A concrete dam retaining 6 m of water is shown in Fig. 3-18(a). The unit weight of the concrete is 23.5 kN/m3. The foundation soil is impermeable. Determine (a) the factor of safety against sliding, (b) the factor of safety against overturning, and (c) the pressure intensity on the base of the dam.

Question

A concrete dam retaining 6 m of water is shown in Fig. 3-18(a). The unit weight of the concrete is 23.5 kN/m³. The foundation soil is impermeable. Determine (a) the factor of safety against sliding, (b) the factor of safety against overturning, and (c) the pressure intensity on the base of the dam. The coefficient of friction between the base of the dam and the foundation soil is 0.48.

Accepted Answer

[latex]F_{H} [/latex] = [latex]\gamma h_{cg} [/latex]A = (9.79)(3)(6 x 1) = 176.2 kN
[latex]F_{V} [/latex]=0

Refer to Fig. 3-18(6).

weight of part 1 of dam = (1) [(2)(7)/2](23.5) = 164.5 kN
weight of part 2 of dam = (1)(2)(7)(23.5) = 329.0 kN

Total weight of dam = 164.5 + 329.0 = 493.5 kN.

(a) [latex]F S_{sliding}=\frac{sliding resistance}{sliding force} [/latex]

[latex]=\frac{(0.48)(493.5)}{176.2} =1.34 [/latex]

(b) [latex]FS_{overturning} =\frac{total righting moment}{total overturning moment} [/latex]

[latex]=\frac{(164.5)(1.333)+(329.0)(3.000)}{(176.2)(2)}=3.42 [/latex]

(c) Resultant (R) on base = [latex]\sqrt{(164.5+329.0)^2+176.2^2}=524 [/latex] kN. Let [latex]\bar{x} [/latex] be the distance from A to the point where R intersects the base of the dam.

[latex]\bar{x} =\frac{\sum{M_{A}} }{R_{y}}=\frac{[(164.5)(1.333)+(329.0)(3.000)]-[(176.2)(2)]}{493.5}=1.730 [/latex] m

[latex]eccentricity=\frac{4}{2}-1.730=0.270m<\frac{4}{6}=0.667 [/latex] m

Therefore, the resultant lies within the middle third of the base.

[latex]p=F/A\pm M_{y}{x}/I_{y}\pm M_{x}y/I_{x} [/latex]

[latex]=\frac{493.5}{(4)(1)}\pm \frac{[(493.5)(0.270)](2)}{(1)(4)^3/12}\pm 0 [/latex]

[latex]p_{A} [/latex] = 123.4 + 50.0 = 173.4 kPa [latex]p_{B} [/latex] = 123.4 – 50.0 = 73.4 kPa

Question 3.20: A concrete dam retaining 6 m of water is shown in Fig. 3-18(...

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