岩体结构面粗糙度各向异性特征及尺寸效应分析

 岩体结构面形貌存在明显的各向异性和尺寸效应特征。由于结构面本身的复杂性,定量表征其属性仍是该领域的研究难点。鉴于此,考虑岩体结构面的地质本质性特征,应用地质统计学原理,提出采用变异函数参数(基台C和变程 )表示结构面粗糙度(JRCv)的方法;然后采用量纲分析法,给出JRCv表达式。应用提出的公式计算结构面上不同尺寸范围(100 Pixel×100 Pixel～1 000 Pixel×1 000 Pixel) 32个方向上的JRCv值,分析结构面粗糙度各向异性及其尺寸效应特征。研究结果表明：(1) 从表观看,沿分析方向,结构面越粗糙,JRCv值越大,JRCv可以定量表征结构面粗糙度及其各向异性特征;(2) 在结构面分析方向上,随尺寸范围的增大,JRCv值逐渐减小,达到一定范围时,JRCv值趋于稳定,通过分析各方向上JRCv值随尺寸范围的变化趋势,可以确定结构面的临界范围;(3) 结构面各向异性特征受结构面研究范围的影响,当研究范围达到一定尺度时,结构面各向异性特征趋于稳定。该研究成果将为定量分析岩体结构面力学性质强弱方向提供依据,为实验室或原位结构面力学试验选择合理尺寸试件提供一种新方法。     

剪切过程中岩石节理粗糙度分形演化及力学特征

在系统测量和试验的基础上，研究了剪切过程中岩石节理粗糙面的分形特征和岩石节理的力学行为，阐述了岩石节理面分形维数Ｄ和截距Ａ与岩石节理在载荷作用下法向、切向变形以及抗剪强度之间的关系，得出岩石节理在剪切过程中由于表面损伤而引起的表面分维Ｄ和截距Ａ的演化规律。研究表明：分维Ｄ和截距Ａ是描述节理面粗糙性的两个重要的参数。前者反映节理粗糙面的不规则程度，后者则与节理面粗糙体（ａｓｐｅｒｉｔｉｅｓ）的坡度密切相关。仅依据分形维数Ｄ不足以确定岩石节理的粗糙性与岩石节理力学行为之间的关系。在许多情况下，岩石节理的力学性质对截距Ａ的依赖程度大于对分维Ｄ的依赖程度     

Experimental and Analytical studies of reinforced crushed limestone

This research study aims at investigating the behavior of spread footings on reinforced crushed limestone using laboratory model tests. The model tests were conducted inside a steel box with dimensions of 1.5 m (length) × 0.91 m (width) × 0.91 m (height) using a steel plate with dimensions of 152 mm × 152 mm (6 in. × 6 in.). The parameters investigated include the number of reinforcement layers and the tensile modulus and type of reinforcement. An analytical solution is also developed to estimate the ultimate bearing capacity of reinforced crushed limestone. The test results show that the inclusion of reinforcement can appreciably improve the bearing capacity of crushed limestone up to a factor of 2.85 at a settlement ratio of 10% and reduce the footing settlement down to 75% at a surface pressure of 5500 kPa. The results also demonstrate that reinforcements with higher tensile modulus performed better than reinforcements with lower tensile modulus and that steel reinforcement performed better than geogrid reinforcement. The proposed analytical solution gave a good predication of experimental results of geogrid reinforced sections, while Huang and Menq's solution (1997) gave a good predication for steel reinforced crushed limestone. The analytical results also showed that the reinforced ratio (R_r) should be high enough to form the “deep footing” effect.     

A laboratory experiment on natural ventilation through a roof cavity for reduction of solar heat gain

The study targets the reduction of roof solar heat gain through the use of natural ventilation in a roof cavity. This study is mainly concerned with factory buildings. Experimental outcomes were obtained from an inclined cavity model which was heated on the upper surface to mimic solar radiation on a roof. The dimensions of the cavity were 4882 mm× 400 mm × 78 mm. The two opposing smallest sides were allotted as the inlet and outlet, and narrowed to simulate resistance of the air flow in practical applications. Temperature and velocity measuring facilities were prepared in the experimental model. A number of measurements were carried out by varying the combinations of different heat production, inclination angles, and opening ratios. It was found that resistance to heat and air flow in the cavity was strongly influenced by the opening size. When the Reynolds number was examined, it showed that the flow belonged to the laminar region. The average velocity reached to 0.25 m/s at the highest in the examined cases. In other words, the cavity air was turned over 184 times in an hour. Natural ventilation in the roof cavity seemed to be effectively applicable to solar incidence discharges in factory buildings.     

