A large excavation is made in a stiff clay whose saturated unit weight is 109.8 lb / ft ^{3}. When the depth of excavation reaches 24.6 ft, cracks appear and water begins to flow upward to bring sand to the surface. Subsequent borings indicate that the clay is underlain by sand at a depth of 36.1 ft below the original ground surface.
What is the depth of the water table outside the excavation below the original ground level?
Making an excavation in the clay creates a hydraulic gradient between the top of the sand layer and the bottom of the excavation. As a consequence, water starts seeping in an upward direction from the sand layer towards the excavated floor. Because the clay has a very low permeability, flow equilibrium can only be reached after a long period of time. The solution must be considered over a short time interval.
The floor of the excavation at depth d is stable only if the water pressure \sigma_{w} at the top of the sand layer at a depth of 36.1 ft is counterbalanced by the saturated weight \sigma_{c} per unit area of the clay above it disregarding the shear strength of the clay.
Let H = total thickness of clay layer = 36.1 ft, d = depth of excavation in clay = 24.6 ft, h = depth of water table from ground surface, \gamma_{s a t}= saturated unit weight of the clay.
(H-d)=36.1-24.6=11.5 ft, the thickness of clay strata below the bottom of the trench.
\sigma_{c}=\gamma_{\text {sat }}(H-d)=109.8 \times 11.5=1263 lb / ft ^{2}
\sigma_{w}=\gamma_{w}(H-h)=62.4 \times(36.1-h) lb / ft ^{2}
cracks may develop when \sigma_{c}=\sigma_{w}
or 1263=62.4(36.1-h), \text { or } h=36.1-\frac{1263}{62.4}=15.86 ft
