Rough Rock Research Articles

An Analytical Model for Two-Order Asperity Degradation of Rock Joints Under Constant Normal Stiffness Conditions

Jointed rock masses during underground excavation are commonly located under the constant normal stiffness (CNS) condition. This paper presents an analytical formulation to predict the shear behaviour of rough rock joints under the CNS condition. The dilatancy and deterioration of two-order asperities are quantified by considering the variation of normal stress. We separately consider the dilation angles of waviness and unevenness, which decrease to zero as the normal stress approaches the transitional stress. The sinusoidal function naturally yields the decay of dilation angle as a function of relative normal stress. We assume that the magnitude of transitional stress is proportionate to the square root of asperity geometric area. The comparison between the analytical prediction and experimental data shows the reliability of the analytical model. All the parameters involved in the analytical model possess explicit physical meanings and are measurable from laboratory tests. The proposed model is potentially practicable for assessing the stability of underground structures at various field scales.

A New Rock Joint Generation Method and Its Verification in PFC2D

The first part of this paper presents the major drawbacks of the traditional methods for generating joints in Particle Flow Code 2D (PFC2D). Violent oscillations in the postpeak shear stress and shear‐induced dilation in the normal direction occur in specimens generated by directly removing bonds in joints and using the discrete fracture network (DFN) method. The specimens generated by the additional wall method can be used to simulate realistic shear mechanical properties in the direct shear test, but it is difficult to achieve a uniform initial stress distribution within the specimen due to the constraint of particle motion. The second part of this paper explores an improved method to generate realistic joints based on the particle grouping technique and the smooth joint model, and the validity of this method is verified by a set of numerical direct shear tests. The numerical results show that the proposed joint generation method can effectively eliminate the oscillation of the postpeak shear stress and shear‐induced dilation in the normal direction. In addition, the mechanical behaviours of the rough jointed rock mass correspond well with the theoretical results obtained from Patton’s and Barton’s models. The proposed model can also simulate the asperity degradation of rough jointed rock masses.

Numerical Investigation on Hydraulic Properties of Artificial-Splitting Granite Fractures during Normal and Shear Deformations

This study explores the effects of normal loading and shearing on hydraulic properties in roughness-walled rock fractures. The geometries of five fractures were measured by the 3D scanning technology. The flow simulation was performed for rough rock fractures with large displacements during normal loading and shearing by finite volume method (FVM). The results demonstrate that the deformation of fracture with increasing normal stress and shear causes nonuniform changes in void space geometry and further influences fracture permeability. Associated with normal displacement are an increase in contact area and a decrease in mechanical aperture. The transmissivity is decreasing by 3 orders of magnitude response to applied normal displacement values of 0.0 mm to 1.8 mm. In contrast, an increase in mechanical aperture and contact ratio that occurs with increasing shear displacement values of 0.0 mm to 4.0 mm is associated with decreasing distinctly transmissivity by 1.5–2 orders of magnitude. Based on the numerical results, an empirical equation is proposed to evaluate the effects of contact area and roughness of fracture on the hydraulic aperture. The good agreement between numerical results and the predicted results by the new model indicates that the proposed model is capable of estimating the hydraulic aperture of rock fractures through parametric analyses, compared with other published models from available literature. In addition, the new model succeeds in predicting the transmissivity in Develi and Babadagli (2014) water flow experiments.

Experimental Study on 3D Roughness and Shear Failure Mechanism of Rock Mass Discontinuity

A set of systematic experimental methods, including 3D accuracy scanning and identification of discontinuous surface topography, physical model construction, and laboratory direct shear experiment under different directions and normal stresses, was proposed to research the influence of discontinuity roughness on strength and deformation of discontinuity. During physical model construction of discontinuity, three types of discontinuity and rough natural rock joint surface models were constructed and moulded. Meanwhile, many influence factors of discontinuity surface topography, such as asperity inclination angle (AIA), asperity height (AH), normal stress (NS), and shear direction (SD), were considered during the direct shear experiment. On the basis of the experimental results, it can be found that there were two types of failure modes under different loading conditions, which were named “failure by shearing through the asperities” and “failure by sliding over the asperities”. The obvious stress concentration phenomenon, climbing, and cutting effects appeared in the process of the direct shear experiment. In addition, the accurate identification of surface topography of natural rough rock joint surface was carried out using three-dimensional sensing system (3DSS) and self-programming software before and after the experiment. The subsamples with the same surface topography as the original samples were moulded using a self-developed instrument. Then, the mechanical behavior of the original samples and subsamples for the natural rough rock joint surface under different shear directions and normal stresses was studied. The results show that the shear displacement under different shear directions and normal stresses is very large before it reaches the failure state. And the residual strength of the original samples is higher than that of the subsamples. In addition, failure modes of the subsamples are main failure by shearing through the asperities due to the significant difference between peak shear strength and residual strength. The failure modes for parts of the original samples are failure by sliding over the asperities. The change ratio of area for the discontinuity after the experiment depends on surface topography, strength of heave on the surface of discontinuity, and particle size of minerals on the surface of discontinuity.

