Textbook Problem

A retaining wall has a vertical back face with a horizontal granular backfill. Given: H = 6 m, γ = 18.5 kN/m³, ${\varphi }^{\prime }=40°$, and ${\delta }^{\prime }=\frac{1}{2}{\varphi }^{\prime }$. Estimate the passive force, P_p, per unit length of the wall using Terzaghi and Peck’s (1967) wedge theory (Figure 14.4).

To determine

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

Answer to Problem 14.1P

The passive force $P_p$ per unit length of the wall using Terzaghi and Peck’s wedge theory is $\underset{\_}{2,997\text{kN/m}}$.

Explanation of Solution

Given information:

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

The soil friction angle ${\varphi }^{\prime }$ is $40°$.

The unit weight $\gamma$ of the granular backfill is $18.5{\text{kN/m}}^{\text{3}}$.

The equation for the angle of wall friction ${\delta }^{\prime }$ is $\frac{1}{2}{\varphi }^{\prime }$.

Calculation:

Determine the angle of wall friction ${\delta }^{\prime }$ using the relation.

${\delta }^{\prime }=\frac{1}{2}{\varphi }^{\prime }$

Substitute $40°$ for ${\varphi }^{\prime }$.

$\begin{array}{c}{\delta }^{\prime }=\frac{1}{2}\left(40°\right)\\ =20°\end{array}$

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

$P_p=\frac{1}{2}{K}_p\gamma H^2$

Here, $K_p$ is the passive earth pressure coefficient.

Refer Figure (14.4) “Variation of $K_p$ with ${\varphi }^{\prime }$ and ${\delta }^{\prime }$ 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 $K_p$, $18.5{\text{kN/m}}^{\text{3}}$ for $\gamma$, and 6.0 m for H.

$\begin{array}{c}{P}_p=\frac{1}{2}\times 9.0\times 18.5\times {6.0}^2\\ =\frac{5,994}{2}\\ =2,997\text{kN/m}\end{array}$

Thus, the passive force $P_p$ per unit length of the wall using Terzaghi and Peck’s wedge theory is $\underset{\_}{2,997\text{kN/m}}$.