Mapping reconstruction of rock mass fracture based on Weierstrass-Mandelbrot function

The reconstruction of rock mass fracture is crucial for accurately constructing fracture rock mass model and obtaining its mechanical properties. To ensure the reconstructed fractures fit the natural state, this paper first proposed the <i>D</i>-<i>n</i>_max threshold formula and modified the Weierstrass-Mandelbrot (W-M) function used in rock mass fracture simulation. Barton’s 10 profile lines were digitized using binarized gray images, and Hurst values for 10 roughness levels were determined using the equi-difference method, trial and error method and comprehensive analysis method. The new parameter Spp, representing the magnitude feature, is obtained by Fourier transforming the 10 profile lines. The parameter Spp is then combined linearly with the standard deviation of the angle <inline-formula id="M1"> <math id="mathml_M1" display="inline" overflow="scroll"> <msub> <mi>σ</mi> <mi>i</mi> </msub></math></inline-formula> to construct a new joint roughness coefficient (JRC) calculation formula. The optimal scaling constant <i>G</i> value corresponding to the target JRC value is obtained using the dichotomy method, establishing the mapping relationship between JRC and the W-M function. The W-M function considers random terms and realizes the differentiation of reconstructed fractures. The roughness quantification research and laboratory tests are conducted to verify the validity of the new parameter Spp, the new JRC formula, and the mapping relationship. This study provides a new approach for expanding the method of obtaining fracture in rock mass, and lays the foundation for studying the mechanical properties of fractured rock mass.