Chapter 15, Problem 15.11P

### Principles of Geotechnical Enginee...

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

Chapter
Section

### Principles of Geotechnical Enginee...

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

# Refer to Figure 15.50. Using the soil parameters given in Problem 15.10, find the height of the slope, H, that will have a factor of safety of 2.95 against sliding. Assume that the critical sliding surface is a plane.15.10 For the finite slope shown in Figure 15.50, assume that the slope failure would occur along a plane (Culmann’s assumption). Find the height of the slope for critical equilibrium. Given: β = 49°, γ = 17.6 kN/m3, ϕ ′ = 19 ° , and c′ = 42 kN/m2.Figure 15.50

To determine

Find the height (H) of the slope that will have a factor of safety of 2.95 against sliding.

Explanation

Given information:

The slope with an inclination β is 49°.

The angle of friction ϕ is 19°.

The cohesion c is 42kN/m2.

The unit weight γ of the soil is 17.6kN/m3.

The factor of safety Fs against the sliding is 2.95.

Calculation:

Determine the cohesion cd develop along the potential failure surface using the relation.

cd=cFs

Substitute 42kN/m2 for c and 2.95 for Fs.

cd=422.95=14.23kN/m2

Determine the angle ϕd of friction that develops along the potential failure surface using the relation.

ϕd=tan1(tanϕFs)

Substitute 19° for ϕ and 2.95 for Fs.

ϕd=tan1(tan19°2

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