ALBERT

Description: Values of the bearing capacity factor Nγ are numerically computed using the method of triangular slices. Three assumptions of the value of ψ, the base angle of the active wedge, are analyzed, corresponding to the following three cases: (1) ψ = ϕ, the internal friction angle; (2) ψ = 45° + ϕ/2; and (3) ψ has a value such that Nγ is a minimum. The location of the critical failure surface is presented and the numerical solutions to Nγ for the three cases are approximated by simple equations. The influence of the base angle on the value of Nγ is investigated. Comparisons of the present solutions are made with those commonly used in foundation engineering practice.Key words: shallow foundation, bearing capacity, bearing capacity factor, limit equilibrium.

Description: A concise algorithm is proposed in this paper for the calculation of the factor of safety of a slope using the MorgensternPrice method. Based on force and moment equilibrium considerations, two expressions are derived for the factor of safety Fs and the scaling factor λ, respectively, both in relatively simple forms. With this algorithm and assumed initial values of Fs and λ, the solutions for Fs and λ are found to converge within a few iterations. Compared to other procedures, the present algorithm possesses the advantages of simplicity and high efficiency in application. It is rather straightforward to implement this algorithm into a computer program.Key words: slope, stability, factor of safety, limit equilibrium method.

Description: By employing the same assumption regarding interslice forces as that used in the Morgenstern-Price method, two concise recurrence relations between interslice forces and interslice moments are derived which satisfy both force and moment equilibrium conditions. The Newton-Raphson method is used for determining the factor of safety and the associated scaling parameter of the interslice force function. Algebraic derivatives required in the solution process are evolved in a recursive manner which can be easily implemented in a computer program. The choices of initial values of safety factor and scaling parameter are suggested. The procedure proposed in this paper proves to be efficient and solutions converge rapidly.Key words: slope, stability, factor of safety, limit equilibrium method.

Description: The Terzaghi superposition assumption has been widely used to determine the bearing capacity of shallow footings. Although this assumption always errs on the safe side, a rigorous procedure to calculate the bearing capacity is still of engineering value. This paper presents such a procedure that is free from errors as a result of the superposition assumption. It demonstrates that the ultimate bearing capacity can be precisely expressed by the Terzaghi equation, except that the bearing capacity factor Nγ is dependent upon the surcharge ratio. A recently developed numerical method, i.e., the critical slip field method, is used to calculate the modification coefficient for modifying Nγ. It is found that this modification coefficient increases with the surcharge ratio at small values of surcharge ratio and then remains constant for large values of surcharge ratio. However, the errors invoked by the superposition assumption do not exceed 10%. On the basis of numerical calculations, a simple closed-form expression of the modification coefficient is proposed that yields the theoretically rigorous ultimate bearing capacity. In the later part of the paper, errors in bearing capacity calculations owing to the use of conventional procedures are analyzed. It is concluded that the continued use of conventional procedures is justified, but the inherent errors should not be neglected in assessing the performance of shallow foundations.Key words: shallow foundation, strip footing, ultimate bearing capacity, critical slip field.

Description: The conventional methods of slices are commonly used for the analysis of slope stability. When anchor loads are involved, they are often treated as point loads, which may lead to abrupt changes in the normal stress distribution on the potential slip surface. As such abrupt changes are not reasonable and do not reflect reality in the field, an alternative approach based on the limit equilibrium principle is proposed for the evaluation of the stability of anchor-reinforced slopes. With this approach, the normal stress distribution over the slip surface before the application of the anchor (i.e., σ0) is computed by the conventional, rigorous methods of slices, and the normal stress on the slip surface purely induced by the anchor load (i.e., λpσp, where λp is the load factor) is taken as the analytical elastic stress distribution in an infinite wedge approximating the slope geometry, with the anchor load acting on the apex. Then the normal stress on the slip surface for the anchor-reinforced slope is assumed to be the linear combination of these two normal stresses involving two auxiliary unknowns, η1 and η2; that is, σ = η1σ0 + η2λpσp. Simultaneously solving the horizontal force, the vertical force, and the moment equilibrium equations for the sliding body leads to the explicit expression for the factor of safety (Fs)or the load factor (λp), if the required factor of safety is prescribed. The reasonableness and advantages of the present method in comparison with the conventional procedures are demonstrated with two illustrative examples. The proposed procedure can be readily applied to designs of excavated slopes or remediation of landslides with steel anchors or prestressed cables, as well as with soil nails or geotextile reinforcements.Key words: slopes, factor of safety, anchors, limit equilibrium method.