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A rectangular footing which has 6m x 8m dimensions and carrying 250 kN/m2 is located at a depth of 3m in a deposit of clay which has 27 m thick. The coefficient of volume compressibility is 4x10^{-4} m2/kN at the ground surface and the reduction in the coefficient of volume compressibility with depth equals depth*0.1*10^{-4} m2/kN. The ground water level is at the ground surface and the unit weight of soil is 18 kN/m3.
a) Determine the consolidation settlement of the clay by dividing the clay layer into four sub-layers (use the approximate method for calculating the increase in stress [at various depths] due to applying the surface load).
b) Find the average degree of consolidation when the soil settlement is 10 cm.
c) Find the pore water pressure at 12 m depth of clay when the degree of consolidation at that depth is 30%.
d) If the uniform coefficient of consolidation of the clay layer is 7.3 m2/year, find the necessary time to reach 50% consolidation for this layer with the assumption of two-way drainage.