A note on the interpretation of Coulomb's analysis of the thrust on a rough retaining wall in terms of the limit theorems of plasticity theory

The author examines Coulomb's analysis of the earth pressure on a vertical retaining wall in the light of modern theory of plasticity. His work was prompted by Heyman's comment that Coulomb's expression cannot be applied when the wall is rough and that the thrust estimates are therefore not strict bounds. He first discusses upper and lower bound theorems and points out that although they hinge critically on the assumption of a normal or associated flow rule, the normal flow rule can still be used to provide upper bounds of the failure loads even when the real soil behaves incompressibly. An account is given of the derivation of formulae for pressures on both smooth and rough retaining walls. The fact that his kinematic argument appears to differ from Heyman's yet yields the same formula is briefly disscussed. An appendix gives a proof of the author's statement that "the internal rate of working of the stresses in any virtual mechanism, compatible with the yield condition, cannot be less than the sum of the rate of the rate of working of the actual body forces and surface tractions with the virtual velocity field. /TRRL/