Shear Behavior of Rough Rock Joints Reinforced by Bolts

Shear Behavior of Rough Rock Joints Reinforced by Bolts

Evaluation Models for the Peak Shear-Strength and Shear-Resistance Components of Rough Rock Joints

Abstract This study aims to present a new model for evaluating the peak shear strength of rock joints and investigate the contribution from different shear components to the total shear resistance. Direct shear tests under constant normal load (CNL) conditions were performed on artificial rock joints with different morphology. Before the shear test, a 3D optical scanner was used to measure the joint morphology, and then two statistical parameters were suggested to characterize the joint roughness. For establishing an evaluation model of peak shear strength of rock joints, a model of peak dilatancy angle was first developed and then incorporated into the Maksimovic criterion. A new peak shear strength model for rock joints was thus established, and a good evaluating precision of the new criterion was found by comparing predictive results with experimental results. Three shear strength components, i.e., basic friction, dilation, and shear-off of asperities were investigated. Results show that the basic friction represents over 50 % of the total shear resistance, and this proportion grows steadily by increasing the normal stress. As the normal stress increases, the percentage of shear-off rises gradually before approaching a stable level, whereas dilation consistently decreases. At a certain normal stress level, the basic friction of joints with a lower roughness makes up more of the contribution to the total shear strength, whereas the shear-off component tends to be greater on rougher rock joints. However, the dilation of joints with different roughness does not show an obvious difference in terms of proportion. The apparent cohesion of sheared rock joints increases as the normal stress increases. The rock joint with a rougher surface has a larger apparent cohesion at a certain normal stress level.

A PREDICTIVE MODEL OF PERMEABILITY FOR FRACTAL-BASED ROUGH ROCK FRACTURES DURING SHEAR

This study investigates the roles of fracture roughness, normal stress and shear displacement on the fluid flow characteristics through three-dimensional (3D) self-affine fractal rock fractures, whose surfaces are generated using the modified successive random additions (SRA) algorithm. A series of numerical shear-flow tests under different normal stresses were conducted on rough rock fractures to calculate the evolutions of fracture aperture and permeability. The results show that the rough surfaces of fractal-based fractures can be described using the scaling parameter Hurst exponent [Formula: see text], in which [Formula: see text], where [Formula: see text] is the fractal dimension of 3D single fractures. The joint roughness coefficient (JRC) distribution of fracture profiles follows a Gauss function with a negative linear relationship between [Formula: see text] and average JRC. The frequency curves of aperture distributions change from sharp to flat with increasing shear displacement, indicating a more anisotropic and heterogeneous flow pattern. Both the mean aperture and permeability of fracture increase with the increment of surface roughness and decrement of normal stress. At the beginning of shear, the permeability increases remarkably and then gradually becomes steady. A predictive model of permeability using the mean mechanical aperture is proposed and the validity is verified by comparisons with the experimental results reported in literature. The proposed model provides a simple method to approximate permeability of fractal-based rough rock fractures during shear using fracture aperture distribution that can be easily obtained from digitized fracture surface information.

Experimental research on the convection heat transfer characteristics of distilled water in manmade smooth and rough rock fractures

Convection heat transfer characteristics in a single rock fracture was experimentally investigated in this work. Distilled water was used as working medium for heat transfer in manmade smooth and rough fractures of sandstone and granite samples. The influence of fracture surface roughness on heat transfer intensity was analyzed. During seepage heat transfer process, evolution of samples external surface temperatures was monitored using six resistance temperature detectors to study the local heat transfer characteristics along the flow direction. Subsequently, heat transfer correlations were proposed on the basis of the experimental results. The results indicate that the roughness of rock fracture surface improves the overall heat transfer intensity to a certain extent, whereas lithology has little influence on the heat transfer intensity. For smooth fractures, the local heat transfer intensity decreases with the increase of the distance from the inlet. For rough fractures, evolution of sample external temperatures along the flow direction exhibits strong nonlinear characteristics with multiple peaks. Nu/Pr1/3 is close to a power function of Re under the experimental conditions in this work. With the increase of experimental temperature, the relationship gradually tends to be linear.

