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Principles of Geotechnical Enginee...

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

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BuyFindarrow_forward

Principles of Geotechnical Enginee...

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

Redo Problem 16.9 with the following: density of soil above the ground water table, ρ = 1800 kg/m3; saturated soil density below the groundwater table, ρsat = 2050 kg/m3; c′ = 36 kN/m3, ϕ = 29 ° , Df = 1.5 m, h = 1.5 m, and B = 2 m.

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.

images

Figure 16.18

To determine

Find the gross allowable load (Qall) that the footing can carry.

Explanation

Given information:

The factor of safety is 4.0.

The density of soil above the ground water table ρ is 1,800kg/m3.

The saturated density of the soil ρsat is 2,050kg/m3.

The value of cohesion c is 36kN/m2.

The soil friction angle ϕ is 29°.

The depth of foundation Df is 1.5 m.

The depth of soil above water table h is 1.5 m.

The width of footing B is 2 m.

Calculation:

Determine the unit weight of soil above the water table γ using the relation.

γ=ρg

Here, g is the acceleration due to gravity.

Substitute 1,800kg/m3 for ρ and 9.81m/s2 for g.

γ=1,800×9.81=17,658N/m3×1kN1,000N=17.65kN/m3

Determine the saturated unit weight of soil γsat using the relation.

γsat=ρsatg

Substitute 2,050kg/m3 for ρsat and 9.81m/s2 for g.

γsat=2,050×9.81=20,110.5N/m3×1kN1,000N=20.11kN/m3

Determine the effective unit weight of soil γ using the relation.

γ=γsatγw

Here, γw is the unit weight of water.

Take unit weight of water as 9.81kN/m3.

Substitute 20.11kN/m3 for γsat and 9.81kN/m3 for γw.

γ=20.119.81=10.3kN/m3

The ground water table is at the foundation level

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