# A retaining wall has a vertical back face with a horizontal granular backfill. Given: H = 6 m, γ = 18.5 kN/m 3 , ϕ ′ = 40 ° , and δ ′ = 1 2 ϕ ′ . Estimate the passive force, P p , per unit length of the wall using Terzaghi and Peck’s (1967) wedge theory (Figure 14.4).

### 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 14, Problem 14.1P
Textbook Problem

## A retaining wall has a vertical back face with a horizontal granular backfill. Given: H = 6 m, γ = 18.5 kN/m3, ϕ ′ = 40 ° , and δ ′ = 1 2 ϕ ′ . Estimate the passive force, Pp, per unit length of the wall using Terzaghi and Peck’s (1967) wedge theory (Figure 14.4).

Expert Solution
To determine

Find the passive force Pp per unit length of the wall using Terzaghi and Peck’s wedge theory.

The passive force Pp per unit length of the wall using Terzaghi and Peck’s wedge theory is 2,997kN/m_.

### Explanation of Solution

Given information:

The height (H) of the retaining wall is 6.0 m.

The soil friction angle ϕ is 40°.

The unit weight γ of the granular backfill is 18.5kN/m3.

The equation for the angle of wall friction δ is 12ϕ.

Calculation:

Determine the angle of wall friction δ using the relation.

δ=12ϕ

Substitute 40° for ϕ.

δ=12(40°)=20°

Calculate passive force Pp per unit length of the wall using Terzaghi and Peck’s wedge theory using the relation.

Pp=12KpγH2

Here, Kp is the passive earth pressure coefficient.

Refer Figure (14.4) “Variation of Kp with ϕ and δ based on the procedure of Terzaghi and Peck’s” in the text book.

Take the passive earth pressure coefficient for the soil having friction angle of 40° and angle of wall friction of 20° as 9.0.

Substitute 9.0 for Kp, 18.5kN/m3 for γ, and 6.0 m for H.

Pp=12×9.0×18.5×6.02=5,9942=2,997kN/m

Thus, the passive force Pp per unit length of the wall using Terzaghi and Peck’s wedge theory is 2,997kN/m_.

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