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.

(b) Strut loads.

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

The struts are placed 12 ft apart center to center horizontally.

Question

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

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

Determine: (a) The earth pressure distribution envelope.

(b) Strut loads.

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

The struts are placed 12 ft apart center to center horizontally.

Accepted Answer

(a) The stability number [latex]N_{s}[/latex] from Eq. (20.57a) is

[latex]N_{s}=\frac{\gamma H}{c} \leq 4[/latex] (20.57a)

[latex]N_{s}=\frac{\gamma H}{c}=\frac{115 imes 25}{800}=3.6<4[/latex]

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

[latex]p_{a}=0.3 imes 115 imes 25=863 lb / ft ^{2}[/latex]

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

(b) Strut loads

Taking moments about the strut head [latex]B_{1}(B)[/latex]

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

Due to symmetry

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

Strut loads are:

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

(c) Moments

The shear force diagram is shown in Fig. 20.18c for sections [latex]D B_{1} ext { and } B_{2} E[/latex]

Moment at [latex]A=\frac{1}{2} imes 5 imes 690 imes \frac{5}{3}=2,875[/latex] Ib-ft/ft of wall

Moment at [latex]m=2848 imes 3.3-863 imes 3.3 imes \frac{3.3}{2}=4699[/latex] Ib-ft/ft

Because of symmetrical loading

Moment at A = Moment at C = 2875 Ib-ft/ft of wall

Moment at m = Moment at n = 4699 Ib-ft/ft of wall

Hence, the maximum moment = 4699 Ib-ft/ft of wall.

The section modulus and the required sheet pile section can be determined in the usual way.

Q. 20.18

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