Limitations of classical bearing theories

Classical bearing capacity theories (Rankine, Prandtl, Reissner, Terzaghi) have several limitations.

• Strip footing assumed. Plane strain is assumed, so shape effects for square, circular and rectangular footings are put in by empirical factors rather than being derived.
• Homogeneous, isotropic soil. Real soil is layered, variable and anisotropic, and the theories cannot deal with it directly.
• Rankine's and Bell's theories ignore the width of the footing and the friction on the base, so they are approximate and conservative.
• Prandtl's theory assumes weightless soil and no surcharge; Reissner's still neglects soil weight.
• Terzaghi's theory ignores the shear strength of the soil above the base (treated only as surcharge) and assumes a rough base and $D_f \le B$, so it is not suited to deep footings.
• General shear assumed. Local and punching shear are handled only by an empirical two-thirds reduction of $c$ and $\tan\phi$.
• Load conditions. Central, vertical, static load only. Eccentric, inclined and dynamic loads are not included in the original form.
• Nγ values differ between authors (Terzaghi, Meyerhof, Hansen, Vesic) because of the uncertainty in the failure surface, giving different results for the same soil.
• Compressibility is ignored. The soil is treated as rigid–plastic, so settlement is not obtained. Settlement may govern the design.
• Water table effect is accounted for only approximately by correction factors.