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On the optimal profile of a slope

Utili, S. and Nova, R. (2007) On the optimal profile of a slope. Soils and foundations, 47 (4). pp. 717-731. ISSN 0038-0806

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The problem of determining the best profile for a c, φ soil slope is tackled, with reference to rigid rotational failure mechanisms. By means of limit analysis, upper bound values of collapse load are determined. A new mathematical function is derived to compute the external work made by the weight of a double spiral shaped soil region sliding away. It is found that a log spiral front is associated with a larger safety factor than a planar one. The obtained results may also explain the log-spiral shape of perimeter walls of some typical Japanese castles.