   Chapter 16, Problem 16.13P Principles of Geotechnical Enginee...

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

Solutions

Chapter
Section Principles of Geotechnical Enginee...

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

A square footing (B × B) must carry a gross allowable load of 1160 kN. The base of the footing is to be located at a depth of 2 m below the ground surface. If the required factor of safety is 4.5, determine the size of the footing. Use Terzaghi’s bearing capacity factors and assume general shear failure of soil. Given: γ = 17 kN/m3, c′ = 48 kN/m2, ϕ ′ = 31 ° .

To determine

Find the size of the footing.

Explanation

Given information:

The gross allowable load (qall) is 1,160 kN.

The location of depth of footing base Df is 2 m.

The factor of safety Fs is 4.5.

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

The value of cohesion c is 48kN/m2.

The soil friction angle ϕ is 31°.

Calculation:

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

qu=1.3cNc+qNq+0.4γBNγ=1.3cNc+γDfNq+0.4γBNγ (1)

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 40.41, Nq as 25.28, and Nγ as 22.65 for the ϕ value of 31°.

Substitute 48kN/m2 for c, 40.41 for Nc, 17kN/m3 for γ, 2 m for Df, 25

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