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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

Use Spencer’s chart (Figure 15.35) to determine the value of Fs for a slope with the following characteristics: H = 25 m, β = 30°, γ = 17 kN/m3, ϕ' = 20°, c' = 27 kN/m2, and ru = 0.25.

To determine

Find the factor of safety Fs for a slope using Spencer’s chart.

Explanation

Given information:

The height (H) is 25 m.

The inclination angle β is 30°.

The unit weight γ is 17kN/m3.

To soil friction angle ϕ is 20°.

The cohesion c value is 27kN/m2.

The non-dimensional quantity ru is 0.25.

Calculation:

Determine the value of cFsγH

Consider the factor of safety Fs value as 1.20.

Substitute 27kN/m2 for c, 1.20 for Fs, 17kN/m3 for γ, and 25 m for H.

cFsγH=271.20(17)(25)=0.0529

Similarly, calculate and tabulate the value of cFsγH by taking the factor of safety value as 1.1, 1.0, and 0.90 as in Table (1).

Determine the factor of safety Fs(calculated) for a slope using Spencer’s chart.

Fs(calculated)=tanϕtanϕd

Here, ϕd angle of friction that develops along the potential failure surface.

Refer Figure (15.35) “Spencer’s solution plot of cFsγH versus β” in the text book

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