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The bearing capacity of soil is a critical factor in determining the adequacy of soil to support structural loads without experiencing excessive settlement or failure. The Terzaghi-Wegman formula and Meyerhof's method are specifically designed for calculating bearing capacity.

The Terzaghi-Wegman formula takes into account various factors including the soil's shear strength, the effective overburden pressure, and the arrangement of loads. Similarly, Meyerhof's method improves upon earlier bearing capacity analyses by incorporating factors such as the depth and width of the footing, and the influence of surcharge pressures above the footing.

These methods are grounded in soil mechanics and are empirical approaches that have been validated through extensive field and laboratory testing. Since they consider the soil type, loading conditions, and environmental factors, they provide a comprehensive means for estimating how much weight the soil can safely support.

In contrast, the other options do not focus explicitly on determining the bearing capacity of soil. Simpson's Rule is a numerical integration technique used in various mathematical applications, Mohr's Circle is utilized for analyzing stress states in materials, and the Factor of Safety method refers to a design principle rather than a specific calculation for bearing capacity.