Flow resistance and hydraulic geometry in contrasting reaches of a bedrock channel

AbstractAssumptions about flow resistance in bedrock channels have to be made for mechanistic modeling of river incision, paleoflood estimation, flood routing, and river engineering. Field data on bedrock flow resistance are very limited and calculations generally use standard alluvial‐river assumptions such as a fixed value of Manning's n. To help inform future work, we measured how depth, velocity, and flow resistance vary with discharge in four short reaches of a small bedrock channel, one with an entirely rock bed and the others with 20–70% sediment cover, and in the alluvial channel immediately upstream. As discharge and submergence increase in each of the partly or fully alluvial reaches there is a rapid increase in velocity and a strong decline in both n and the Darcy‐Weisbach friction factor f. The bare‐rock reach follows a similar trend from low to medium discharge but has increasing resistance at higher discharges because of the macroroughness of its rock walls. Flow resistance at a given discharge differs considerably between reaches and is highest where the partial sediment cover is coarsest and most extensive. Apart from the effect of rough rock walls, the flow resistance trends are qualitatively consistent with logarithmic and variable‐power equations and with nondimensional hydraulic geometry, but quantitative agreement using sediment D84 as the roughness height is imperfect.

Distributed snow and rock temperature modelling in steep rock walls using Alpine3D

Abstract. In this study we modelled the influence of the spatially and temporally heterogeneous snow cover on the surface energy balance and thus on rock temperatures in two rugged, steep rock walls on the Gemsstock ridge in the central Swiss Alps. The heterogeneous snow depth distribution in the rock walls was introduced to the distributed, process-based energy balance model Alpine3D with a precipitation scaling method based on snow depth data measured by terrestrial laser scanning. The influence of the snow cover on rock temperatures was investigated by comparing a snow-covered model scenario (precipitation input provided by precipitation scaling) with a snow-free (zero precipitation input) one. Model uncertainties are discussed and evaluated at both the point and spatial scales against 22 near-surface rock temperature measurements and high-resolution snow depth data from winter terrestrial laser scans.In the rough rock walls, the heterogeneously distributed snow cover was moderately well reproduced by Alpine3D with mean absolute errors ranging between 0.31 and 0.81 m. However, snow cover duration was reproduced well and, consequently, near-surface rock temperatures were modelled convincingly. Uncertainties in rock temperature modelling were found to be around 1.6 °C. Errors in snow cover modelling and hence in rock temperature simulations are explained by inadequate snow settlement due to linear precipitation scaling, missing lateral heat fluxes in the rock, and by errors caused by interpolation of shortwave radiation, wind and air temperature into the rock walls.Mean annual near-surface rock temperature increases were both measured and modelled in the steep rock walls as a consequence of a thick, long-lasting snow cover. Rock temperatures were 1.3–2.5 °C higher in the shaded and sunny rock walls, while comparing snow-covered to snow-free simulations. This helps to assess the potential error made in ground temperature modelling when neglecting snow in steep bedrock.

Quantitative Estimates of Normalized Transmissivity and the Onset of Nonlinear Fluid Flow Through Rough Rock Fractures

Quantitative Estimates of Normalized Transmissivity and the Onset of Nonlinear Fluid Flow Through Rough Rock Fractures

Rock fracture grouting with microbially induced carbonate precipitation

AbstractMicrobially induced carbonate precipitation has been proposed for soil stabilization, soil strengthening, and permeability reduction as an alternative to traditional cement and chemical grouts. In this paper, we evaluate the grouting of fine aperture rock fractures with calcium carbonate, precipitated through urea hydrolysis, by the bacteria Sporosarcina pasteurii. Calcium carbonate was precipitated within a small‐scale and a near field‐scale (3.1 m2) artificial fracture consisting of a rough rock lower surfaces and clear polycarbonate upper surfaces. The spatial distribution of the calcium carbonate precipitation was imaged using time‐lapse photography and the influence on flow pathways revealed from tracer transport imaging. In the large‐scale experiment, hydraulic aperture was reduced from 276 to 22 μm, corresponding to a transmissivity reduction of 1.71 × 10−5 to 8.75 × 10−9 m2/s, over a period of 12 days under constantly flowing conditions. With a modified injection strategy a similar three orders of magnitude reduction in transmissivity was achieved over a period of 3 days. Calcium carbonate precipitated over the entire artificial fracture with strong adhesion to both upper and lower surfaces and precipitation was controlled to prevent clogging of the injection well by manipulating the injection fluid velocity. These experiments demonstrate that microbially induced carbonate precipitation can successfully be used to grout a fracture under constantly flowing conditions and may be a viable alternative to cement based grouts when a high level of hydraulic sealing is required and chemical grouts when a more durable grout is required.

