing is caIculated by assuming linearly elastic actioc ::"pression, but no tensile strength across the contact between the footing and the sc~column load is applied at, or near, the rniddle of the footing, as shown in Fig. :-_stress, q, under the footing is

P Myq=-j;-A I

p

Centroidal axis

~(a) Loads on tooting.

(b) Soil pressure distribution.

(c) Kern dimensions.


where

P = verticalload,positivein compressionA = area of the contact surface between the soil and the footingI = moment of inertia of this area

M = moment about the centroidal axis of the area

y = distance from the centroidal axis to the point where the stresses are beingcalculated

The moment, M, can be expressed as Pe, where e is the eccentricity of the load rela-tive to the centroidal axis of the area A. The maximum eccentricity e for which (16-4) ap-plies is that which first causes q = O at some point. Larger eccentricities will cause aportion of the footing to lift off the soil, since the soil-footing interface cannot resist ten-sion. For a rectangular footing, this occurs when the eccentricity exceeds

(16-5)

This is referred to as the kern distance. Loads applied within the kern, the shaded area inFig. 16-4c, will cause compression over the entire area of the footing, and (16-4) can beused to compute q.

Various pressure distributions for rectangular footings are shown in Fig. 16-5. If theload is applied concentrically, the soil pressure q is qavg = P/A. If the load acts throughthe kern point (Fig. 16-5c), q = Oat one side and q = 2qavgat the other. If the load fallsoutside the kern point, the resultant upward load is equal and opposite to the resultantdownward load, as shown in Fig. 16-5d. Generally, such a pressure distribution would notbe acceptable, since it makes inefficient use of the footing concrete, tends to overload thesoil, and may cause tilt.

Elastic and Plastic Soil-Pressure Distributions

The soil-pressure diagrams in Fig. 16-5 are based on the assumption that the soil pressureis linearly distributed under a footing. This is a satisfactory assumption at service-load lev-els and for footings on rock or dense glacial til!. For yielding soils, the soil-pressure distri-bution will approach a uniform (plastic) distribution over part of the base of the footing insuch a way that the resultant load on the footing and the resultant of the soil pressure coin-cide as is required for equilibrium.

For the design of concentrically loaded footings, the distribution of soil pressures istaken to be uniform over the entire contact area, as shown in Fig. 16-5a. For the structural de-sign of eccentrically loaded footings, such as those for retaining walls or bridge abutments,two pressure distributions may be considered [16-2]. The first of these is a uniform, fully

plastic pressure, qp' over a portion, Ap, of the area of the contact surface. The area Ap is cho-sen such that the centroid of Ap and the resultant of the applied loads coincide. The secondpressure distribution is a linearly varying distribution like the one in Fig. 16-5d, again withthe resultant of the soil pressure coincident with the resultant of the applied loads.

The examples in this chapter are limited to the predominant case of concentric loadsand a uniform or linear soil-pressure distribution over the entire contact area.

Load and Resistance Factors for Footing Design

ln 1995, the ACI Code added a second set of load and resistance factors for reinforcedconcrete design to the traditional ACI load factors and resistance factors. In the 2002 ACICode, the two sets of factors were interchanged: the new factors were given in ACI


Fig. 16-5Pressures under an eccentri-cally loaded footing.

P

q < PIA q> PIA

q = PIA = qavg

(a) Concentric load, e = O.

(b) e < ek.

P

q = 2qavg

I. eI

M

P

Resultant 01 loads

on the looting.

q > 2PIA

Resultant 01 /'soil pressures

(d) e > ek.

Sections 9.2 and 9.3 and the traditional ACI load and resistance factors in Append..the 2002 code, both sets of load and resistance factors are acceptable for desig::ACI318.

The first three examples in this chapter are based on the load and resistancein ACI 2002 Sections 9.2 and 9.3. Example 16-4 uses the factors in ACI Appende: :

Gross and Net Soil Pressures

Figure 16-6a shows a 2-ft-thick spread footing with a column at its center and \\i'-..=.surface located 2 ft below the ground surface. There is no column load at this ~:total downward load from the weights of the soil and the footing is 540 psf. This is ~.


2 ft of soil@ 120 Iblft3 240 Iblft2

300 Iblft2

540 Ib/ft2

(a) Seli weight and soil surcharge.

Gross soil

{pressure =540 + qn Ib/ft2

(b) Gross soil pressure.

Net soil pressure {i i i i i i i i qn = PclA

)il pressures. (c) Nel soil pressure.

by an equa!,but opposite, upward pressure. As a result, the net effect on the concrete foot-ing is zero. There are no moments or shears in the footing due to this loading.

When the column load Pc is added, the pressure under the footing increases byqn = PclA, as shown in Fig. 16-6b. The total soil pressure is q = 540 + qll' This is re-

ferred to as the gross soUpressure and must not exceed the allowable soil pressure, qa'When moments and shears in the concrete footing are calculated, the upward and down-ward pressures of 540 psf cancel out, leaving only the ne! soUpressure, q", to cause inter-nal forces in the footing, as shown in Fig. 16-6c.

ln design, the area of the footing is selected so that the gross soUpressure does notexceed the allowable soil pressure. The flexural reinforcement and the shear strength of the

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Footings Soil Pressure