# Refer to the infinite slope shown in Figure 15.46. Given: β = 19°, γ = 20 kN/m 3 , ϕ ′ = 33 ° , and c ′ = 47 kN/m 2 . Find the height, H , such that a factor of safety, F s , of 3.1 is maintained against sliding along the soil-rock interface. Figure 15.46

### Principles of Geotechnical Enginee...

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

### Principles of Geotechnical Enginee...

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

#### Solutions

Chapter
Section
Chapter 15, Problem 15.1P
Textbook Problem

## Refer to the infinite slope shown in Figure 15.46. Given: β = 19°, γ = 20 kN/m3, ϕ ′ = 33 ° , and c′ = 47 kN/m2. Find the height, H, such that a factor of safety, Fs, of 3.1 is maintained against sliding along the soil-rock interface.Figure 15.46

Expert Solution
To determine

Find the height (H) of the soil-rock interface.

The height of the soil-rock interface is 6.28m_.

### Explanation of Solution

Given information:

The slope rise at an angle β with the horizontal line is 19°.

The unit weight γ of the soil is 20kN/m3.

The angle of friction ϕ is 33°.

The cohesion c is 47kN/m2.

The factor of safety Fs is 3.1.

Calculation:

Determine the height of the soil-rock interface using the formula.

Fs=cγHcos2βtanβ+tanϕtanβ

Substitute 3.1 for Fs, 47kN/m2 for c, 20kN/m3 for γ, 19° for β, and 33° for ϕ.

3.1=4720Hcos2(19°)tan(19°)+tan(33°)tan(19°)3.1=7.634H+1.8863.1=7.634+1.886HH3.1H=7.634+1.886H

3.1H1.886H=7.6341.214H=7.634H=7.6341.214H=6.28m

Thus, the height of the soil-rock interface is 6.28m_.

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