Bearing capacity analysis using the method of characteristics

Abstract

Using the method of characteristics, the bearing capacity for a strip footing is analyzed. The method of characteristics leads to an exact true limit load when the calculations of the three terms in the bearing capacity formula are consistent with one collapse mechanism and the soil satisfies the associated flow rule. At the same time, the method of characteristics avoids the assumption of arbitrary slip surfaces, and produces zones within which equilibrium and plastic yield are simultaneously satisfied for given boundary stresses. The exact solution without superposition approximation can still be expressed by Terzaghi’s equation of bearing capacity, in which the bearing capacity factor N _γλ is dependent on the dimensionless parameter λ and the friction angle φ. The influence of groundwater on the bearing capacity of the shallow strip footing is considered, which indicates that when the groundwater effect is taken into account, the error induced by the superposition approximation can be reduced as compared with dry soil condition. The results are presented in the form of charts which give the modified value $(N_{\gamma ^{\lambda _c } }^W /N_{\gamma ^{\lambda _c } } )$ of bearing capacity factor. Finally, an approximated analytical expression, which provides results in close agreement with those obtained by numerical analysis in this paper, has been suggested for practical application purposes.