Abstract
BackgroundThe 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.ResultsThe numerical solution of Nγ are consistent with published complete solutions based on cohesionless soil with no surcharge load. The relationship of Nγ between smooth and rough foundations is discussed which indicates that the value of Nγ 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 Nγ is studied. Finally, a curve-fitting formula that simultaneously considers both ϕ and λ is proposed and is used to produce a series of Nγ versus λ curves.ConclusionsThe surcharge ratio λ and roughness of the footing base both have significant impacts on Nγ. 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 Nγ 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 %.
Highlights
The method of characteristics is used to calculate the bearing capacity of strip footings on ponderable soil
When the bearing capacity is computed on general c–φ–γ soil without superposition and the result is still written in the form of Eq (1), the bearing capacity factor Nγ is not the value that computed by superposition method
The present values when λ is 0 in Table 1 are equivalent to complete solutions given by Martin (2005) and Smith (2005), which indicates that the results by present method can be treated as exact solutions
Summary
The numerical solution of Nγ are consistent with published complete solutions based on cohesionless soil with no surcharge load. The relationship of Nγ between smooth and rough foundations is discussed which indicates that the value of Nγ 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 Nγ is studied. A curve-fitting formula that simultaneously considers both φ and λ is proposed and is used to produce a series of Nγ versus λ curves
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