One of the distinguishing features of rocks is their different tensile and compression strength. The paper considers the regularities in the stress-deformed condition of rocks taking into account the said feature. It is shown that the effect of the different tensile and compression strength is manifested in the fact that shear deformation is dependent on the omnidirectional pressure, While volume deformation depends on shear stress (which causes loosening). The deformation equation and its parameters can be obtained from diagrams of uniaxial compression and tension of the rock. Cases are discussed where these diagrams are described by the linear and exponential laws (with different moduli in compression and tension). The problem of the stress-deformed condition of a rock massif under the action of a concentrated force and a strip load is solved for these cases.


Une des particularites distinctives des roches est la difference de leur resistance à la compression et à la traction. L'article envisage la regularite de la condition des contraintes et des deformations des roches avec consideration de cette particularite. On demontre que l'influence de l'inegalite de la resistance à la compression et à la traction se manifeste dans le fait, que la deformation de cisaillement depend de la pression hydrostatique et la deformation de volume depend de l'effort de cisaillement (lequel provoque la dilatabilite). L'equation de la deformation et les paramètres qu'elle contient peuvent être deduits à l'aide des diagrammes de la pression et la traction uniaxiale de la roche. On examine les cas, quand ces diagrammes sont decrits par les lois lineaires et puissancielles (avec des modules differents durant la pression et la traction). Pour ces cas nous avons resolu le problème de la condition des contraintes et des deformations d'un massif de roche sous l'influence d'une charge concentree et repartie.


Eine der besonderen Eigenschaften von Felsen ist ihre verschiedene Drueck- und Zugfestigkeit. Im Artikel wird die Gesetzmassigkeit des gespannt-deformierten Zustandes von Felsen mit Ruecksicht auf ihre erwahnte Eigenschaft untersucht. Es wird gezeigt, dass sich der Einfluss der nicht gleichen Drueckcund Zugfestigkeit in dem Umstand aussert, dass die scherverformung von hydrostatischer Druck und die Volumenanderung von Scherspannung (welche eine Volumvergrösserung verursacht) abhangig ist. Die Gleichung der Verformung und die Parametern, die diese Gleichung enthalt, können auf dem Grunde von Diagrammen einaxialer Zusammendrueckung und Spannung von Felsen erhalten sein. Es werden Falle untersucht, das diese Diagrammen durch lineare und potenziale Gesetze (mit verschiedenen Modulen bei Zusammendrueckung und Spannung) beschrieben sind. Fuer diese Falle ist die Aufgabe ueber gespannt-deformierten Zustand eines Felsmassiven, unter Einwirkung der konzentrienen und verteilten Last, gelost.

One of the distinguishing features of rocks is their different tensile and compression strength. The paper considers the effect of this feature on the stress-deformed condition. In usual cases, where a material offers equal resistance to tension and compression, the diagram of relationship between σiand εi is invariant relative to the stressed condition (Fig. 1a), and the parameter χ can be obtained from a test for uniaxial compression, as well as tension or shear. It was, however, shown as far back 1939 by a A. I. BOTKIN [1], on the basis of experiments on triaxial compression, and later by other authors [2, 3, 4, 5], that for rocks shear deformations depend not only on σ i but also on the mean pressure σ(Fig. 1b), white volume deformation depends not only on σ, but on σi as well. Here, the term φ1(εi) characterizes the resistance of the medium to pure shear, the term φ2 (εi) Ф (σ) the variation of this resistance due to the effect of σ; the term f 1(ε) reflects the resistance to omnidirectional compression, and the term f2(ε) Ψ (a,) the variation of this resistance due to the influence of σi. The expressions (2) should be substituted into the Eqs. (1) as a result of which we will obtain relations taking into account the different tensile and compression strength of rocks. Developing [5] further, we will show that the relationships between the shape variation and the mean pressure and between volume deformation and shear stress (2) depend on the different tensile and compression strength of the medium. Substituting the expressions (4) into Eqs. (5), we can determine the functions (2). We should set some additional conditions which would enable the type of the functions Ф and Ψ to be found. It should be noted that all these functions can be determined directly from experiments in a complex stressed condition (for instance, experiments on triaxial compression). We will consider the simplest case where the compression and tension diagram is approximated (in a certain stress range) by linear functions, but with different deformation moduli (see Fig. 3). As can be seen from Eqs (7), the different tensile and compression strength leads to a decrease in both shear and volume deformations.

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