   Chapter 15, Problem 15.23P 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

Repeat Problem 15.22 with the following slope characteristics: 1H:1V, γ = 18 kN/m3, ϕ' = 18°, H = 12 m, and c' = 30 kN/m2.15.22 Refer to Figure 15.52. Using Taylor’s stability chart (Figure 15.21), determine the factor of safety, Fs, against sliding for a slope with the following characteristics: 1.75 H: 1 V, γ = 19 kN/m3, ϕ' =22°, H = 24 m, and c' = 25 kN/m2 To determine

Find the factor of safety Fs against sliding for a slope using Taylor’s stability chart.

Explanation

Given information:

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

The unit weight γ is 18kN/m3.

To soil friction angle ϕ is 18°.

The height (H) of the retaining wall is 12 m.

The cohesion c value is 30kN/m2.

Calculation:

Determine the inclination angle β using the formula.

β=tan1(yx)

Substitute 1 for y and 1 for x.

β=tan1(11)=45°

Take the angle of friction ϕd that develops along the potential failure surface ϕd value as 8°.

Determine the factor of safety Fϕ with respect to friction using the formula.

Fϕ=tanϕtanϕd

Substitute 18° for ϕ and 8° for ϕd.

Fϕ=tan18°tan8°=2.31

Similarly, calculate and tabulate the factor of safety Fϕ with respect to friction for the remaining angle of friction ϕd that develops along the potential failure surface as in Table (1).

Determine the cohesion per unit area developed using the relation.

cd=mγH

Here, m is the stability number.

Refer Figure 15.21 “Taylor’s stability number” in the text book.

Take the stability number as 0.115 when the soil friction angle is 8° and the inclination angle is 45°.

Similarly, take and tabulate the stability number for the remaining angle of friction ϕd as in Table 1.

Substitute 0.115 for m, 18kN/m3 for γ, and 12 m for H

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