Uncertainties in estimating the roughness coefficient of rock fracture surfaces

Joint roughness has a critical role in the deformation behavior of discontinuous rock masses. Several subjective (visual comparison) and quantitative (statistical and fractal) approaches have been proposed for estimating rock joint roughness coefficient (JRC). Using a large collection of 223 published joint profiles, this study investigates variability of the JRC estimates by these approaches. Among the profile parameters, maximum height (R _z), ultimate slope (λ), and fractal dimension (D _h–L, determined using the hypotenuse leg method) show a lower sensitivity to the sampling interval than the root mean square of the first deviation (Z ₂), profile elongation index (δ), fractal dimension (D _c, determined using the compass-walking method), and standard deviation of the angle i (σ _i ). Accordingly, this study proposes two separate sets of equations for quantitatively estimating JRC. The performances of these equations are examined by performing direct shear tests on 23 rock joint samples. The subjective approach is found to underestimate JRC by less than two units because it ignores (1) the main trend of the compared profile and (2) the limited scope of the standard profiles. Following these results, the visual comparison chart is updated by explicitly adding a scale bar for the y-axes of the standard profiles. Several basic rules for visual comparisons are also proposed.

     

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。     

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...     

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.     

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。     

Experimental studies on fragmentation of rock falls on impact with rock surfaces

Rock fall is a common natural hazard causing significant damage to infrastructure and loss of life. Rock fragmentation is frequently observed during rock fall events and several authors have raised issues related to the impact of fragments on the protection structure. However, this phenomenon is not accounted for when designing the protection barriers. The paper presents the results of 20 rockfall tests performed in a quarry in Italy to provide new insight into the fragmentation phenomenon, especially in the case of foliated materials. The results have shown that the impacting angle plays a key role in the fragmentation of foliated rocks whereas the effect of the impacting energy tends to be of second order. No threshold in impacting energy could be defined to explain what triggers the fragmentation. It has been noticed that the proportion of impacting energy dissipated during fragmentation is relatively constant and depends on the choice of the normal restitution coefficient.     

Effects of loading rate on rock fracture

By means of a wedge loading applied to a short-rod rock fracture specimen tested with the MTS 810 or SHPB (split Hopkinson pressure bar), the fracture toughness of Fangshan gabbro and Fangshan marble was measured over a wide range of loading rates, =10⁻²–10⁶ MPa m^1/2 s⁻¹. In order to determine the dynamic fracture toughness of the rock as exactly as possible, the dynamic Moiré method and strain–gauge method were used in determining the critical time of dynamic fracture. The testing results indicated that the critical time was generally shorter than the transmitted wave peak time, and the differences between the two times had a weak increasing tendency with loading rates. The experimental results for rock fracture showed that the static fracture toughness K_Ic of the rock was nearly a constant, but the dynamic fracture toughness K_Id of the rock ( ≥10⁴ MPa m^1/2 s⁻¹) increased with the loading rate, i.e. log(K_Id)=a log +b. Macroobservations for fractured rock specimens indicated that, in the section (which was perpendicular to the fracture surface) of a specimen loaded by a dynamic load, there was clear crack branching or bifurcation, and the higher the loading rate was, the more branching cracks occurred. Furthermore, at very high loading rates ( ≥10⁶ MPa m^1/2 s⁻¹) the rock specimen was broken into several fragments rather than only two halves. However, for a statically fractured specimen there was hardly any crack branching. Finally, some applications of this investigation in engineering practice are discussed.     

