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

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 + ccot 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 %.