Two columns, A and B, are spaced 4.0 meters apart. Column A carries a load ($P_A$) of $1000 \text{ kN}$. Column B carries a load ($P_B$) of $1500 \text{ kN}$. Column A is located on a property line, so the footing cannot extend beyond its centerline. The allowable bearing capacity of the soil is $q_{allow} = 150 \text{ kPa}$. Determine the required length ($L$) and width ($B$) of a rectangular combined footing to ensure uniform soil pressure. (Ignore the weight of the footing for this example).

A $15 \text{ m} \times 20 \text{ m}$ mat foundation is to be constructed for a heavy building. The foundation will be placed at a depth of $D_f = 4.0 \text{ m}$ in a stiff clay deposit. The total building load (including the mat itself) is $Q_{bldg} = 24,000 \text{ kN}$. The unit weight of the excavated soil is $\gamma = 19 \text{ kN/m}^3$. Calculate the net bearing pressure ($q_{net}$) applied to the soil underlying the mat.

A plate load test is performed using a standard $0.3 \text{ m} \times 0.3 \text{ m}$ square plate on a sandy soil. Under an applied pressure of $q = 150 \text{ kPa}$, the plate settles by $\delta = 5 \text{ mm}$ ($0.005 \text{ m}$). Calculate the coefficient of subgrade reaction ($k_{0.3}$) for the test plate, and estimate the adjusted coefficient ($k_B$) for a full-size square footing of width $B = 2.0 \text{ m}$.

A flexible rectangular footing ($2.0 \text{ m} \times 4.0 \text{ m}$) is placed on the surface of a deep, uniform clay deposit and subjected to a uniform pressure of $q_0 = 120 \text{ kPa}$. The clay has an undrained modulus of elasticity $E_s = 25 \text{ MPa}$ ($25,000 \text{ kPa}$) and a Poisson's ratio $\mu = 0.5$. Calculate the immediate settlement ($S_i$) at the center of the footing. The shape/influence factor for the center of a flexible rectangular footing with $L/B = 2$ is $I_s \\approx 1.53$.

The Leaning Tower of Pisa is the most famous example of foundation failure due to differential settlement. The circular mat foundation of the tower was constructed on a stratified profile of weak, highly compressible clays and fine sands.

A 50-story skyscraper was designed to be built in a coastal city situated on extremely deep, soft, compressible marine clay. Conventional spread footings or standard mat foundations would result in meters of catastrophic settlement. Driving piles to bedrock was deemed economically unfeasible due to the extreme depth.