A 5 m normally consolidated clay layer is sandwiched betweentwo sand layers. A 3 m sand layer is above the clay layer, and adeep sand layer is under the clay layer. The water table is at thetop surface of the clay layer (i.e. 3 m below the soil surface).The sand layer above clay is dry with a unit weight of d = 17.5kN/m3. The clay under the water table has a saturated unitweight of sat = 18.5 kN/m3, water content of w = 22%,compression index of Cc = 0.30 and specific gravity of Gs = 2.70.A surface loading of 100 kPa is placed at the soil surface.(a) Find the effective stress and pore pressure at the top (A),centre (C) and bottom (B) of the clay layer before thesurface loading;(b) Find the effective stress and pore pressure at the top,centre and bottom of the clay layer immediately after thesurface loading (i.e. t = 0)

(a) Before the surface loading:

At the top of the clay layer (A): The effective stress (σ') is the total vertical stress (σ) minus the pore water pressure (u). The total vertical stress at the top of the clay layer is the weight of the overlying dry sand layer, which is the product of its depth and unit weight (3m * 17.5 kN/m³ = 52.5 kPa). Since the water table is at the top of the clay layer, the pore water pressure is zero. Therefore, the effective stress at A is 52.5 kPa.

At the center of the clay layer (C): The total vertical stress is the weight of the overlying sand layer plus half the weight of the clay layer (52.5 kPa + 0.5 * 5m * 18.5 kN/m³ = 52.5 kPa + 46.25 kPa = 98.75 kPa). The pore water pressure is the weight of the overlying half clay layer (0.5 * 5m * 9.81 kN/m³ = 24.525 kPa). Therefore, the effective stress at C is 98.75 kPa - 24.525 kPa = 74.225 kPa.

At the bottom of the clay layer (B): The total vertical stress is the weight of the overlying sand layer plus the weight of the clay layer (52.5 kPa + 5m * 18.5 kN/m³ = 52.5 kPa + 92.5 kPa = 145 kPa). The pore water pressure is the weight of the overlying clay layer (5m * 9.81 kN/m³ = 49.05 kPa). Therefore, the effective stress at B is 145 kPa - 49.05 kPa = 95.95 kPa.

(b) Immediately after the surface loading (t = 0):

At the top of the clay layer (A): The total vertical stress is the weight of the overlying sand layer plus the surface loading (52.5 kPa + 100 kPa = 152.5 kPa). The pore water pressure is still zero because the clay is impermeable and the water has no time to drain. Therefore, the effective stress at A is 152.5 kPa.

At the center of the clay layer (C): The total vertical stress is the weight of the overlying sand layer, half the weight of the clay layer, plus the surface loading (98.75 kPa + 100 kPa = 198.75 kPa). The pore water pressure is still the weight of the overlying half clay layer (24.525 kPa). Therefore, the effective stress at C is 198.75 kPa - 24.525 kPa = 174.225 kPa.

At the bottom of the clay layer (B): The total vertical stress is the weight of the overlying sand layer, the weight of the clay layer, plus the surface loading (145 kPa + 100 kPa = 245 kPa). The pore water pressure is still the weight of the overlying clay layer (49.05 kPa). Therefore, the effective stress at B is 245 kPa - 49.05 kPa = 195.95 kPa.