基于分形理论构建随机粗糙节理模型的方法研究

粗糙节理三维形貌特征是影响岩体沿节理面剪切力学性质的关键因素。采用3D扫描方法重构巴西劈裂试验得到的砂岩张节理表面形貌模型。根据粗糙节理表面统计自相似性质,引入地形学领域广泛应用的随机分形数字高程模型生成方法,通过调节不同的随机参数d,采用"菱形–正方形"算法迭代生成一系列不同形貌特征的分形粗糙表面数字高程模型,并将其与天然砂岩张节理进行形貌特征比较。采用三维盒维数法计算天然砂岩张节理以及随机构建的分形高程模型的分形维数,并基于选定的剪切方向统计2种模型的视倾角统计分布规律。分别以分形维数以及视倾角统计分布标准差为表征粗糙模型三维形貌特征的参数,确定了该天然张节理的形貌特征参数对应的粗糙度水平符合随机参数d=2~3 mm范围的分形高程模型的粗糙度水平,验证了基于分形理论构建随机数字高程模型的方法在模拟构建粗糙节理表面模型方面的可行性。     

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.     

Requirements for accurate quantification of self-affine roughness using the roughness–length method

Self-affine fractals have the potential to represent rock joint roughness profiles. Fractional Brownian profiles (self-affine profiles) with known values of fractal dimension, D, input standard deviation, σ, and data density, d, were generated. For different values of the input parameter of the roughness–length method (window length, w), D and another associated fractal parameter A were calculated for the aforementioned profiles. The calculated D was compared with the D used for the generation to determine the accuracy of calculated D. Suitable ranges for w were estimated to produce accurate D (within ±10% error) for the generated profiles. The results showed that to obtain reliable estimates for fractal parameters of a natural rock joint profile, it is necessary to choose a unit for the profile length to satisfy a data density (d) greater than or equal to 5.1. For roughness profiles having 5.1≤d≤51.23 and 1.2≤D≤1.7, w values between 2.5% and 10% of the profile length were found to be highly suitable to produce accurate fractal parameter estimates. It is recommended to use at least seven w values between the estimated minimum and maximum suitable w values in estimating fractal parameters of a natural rock joint profile. It was found that σ and a global trend of a roughness profile have no effect on calculated D. The estimated A was found to increase with both D and σ. The parameter D captures the auto-correlation and A captures the amplitude of a roughness profile at different scales. Therefore, the parameters D and A are recommended to use with the roughness–length method in quantifying rock joint roughness. In addition, at least one more parameter is required to quantify the global trend of a roughness profile, if it exist; in many cases just the inclination or declination angle of the roughness profile in the direction considered would be sufficient to estimate the global trend. Calculated cross-over lengths (segment length of a profile at which a self-affine profile becomes self-similar) for the profiles investigated were found to be extremely small (less than 0.6% of the profile length) indicating that laser profilometers are required to make roughness measurements at interval lengths comparable to the cross-over lengths of the natural rock joint profiles. To calculate rock joint roughness parameters accurately using the self-similar techniques, it is necessary to have roughness measurements made at interval lengths comparable to the cross-over length of the profile. This indicate clearly the difficulty of using self-similar techniques such as the divider method in estimating rock joint roughness accurately.     

岩石模型结构面的取样代表性试验研究

岩石结构面的代表性取样是开展不同尺寸模型结构面直剪试验的前提条件,直接影响到结构面抗剪强度尺寸效应试验结果的有效性和可靠性。通过对取样尺寸为10 cm的18组岩石结构面粗糙度系数(JRC)的测量和统计分析,得到该尺寸岩石结构面试样的粗糙度系数分布规律,表明模型结构面取样代表性评价的必要性。基于结构面粗糙度系数非均一性分布特点,以及对简单随机取样法和分层取样法2种概率取样方法的比较分析,提出基于分层取样法的岩石模型结构面代表性取样方法,该方法采用JRC四分位法确定各层样本的数量比例,再利用分层取样公式计算样本的取样数量。通过岩体结构面抗剪强度的力学机制分析,对试样取样代表性和力学可靠性进行校验,结果表明,采用该取样方法能较好地代表该尺寸的表面形态分布,取样结果也较好地满足力学试验的统计精度要求。     

Topography of natural and artificial fractures in granitic rocks: Implications for studies of rock friction and fluid migration

