A reservoir is to be built to contain a slurry as shown in Figure 2.58. It is pr

Question

A reservoir is to be built to contain a slurry as shown in Figure 2.58. It is proposed that the retaining wall of the reservoir be 3 m high, 1 m thick, and be made of concrete with a density of 2800 kg/m3 . A review of site conditions indicates that the coefficient of friction between the concrete wall and the underlying soil is equal to 0.35. It is expected that the slurry will have a density of 1500 kg/m3 . (a) Estimate the height, h, of slurry that will cause the wall to fail by sliding over the soil, i.e., shear failure. (b) Estimate the height, h, of slurry that will cause the wall to topple over by rotating about the point P. Which is the more likely failure mode?

Explanation / Answer

For Caculation we take weight per unit lenth of wall

the pressure due to slurry is triangular with force acting at one third of height from base

Weight per unit lenth of wall = Density * Area

Weight per unit lenth of wall = 2800 *1 *3 = 8400kg/m = Normal reaction due to weight of wall

Now FOR SHEAR FAILURE

FRICTION FORCE = HORIZONTAL FORCE BY SLURRY

coefficent of friction * Normal reaction due to weight of wall = 0.5 *density of slurry * g* height of slurry2

0.35 * 8400 = 0.5 * 1500 * 9.8 * h2

calculating         h = 1.97 m say 2 mts

For topple about P we need to find moment about p

then Moment due to weight of wall = 8400 * g * 0.5 clockwise

Moment due to force from slurry = 0.5 *density of slurry * g* height of slurry2 * (h/3)

so

8400 * g * 0.5 = 0.5 * 1500 * g * h3 / 3

solving         h = 2.56 m

The probable failure mode is due to shear as height of slurry reqiured is less as compared due to topple failue..

the wall would already be failed till it reaches toppling condition

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