岩石断裂和损伤的研究现状

从岩石断裂和损伤力学角度以及细观角度对岩石的断裂和损伤理论的研究现状进行了综述分析,指出岩石强度理论的研究由经典强度理论向断裂强度理论、损伤强度理论发展。     

Effects of high temperatures on dynamic rock fracture

The dynamic fracture toughness of Fangshan gabbro and Fangshan marble subjected to high temperature was measured by means of the split Hopkinson pressure bar (SHPB) system. The specimens for measuring the fracture toughness were manufactured according to the requirements for the Short Rod (SR) specimen suggested by ISRM. Two cases were investigated: (1) the SR specimens of the gabbro and marble were fractured at high temperature (100–330°C), and (2) the specimens of the rocks were first pre-heat-treated at 200°C for the marble and 600°C for the gabbro, and then fractured at room temperature. The experimental results showed that under dynamic loading the fracture toughness of both the gabbro and the marble tested in the above-mentioned cases increased with increasing loading rates. The relationship between the fracture toughness and the loading rates in the two cases is similar to that obtained in the room temperature environment, i.e., without high temperature. (This is defined as the third case.) It can be concluded that temperature variation affects the dynamic fracture toughness of the two rocks to a limited extent within the temperature ranges tested. This is different from the results obtained under the static loading condition. Furthermore, by means of the scanning electronic microscope (SEM), the vertical sections of the fracture surfaces for some gabbro specimens were examined. In addition, the fractal dimensions of the fracture surfaces of some specimens were measured by means of fractal geometry. The results showed that under dynamic loading: (1) macro-crack branching near the fracture surfaces was universal; (2) the fractal dimensions increased with increasing loading rates; (3) in the sections of the specimens tested at high temperature there were many micro-cracks that were probably induced by thermal cracking. On the basis of the above macro- and micro-experimental investigation, an energy analysis of the process of dynamic rock fracture was performed. The results showed that the energy utilisation in dynamic fracture was much lower than that in static fracture.     

Investigation of fracture behaviour during rock mass failure

The main characteristic behaviour of rock mass fractures are studied. Their importance in the application and investigation of rock mass failure is demonstrated through some preliminary investigation of rock mass fracture mechanics by the authors. Firstly, in the study of rock fracture features, the mechanisms and non-linear phenomenon of a fragmented belt of rock fracturing have been investigated. Several new ideas can be used to construct a new system of rockmass fracture mechanics. Secondly, in the investigation of rock mass structure controlled rock mass fracturing, the importance of true mixed mode fracturing is emphasized. A primary criterion to predict the propagation of rock mass cracks has been established. Thirdly, in the investigation of non-singular stress effects on rock mass fracture, a new fracture criterion for the generalized crack opening displacement of rock is proposed. This can be used to analyze the influence of the normal stress and the crack orientation on the fracturing process in a rock mass. Finally, the rock mass fracture mechanics investigation and methodology was used to analyze the stability of the Mabukan high slope in the upper reaches of a large hydro-power station in the south-west of China. It is shown that the results of this study have created a more solid foundation for the application of rock mass fracture mechanics to rock engineering.     

Effects of loading rate on rock fracture: fracture characteristics and energy partitioning

By means of the Scanning Electron Microscope (SEM), an examination was performed of the fracture surfaces (including their vertical sections) of both Fangshan gabbro and Fangshan marble specimens fractured at the loading rates MPa m^1/2 s⁻¹. The results showed that one or more branching cracks near the fracture surfaces of dynamic rock specimens were clear and the cracks increased with increasing loading rates. However, such branching cracks were rarely seen near the static fracture surfaces. In addition, with the aid of the Split Hopkinson Pressure Bar (SHPB) testing system and a high-speed framing camera, the energy partitioning in the dynamic fracture process of a short rod (SR) rock specimen was analysed quantitatively. The total energy W_L absorbed by an SR specimen in the dynamic fracture process mainly consisted of the fracture and damage energy W_FD and the kinetic energy W_K of flying fragments. The energies W_L and W_K could be quantitatively calculated through stress wave measurement and high-speed photography in the SHPB testing system. Thus, the fracture and damage energy W_FD could be obtained. The results showed that: (1) the energy W_K increased with an increase in the impact speed of the striker bar or the loading rate; (2) the energy W_FD for dynamic rock fracture was markedly greater than that for static rock fracture, and the W_FD increased with an increase in the impact speed of the striker bar or the loading rate; and (3) the value W_L/W_B (W_B is the energy input into the loading system) in the case of dynamic fracture is much lower than that in the case of static fracture. In addition, the ratio decreases with an increase in the loading rate or the impact speed of the striker bar. This means that the energy utilisation decreases when the loading rate or the impact speed of the striker bar rises. Finally, some application problems are discussed in the paper.     

