ABSTRACT:

A method for determination of the effective deformation properties of stratified and jointed rocks is given. It is based on the asymptotic method of averaging of partial differential equations with periodical rapidly fluctuating coefficients and uses the Goodman's model of joints. The asymptotic method is especially useful in cases when traditional tests are not applicable because of both large size of heterogeneity elements and the scale effect. By considering some factors (stiffness parameters of joints, stress state) the method gives nonlinear relationships between stress and strain. A comparison of numerical results with the data of laboratory tests is carried out.

RESUME:

Les auteurs presentent une methode determination des caracteristiques effectives de deformabilite des roches stratiformes et fissurees. Cette methode se base sur une methode asymptotique d'egalisation des equations differentielles partielles avec les coefficients periodiques rapidement variables et on utilise un modèle des fissures de Goodman. La methode asymptotique est particulièrement utile quand on ne peut pas effectuer les essais traditionnelles à cause de grands dimensions des elements d'heterogeneite on à cause d'effet spatial. En envisagant les differents facteurs (rigidite des fissures, etat des contraintes), la methode donne le rapport non lineaire des contraintes et des deformations. On presente la comparaison des resultats de calcul avec les resultats des essais laboratorres.

ZUSAMMENFASSUNG:

Es wird ein Method fuer eine Bestimmer Integral verformungkennwerte einer Schicht- und einer Sprungsgesteinschlicht ausfuehrlich beschrieben. Das beruht auf ein Assimptote Method kennwerte und benutz eine Modelle von Goodman fuer eine Sprungsgesteinschicht. Das Method ist besonderes gut, wenn einfache Laborversuchen wegen groβer Elemente der Gleichartigkeit und des Maβstabeffektes nicht durchgefuert werden. Beim Beruecksichtigen verschiedene Faktoren Sprungheftigkeit, Spannungzustand ergibt sich eine unlineare Korelation zwieschen Spannungen und Verformungen. Es wird von einem vergleichen zwieschen Berechnen- und Laborergebnisse mitgeteilt.

1 INTRODUCTION:

The computation of structures that interact with stratified and jointed beds is divided into two problems:

  1. determination of the characteristics of the bed;

  2. design of the structure and bed.

There will be given here a discussion about conditional (so-called effective) characteristics of the deformation properties, i.e. quantities that generally characterize the deformability of a certain imaginary homogeneous material (for example, transversely isotropic) in the volume of rock under investigation and the adequate deformability of real rock. The corresponding effective characteristics of rock de formation properties will depend heavily on the correctness of averaging the actual characteristics.

2 CONSTITUTIVE EQUATIONS:

In order to solve the problem of determination the effective characteristics of the deformation properties in inhomogeneous rock represented by an equivalent homogeneous medium, it is necessary that the displacements and stresses at any point of this medium, which are calculated for given boundary conditions, should correspond to displacements and stresses in the initial inhomogeneous medium. In the mechanics of composition materials, this condition is known as the hypothesis of equivalent homogeneity. One of the methods to solve this problem, which is based on the asymptotic method of averaging of exact equations due the theory of elasticity with rapidly fluctuating coefficients, has been proposed by Bakhvalov (1975, 1984). The effective characteristics obtained with this method (asymptotic method of averaging) ensure closeness between the computed and actual displacements, strains and stresses, with an accuracy of the order of (/L)m, where is a characteristics dimension (cell) of inhomogeneity, L is the characteristic dimension of rock specimen, and m is a whole positive integer. The method makes it possible to analyse the three dimensional problem and does not need under attenuating conditions.

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