Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939



Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

If the water table in Problem 16.9 drops down to 0.25 m below the foundation level, what would be the change in the factor of safety for the same gross allowable load?

16.9 A square footing is shown in Figure 16.18. Determine the gross allowable load, Qall, that the footing can carry. Use Terzaghi’s equation for general shear failure (Fs = 4). Given: γ = 17 kN/m3, γsat = 19.2 kN/m3, c′ = 32 kN/m3, ϕ = 26 ° , Df = 1 m, h = 0.5 m, and B = 1.5 m.


Figure 16.18

To determine

Find the change in factor of safety for the estimated gross allowable load.


Given information:

The factor of safety Fs is 4.0.

The unit weight of the soil γ is 17kN/m3.

The saturated unit weight of the soil γsat is 19.2kN/m3.

The value of cohesion c is 32kN/m2.

The soil friction angle ϕ is 26°.

The depth of foundation Df is 1.0 m.

The depth of soil above water table h is 0.5 m.

The drop down depth of water table D is 0.25 m.

The width of footing B is 1.5 m.


For depth of water table at 0.5 m.

Determine the magnitude of q using the relation.

q=γ(Dfh)+γh=γ(Dfh)+(γsatγw)h (1)

Here, γ is the effective unit weight of soil and γw is the unit weight of water.

Take unit weight of water as 9.81kN/m3.

Substitute 17kN/m3 for γ, 1.0 m for Df, 0.5 m for h, 19.2kN/m3 for γsat, and 9.81kN/m3 for γw in Equation (1).


Determine the ultimate bearing capacity of the soil (qu) using the relation.


Here, Nc is the contribution of cohesion, Nq is the contribution of surcharge, and Nγ is the contribution of unit weight of soil.

Refer Table 16.1, “Terzaghi’s bearing-capacity factors–Nc, Nq, and Nγ” in the textbook.

Take the Nc as 27.09, Nq as 14.21, and Nγ as 9.84 for the ϕ value of 26°.

Substitute 32kN/m2 for c, 27.09 for Nc, 13.19kN/m2 for q, 14.21 for Nq, (19.29.81)kN/m3 for γ, 1.5 m for B, and 9.84 for Nγ.


Determine the gross allowable load (qall) that the footing can carry using the relation.


Substitute 1,369.81kN/m2 for qu, 1.5 m for B, and 4.0 for Fs.


For drop down depth of ground water table at 0

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