Analytic solutions for the stress field in static sandpiles

•Analytical solutions for the stress field in static sandpiles is presented.•The material is governed as continuum composed by cohesionless granular material.•The material is governed by the Mohr Coulomb yield condition.•A simple examples are presented.•Comparison with test results are discussed.

In the present paper we propose a new class of analytical solutions for the equilibrium problem of a prismatic sand pile under gravity, capturing the effects of the history of the sand pile formation on the stress distribution. The material is modeled as a continuum composed by a cohesionless granular material ruled by Coulomb friction, that is a material governed by the Mohr–Coulomb yield condition. The closure of the balance equations is obtained by considering a special restriction on stress, namely a special form of the stress tensor relative to a special curvilinear, locally non-orthogonal, reference system.This assumption generates a class of closed-form equilibrium solutions, depending on three parameters. By tuning the value of the parameters a family of equilibrium solutions is obtained, reproducing closely some published experimental data, and corresponding to different construction histories, namely, for example, the deposition from a line source and by uniform raining. The repertoire of equilibrated stress fields that we obtain in two special cases contains an approximation of the Incipient Failure Everywhere (IFE) solution and a closed-form description of the arching phenomenon.