Modelling weathering induced retreat of c-φ cliffs with limited tensile strength

Natural cliffs subject to weathering induced retreat are typically made of hard soils and / or weak rocks exhibiting limited tensile strength. In this paper, the morphologic evolution of uniform c, φ slopes subject to weathering is investigated for a range of values of tensile strengths employing the limit analysis upper bound method. This paper extends the analytical framework set up in [1, 2] by accounting for the limited tensile strength of the ground which was previously disregarded. The solutions were obtained by employing the kinematic method of limit analysis providing rigorous upper bounds to the true collapse values. The inclusion of tension cracks leads to modified analytical expressions of the energy balance equation (the balance between external work and dissipated energy) and as a consequence, of the function whose minimum provides the solution in terms of failure mechanisms and associated values of soil strength. Pre-existing cracks are considered, as well as cracks that form as part of the failure mechanism. It turns out that the presence of tension cracks may significantly alter the size of each landslide contributing to the retrogression of the slope. Results in the form of dimensionless ready-to-use charts are produced for any value of engineering interest of friction angle and slope inclination for the case of dry cracks. Moreover, upper bounds for values not included in the charts can be achieved either by interpolation from the charts or by running the minimisation of the analytical functions provided in the paper.