The Effect of Loading Inclination and Eccentricity on the Bearing Capacity of Shallow Foundations: A Review

Abstract

AbstractThis paper provides a comprehensive review on the effect of load inclination and eccentricity on the bearing capacity of shallow foundations. Regarding load eccentricity, Meyerhof’s intuitive formula $${B}{\prime}=B-2{e}_{b}$$ B ′ = B - 2 e b aligns well with finite element analyses, though it is slightly conservative. Analysis using finite element results revealed the more accurate formula $$B-1.9{e}_{b}$$ B - 1.9 e b . Concerning load inclination factors, numerous such factors exist in the literature. However, most are either intuitive or derived from small-scale experimental results, rendering them unreliable due to the significant impact of model scale on the bearing capacity of footings. Based on numerical results, it is proposed that all inclination factors (namely $${i}_{c}$$ i c , $${i}_{\gamma }$$ i γ and $${i}_{q}$$ i q ) can be reliably expressed by a formula of the form $${\left(1-{f}_{1}\cdot {\tan }\left({f}_{3}\delta \right)\right)}^{{f}_{2}}$$ 1 - f 1 · tan f 3 δ f 2 , where $$\delta$$ δ is the inclination angle of the loading with respect to the vertical, $${f}_{1}$$ f 1 and $${f}_{3}$$ f 3 are coefficients and $${f}_{2}=3$$ f 2 = 3 . The latter ensures smooth transition from the bearing capacity failure to the sliding failure as $$\delta$$ δ increases. It is also observed that many $$i-$$ i - factors in the literature and various design standards employ an impermissible combination of sliding resistance at the footing-soil interface and Mohr–Coulomb bearing capacity failure under the footing. Moreover, it is shown that only the $${i}_{c}$$ i c factor depends on the angle of internal friction of soil. Finally, Vesic’s 1975 “m” interpolation formula largely falls short in accurately representing the effect of the direction of the horizontal loading.