The problem of determining the displacements of the contour of a mine working with an arbitrary cross-section, after their completion on the site by the moment of its creation, is considered. To solve the problem, the method of slotted unloading is used. A contour similar to that of the investigated working with a subsequent unloading is drawn on the exposed surface of the rock massif. The displacements are measured both at the resulting core boundary and at the contour of the created hole, imitating the mine working contour. It is shown that these displacements differ not only in direction but also in magnitude. In order to determine the total displacements at the mine working boundary, it is necessary to sum them up. Then they are used both to estimate the stress-strain state of the rock massif around the mine working and the external loads applied to the rock massif as a whole. A solution in the elastic case for a circular cylindrical mine working is proposed, with the displacements of the arbitrary type defined on its contour.

This paper is devoted to the problem of determining critical loads for stability loss of mine working contours under conditions of elastoplastic strain. Stability loss results in such processes as soil heave, distortion of the roof profile, expulsion of the developed material into the mined-out space. The mathematical model of stability loss is based on the Leibenzon-Ishlinsky method, which considers this process as adjacent to the basic process of rock mass deformation. Also the Shenly hypothesis is applied, suggesting continuous loading at the moment of contour stability loss. The problem is solved within the framework of plastic flow theory and the theory of plasticity.

During the operation of certain structures, two questions arise: about the stress-strain state (SSS) at a point and in its neighborhood on the surface of the object under study and in its bulk, and about the remaining material strength in the considered area. The values of stresses and strains not at a point, but in a neighborhood, make it possible to use the results of the proposed research to test existing numerical and analytical calculation schemes, to find the direction of growth or decrease of the quantities under consideration, and to predict catastrophic events. It is proposed to assess the state of the material using classical formulations and methods of solid mechanics, which guarantee the existence and uniqueness of the solution and continuous dependence on the input data. To determine the SSS of the material in the neighborhood of the point, we start with the full unload of the latter in order to determine the unloading displacements at the boundary. The SSS within the area, including stresses at the boundary, is found from the known boundary displacements. When studying the SSS inside the body, it is proposed to install elongated reference elements with their ends reaching the surface. To measure unloading displacements, the existing optical, mechanical, and tensometric systems are used. The uniqueness of the proposed approach is in considering not only radial displacements, but also tangential ones. The aim of the work is experimental and analytical determination of the SSS at any point of the structure and at any time of its non-stop operation.

Аннотация.Под действием нагрузок среда разбивается на блоки.При скольжении блоков образуется эффект дилатансии.Увеличение объема происходит за счет раскрытия пор.Материал теряет жесткостные свойства как вдоль, так и поперек направлений скольжения.Потерю жесткостных свойств предлагается описывать с

Rock testing data are used to determine proper bases of tensors where strains along the unit vectors are only governed by stresses along them. The obtained curves along the unit vectors-one curve is proportional and the other curve is nonlinear, and both are independent of loading history and mechanism-are used to solve geomechanical problems. In planar post-limit deformation, these curves lead to a hyperbolic system of differential equations with four real functions and four relations to find four unknown functions: average stress, maximum shear stress, rotation angle and angle of directions of principal stress tensor axes. For finding their boundary values, the Cauchy stress vector and the displacement vector are assigned simultaneously at one and the same boundary. The authors propose an algorithm of finding these four functions within the post-limit deformation domain.

A method is proposed for estimating the stress-strain state of a rock mass both on the contour of the working itself and in its vicinity, based on the unloading method (VNIMI, Khast, Liman), characterized by the formation of a gap that repeats the contour of the studied working. When measuring the displacements of the outer contour of the slot, which coincides in shape with the destressed contour of the working, the necessary information is obtained to predict the behavior of the rock mass both on the contour of the working and near it.

The problem of determining the resistance of the medium is solved, taking into account the viscous term according to the data of full-scale measurements of the penetration depth and time to stop under impact. A system of equations has been constructed and a solution has been obtained for estimating the resistance parameters. A series of experiments was carried out on throwing a hand-held pile driver into the ground.

The authors construct an exact solution to the problem on the stress–strain behavior of rock mass at the boundary of an underground excavation of an arbitrary geometry if the vectors of the Cauchy stresses and displacements are assigned simultaneously at this boundary. All explicit components of stress and strain tensors, as well as the components of rotation vector are determined as functions of the elastic characteristics of rocks, values of the preset functions and differential properties of the boundary.

In the framework of the Leibenzon-Ishlinsky approach, the problem of the loss of stability of a pillar of a cylindrical mine working is solved. The pillar material was assumed with an initial anisotropy corresponding to the layered structure. A criterion for loss of stability is being constructed, a solution to the system of differential equations of the problem in the form of combinations of cylindrical and trigonometric functions is determined. From the fact that the determinant of a system of homogeneous algebraic equations is equal to zero, the critical load value is found at which, along with the main continuation of the deformation of the pillar, something else is possible with a changed surface geometry. The influence of the initial anisotropy, the parameters of the pillar (height, radius) on the values of the ultimate load is investigated.

A plastically deformable half-plane with initial anisotropy is considered. It is assumed that the elastic tensors for both the state of elasticity and the state of plasticity coincide. Within the framework of this hypothesis, the problem of penetrating a wedge into a given half-plane is solved. The ultimate load is found, its values are studied depending on the initial anisotropy.

For media with periodic changes in Young's modulus and yield strength, the problems of stress, strain and displacement distribution around single excavation of spherical and cylindrical shape are solved. The density of the medium is determined by the difference between the elastic modules and the yield strength in the blocks and interblock space. In each case analytical solutions are obtained. Influence of blocks quantity on length unit and differences in properties of blocks and interlayers on the nature of changes in stress, strains and displacements was studied. It is noted that blockness is one of the factors that form zonal disintegration around excavations.

The problem of defining the stress-strain state of a rock mass near the working contour is solved by the Cauchy stress vector and the displacement vector set on it. To do this, you also need to know the elastic properties and the passport curve of the material “tangent stress – shift” with a section of extreme deformation. The information obtained in solving the problem allows us to judge the condition and remaining reserve of strength of the material both on the contour of the rock mass itself and in its vicinity.

Ideally plastic state of material under conditions of Mises plasticity, proportionality of stress and strain deviators (deformation theory of plasticity) and elastic volume change is considered. Given the Cauchy stress and displacement vectors specified on the body surface (with indicated state) or its area, all six components of the stress tensor, all six components of the strain tensor, and also three components of the rotation vector are restored on this surface. This method for determining the stress-strain state can be related to the methods of rapid assessment of the structure state (body surface), since differential equations inside the body are not involved.

The problem of determining the stress-strain state in the vicinity of an opening with an arbitrary shape using the measurements of the Cauchy stress vector and displacement vector is solved. The states of elasticity, plasticity, and post-limiting straining are considered. The obtained results allow rapid determining of the resource capabilities of rock mass resistance to failure on the boundary both in a buried opening and in opencast mining.

Россия 2 Новосибирский государственный университет экономики и управления ул.Каменская 52, г