Several Scales Analysis On Rock Fracture Surfaces Under Different Loading Modes

In order to realize that rock mechanics mechanism of rock deformation and fracture can be derived from morphology characterization of rock fracture surfaces, morphology characteristic differences among rock fracture surfaces under different loading modes are researched in the thesis. A classic rock mechanics testing(Brazilian test) is used to load to granite Brazilian discs with diameter112mm, height28mm, diameter50mm, height20mm and marble, sandstone ones with diameter50mm, height25mm. Brazilian discs are loaded to fracture failure with MTS (Mechanics Testing Systems) under different loading rates. And Brazilian discs are loaded to1/2,2/3or3/4of fracture strength threshold with MTS. Successively, after the Brazilian discs being rotated30degrees angles or45degrees angles(abbreviation: Pre-loading angle) and the Brazilian discs are loaded to fracture. The concepts about normal vector of center profile curve on rock fracture surface and deviation normal distribution coefficient(abbreviation: DNDC) are self-defined in this dissertation. Data collected by testing devices are analysed by several advanced mathematical models, for example, statistics, wavelet analysis and fractal theory. The six conclusions are acquired in the dissertation through researching.1) Angles data distribution of center profile curves’normal vectors on granite fracture surfaces obviously depends on scale effecting. That is to say, angle data samples’distribution of normal vectors more and more approximates normal distribution along with increase of measure scale;2) DNDC of center profile curves on granite fracture surfaces has obvious scale effecting. As measure scale reduces, DNDC will increase, which indicates roughness of center profile curve more and more deviates from self-defined standard roughness. The case that changes of loading rates in static loading range don’t give rise to obvious changes of DNDC is discovered through the comparison of three loading rates in granite testing. Changes of DNDC isn’t rather obvious to sensitivity of loading rates’change in static loading range, which illustrates roughness change of rock fracture surface isn’t rather obvious to sensitivity of loading rates’changes in static loading range;3) Modulus maximum method of wavelet transform, including a new self-defined power algorithm and signal to noise ratio, and fractal variation method are used to determine the differences in rock fracture surfaces’morphology characterization under different loading directions and rates. The result illustrates that both modulus maximum and fractal variation method can detect anisotropy of rock fracture failure. Compare to modulus maximum method, fractal variation method shows stronger sensitivity to the change of loading rates, which is more suitable to differentiate the rock fracture surface’s morphology characterization under different loading modes;4) The Pre-loading from other direction that is about1/2,2/3or3/4of mean fracture strength threshold has made inner of rock damaged to some extent and emerged many micro cracks in inner of rock through comparison;5) Mean fractal variation of marble fracture surfaces is more than that of sandstone under the same loading mode, which illustrates roughness of marble fracture surface is more greater than that of sandstone fracture surface under the same loading mode. And roughness changes of marble fracture surface is clearer than that of sandstone to sensitivity of Pre-loading angle’s change;6) From purely theoretical mathematics, fractional calculus of fractal interpolation function is researched and the result indicates that fractional integral of fractal interpolation function is continuous on closed interval and it is still a fractal interpolation function. Fractional calculus of fractal interpolation function is attempted to be applied in researching morphology characterization of rock fracture surface in the future.