Three-dimensional yield strength properties of jointed rock mass as a homogenized medium

A comprehensive three-dimensional formulation for the strength criterion of regular jointed rocks is derived in this paper. The approach is based upon the implementation of the homogenization method of periodic media within the framework of the yield design theory. A rigorous explicit expression of the macroscopic criterion is given as a function of the strength properties of the intact rock and of the joints modelled as interfaces. Attention is focused on the particular case of an infinitely resistance intact rock. It is shown in particular how the relevant velocity jumps for the homogenized medium can be characterized from the introduction of the set of admissible stress vectors acting upon an elementary surface. The results make it possible to perform the static and kinematic approaches in order to address the stability analysis of rock masses cut by sets of regular joints, even for the three-dimensional geometries.

[1]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[2]  Evert Hoek,et al.  Fracture of Anisotropic Rock , 1964 .

[3]  K. Gray,et al.  The Mechanical Behavior of Anisotropic Sedimentary Rocks , 1967 .

[4]  A. Taliercio,et al.  A failure condition for layered rock , 1988 .

[5]  J. P. Boehler,et al.  On yielding of oriented solids , 1977 .

[6]  J. C. Jaeger.  Shear Failure of Anistropic Rocks , 1960, Geological Magazine.

[7]  C. Gerrard,et al.  EQUIVALENT ELASTIC MODULI OF A ROCK MASS CONSISTING OF ORTHORHOMBIC LAYERS , 1982 .

[8]  Nick Barton,et al.  Review of a new shear-strength criterion for rock joints , 1973 .

[9]  Z. Bieniawski.  Estimating the strength of rock materials , 1974 .

[10]  Evert Hoek,et al.  Strength of jointed rock masses , 1983 .

[11]  F. Donath.  EXPERIMENTAL STUDY OF SHEAR FAILURE IN ANISOTROPIC ROCKS , 1961 .

[12]  D. Bernaud,et al.  Numerical simulation of the convergence of a bolt‐supported tunnel through a homogenization method , 1995 .

[13]  P. A. Cundall,et al.  FORMULATION OF A THREE-DIMENSIONAL DISTINCT ELEMENT MODEL - PART I. A SCHEME TO DETECT AND REPRESENT CONTACTS IN A SYSTEM COMPOSED OF MANY POLYHEDRAL BLOCKS , 1988 .

[14]  R. Nova,et al.  The failure of transversely isotropic rocks in triaxial compression , 1980 .

[15]  S. D. Priest,et al.  The use of inclined hemisphere projection methods for the determination of kinematic feasibility, slide direction and volume of rock blocks , 1980 .

[16]  P. Cundall,et al.  FORMULATION OF A THREE-DIMENSIONAL DISTINCT ELEMENT MODEL - PART II. MECHANICAL CALCULATIONS FOR MOTION AND INTERACTION OF A SYSTEM COMPOSED OF MANY POLYHEDRAL BLOCKS , 1988 .

[17]  Modified borehole jack method for elastic property determination in rocks , 1978 .

[18]  P. Warburton.  Vector stability analysis of an arbitrary polyhedral rock block with any number of free faces , 1981 .

[19]  N. Barton,et al.  The shear strength of rock joints in theory and practice , 1977 .