   Chapter 15, Problem 15.1P 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

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

To determine

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

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

Explanation

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_.

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 