Design of Shallow Foundations

The design of shallow foundations requires satisfying two primary criteria:

1. The applied bearing pressure must not exceed the allowable bearing capacity of the soil.
2. The anticipated settlement (both total and differential) must be within acceptable limits for the supported structure.

Engineers must select from isolated, combined, strap, or mat foundations based on load magnitudes, column spacing, and soil conditions to meet these safety criteria economically.

The choice of shallow foundation depends primarily on the column loads, soil conditions, and spatial constraints (like property lines).

The structural design of the foundation slab depends on its relative stiffness compared to the soil.

• Rigid Approach: Assumes the foundation is infinitely stiff compared to the soil. Settlement is uniform, but soil contact pressure distribution is non-uniform (higher at edges in cohesive soils, higher in the center for granular soils). Most structural designs simplify this by assuming uniform or linear pressure to calculate bending moments.
• Flexible Approach: Assumes the foundation deforms with the soil. A uniformly loaded flexible footing exerts uniform contact pressure, but experiences non-uniform settlement (dishing in the center).

Concrete footings generally fall somewhere in between, but are typically designed using the rigid assumption for simplicity unless they are very large mats.

Mats are typically employed under specific challenging conditions:

A compensated foundation is a specific design strategy for mat foundations on highly compressible soils (like deep soft clays). The mat is placed at a depth ($D_f$) such that the weight of the excavated soil roughly equals the total weight of the new structure. This results in nearly zero net increase in pressure ($q_{net}$) on the soil below, dramatically minimizing anticipated consolidation settlement.

The Winkler model idealizes the soil beneath a mat foundation as a bed of closely spaced, independent linear elastic springs. The stiffness of these imaginary springs is defined by the Coefficient of Subgrade Reaction ($k$).

This approach allows structural engineers to analyze the mat foundation as a structural slab supported on elastic supports, calculating internal bending moments and shears more accurately than assuming uniform soil pressure.

Bearing capacity alone does not guarantee a safe design. A foundation must also satisfy settlement criteria to prevent structural damage or functional impairment. Total settlement consists of three components.

Before any settlement (immediate or consolidation) can be calculated, engineers must determine how the applied foundation pressure ($q_0$) dissipates with depth ($z$).

• Boussinesq's Point Load Theory: The foundational theory for calculating the vertical stress increase $\Delta \sigma_z$ at any depth $z$ and radial distance $r$ from a concentrated point load $P$ on an elastic half-space. It forms the basis for integrating stress beneath continuous foundations.
• 2:1 Method (Approximate Method): A rapid, empirical method assuming the stress zone spreads outward at a slope of 2 vertical to 1 horizontal. For a rectangular footing of dimensions $B \times L$ carrying a total load $Q$, the average stress increase at depth $z$ can be estimated quickly.

Immediate settlement in granular soils or unsaturated cohesive soils is estimated using elastic theory.