The article deals with direct methods for solving the variational problem in stresses for multicriteria estimation of the bearing capacity of a geomaterial sample in the current configuration, which can be both reference (undeformed) and actual (deformed). The problem is to minimize the integral quadratic functional from the various stress components in the selected control subdomain on a set of stress fields statically balanced with external influences. For the simplest configurations of the sample, it is proposed to use the method of generalized Fourier series in Hilbert spaces. For complex configurations of a sample with stress concentrators, it is suggested to use finite element approximation with the subsequent minimization of a finite-dimensional quadratic function with linear constraints of equalities. A substantial numerical example is given for estimating the bearing capacity of a sample from a geomaterial under pure compression.
In the article the problem of an estimation of bearing capacity of geomaterials as a deform-able solid is considered in the current configuration, which may be as the reference (undeformed) or the actual (deformed). We propose an original variational approach to the problem for stresses in selected subdomains, in which, depending on different engineering considerations, average in-tegral values of different component of stresses are estimated and from their aggregate the bearing capacity of the current configuration of the solid is estimated regarding to given external influ-ences. In each of the selected subdomain the weakest stress field is obtained which is globally bal-anced with external influences. For example, the assessment of the average integral hydrostatic pressure is needed for study of bearing capacity of geomaterials.
