A method is presented for calculating the stabilizing pressures that must be applied against the exposed surface of an excavation in an incompetent rock medium to prevent shear failure of the rock mass, either along the surface of a rock joint or along a potential surface of rupture through the intact rock. The solution to several example problems shows that the magnitude and distribution of the stabilizing pressure, which varies around the opening, depends on the strengths of rock and joints, the orientations of the joints, the geometry of the excavation, and the geostatic stress field.
On présente une méthode pour calculer des pressions stabilisatrices qu'il faut appliquer a la paroi d'un creusement dans un massif rocheux incompétent, pour empêcher la rupture cisaillement le long des joints ou le long des surfaces potentielles de ruptures de la roche intacte. Par le calcul de quelques exemples on montre que l'intensité et la distribution des pressions stabilisatrices sont variables autour de la périphérie du creusement et sont les fonctions de la résistance cisaillement de la roche et celui des joints, l'orientation des joints, la géométrie du creusement, et les contraintes geostatiques.
Ein Berechnungsverfahren zur Ermittlung von Druecken, die zur Stabilisierung von Hohlraumbauten im ungenuegend standfesten Gebirge notwendig sind und den Bruch entlang vorgegebener Kluftflaechen bzw. entlang potentieller Gleitflaechen verhindern sollen, wird in diesem Aufsatz beschrieben. Wie von den Resultaten mehrerer angefuehrter Berechnungsbeispiele bestaetigt wird, sind die zur Stabilisierung des Gebirges notwendigen Druecke ungleichmaessig entland des Hohlraumes verteilt und ihrer Groesse bzw. Verteilung nach von der Festigkeit des Gesteines und der Kluefte, der Kluftlage und Geometrie des Hohlraumes und auch vom geostatischen Spannungsfeld abhaengig.
A problem of general interest in rock mechanics involves analysis of the stability, or the support required, for an excavation in an incompetent rock medium. Tunnels for mining purposes or for civil works frequently must pass through highly fractured, sheared, or faulted rock masses. The solution to this problem remains elusive. Several methods of analysis have been developed; an excellent review of these methods is given by Szechy (1973). Two main approaches have evolved. The first approach is to analyze the nonlinear behavior of the opening to determine the stresses and deformations of the rock mass (Fedotov, 1971); the tunnel lining is designed to withstand the deformation of the rock cavity without failing. The second approach is to determine the pressures that must be applied against the excavation surface to achieve stability (Daemen and Fairhurst, 1972, and Gasiev, 1970); the support is designed to withstand these pressures without failing. Past efforts to make this problem tractable rely on extremely idealized rock mass behavior, which are incapable of taking account of important physical variables such as irregular loading and geometry, inhomogeneity and anisotropy, and geologic discontinuities, such as fractures and joints. The solution procedure employed herein consists of constructing a finite-element representation of the rock structure, subjecting the model to a prescribed loading condition, evaluating the stress condition along the exposed surface of the excavation, calculating and applying the confining (stabilizing) pressures necessary to prevent shear failure from initiating at the exposed rock surface, reevaluating the stress condition on the boundary, and iterating this procedure until a convergent solution is obtained for the stabilizing pressures. Example analyses of circular underground openings are included to show the influence of geostatic loads and material properties on the distribution and magnitude of the stabilizing pressures. The method can be used for determining active rock loads on support structures such as tunnel and drift linings. A subsequent report will give computer programming details and user information necessary for the computer analysis. A planned extension of this investigation will include nonlinear rock mass behavior.
The rationale applied in developing equations for calculating the pressures required to stabilize rock at an exposed excavation surface is based on the shearing failure of rock in the triaxial test, which is well known in soil and rock mechanics. In this test, a radial constraining (stabilizing) pressure p is maintained all around a cylindrical test specimen while the axial pressure ó, is increased until failure (in shear) occurs.
The present analysis procedure treats a two-dimensional continuum. The influence of rock joints can be analyzed without the need for explicitly representing them in the finite-element model as done by Goodman et al. (1968). However, discrete joint elements can be incorporated in the analysis, if desired. The analysis considers potential shear failure that might initiate on the boundary of the opening, in the intact rock as well as along rock joints or other planes of weakness.