A new method for estimating the earth pressures on retaining walls has been developed. It is an extension of Coulomb's earth pressure theory for non cohesive materials that can follow a non-linear strength criterion. This was previously done by the authors (Serrano et al, 2007) for some basic assumptions that have now been extended. The method is valid for materials that may have either a linear or non-linear strength criterion (parabolic or Hoek-Brown), a non-horizontal surface and an earth-wall friction angle. The method considers the material dilatancy. Moreover, the failure surface does not need to be plane, as in previously developed methods, but its shape is obtained as a result of the calculus, by applying Euler's variational method that obtains the extremal thrust.


This study is an extension of coulomb's classic method of calculating thrust on incoherent materials with a non linear strength criterion At the present time the calculation of thrusts on these materials requires a previous linearization of the failure criterion. This linearization is always problematical as its success depends on the election of a carefully chosen range of stresses. The fundamental hypothesis of the Coulomb method was abandoned -the adoption of a plane for the failure surface- and this is obtained directly by Euler's variational method making the thrust extremal. The results of this study allow determination of the thrusts on walls due to materials such as armourstone, highly fractured rock masses, pyroclasts, etc., whose mechanical behaviour is clearly non linear.

2.1 Geometrical (cf Fig. 1a)
  1. The wall is assumed to be indefinite so that it is a two-dimensional problem in plane deformation condition.

  2. The earth surface is plane, forming an α angle with the horizontal.

  3. The wall has a vertical backfilling.

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