基于多重分形特征的岩体结构面剪切强度研究

Shear strength research on rock joint surfaces based on multifractal theory

Barton剪切强度模型是目前工程实践中普遍采用的强度公式,而实践应用时,该模型中结构面粗糙性系数(JRC)的评估存在主观性和片面性的缺点。鉴于此,应用多重分形理论,提出了采用多重分形参数准确量化JRC的方法。首先应用数字图像处理技术获取了结构面三维形貌数据信息;然后采用投影覆盖法进行了结构面的分形维数计算,重点对结构面的多重分形特征进行了分析,通过对比分析了构造的15个结构面的多重分形特征值。结果表明:结构面越粗糙,多重分形特征参数△D(q)和△a(q)值越大,△D(q)或△a(q)能够很好地描述结构面的形貌特征。最后对9组石膏试件进行了剪切试验,通过不同正应力下对应的剪应力数据分析,结合结构面形貌多重分形参数△D(q)或△a(q),以Barton剪切强度公式为基础,应用最小二乘法原理,给出了JRC与△D(q)及JRC与△a(q)关系。这样在工程实际中,可以用参数△D(q)或△a(q)对JRC进行估算,克服了JRC人为估值主观性及采用二维标准轮廓线评估片面性的缺点,为准确评估结构面粗糙度提供了一条新的途径。在此基础上,应用Barton模型可准确估算岩体结构面的剪切强度。

The Barton＇s shear strength criterion is widely used in engineering practice. However, the estimation of joint surface roughness coefficient（JRC） is subjective and one-sided in this method. Therefore, a method is proposed to estimate JRC with multifractal parameters based on multifractal theory. Firstly, 3D data of joint surface are obtained with digital image processing（DIP）technique. Secondly, the fractal dimension of surface is calculated with the projective covering method（PCM）. Particularly the multifractal parameters of fifteen joint surfaces are computed. The results show that the rougher the surface, the larger the parameters of △D（q） and △a（q）. Both multifractal parameters △D（q） and △a（q） can well describe the morphology of joint surface. At last, nine groups of gypsum specimens are used for direct shear tests under different normal stresses. The relationship between the multifractal parameters and the JRC is examined with the principle of least square method according to the experimental data of shear strength. Thus, the JRC can be estimated accurately using parameters of △D（q） and △a（q）. The results provide a new approach to study surface roughness of rock joints. On the basis, the shear strength of rock joints can be accurately estimated.