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Background  The method of characteristics (also called as the slip-line method) is used to calculate the bearing capacity of strip footings on ponderable soil. The soil is assumed to be a rigid plastic that conforms to the Mohr–Coulomb criterion. The solution procedures proposed in this paper is implemented using a finite difference method and suitable for both smooth and rough footings. By accounting for the influence of the cohesion  c , the friction angle  ϕ  and the unit weight  γ  of the soil in one failure mechanism, the solution can strictly satisfy the required boundary conditions.    Results  The numerical solution of  N   γ   are consistent with published complete solutions based on cohesionless soil with no surcharge load. The relationship of  N   γ   between smooth and rough foundations is discussed which indicates that the value of  N   γ   for a smooth footing is only half or more of that for a rough footing. The influence of  λ  ( λ  = ( q  +  c cot  ϕ )/ γB ) on  N   γ   is studied. Finally, a curve-fitting formula that simultaneously considers both  ϕ  and  λ  is proposed and is used to produce a series of  N   γ   versus  λ  curves.    Conclusions  The surcharge ratio  λ  and roughness of the footing base both have significant impacts on  N   γ  . The formula for the bearing capacity on  c – ϕ – γ  soil can be still expressed by Terzaghi’s equation except that the bearing capacity factor  N   γ   depends on the surcharge ratio  λ  in addition to the friction angle  ϕ . Comparisons with the exact solutions obtained from numerical results indicate that the proposed formula is able to provide an accurate approximation with an error of no more than ±2 %.

The bearing capacity factor N γ of strip footings on c–ϕ–γ soil using the method of characteristics