Experimental Study on Relationship Between Mechanical, Seepage Characteristics and 3D Morphology Parameters of Marble Joint

In order to investigate the influence of 3D morphology parameters of marble joint surface on its mechanical and seepage characteristics, artificial joints of coarse-grained marbles were scanned by Tianyuan OKIO-typed 3D laser scanner; and then, the professional software was used to obtain the 3D morphology parameters of marble joint surface. Tests of water flowing through a single joint were conducted under different normal stress and feeding water head by using self-developed radial flowing system, and the exponential function between flow rate per head and normal stress, the linear relation between equivalent hydraulic aperture and mechanical aperture, and the linear relation between joint closure and normal stress were obtained. The relationships between regression parameters in above three formulas and 3D morphology parameters of joint surface were also studied by fitting method. All in all, the results may provide a reference to understand the mechanical and seepage characteristics of rough rock joint.

Hybrid finite-discrete element modelling of asperity degradation and gouge grinding during direct shearing of rough rock joints

A hybrid finite-discrete element method was implemented to study the fracture process of rough rock joints under direct shearing. The hybrid method reproduced the joint shear resistance evolution process from asperity sliding to degradation and from gouge formation to grinding. It is found that, in the direct shear test of rough rock joints under constant normal displacement loading conditions, higher shearing rate promotes the asperity degradation but constraints the volume dilation, which then results in higher peak shear resistance, more gouge formation and grinding, and smoother new joint surfaces. Moreover, it is found that the joint roughness affects the joint shear resistance evolution through influencing the joint fracture micro mechanism. The asperity degradation and gouge grinding are the main failure micro-mechanism in shearing rougher rock joints with deeper asperities while the asperity sliding is the main failure micro-mechanism in shearing smoother rock joints with shallower asperities. It is concluded that the hybrid finite-discrete element method is a valuable numerical tool better than traditional finite element method and discrete element method for modelling the joint sliding, asperity degradation, gouge formation, and gouge grinding occurred in the direct shear tests of rough rock joints.

Normal Deformation and Formation of Contacts in Rough Rock Fractures and Their Influence on Fluid Flow

AbstractRock fracture flow was initially modeled according to the parallel plate model, which does not consider the undulating nature of fracture surfaces. The conventional parallel plate model or cubic formula was later modified to obtain precise predictions by considering the joint roughness coefficient (JRC) of the fracture walls. However, the real flow characteristics through a relatively long rough rock joint can still be modeled accurately via a two-dimensional analysis, which enables the spatial irregularity of rock fracture apertures to be considered with the fracture contacts, which act as obstacles to the flow. In this study, a new two-dimensional flow model for deformable fracture walls to predict the volumetric flow changes that result from effective normal stress fluctuations is proposed. This model was solved using the finite-volume method via a new program developed by the authors. It captures the existing contacts and newly formed contacts that occur while fracture aperture deformations ta...

Rate-dependent mechanical behavior of rough rock joints

The influence of shear rate on the mechanical behavior of rough rock joints prepared using a molding method was examined by testing jointed samples of four rock joint groups, which were obtained from the underground caverns of the Huangdao State Oil Reserves in China. The tests were performed using a JAW-600 coupled shear-flow machine under constant normal load (CNL) conditions. Shear rate and joint roughness coefficient (JRC) were the two primary considerations in this study. The results indicate that the peak shear strength is controlled by shear rate and joint roughness. Shear rate has a nonlinear relationship with the peak shear strength, whereas joint roughness exhibits good linearity with a high correlation coefficient (>0.97, except for results under a shear rate of 24.0mm/min). Furthermore, shear rate affects the damage incurred by the rock joints, as illustrated by the acoustic emission of rock joints monitored by a PAC acoustic emission system. The joint surface breaks earlier with increased shear rate. Furthermore, because of the more rapid generation of macrocracks under higher shear rate, the corresponding cumulative acoustic emission (AE) count and AE energy are inversely proportional to the shear rate. A new shear strength criterion that considers both shear rate and joint roughness was developed based on the experimental results and Barton’s shear strength criterion. Then, the validity of this proposed criterion was verified with an average estimated error of 10.539% using the shear strength values of rock joints proposed by Barton, indicating that the new criterion is capable of providing an accurate estimate of shear strength for rough rock joints under different shear rates.