The topography of fractures and joints has a strong influence on their frictional strength and fracture permeability. Important aspects of the surfaces are the size, distribution and density of contact spots between the surfaces, which can be calculated using topographic data. For a variety of tensile fracture surfaces in granite, including both natural joints and man-made fractures, spectral and statistical properties are similar, suggesting that man-made fractures in granites can be acceptable substitutes for natural fractures in some experimental situations. The topographic data indicate that fracture surfaces at scales from 0.1 to 200 mm are approximately fractal and statistically self-affine. A log-log plot of power spectral density vs spatial frequency, calculated from the fracture surfaces indicates a spectral slope of −2.3 ± 0.2, yielding a fractal dimension D between 2.25 and 2.45. Shear fracture surfaces are also fractal, but have anisotropic roughness, which develops during the fracture initiation process. The amount of anisotropy that develops on the shear fracture surfaces is small in comparison to that exhibited by natural fault surfaces, which include anisotropy that results from post failure wear and from surface evolution. For fractures like those measured in this study, simple simulations indicate that the aperture, size and number density of wall-to-wall contacts between the surfaces change non-linearly with relative shear displacement of the surfaces. It is possible to make preliminary estimates of how the permeability and frictional properties of fractures and joints depend on the size, distribution and character of the contact spots. Furthermore, given that artificial fractures can be generated numerically with statistical properties similar to those of natural or man-made fractures, it is reasonable for systematic studies of the effects of roughness on friction and fluid flow to use computer designed surfaces to provide a range of variability that is not easily accessible in the laboratory.     

3-D Degradation analysis of railroad ballast

Degradation behaviour of aggregate particles of the size of railroad ballast (32–63 mm) is examined using Los Angeles (LA) milling and 3-D scanning techniques. Seven different rock types were tested at four stages of milling. For the analytical geometry and topography characterization, a new method based on Fourier and power spectra was used. The results are compared with those obtained using geometrical methods and traditional manual measurements. Diminishing of surface roughness and dimensions is evident. The change in roughness was 20–35% and for maximum dimensions of less than 10% in the case of hard rock types. The LA value was less than 15. For the weaker particles values of more than 40% and more than 20%, respectively, were obtained. The fractal dimension approached a value of 2 as a function of milling rates. Electronic Publication     

节理在不同接触状态下的渗流特性

 将取自雅砻江水电站锦屏二期工程施工现场的白色大理岩,采用劈裂法制成张拉性人工节理试件,用TJXW–3D型岩石节理表面形貌仪测量节理的表面形貌,并采用自行编制的表面形貌和组合形貌参数计算软件,分析其用以表征节理表面形貌的节理面二维分形维数,以及用以表征组合形貌的节理内空腔的三维分形维数。对节理面进行错位,以改变其接触状态,然后进行不同接触状态下节理的渗流试验。将试验实测结果与传统的经验公式及各种修正公式的计算值进行比较,发现利用现有经验公式分析试验结果存在较大的偏差。通过对实测数据做进一步分析,发现表征节理表面形貌和组合形貌特征的分形维数也是影响节理渗透率的重要因素之一。综合考虑节理透过率以及表征节理形貌的分形维数等因素对节理渗透特性的影响,得到更为合理的节理渗流经验公式,该公式具有更广阔的应用前景。     

基于数字图像处理技术的岩石节理分形描述

岩石节理的粗糙度对结构面的剪切强度起着重要的作用.分形维数对节理的次级细微粗糙结构能够进行很好的描述,而对节理的一级起伏结构体现并不明显.考虑了节理形态的层次性,用分形维数代表节理的次级精细结构,即节理的粗糙度;用起伏度表示节理的一级波状形态,据此提出用分形维数D和起伏度W_d两个指标来描述JRC(节理粗糙度系数),并给出相应的计算公式.另外,针对工程实践中分形维数准确快速量测存在的困难,本文以摄影测量为基础,借助数字图像处理技术,在VC++平台下开发了节理轮廓线分形维数计算程序,为分维较准确方便地应用于工程实践做了有益的探索.     

非贯通节理Jennings强度准则的岩桥弱化和节理面起伏角修正

 通过对具有不同粗糙程度(以节理面起伏角表示)的共面非贯通人工节理进行不同法向应力水平下的直剪试验,研究节理面起伏角对非贯通节理剪切强度的影响,分析在剪切过程中岩桥力学参数的弱化机制。现有Jennings准则将岩桥视为完整岩块,计算所得的剪切强度与直剪试验结果存在较大偏差。在试验结果的基础上,考虑剪切过程中岩桥力学参数的弱化和节理面起伏角的影响,对Jennings准则进行修正。将修正Jennings准则计算的非贯通节理剪切强度结果与直剪试验结果对比,结果表明：修正Jennings准则的计算结果与试验结果吻合较好,能较好地预测具有规则起伏角的非贯通节理剪切强度。     

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.     

Effect of shear-induced contact area and aperture variations on nonlinear flow behaviors in fractal rock fractures

This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus. A series of fluid flow and visualization tests is performed on four transparent fracture specimens with various shear displacements of 1 mm, 3 mm, 5 mm, 7 mm and 10 mm under a normal stress of 0.5 MPa. Four granite fractures with different roughnesses are selected and quantified using variogram fractal dimensions. The obtained results show that the critical Reynolds number tends to increase with increasing shear displacement but decrease with increasing roughness of fracture surface. The flow paths are more tortuous at the beginning of shear because of the wide distribution of small contact spots. As the shear displacement continues to increase, preferential flow paths are more distinctly observed due to the decrease in the number of contact spots caused by shear dilation; yet the area of single contacts increases. Based on the experimental results, an empirical mathematical equation is proposed to quantify the critical Reynolds number using the contact area ratio and fractal dimension.     

