Investigation Of Roughness Characteristics Of Natural Rock Joints Based On Statistical And Fractal Methods

The strength,deformation and flow characteristics of rock discontinuity are largely determined by joint surface roughness.Rock mass,as a large composite medium,includes intact rocks and several structural features,such as discontinuous folds（joints,bedding planes,faults）.Therefore,the mechanical behavior of rock mass is determined by the comprehensive influence of rock properties,anisotropy and discontinuity.The geometrical shape,strength and deformation capacity of the convex body in rock mass discontinuous plane determine the mechanical properties of rock,and the spatial distribution of surface pore size controls the hydraulic properties.The roughness of joints is the representative characteristic of discontinuous plane and surface pore size.Therefore,accurate quantification of rock joint surface roughness is of great significance for simulating and predicting rock joint strength,deformation capacity and permeability behavior.Based on four two-dimensional(root mean square of the slope of the profile Z₂,structural function SF,roughness profile index Rp,Grasselli modelθ^*_Max/[C+1])_2D)and two three-dimensional(root mean square of slope Z_2s and surface tortuosity Ts)roughness slope slope and amplitude statistical parameters,a case study of slate structural surface in A quarry in Qingshi Town,Zhejiang Province was presented.The surface roughness of 1000 x 1000 mm2 joint was quantified by 3d laser scanning.In addition,the variational function method（fractal dimension D,amplitude parameter Kv,combined parameter Dx Kv）is used to describe the roughness of structural plane from fractal Angle,and the superiority of fractal method in quantifying roughness is discussed compared with JRC,statistical parameters and functions.Based on the above two kinds of methods,linear profile roughness（2D）,surface roughness（3D）and fractal Angle analysis were carried out respectively,and the non-stationary,sampling interval effect,non-uniformity,joint size effect and anisotropy characteristics of joint surface roughness were identified.A total of 3230 profiles were calculated,and all calculations were tested by regression analysis.This research has higher theoretical significance and research value for accurate description of mechanical properties of rock discontinuous plane and practical engineering application.The main research results are as follows:（1）Based on the two-dimensional statistical parameters and variogram method,the results of the four two-dimensional parameters are highly consistent,and the non-stationary caused by the global linear trend has no effect on the two-dimensional roughness parameters calculated by z-X and Z-Y profiles.The linear trend（-1.9°-+1.0°）has no effect on the calculation of fractal parameters of variogram.The z-Y profile shows obvious roughness inhomogeneity at250 mm and 500 mm.（2）Sampling interval plays an important role in roughness evaluation.The values of two-dimensional parameters Z₂,Rp andθ^*_Max/[C+1])_2D decrease with the increase of sampling interval,while SF increases significantly with the increase of sampling interval and its variability is obviously higher than other parameters.Compared with the Z-X profile,the observation results of the Z-Y profile are more significant.With the increase of sampling interval,the roughness variability in z-Y profile decreases gradually.The roughness values of Z2s and Ts quantized regions decrease obviously with the increase of sampling interval.（3）The surface of rock joints shows obvious heterogeneity,and the heterogeneity of Z-Y profile set is significantly higher than that of Z-X profile set.For z-Y contour only,for any X value,it is found that the Y（750-1000 mm）part is significantly rougher and uneven compared with the Y（0-750 mm）part.（4）The joint size has no effect on the quantification of roughness.No size effect was found in the study of joint size effect of z-Y profile compared to uniform lumped profile.The non-uniformity of the z-Y profile is obviously higher than that of the Z-X profile.No obvious joint size effect is observed in the Z-X profile,while the joint size effect is relatively higher in the Z-Y profile.The results based on statistical and fractal methods show that the roughness surface non-uniformity or uniformity plays a major role in the scale effect caused by joint size.（5）The calculated roughness parameters of rock joint surface show significant anisotropy.The roughness of the joint plane along the axis of the ridge groove（X direction）is obviously smaller than that of the vertical axis of the ridge groove（Y direction）.It shows that the joint surface is composed of shear joints with X direction as shear direction.