A layer of sand extends from ground level to a depth of 11m and overlies a layer
ID: 1822472 • Letter: A
Question
A layer of sand extends from ground level to a depth of 11m and overlies a layer of clay, of very low permeability, 8m thick. The water table is 7m below the surface of the sand. The saturated unit weight of the sand is 19kN/m3 and that of the clay 20kN/m3; the unit weight of the sand above the water table is 16kN/m3. Over a short period of time the water table rises of 3m and is expected to remain permanently at this new level. Determine the effective vertical stress at depths of 8m and 12m below ground level (a) immediately after the rise of water table and (b) several years after the rise of the water table.Explanation / Answer
The depth of sand = 11 m
Depth of clay = 8 m
Total depth = 19 m
Initial water table is at a depth 0f 7m
final water table is at depth of 4m
(a) Immediately after the rise of water table.
At 8 m
stress = 16*4 + 19*4 = 140 Kn/m^2
= 9.81*(8-4)*1000 = 39.24 Kn/m^2
[ height of water table upto depth 8 m = 4 m]
Effective stress = stress - = 140-39.24 = 100.76 Kn/m2
At 12m depth
since the stresses in clay zone does not change immediately, we calculate the stress at 12 m before raise of water table.
stress = 16*7 + 19*4+ 20 *1 = 208 Kn/m2
= 9.81*(5)*1000 = 49.05 kn/m2
Effective stress = stress - = 208 - 49.05 = 158.95 Kn/m2
(b)several years after rise
At 8 m
stress = 16*4 + 19*4 = 140 Kn/m^2
= 9.81*(8-4)*1000 = 39.24 Kn/m^2
[ height of water table upto depth 8 m = 4 m]
Effective stress = stress - = 140-39.24 = 100.76 Kn/m2
At 12m depth
stress = 16*4 + 19*7 + 20 *1 = 217 Kn/m2
= 9.81*10*1000 = 98.1 kn/m2
Effective stress = stress - = 217 -98.1 = 118.9 Kn/m2
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