Summary

We consider first the case of a vertical point load in an infinite media with horizontal planes of discontinuity and obtain the distribution of stresses and displace. meats. By means of an integral we come upon the effect on a vertical plane of a uniform vertical load along a straight line perpendicular to such a plane. Following this same line of thought and as a consequence we study the case of a uniform tangential load acting along a straight line on the surface of a half-space. We present at the same time the equations of displacements and stresses due to the action of a uniform straight line load in a vertical direction on the surface of a halfspace.

Resume

On considère d'abord Ie cas d'une charge verticale dans un milieu indefini avec des plans horizontaux de discontinuite, ensuite les distributions des contraintes et des deplacements sont obtenues. Par integration on arrive à la solution du problème d'une charge verticale uniforme qui agit Ie long d'une droite indefinie. En suivant cette ligne de pensee on etudie Ie cas d'une charge tangentielle le long d'une droite de fa surface d'un solide semi-indefini. On presente au même temps les equations des deplacements et des contraintes dûs à l'action d'une charge verticale uniforme le long d'une droite de la surface du même solide semi-indefini.

Zusammenfassung

Wir betrachten an erster Stelle den Fall liner punktualen, vertikalen Last in einem unendlichen Milieu mit horizontalen, unterbrochenen Flaechen und erhalten die Spannungsverteilung und die Verschiebungen. Mittels einer Integralrechnung kommen wir bei einer vertikalen Flaeche auf die Wirkung, die eine gleichfoermtge, vertikale Last laengs einer zu dieser Flaeche lotrechten Geraden ausuebt. Wir verfolgen diesen Gedankenzug und als Folgerung dessen studieren wir den Fall einer tangentialen, gleichfoermigen Last, die entlang einer Geraden auf der Oberflaeche des Halbraumes wirkt. Wir geben zur gleichen Zeit die Gleichungen der Verschiebungen und der Spannungen, die durch die Wirkung einer gleichfoermigen, geradlinigen Last in vertikaler Richtung auf der Oberflaeche des Halbraurnes hervorgerufen werden.

The foundation ground was considered, until very recent times, homogeneous and mechanically isotropic in studies dealing with stress-distributions. Minerals in crystalline structure are internally anisotropic but' we are interested in macroscopic or mechanical anisotropy or in other words anisotropic behavior of the rock mass under loads, reflected in variation of the modulus of elasticity with direction. We find isotropic behavior in granitic masses with orthogonal systems of joints, in very thick strata of limestone, sandstone and quartzite, in loose sediments of clay, sand and marl, in alluviums and in top soils. But quite frequently rock masses present discontinuities that produce anisotropy. These discontinuites have two principal sources: sedimentation and jointing (schistosity will be considered as a particular case of jointing). Rock masses with a particular joint pattern due to sedimentation as in «flysch» and many types of limestone and sandstone or to the existence of a predominant direction of fissures as in slates, schists, gneiss, micacites and in any rock in a fault zone should be studied taking into account its heterogeneity and anisotropy. We will study the effects of such anisotropic behavior neglecting the influence of the lack in homogeneity. We will not consider the case of anisotropy of the general form but a more particular one of transversal or cross anisotropy defined by five independent elastic constants that reflects the case in Nature where isotropy exists in a system of parallel planes and the elastic properties are different in perpendicular direction. We relay on the hypothesis of perfect elasticity and infinite strength of the media. In this state of plane deformation the result is also valid for the anisotropy at a right angle to the previous one and only the parameters will change. MEDEDELIGEN(1) solved the case of a vertical point load on the surface of a half space with horizontal planes of discontinuity and integrating the expressions for stresses in a similar manner we find the stress distribution in state of plane deformation. Now the problem of a tangential load along a straight line on the surface of a half-space can be solved by adding to the expression for the infinite space the effect of a hyperbolic load on the same surface (Fig. 3). If we now think that beyond a certain distance D(big enough in relation to y) the displacements are zero we can substract the mathematical expressions for Wo at distances from the origin y and D and arrive to which can be used in the interpreting of in-situ tests. The general case of plane deformation was solved by LEKHNITSKII (2) and others. They arrive to a radial distribution of stresses and it can be shown that our solution do also have this property. The formula for w at the surface may be useful and the value D found, for practical applications.

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