Terzaghi's Bearing Capacity Theory

Terzaghi's bearing capacity theory is a fundamental concept in foundation engineering used to calculate the ultimate bearing capacity of shallow foundations on soil. The theory combines soil shear strength parameters (cohesion $c$ and internal friction angle $\phi$), foundation geometry (width $B$ and depth), and loading conditions (effective vertical stress $\sigma'$) to predict the maximum load soil can sustain before failure. The ultimate bearing capacity is calculated using the equation $q_u = c N_c + \sigma' N_q + 0.5 \gamma B N_\gamma$, where , , and are bearing capacity factors dependent on , and is the soil unit weight. These factors increase with soil friction angle and are referenced in geotechnical tables. The theory assumes a rough, shallow footing on a homogeneous, isotropic cohesion-shear soil under vertical loading, with generalized shear failure mode. A safety factor (normally 2.5 to 3) is applied to ensure design reliability by reducing the ultimate capacity to an allowable bearing capacity. Practical design may include corrections for footing shape, load inclination, water table presence, and load eccentricities. Understanding Terzaghi's theory is critical for safe foundation design to prevent failure modes such as shear failure and excessive settlement, and it serves as the basis for advanced soil-structure interaction analyses and foundation design codes.