Soil bearing capacity, retaining wall stability, and earthwork excavation.
Calculate trench/pit in-situ cut volume, loose soil swell expansion, and dump truck haul trips.
V_{bank} = L times W times D; quad V_{loose} = V_{bank} times S_{factor}; quad text{Trips} = leftlceil frac{V_{loose}}{text{Truck Capacity}} rightrceil
Calculate ultimate and safe bearing capacity of strip, square, and circular shallow footings using Terzaghi theory.
q_{ult} = c N_c s_c + gamma D_f N_q + 0.5 gamma B N_gamma s_gamma; quad q_{safe} = frac{q_{ult} - gamma D_f}{FS} + gamma D_f
Evaluate Rankine lateral active earth pressure, overturning safety factor, and sliding stability resistance.
K_a = frac{1 - sinphi}{1 + sinphi}; quad P_a = frac{1}{2} K_a gamma H^2 + K_a q H; quad FS_{OT} = frac{sum M_{resisting}}{sum M_{overturning}} ge 2.0