节理粗糙度与分维

岩体节理粗糙度JRC不但是估算节理抗剪强度和变形指标最重要的参数,而且对于研究岩石的剪胀效应和渗流性质等具有重要意义.笔者主要回顾了近年来国内外对岩石节理粗糙度系数(JRC)研究的进展,以及所取得的成果,尤其将分形理论应用于研究岩石节理的粗糙度以后,使得对岩体节理粗糙度的描述取得了一定的发展,并得出了JRC与维数的一系列的关系.     

Multifractal characterization of rock fracture surfaces

The multifractal behavior of rock fracture surfaces is studied taking into account fractal heterogeneity and anisotropy of surface structures. A projective covering method (PCM) is proposed and used to estimate directly the fractal dimension D_s[2, 3) of a fracture surface. The study indicates that the multifractal spectrum of the fracture surfaces provide much additional information on the fracture mechanism and the distribution of asperity concentration on the surface. The fracture surfaces induced in rocks under different failure mechanisms display distinct multifractal behavior.     

岩体裂隙面粗糙度对其渗流特性的影响研究

为了研究岩体裂隙面的粗糙程度与渗流机制间的相互关系,将裂隙沿长度方向均匀分割成若干段,通过设置每一段末端的随机高度,生成两侧对称的粗糙裂隙面。基于格子Boltzmann方法,采用不可压缩流体的D2G9模型,验证了经典的Poiseuille流,计算了不同相对粗糙度岩体裂隙的渗流特性,讨论了裂隙面粗糙度对渗流流态的影响。研究结果表明:裂隙结构壁面对流体的阻碍作用,使得流体在壁面附近的流动产生急剧调整,同时随着裂隙相对粗糙度的增加,在裂隙隙宽急剧变化的部位,局部伴随着旋涡的形成,导致流体内部摩擦阻力作用增大。在单位时间截面渗流流量及每一段平均隙宽相等的条件下,将本数值解与多平行板理论解进行了对比,对于相对粗糙度δ=0.01674的裂隙方案,由于多平行板理论解忽略了粗糙裂隙隙宽变化而引起的局部压降,其裂隙中线处压降产生的最大误差达到15.2%。当相对粗糙度较小时,裂隙中线处的压力与光滑平板流相类似,近似呈线性变化。随着裂隙相对粗糙度增大,压力变化偏离直线方向,且在断面由窄突然变宽的部位,压力变化偏离线性尤为显著。     

Field measurements for estimating the convective heat transfer coefficient at building surfaces

To establish a comprehensive and qualitative prediction basis for the convective heat transfer coefficient (CHTC) for various urban canopy surfaces mainly consisting of building envelopes, a series of outdoor experiments were performed. Multi-point measurements of surface heat balance lead to a distribution of the CHTC on an actual building envelope. Several turbulent statistical values acquired at two different sites enabled the development of an experimental equation depicted by non-dimensional numbers that express a relationship between CHTC and wind velocity containing a turbulent factor. An important thing is the fact that the two measuring sites, one a rooftop slab and the other the vertical wall of a test dwelling, have different scales and different surface directions facing the wind.     

Assessment of rock fracture surface roughness using Riemannian statistics of linear profiles

The mechanical behaviour of rock masses is complex, due partly to the presence of discontinuities within them. Of the geometrical parameters of discontinuities, surface roughness, which encapsulates the topographical features of a rock surface, is known to play a significant role. Here, a new parameter for quantitative roughness determination based on the distribution of unit normal vectors to a rock profile is presented.The analysis of unit normal vectors in terms of directional statistics is customarily performed in Euclidean space using a Cartesian co-ordinate system. Here, the analysis is developed using Riemannian geometry, with Mahalanobis distances being proposed for discrimination between different rock profiles. Statistical parameters on the unit circle are extracted using Riemannian geometry, and from that a roughness parameter, D_R1, is obtained. This parameter corresponds to 1D Riemannian dispersion, and as such D_R1 increases as profile roughness increases.D_R1 is applied to the analysis of synthetic profiles and some real rock profiles. Conclusions are drawn that demonstrate the advantages of the new method in terms of investigating the scale effect in roughness determination as well as in comparing different profiles.A preliminary study into the correlation between D_R1 and the shear strength of a fracture, using analytical and numerical investigation of the strength of profiles comprising symmetric triangular asperities sheared at different normal stress levels, shows a clear relation between Riemannian roughness parameter and profile shear strength.     

Estimation of the joint roughness coefficient (JRC) of rock joints by vector similarity measures

Bulletin of Engineering Geology and the Environment - Accurate determination of joint roughness coefficient (JRC) of rock joints is essential for evaluating the influence of surface roughness on...     