天然岩体结构面粗糙度各向异性、尺寸效应、间距效应研究

为了研究天然岩体结构面粗糙度评价结果影响因素,以重庆武隆地区大尺寸岩体结构面为例,运用三维激光扫描技术,基于Grasselli改进法描述粗糙度在不同采样方向、尺度与精度下的变化规律。结果显示:所选用的天然岩体结构面具有明显的各向异性、正尺寸效应和间距效应,因此在进行粗糙度评价时,采样方向务必与剪切方向保持一致,采样尺寸与采样间距应大于等于和小于等于有效采样尺寸与间距;为便于不同评价方法间结果对比,应保证在相同的采样参数下开展研究。     

煤体爆破破碎分维评价方法的研究

 提出了煤体爆破破碎分维评价方法和分维比概念, 考虑了煤体原始结构特征对煤体爆破破碎效果的影响。通过主因素分析, 明确了爆破参数与分形维数、分维比的相关关系以及影响的显著性大小, 探讨了不同分维和分维比的表征含义。在单自由面深孔煤体爆破的条件下, 爆破块度相似分维与分维比体现了顶煤预爆破破裂裂隙的整体分布, 可作为定量评价爆破方案的主要指标, 表面裂隙分维测量计算简易, 是煤体内部裂隙的外在表现, 可作为初步评价爆破方案的定量指标。应用煤体爆破破碎分维评价方法对大同矿务局忻州窑矿坚硬顶煤进行了预爆破研究, 取得了很好的经济效益。     

Predicting the settling velocity of flocs formed in water treatment using multiple fractal dimensions

Here we introduce a distribution of floc fractal dimensions as opposed to a single fractal dimension value into the floc settling velocity model developed in earlier studies. The distribution of fractal dimensions for a single floc size was assumed to cover a range from 1.9 to 3.0. This range was selected based on the theoretically determined fractal dimensions for diffusion-limited and cluster-cluster aggregation. These two aggregation mechanisms are involved in the formation of the lime softening flocs analyzed in this study. Fractal dimensions were generated under the assumption that a floc can have any value of normally distributed fractal dimensions ranging from 1.9-3.0. A range of settling velocities for a single floc size was calculated based on the distribution of fractal dimensions. The assumption of multiple fractal dimensions for a single floc size resulted in a non-unique relationship between the floc size and the floc settling velocity, i.e., several different settling velocities were calculated for one floc size. The settling velocities calculated according to the model ranged from 0 to 10 mm/s (average 2.22 mm/s) for the majority of flocs in the size range of 1-250 μm (average 125 μm). The experimentally measured settling velocities of flocs ranged from 0.1 to 7.1 mm/s (average 2.37 mm/s) for the flocs with equivalent diameters from 10 μm to 260 μm (average 124 μm). Experimentally determined floc settling velocities were predicted well by the floc settling model incorporating distributions of floc fractal dimensions calculated based on the knowledge of the mechanisms of aggregation, i.e., cluster-cluster aggregation and diffusion-limited aggregation.     

Numerical studies of the influence of microstructure on rock failure in uniaxial compression — Part II: constraint, slenderness and size effect

Numerical simulations of uniaxial compression have been conducted to evaluate the effects of the loading system and specimen geometry on the deformation and failure behavior of brittle and heterogeneous rock. This was done using the Rock Failure Process Analysis program (RFPA^2D). Numerical model specimens with different Young’s modulus ratios of platen to specimen (Ep/Es=0, 0.1, 1, 2, and 10), different slenderness in terms of height to width ratios (H/W=0.5, 0.67, 1, 1.5, and 3), and different sizes (H×W=30×20, 100×67, 120×80, 150×100, and 190×127 mm) have been numerically analyzed. The numerical simulations not only qualitatively reproduce the experimentally observed pre- and post-peak failure phenomena of the loaded specimens, but also provide a quantitative evaluation of the influence of the parameters studied on the complete stress–strain curves and the strength characteristics. The results presented here indicate that a more ductile response is simulated and the peak strength increases when the end constraint increases. The crack patterns show that almost-vertical splitting cracks develop in specimens loaded with softer loading platens, and the well-known hour-glass failure mode develops in specimens loaded with stiffer loading platens. The peak stress sustained by a specimen decreases with increasing slenderness of the specimen. The pre-peak portion of the stress–strain curves shows no significant dependence on slenderness; however, the post-peak curves are highly dependent on the ratio of specimen height to width. As far as the effect of size is concerned, numerical results reveal a strength reduction with an increase in specimen size, whereas the change of the specimen size does not obviously change the failure patterns.