Two-order Roughness Of Natural Rock Joints In Various Scales

The mechanical properties of rock joints greatly affect the deformation,strength and permeability of discontinuous rock masses.The slide or shear behaviour of a rock joint is strongly affected by the surface roughness.Due to geological effects,surface roughness inherently exists in natural joints of various sizes from millimeters to kilometers.Disclosing how the joint roughness vary as the joint size increases from the laboratory-scale to the large-scale in workfield is crucial for learning about the mechanical behaviour of rock masses and early warning of safety accidents in the practical engineering application.Although many experiences and methods have been proposed to explore the scale effect of rock joint roughness,conflicting results including positive scale effect,negative scale effect,and no scale effect have been obtained.In addition,some studies claim that there is a stationarity threshold with the size increasing.The surface roughness is comprised of large-scale?waviness?and small-scale?unevenness?components.These controversial results of scale effect maybe due to the fact that the two-order roughness was not separated,so that waviness and unevenness superimposed on the final result.Therefore,it is necessary to further study how to realize the quantitative separation of the rock joint two-order roughness and the independent characterization of scale effect for waviness and unevenness respectively.This thesis aims to separate thefirst-order waviness and second-order unevenness using triangular prism surface area method?TPM?and traditional sampling interval difference method and to calculate the fractal dimension D_w?D_u of waviness and unevenness through TPM method?PSD method and improved RLM method,taking the measured natural granite joint surfaces with resolutions of 0.5 mm?1.0 mm and 2.0 mm as examples.Samples of different joints with window sizes ranging from 100 mm×100 mm to 1000 mm×1000 mm corresponding to each resolution were selected to calculate the fractal dimension to explore the size effect and measurement resolution of the dual roughness fractal feature.Finally,the polar diagram of dual roughness parameters in various analysis directions are used to explore the anisotropy characteristics of waviness and unevenness of joint surfaces,and the scale effect and resolution effect of the anisotropic parameters for dual roughness are studied.The main findings of this article indicate:?1?The TPM principle isused to separate the dual roughness through transforming the grid size?to calculate the surface area S???of the 3D rock joint surface and drawing the double logarithmic coordinate graph of?-S???,then we can clearly observe the straight line slope turning point.It is the critical point of quantitative separation of the dual roughness.In this paper,?=30 mm is determined as the cut-off parameter for separation.This confirms the feasibility of quantitative separation of dual roughness,and provides support for the subsequent realization of the fractal dimension of waviness and unevenness,respectively.?2?Fractal dimensions D_w and D_u of dual roughness with different numerical values fully prove the feasibility and rationality of characterizing the fractal features of dual roughness of rock joint surface.The fractal dimension of the dual roughness of natural rock joints has been affected by both size effect and measurement resolution.Compared with the first-order waviness,the second-order unevenness is more sensitive to resolution,but the scale-dependent appears without generalised trends.No obvious stationarity threshold has been found for the three rock joint samples,indicating the surface roughness of natural rock joints should be quantified at the scale of the rock mass in the field or at the specific scale of the rock mass in-situ.The controversial results regarding the size effect,on the one hand,may be due to the composition of the roughness scaling of waviness and unevenness,on the other hand,it may be related to the combined effect of the sample size and resolution.This suggests that we should characterize first-order waviness and second-order unevenness with appropriate and consistent measurement resolution on the field scale of the rock mass.?3?The ellipses drawn in polar coordinates between the parameter?^*_max?7?C?10?1?8?and the analysis direction t can intuitively and clearly reflect the different anisotropy of dual roughness.The anisotropy of the first-order waviness is more obvious than that of the second-order unevenness.The value of the anisotropic parameter of dual roughness presence distinct size effect and is also affected by the measurement resolution.Since the shape of the ellipse of anisotropy does not change much with size and resolution,the anisotropy feature with multi-direction is little affected by the joint surface size and measurement resolution.The variation of the anisotropy characteristics of the second-order unevenness with the size is approximately negligible,and the first-order wavinessis more sensitive to the joint surface size.The anisotropy parameter value of first-order wavinessis bounded by a certain joint surface size.Under the size it shows a positive size effect and above the size it shows a negative size effect.The measurement resolution has a positive effect on the anisotropy parameter value of the second-order unevenness,and the anisotropy characteristic gradually weakens as the resolution increases.The first-order waviness are hardly affected by the resolution.