岩石断裂面的各向异性分形和多重分形研究

针对表面结构的分形各向异性和奇异性特征，对岩石断裂表面的多重分形性质进行了研究。提出了一种新的分形测量方法---投影覆盖法，直接测量断裂表面的多重分形维数Ｄ∈［２，３），并引入粗糙性概率度量表面不规则性。研究表明，断裂表面的多重分形谱可提供有关断裂机制的更丰富的信息，不同载荷条件和断裂模式下形成的岩石断裂面具有明显不同的多重分形谱函数特征。     

Influence of range measurement noise on roughness characterization of rock surfaces using terrestrial laser scanning

The application of laser scanning in studying rock surfaces is limited by the range measurement noise inherent in the laser scanner data. In this paper we investigate the influence of range measurement noise on the quantification of rock surface roughness. Roughness measures derived from the laser scanner data are compared with those derived from manual measurements. The comparison shows that the presense of noise in range measurements leads to an overestimation of the fractal dimension and amplitude of roughness profiles. Experiments with wavelet decomposition and thresholding methods for reducing noise in the laser range data are presented. The results indicate that wavelet de-noising methods in general lead to more realistic estimates of the roughness of the laser profiles.     

Data-driven estimation of joint roughness coefficient

Joint roughness is one of the most important issues in the hydromechanical behavior of rock mass. Therefore, the joint roughness coefficient (JRC) estimation is of paramount importance in geomechanics engineering applications. Studies show that the application of statistical parameters alone may not produce a sufficiently reliable estimation of the JRC values. Therefore, alternative data-driven methods are proposed to assess the JRC values. In this study, Gaussian process (GP), K-star, random forest (RF), and extreme gradient boosting (XGBoost) models are employed, and their performance and accuracy are compared with those of benchmark regression formula (i.e. Z₂, R_p, and SD_i) for the JRC estimation. To analyze the models’ performance, 112 rock joint profile datasets having eight common statistical parameters (R_ave, R_max, SD_h, i_ave, SD_i, Z₂, R_p, and SF) and one output variable (JRC) are utilized, of which 89 and 23 datasets are used for training and validation of models, respectively. The interpretability of the developed XGBoost model is presented in terms of feature importance ranking, partial dependence plots (PDPs), feature interaction, and local interpretable model-agnostic explanations (LIME) techniques. Analyses of results show that machine learning models demonstrate higher accuracy and precision for estimating JRC values compared with the benchmark empirical equations, indicating the generalization ability of the data-driven models in better estimation accuracy.     

Estimating the joint roughness coefficient of discontinuities found in metamorphic rocks

The paper presents the results of different methods of determining the roughness of joints in quartzites, metagreywackes and phyllites obtained from road cuts in central Portugal. The evaluation of the joint roughness coefficient (JRC) was carried out using graphical and analytical procedures. Differences were found between the JRC graphic and the JRC calculated, depending on the method used. The JRC calculated values obtained by the tilt tests and the Schmidt rebound hammer tests were compared to the JRC calculated values established from the rock joint shear tests. It is concluded that if JRC is to be used, it is essential to specify how it was established.      

桥面不平整度对桥梁冲击系数的影响研究

采用有限元方法,研究了桥面不平整度对不同跨度及宽度简支梁桥冲击系数的影响,结果表明,桥面不平整对桥梁冲击系数影响显著,且与桥梁的宽跨比有关;当宽跨比小于1.0,桥面不平整时冲击系数随着桥梁宽跨比变化明显,而当宽跨比在2.0~3.0之间时,冲击系数的变化趋势减缓,相对稳定,宽跨比的影响可以忽略。     

Numerical modeling of closure effect of natural fracture surfaces of rock on behavior of fluid flow

Bulletin of Engineering Geology and the Environment - It is essential to understand the hydraulic behavior of rock apertures as the fluid flow path in the rock mass. The geometric parameters of...     

岩石中断裂力学的研究

在断裂力学的基础上,研究了岩石破坏类型和受压裂缝的扩展,并对微裂缝演化进行了探讨,提出利用断裂力学中的裂纹尖端应力和应变场的分布情况,可以预测和制止岩体的失稳。基于能量平衡建立岩石裂纹的扩展条件,进而导出断裂稳定性准则。指出岩石断裂力学中存在的一些问题,并对研究要点进行了总结,为岩石断裂问题研究提供了理论依据。     

Influence of interface roughness on dynamic shear behavior in jointed rock

An interlock/friction model is used to predict the behavior of natural jointed rock specimens subject to static normal stress and dynamic shear. The friction part of the model is based on the simple Coulomb friction formulation. The interlock part of the model is shown to be related to the degree of interface matching that is present between two surfaces of a jointed rock pair. The interlock/friction model adequately predicts the offset phenomenon in the hysteresis results of well-matched jointed rocks. The offset phenomenon is recognized as an increase in shear stress required for shear displacement away from the naturally-aligned rock positions and a decrease in shear stress upon shear displacement back toward the naturally-aligned location. The parameters of the interlock/friction model are shown to be empirically related to rock interface roughness properties. Prediction of the shear stress vs shear displacement hysteresis including the offset phenomenon is possible for welded tuff specimen pairs using the measured interface roughness amplitude and the interface coherence between jointed rocks. Model parameters were verified by an experiment on molded mortar specimens. The data from the mortar specimens indicate that the empirically determined relations may be valid for jointed rock pairs that have dramatically different strength properties than welded tuff.     