Rock Fracture Centerline Extraction based on Hessian Matrix and Steger Algorithm

The rock fracture detection by image analysis is significant for fracture measurement and assessment engineering. The paper proposes a novel image segmentation algorithm for the centerline tracing of a rock fracture based on Hessian Matrix at Multi-scales and Steger algorithm. A traditional fracture detection method, which does edge detection first, then makes image binarization, and finally performs noise removal and fracture gap linking, is difficult for images of rough rock surfaces. To overcome the problem, the new algorithm extracts the centerlines directly from a gray level image. It includes three steps: (1) Hessian Matrix and Frangi filter are adopted to enhance the curvilinear structures, then after image binarization, the spurious-fractures and noise are removed by synthesizing the area, circularity and rectangularity; (2) On the binary image, Steger algorithm is used to detect fracture centerline points, then the centerline points or segments are linked according to the gap distance and the angle differences; and (3) Based on the above centerline detection roughly, the centerline points are searched in the original image in a local window along the direction perpendicular to the normal of the centerline, then these points are linked. A number of rock fracture images have been tested, and the testing results show that compared to other traditional algorithms, the proposed algorithm can extract rock fracture centerlines accurately.

Influence of scale and matedness on the peak shear strength of fresh, unweathered rock joints

It is widely recognized that the mechanical parameters for unfilled and rough rock joints, such as the peak shear strength, can vary with scale. However, due to contradictory results concerning the extent and nature of the scale effect reported in the literature, it is still a debated subject. A conceptual model developed by Johansson and Stille 2014 suggests how roughness and matedness at different scales influences the peak shear strength for fresh, rough and unweathered joint. However, the model's ability to predict how the roughness and matedness affects the peak shear strength at different scales was not verified. The aim of this paper is to investigate the ability of the conceptual model to estimate the peak shear strength at different degrees of matedness and scales. A series of direct shear test were carried out at two different scales and two different degrees of matedness. The peak shear strength from the tests was compared to the peak shear strength calculated with the conceptual model. The results showed that the model can predict the peak shear strength for both the perfectly mated and the unmated joints. No scale effect was observed in the shear tests, which is in line with the predictions using the model. The influence of matedness in combination with scale might explain some of the contradictory findings regarding the scale effect.

Snow as a driving factor of rock surface temperatures in steep rough rock walls

Observations show that considerable amounts of snow can accumulate in steep, rough rock walls. The heterogeneously distributed snow cover significantly affects the surface energy balance and hence the thermal regime of the rock walls.To assess the small-scale variability of snow depth and rock temperatures in steep north and south facing rock walls, a spatially distributed multi-method approach is applied at Gemsstock, Switzerland, combining 35 continuous near-surface rock temperature measurements, high resolution snow depth observations using terrestrial laser scanning, as well as in-situ snow pit investigations.The thermal regime of the rock surface is highly dependent on short- and longwave radiation, albedo, surface roughness, snow depth and on snow distribution in time and space. Around 2m of snow can accumulate on slopes with angles up to 75°, due to micro-topographic structures like ledges. Hence, contrasts in mean annual rock surface temperature between the north and the south facing slopes are less than 4°C. However, significant small-scale variability of up to 10°C in mean daily rock surface temperature occurs within a few metres over the rock walls due to the variable snow distribution, revealing the heterogeneity and complexity of the thermal regime at a very local scale. In addition, multiple linear regression could explain up to 77% of near‐surface rock temperature variability, which underlines the importance of radiation and snow depth and thus also of the topography.In the rock faces the thermal insulation of the ground starts with snow depths exceeding 0.2m. This is due to the high thermal resistance of a less densely packed snow cover, especially in the north facing slope. Additionally, aspect induced differences of snow cover characteristics and consequently thermal conductivities are observed in the rock walls.

A modified shrinking core model for the reaction between acid and hetero-granular rough mineral particles

The liquid–solid heterogeneous non-catalytic reaction between acid and minerals is the foremost principle of matrix acidizing. Previous mathematical models failed to describe the acid etching issue of rock particle clusters with the property of fractal surface in a three-dimensional space. We apply fractal geometry principles to characterize the area and volume of the rough rock particles on the basis of a mathematical model of a single particle. Based on chemical reaction kinetics and mass transfer theory, we present a modified shrinking core model for the acid–rock reaction of a mineral particle cluster that is undergoing a surface reaction. Using logarithmic normal distribution functions to describe the grain distribution of rocks, we describe the variations of the extent of leaching under surface reaction control. Our analysis indicates that clusters with larger fractal dimensions, smaller mean sizes and less disperse particles will be less dissolved when most of the other factors are kept constant.