   Chapter 15, Problem 15.30P 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

The following parameters are given for a slope with steady-state seepage. Slope angle: 2H: l V,  ϕ′ = 24°, c′ = 42 kN/m2,  γ = 19.3 kN/m3, H = 14 m, and ru = 0.5. Determine the factor of safety, Fs, using Spencer’s solution (Figure 15.35).

To determine

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

Explanation

Given information:

The inclination of the slope is 2H:1V.

The height (H) is 14 m.

The unit weight γ is 19.3kN/m3.

To soil friction angle ϕ is 24°.

The cohesion c value is 42kN/m2.

The non–dimensional quantity ru is 0.5.

Calculation:

Determine the inclination angle using the formula.

β=tan1(yx)

Substitute 1 for y and 1 for x.

β=tan1(12)=26.56°

Determine the value of cFsγH

Consider the factor of safety Fs value as 1.50.

Substitute 42kN/m2 for c, 1.50 for Fs, 19.3kN/m3 for γ, and 14 m for H.

cFsγH=421.50(19.3)(14)=0.103

Similarly, calculate and tabulate the value of cFsγH by taking the factor of safety value as 1.6, 1.7, and 1.8 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

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