QUESTION 4 The cantilever retaining wall shown in Figure Q4 is filled with granu

Question

QUESTION 4 The cantilever retaining wall shown in Figure Q4 is filled with granular material having a unit weight = 19 kNm-3 and an angle of internal friction, = 300, Assume the allowable bearing pressure of the soil to be 150 kNm-2, sliding friction coefficient 0.35 and the unit weight of reinforced concrete = 24 kN-3 and weep holes are provided behind the wall. (i) Determine the factors of safety against sliding and overturning. (ii) Calculate ground bearing pressure. (ii) Determine the main flexural reinforcement steel for the Stem and Base of the wall. (10) Take feu-30 kNm-2, fy = 450 kNm-2 and the cover to reinforcement in the wall and base as 50 mm. unit wt = 19 kN/n G-30 700 ! 2900 400 Figure Q4: cantilever retaining wall

Explanation / Answer

Solution:-

Density of concrete = 24 kN/m3

Weight of wall (W1) = 5 *0.4 *1 *24=48 KN

Act at 3.1 m from heel point B

W2 = 0.4 * 4 * 1 * 24 = 38.4 kN  

Act at 2m

Weight of earth (W3) = 5*2.9 * 1 * 19 = 275.5 KN

Act at 1.45 meter

Total earth pressure

Pa = ½ * Ca * y * H2

    = 1/2 * 0.33 * 19 * (5)2 = 78.37 KN

Where Ca = (1-sin30)/(1 +sin30) = 0.33

Act at H/3 = 5/3 = 1.66 m

Vertical component of earth pressure (Pv) = 78.37sin30 =39.16 KN

Ph = 78.37cos30 = 67.87 KN

Taking moment of all the forces above point B and dividing by the total vertical forces

X = (48*3.1 + 38.4 * 2 + 275.5 * 1.45 + 67.87 *1.66)/(48 +38.4 + 275.5 + 39.16)

X = 1.83 m

e = 1.83 – 4/2 = -0.17 m

The pressure on the toe and heel are given by

P = W/(bl)*(1 +- 6*e/4)

Pressure at toe = 429.77/(1 *4) *(1 + 6 (-0.17)/4) = 102.87 KN/m2     Answer

Less than 150 KN/m2 Safe

Pressure at heel = 429.77/4 *(1 – 6 (-0.17)/4) = 134.84 KN/m2 less than 150 KN/m2   Safe      Answer

(i)

Resisting moment about point A at toe

Wx1 =48 *0.9 + 38.4 *2 + 275.5 *2.55 = 822.52 KN –m

Overturning moment about point A = Ph H/3 = 67.87 * 1.66 = 112.66 KN-m

Factor of safety against overturning = Wx1/(PhH/3)

                                                                  = 822.52/(112.66)

                                                                  = 7.3     less than 1.5 Safe Answer

Check against sliding

Resisting force = µ W = 0.35 * 361.9 = 126.66 KN

Sliding force =Ph = 67.87 KN

Factor of safety against sliding = µW/Ph = 126.66/67.87 =1.86    less than 1.5

So safe     Answer

(iii)Reinforcement in retaining wall

Mu = 0.87 fyAst(d – fyAst/(fck*b))

1.5*112.66 *106 = 0.87*450 * Ast*(400 – 450*Ast/(30*1000))

Ast = 1126 mm2

Provide 12 mm diameter bars @160mm c/c spacing

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