A new warehouse is to be built on a 4 m thick layer of compressible clay. The warehouse floor will exert a permanent uniform load of $\\Delta p = 50 \text{ kPa}$. The clay has a consolidation coefficient $c_v = 1.2 \text{ m}^2/\text{month}$. The target settlement is $100\%$ of primary consolidation ($U = 100\%$). To accelerate this, a surcharge load ($\\Delta p_s$) will be added. The total preload is $p_f = \\Delta p + \\Delta p_s = 80 \text{ kPa}$. Determine the required degree of consolidation ($U_{surcharge}$) under the $80 \text{ kPa}$ load to achieve the equivalent $100\%$ settlement of the $50 \text{ kPa}$ load.

Prefabricated Vertical Drains (PVDs) are being used to accelerate consolidation. The PVDs have a width $a = 100 \text{ mm}$ ($0.1 \text{ m}$) and a thickness $b = 5 \text{ mm}$ ($0.005 \text{ m}$). They are installed in a triangular grid pattern with a spacing of $S = 1.5 \text{ m}$. Calculate the equivalent diameter of the drain ($d_w$) and the diameter of the influence zone ($d_e$).

Using the PVDs from the previous example ($d_e = 1.575 \text{ m}$, $d_w = 0.0668 \text{ m}$), the horizontal coefficient of consolidation of the clay is $c_h = 2.0 \text{ m}^2/\text{month}$. Calculate the time required to achieve $90\%$ average degree of radial consolidation ($U_r = 0.90$). Assume no smear or well resistance for simplicity.

A new power plant is being constructed near a river delta. The upper 10 meters of the site consists of very loose, saturated, clean sand. Seismic analysis indicates a very high risk of liquefaction during an earthquake.

A sensitive, highly plastic clay slope adjacent to a critical railway line was experiencing slow, continuous creeping movement due to high internal pore water pressures. Traditional drainage methods were ineffective because the clay's permeability was extremely low ($k < 10^{-9} \text{ m/s}$).