Depending on the soil's relative density or stiffness, failure can occur in one of three primary modes:

• General Shear Failure: Occurs in dense sands or stiff clays. It is characterized by a well-defined, continuous slip surface that extends all the way to the ground surface, resulting in sudden, catastrophic heaving on one or both sides of the footing.
• Local Shear Failure: Occurs in medium dense sands or medium stiff clays. The slip surface extends only a short distance into the soil mass before terminating. Settlement is significant before any clear failure surface reaches the ground.
• Punching Shear Failure: Occurs in loose sands or very soft clays. The footing simply punches downward into the soil with excessive settlement. No heave is observed at the surface, and the failure planes are strictly vertical beneath the footing edges.

Terzaghi's classical derivation rests on several simplifying assumptions:

• The foundation is a continuous strip footing (length $L \gg B$).
• The foundation depth is shallow ($D_f \le B$).
• The soil beneath the foundation is homogeneous and semi-infinite.
• General shear failure governs the failure mechanism.
• The base of the footing is rough, preventing soil from sliding along it.
• The soil above the base of the footing ($D_f$) only provides weight (surcharge $q = \gamma D_f$), offering no shear resistance.

Because Terzaghi's original equation was explicitly derived for an infinitely long strip footing, empirical shape factors are applied to modify the equation for other common foundation geometries:

Square Footing ($B \times B$):

Circular Footing (Diameter $B$):

To account for inherent soil variability and uncertainties in load estimation, the design load must provide an adequate Factor of Safety ($FS$) against catastrophic shear failure.

• Net Allowable Bearing Capacity ($q_{all(net)}$): Represents the additional pressure the soil can safely take above the original in-situ overburden pressure.

• Case 1: Water table at or above the ground surface ($D_w = 0$): The soil is completely submerged. Use the buoyant unit weight ($\gamma' = \gamma_{sat} - \gamma_w$) in all terms (for both $q$ and the wedge term). This effectively halves the bearing capacity.
• Case 2: Water table exactly at foundation level ($D_w = D_f$): Use the moist/dry unit weight ($\gamma$) to calculate the surcharge term ($q$). However, use the buoyant unit weight ($\gamma'$) for the wedge term ($0.5 \gamma' B N_\gamma$) since the failure wedge is fully submerged.
• Case 3: Water table at depth $D_w \ge D_f + B$: The water is too deep to intersect the theoretical failure surface. No correction is needed. Use the moist/dry unit weight ($\gamma$) in all terms.
• Intermediate Case ($D_f < D_w < D_f + B$): Linearly interpolate an effective unit weight for the wedge term based on the exact depth of the water.

To calculate bearing capacity under eccentric loading, Meyerhof proposed assuming the load is concentric on a smaller, fictitious effective area ($B' \times L'$).

1. Calculate Eccentricity: $e = M / P$.
2. Determine Effective Dimensions:
   • $B' = B - 2e$ (if eccentricity is along the width).
   • $L' = L - 2e$ (if eccentricity is along the length).
3. Calculate Ultimate Capacity ($q_u'$): Use the General Bearing Capacity Equation substituting $B'$ for $B$, and calculating shape factors based on $B'/L'$.
4. Calculate Total Ultimate Load ($Q_{ult}$): Multiply $q_u'$ by the effective area.

1. Immediate (Elastic) Settlement ($S_e$): Occurs instantaneously as the load is applied, primarily due to elastic distortion of soil particles. Dominant in coarse-grained granular soils.

2. Consolidation Settlement ($S_c$): Time-dependent settlement caused by the slow, gradual expulsion of pore water from the voids in fine-grained cohesive soils (clays). (Detailed in the Compressibility chapter).