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## Q. 20.18

Fig. Ex. 20.18a gives the section of a long braced cut. The sides are supported by steel sheet pile walls with struts and wales. The soil excavated at the site is stiff clay with the following properties

$c=800 lb / ft ^{2}, \phi=0, \gamma=115 lb / ft ^{3}$

Determine: (a) The earth pressure distribution envelope.

(c) The maximum moment of the sheet pile section.

The struts are placed 12 ft apart center to center horizontally. ## Verified Solution

(a) The stability number $N_{s}$ from Eq. (20.57a) is

$N_{s}=\frac{\gamma H}{c} \leq 4$ (20.57a)

$N_{s}=\frac{\gamma H}{c}=\frac{115 \times 25}{800}=3.6<4$

The soil is stiff fissured clay. As such the pressure envelope shown in Fig. 20.28(c) is applicable. Assume $p_{a}=0.3 \gamma H$

$p_{a}=0.3 \times 115 \times 25=863 lb / ft ^{2}$

The pressure envelope is drawn as shown in Fig. Ex. 20.18(b).

Taking moments about the strut head $B_{1}(B)$

\begin{aligned}&R_{A} \times 7.5=\frac{1}{2} 863 \times 6.25\left(\frac{6.25}{3}+6.25\right)+863 \times \frac{(6.25)^{2}}{2} \\&=22.47 \times 10^{3}+16.85 \times 10^{3}=39.32 \times 10^{3} \\&R_{A}=5243 lb / ft \\&R_{ B 1}=\frac{1}{2} \times 863 \times 6.25+863 \times 6.25-5243=2848 lb / ft\end{aligned}

Due to symmetry

\begin{aligned}&R_{A}=R_{C}=5243 lb / ft \\&R_{B 2}=R_{B 1}=2848 lb / ft\end{aligned}

\begin{aligned}&P_{A}=5243 \times 12=62,916 lb =62.92 kips \\&P_{B}=2 \times 2848 \times 12=68,352 lb =68.35 kips \\&P_{C}=62.92 kips\end{aligned}

(c) Moments

The shear force diagram is shown in Fig. 20.18c for sections $D B_{1} \text { and } B_{2} E$

Moment at $A=\frac{1}{2} \times 5 \times 690 \times \frac{5}{3}=2,875$ Ib-ft/ft of wall

Moment at $m=2848 \times 3.3-863 \times 3.3 \times \frac{3.3}{2}=4699$ Ib-ft/ft