Example Problem 1: A square footing $2m \times 2m$ carries a column load of $1000 \, kN$. Calculate the stress increase at a depth of $4m$ below the footing using the 2:1 method.

Example Problem 2: A point load of $500 \, kN$ acts on the ground surface. Calculate the vertical stress increase at a depth of $5m$ directly under the load ($r=0$) using Boussinesq's theory.

Example Problem 3: A rectangular footing measuring $2 \, m$ by $3 \, m$ transmits a uniform contact pressure of $150 \, kPa$ to the soil. Using the approximate 2:1 stress distribution method, calculate the increase in vertical stress at a depth of $4 \, m$ below the center of the footing.