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the multifractal behavior of rock fi'acture surfaces is sludied taking into account fractal heterogeneity and anisotropy of surface structures. a projective covering method (pcm) is proposed and used to estimate directly the fractal dimension d[2, 3) of a fracture surface. the study indicates that the multifractal spectrum of the fracture surfaces provide much additional information on the fracture mechanism and the distribution of asperity concentration on the surface. the fracture surfaces induced in rocks under different failure mechanisms display distinct multifractal behavior.

experimental results indicate that propagation paths of cracks in geomaterials are often irregular, producing rough fracture surfaces which are fractal. a formula is derived for the fractal kinematics of crack propagation in geomaterials. the formula correlates the dynamic and static fracture toughness with crack velocity, crack length and a microstructural parameter, and allows the fractal dimension to be obtained. from the equations for estimating crack velocity and fractal dimension it can be shown that the measured crack velocity (v0) should be much smaller than the fractal crack velocity (v). it can also be shown that the fractal dimension of the crack propagation path can be calculated directly from vo and from the fracture toughness.

extensive studies show that the naturally developed rock joint surfaces have the properties of fractals. the surface roughness of rock joints can be well described within the framework of fractal geometry. to give a better understanding of the roughness of rock fracture surfaces in relation to the mechanical properties and behavior of rock joints in loading, a systematic investigation has been carried out. by means of a laser scanning instrument, the fracture surfaces induced in rocks are measured. the fractal characters of rough fracture surfaces of rocks are analysed according to the variogram method, which elaborates explicitly the importance of the geometric parameters-fractal dimension d and the intercept a. investigation extends to the anisotropy and heterogeneity of rock fracture surfaces, and the scale effect on the fractal estimation. the shear tests on rock joints show a combined effect of the fractal parameters on the mechanical properties and behavior of rock joints. to control the roughness and show the effects in a direct manner, a series of fractal joints with different fractal dimensions are generated on the basis of the weierstrass-mandelbrot function and then manufactured in the polycarbonate plates. by using the photoelastic method, the manners of normal and shear deformation, the stress field in the vicinity of the joint surface and the contact behaviour of the fractal joints have been studied in detail under uniaxial compression and direct shear. based on the experimental results, the dependence of deformation stiffness on the fractal dimensions of rock joints has been recognized. the empirical criteria of shear strength and the evolution law of surface damage during the shear process are developed.

by employing a mercury injection porosimetry, the evolution of micro-pores in marbles is measured as a function of the stresses experienced. based on the fractal model for porous media, the fractal dimensions of micro-pores under different stress levels are estimated. the study shows that porous rocks are actually fractal structures, the fractal dimension of the pore volume increases with the increase of load. this suggests that the fractai dimension of the pore volume could be used as an indicator of damage in the material, which provides a new way of defining the damage variable.