Accuracy of the spectral method in estimating fractal/spectral parameters for self-affine roughness profiles

Accurate quantification of roughness is important in modeling strength, deformability and fluid flow behaviors of rock joints. Self-affine fractals seem to have the potential to represent rock joint roughness profiles. Both stationary and non-stationary fractional Brownian profiles (self-affine profiles) with known values of fractal dimension, D, and input standard deviation, σ, were generated at different generation levels. A few smoothing techniques were used with the spectral method to calculate D, and two other spectral parameters K_s (a proportionality constant; see the text for the details) and CD (the cross-over dimension of the profile) for the fractional Brownian profiles. The effects of smoothing, generation level of the profile, seed value used in the generation, non-stationarity of the profile and σ on the accuracy of the calculated D were examined using the spectral method. The following conclusions were obtained: (a) To obtain accurate estimates for D, K_s and CD, it seems necessary to have at least 10 data points per unit length for a profile having a total length of 100 units (this is equivalent to a generation level of 10). (b) For accurate estimation of D, K_s and CD, the non-stationarity of profiles should be removed, if it exists. (c) The parameter combinations D and K_s, (which has the potential to capture scale effects), and D and CD are recommended for quantification of stationary roughness; in addition, extra parameters are required to quantify the non-stationarity. (d) Both the Parzen and Hanning smoothing techniques seem suitable to use with the spectral technique to obtain accurate estimates for D, K_s and CD. (e) To obtain accurate estimates for D, K_s, and CD, it is necessary to use a suitable bandwidth for the Parzen window and a suitable number of interactions for the Hanning window; this paper provides guidelines to choose these suitable values. (f) Seed value has negligible effect on the accuracy of estimated D, K_s and CD.     

Estimating the relation between surface roughness and mechanical properties of rock joints

Discontinuities in rock masses have an important influence on deformational behaviour of blocky rock systems. For a single rock joint, the roughness of its surface is of paramount importance to its mechanical and hydraulic properties, such as friction angle, shear strength, and dilatancy/aperture. Many methods have been used to characterize the surface roughness of rock joints, such as joint roughness coefficients (JRC), root mean square (RMS) value, structure function (SF) etc. However, most of these methods can only be used in the 2-D models. In this study, we carried out direct shear experiments on rock joints under both constant normal load (CNL) and constant normal stiffness (CNS) conditions, and measured the surfaces of rock joints before and after shearing, using a 3-D laser scanning profilometer system. By using a 3-D fractal evaluation method of roughness characterization, the projective covering method (PCM) and a direct shear apparatus of high accuracy, the relation between mechanical properties of rock joints under different boundary conditions and the change of their fractal dimensions in both 2-D and 3-D models have been examined, which gives a new approach to accurately evaluate the evolution of roughness of rock joint surfaces and its influence on the hydro-mechanical behaviours of rock joints.     

Influence of fracture roughness on shear strength,slip stability and permeability:A mechanistic analysis by three-dimensional digital rock modeling

Subsurface fluid injections can disturb the effective stress regime by elevating pore pressure and potentially reactivate faults and fractures.Laboratory studies indicate that fracture rheology and permeability in such reactivation events are linked to the roughness of the fracture surfaces.In this study,we construct numerical models using discrete element method(DEM) to explore the influence of fracture surface roughness on the shear strength,slip stability,and permeability evolution during such slip events.For each simulation,a pair of analog rock coupons(three-dimensional bonded quartz particle analogs) representing a mated fracture is sheared under a velocity-stepping scheme.The roughness of the fracture is defined in te rms of asperity height and asperity wavele ngth.Results show that(1) Samples with larger asperity heights(rougher),when sheared,exhibit a higher peak strength which quickly devolves to a residual strength after reaching a threshold shear displacement;(2) These rougher samples also exhibit greater slip stability due to a high degree of asperity wear and resultant production of wear products;(3) Long-term suppression of permeability is observed with rougher fractures,possibly due to the removal of asperities and redistribution of wear products,which locally reduces porosity in the dilating fracture;and(4) Increasing shear-parallel asperity wavelength reduces magnitudes of stress drops after peak strength and enhances fracture permeability,while increasing shear-perpendicular asperity wavelength results in sequential stress drops and a delay in permeability enhancement.This study provides insights into understanding of the mechanisms of frictional and rheological evolution of rough fractures anticipated during reactivation events.