Shear fracture (Mode II) of brittle rock

Mode II fracture initiation and propagation plays an important role under certain loading conditions in rock fracture mechanics. Under pure tensile, pure shear, tension- and compression-shear loading, the maximum Mode I stress intensity factor, K_Imax, is always larger than the maximum Mode II stress intensity factor, K_IImax. For brittle materials, Mode I fracture toughness, K_IC, is usually smaller than Mode II fracture toughness, K_IIC. Therefore, K_Imax reaches K_IC before K_IImax reaches K_IIC, which inevitably leads to Mode I fracture. Due to inexistence of Mode II fracture under pure shear, tension- and compression-shear loading, classical mixed mode fracture criteria can only predict Mode I fracture but not Mode II fracture. A new mixed mode fracture criterion has been established for predicting Mode I or Mode II fracture of brittle materials. It is based on the examination of Mode I and Mode II stress intensity factors on the arbitrary plane θ,K_I(θ) and K_II(θ), varying with θ(−180°θ+180°), no matter what kind of loading condition is applied. Mode I fracture occurs when (K_IImax/K_Imax)<1 or 1<(K_IImax/K_Imax)<(K_IIC/K_IC) and K_Imax=K_IC at θ_IC. Mode II fracture occurs when (K_IImax/K_Imax)>(K_IIC/K_IC) and K_IImax=K_IIC at θ_IIC. The validity of the new criterion is demonstrated by experimental results of shear-box testing.Shear-box test of cubic specimen is a potential method for determining Mode II fracture toughness K_IIC of rock since it can create a favorable condition for Mode II fracture, i.e. K_IImax is always 2–3 times larger than K_Imax and reaches K_IIC before K_Imax reaches K_IC. The size effect on K_IIC for single- and double-notched specimens has been studied for different specimen thickness B, dimensionless notch length a/W (or 2a/W) and notch inclination angle α. The test results show that K_IIC decreases as B increases and becomes a constant when B is equal to or larger than W for both the single- and double-notched specimens. When a/W (or 2a/W) increases, K_IIC decreases and approaches a limit. The α has a minor effect on K_IIC when α is within 65–75°. Specimen dimensions for obtaining a reliable and reproducible value of K_IIC under shear-box testing are presented. Numerical results demonstrate that under the shear-box loading condition, tensile stress around the notch tip can be effectively restrained by the compressive loading. At peak load, the maximum normal stress is smaller than the tensile strength of rock, while the maximum shear stress is larger than the shear strength in the presence of compressive stress, which results in shear failure.     

Borehole seismic characterization of a heterogeneous rock

Borehole reflection seismology can provide very high-resolution subsurface images around the borehole. In the oil and gas industry, the method has been aggressively used for imaging complex structure in and around an oil and gas reservoir. In the civil engineering field, there have been few attempts to apply these methods, although there are many potential needs for this type of technology. Intending to promote utilization of the method in civil engineering applications, we have developed data acquisition and processing techniques, and conducted field experiments to study its feasibility.In the borehole seismic measurement system, we use OYO's OWS as a downhole source and borehole shuttle as a receiver. We have increased the source energy of OWS by 3 times the conventional one to obtain greater transmission power. We have devised a tube wave damper for reducing tube waves in borehole acquisition. For the data processing, we have developed a prestack directional migration technique using three-component data for processing reflection waves arriving at the receiver from all directions around the borehole.To study the feasibility for civil engineering applications, we conducted single- and cross-well seismic reflection surveys in tertiary sedimentary and volcanic rocks. The reflection images obtained in the cross- and single-well seismic reflection surveys clearly showed fine layering in a rock and a steeply dipping geological boundary about 20 m away from the borehole, respectively.     

Determination of fracture depth of rock blocks from P-wave velocity

The quality of large rock blocks produced from quarries depends significantly on the fractures and the extent to which they penetrate into the rock. The paper reports a laboratory study to evaluate the possibility of the determining fracture depth in rock blocks from P-wave velocity. Three igneous, three sedimentary and three metamorphic rocks were studied. Inverse linear relations were found between the fracture depths and the P-wave velocities. Although, the slope of the regression lines is approximately the same for the rocks belonging to one rock class, different trends are seen for the different rock types. In addition, some correlation was found between the slopes of the regression lines and the physical properties of the rocks.      

Directional rock mass rating (DRMR) for anisotropic rock mass characterization

Bulletin of Engineering Geology and the Environment - Rock mass classification systems are used to categorize and estimate the role of the most significant parameters influencing rock mass behavior...