基于Weierstrass-Mandelbrot函数的岩体裂隙映射重构  

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

作　　者：刘宏伟 陈世江 许有俊 张旭[1,2,3] 鲍先凯 LIU Hong-wei;CHEN Shi-jiang;XU You-jun;ZHANG Xu;BAO Xian-kai(School of Civil Engineering,Inner Mongolia University of Science and Technology,Baotou,Inner Mongolia 014010,China;Academician Workstation of Mine Safety and Underground Engineering,Inner Mongolia University of Science and Technology,Baotou,Inner Mongolia 014010,China;Engineering Research Center of Urban Underground Engineering at Universities of Inner Mongolia Autonomous Region,Inner Mongolia University of Science and Technology,Baotou,Inner Mongolia 014010,China;School of Mining and Mechanical Engineering,Liupanshui Normal University,Liupanshui,Guizhou 553004,China)

机构地区：[1]内蒙古科技大学土木工程学院,内蒙古包头014010 [2]内蒙古科技大学矿山安全与地下工程院士工作站,内蒙古包头014010 [3]内蒙古科技大学内蒙古自治区高校城市地下工程研究中心,内蒙古包头014010 [4]六盘水师范学院矿业与机械工程学院,贵州六盘水553004

出　　处：《岩土力学》2024年第10期3058-3070,共13页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.51564038);内蒙古自治区高等学校科学技术研究项目(No.NJZY22442);六盘水师范学院高层次人才引进科研启动专项(No.LPSSYKYJJ202308);内蒙古科技大学基本科研业务费专项资金(No.2023QNJS165)。

摘　　要：重构岩体裂隙对精准构建裂隙岩体模型以及准确获取其力学性质具有重要意义。鉴于此,为使重构裂隙与天然状态相吻合,提出了D-n_(max)阈值公式,修正了用于岩体裂隙模拟的Weierstrass-Mandelbrot(W-M)函数。通过二值化灰度图像对Barton10条剖面线进行数字化,经试错法及综合分析法,以等差方式确定10个粗糙度水平的Hurst值。通过对10条剖面线进行傅里叶变换得到了幅值特征新参数Spp,结合起伏角标准差σ_i线性构建新裂隙粗糙度系数(joint roughness coefficient,简称JRC)计算公式。采用二分法获得目标JRC值对应W-M函数的最佳尺度常数G值,建立了JRC与W-M函数的映射关系。W-M函数考虑了随机项,实现了重构裂隙的差异化。对重构裂隙进行粗糙度定量化研究和室内试验,验证了新参数Spp、新JRC计算公式及映射关系的有效性。所作研究为拓展岩体裂隙获取方法提供了新的思路,为裂隙岩体力学性质研究奠定了基础。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 D-nmax 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 isto construct a new joint roughness coefficient(JRC)calculation formula.The optimal scaling constant G 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.

关 键 词：岩体裂隙 自仿射分形 Weierstrass-Mandelbrot函数 裂隙粗糙度系数(JRC) 映射重构 

分 类 号：TU452[建筑科学—岩土工程]