Advances in joint roughness coefficient (JRC) and its engineering applications

The joint roughness coefficient (JRC), introduced in Barton (1973) represented a new method in rock mechanics and rock engineering to deal with problems related to joint roughness and shear strength estimation. It has the advantages of its simple form, easy estimation, and explicit consideration of scale effects, which make it the most widely accepted parameter for roughness quantification since it was proposed. As a result, JRC has attracted the attention of many scholars who have developed JRC-related methods in many areas, such as geological engineering, multidisciplinary geosciences, mining mineral processing, civil engineering, environmental engineering, and water resources. Because of such a developing trend, an overview of JRC is presented here to provide a clear perspective on the concepts, methods, applications, and trends related to its extensions. This review mainly introduces the origin and connotation of JRC, JRC-related roughness measurement, JRC estimation methods, JRC-based roughness characteristics investigation, JRC-based rock joint property description, JRC's influence on rock mass properties, and JRC-based rock engineering applications. Moreover, the representativeness of the joint samples and the determination of the sampling interval for rock joint roughness measurements are discussed. In the future, the existing JRC-related methods will likely be further improved and extended in rock engineering.

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,Rp,and SDi)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),iave,SD_(i),Z_(2),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.

Investigation on the Indeterminate Information of Rock Joint Roughness through a Neutrosophic Number Approach

To better estimate the rock joint shear strength,accurately determining the rock joint roughness coefficient(JRC)is the first step faced by researchers and engineers.However,there are incomplete,imprecise,and indeterminate problems during the process of calculating the JRC.This paper proposed to investigate the indeterminate information of rock joint roughness through a neutrosophic number approach and,based on this information,reported a method to capture the incomplete,uncertain,and imprecise information of the JRC in uncertain environments.The uncertainties in the JRC determination were investigated by the regression correlations based on commonly used statistical parameters,which demonstrated the drawbacks of traditional JRC regression correlations in handling the indeterminate information of the JRC.Moreover,the commonly used statistical parameters cannot reflect the roughness contribution differences of the asperities with various scales,which induces additional indeterminate information.A method based on the neutrosophic number(NN)and spectral analysis was proposed to capture the indeterminate information of the JRC.The proposed method was then applied to determine the JRC values for sandstone joint samples collected from a rock landslide.The comparison between the JRC results obtained by the proposed method and experimental results validated the effectiveness of the NN.Additionally,comparisons made between the spectral analysis and common statistical parameters based on the NN also demonstrated the advantage of spectral analysis.Thus,the NN and spectral analysis combined can effectively handle the indeterminate information in the rock joint roughness.

Effect of roughness on the shear behavior of rock joints subjected to impact loading

The shear behavior is regarded as the dominant property of rock joints and is dramatically affected by the joint surface roughness.To date,the effect of surface roughness on the shear behavior of rock joints under static or cyclic loading conditions has been extensively studied,but such effect under impact loading conditions keeps unclear.To address this issue,a series of impact shear tests was performed using a novel-designed dynamic experimental system combined with the digital image correlation(DIC)technique.The dynamic shear strength,deformability and failure mode of the jointed specimens with various joint roughness coefficients(JRC)are comprehensively analyzed.Results show that the shear strength and shear displacement characteristics of the rock joint under the impact loading keep consistent with those under static loading conditions.However,the temporal variations of shear stress,slip displacement and normal displacement under the impact loading conditions show obviously different behaviors.An elastic rebound of the slip displacement occurs during the impact shearing and its value increases with increasing joint roughness.Two identifiable stages(i.e.compression and dilation)are observed in the normal displacement curves for the rougher rock joints,whereas the joints with small roughness only manifest normal compression displacement.Besides,as the roughness increases,the maximum compression tends to decrease,while the maximum dilation gradually increases.More-over,the microstructural analysis based on scanning electron microscope(SEM)suggests that the roughness significantly affects the characteristics of the shear fractured zone enclosing the joint surface.

Anisotropic surface roughness and shear behaviors of rough-walled plaster joints under constant normal load and constant normal stiffness conditions

In this context,we experimentally studied the anisotropic mechanical behaviors of rough-walled plaster joints using a servo-controlled direct shear apparatus under both constant normal load(CNL)and constant normal stiffness(CNS)conditions.The shear-induced variations in the normal displacement,shear stress,normal stress and sheared-off asperity mass are analyzed and correlated with the inclination angle of the critical waviness of joint surfaces.The results show that CNS condition gives rise to a smaller normal displacement due to the larger normal stress during shearing,compared with CNL condition.Under CNL conditions,there is one peak shear stress during shearing,whereas there are no peak shear stress for some cases and two peaks for other cases under CNS conditions depending on the geometry of joint surfaces.The inclination angle of the critical waviness has been verified to be capable of describing the joint surface roughness and anisotropy.The joint surface is more significantly damaged under CNS conditions than that under CNL conditions.With increment of the inclination angle of the critical waviness,both the normal displaceme nt and shea red-off asperity mass increase,following power law functions;yet the coefficient of deternination under CNL conditions is larger than that under CNS conditions.This is because the CNS condition significantly decreases the inclination angle of the critical waviness during shearing due to the larger degree of asperity degradation.

Relationship between soil surface roughness and hydraulic roughness coefficient on sloping farmland

The soil surface roughness and hydraulic roughness coefficient are important hydraulic resistance characteristic parameters. Precisely estimating the hydraulic roughness coefficient is important to understanding mechanisms of overland flow. Four tillage practices, including cropland raking, artificial hoeing, artificial digging, and straight slopes, were considered based on the local agricultural conditions to simulate different values of soil surface roughness in the Loess Plateau. The objective of this study was to investigate the relationship between the soil surface roughness and hydraulic roughness coefficient on sloping farmland using artificial rainfall simulation. On a slope with a gradient of 10°, a significant logarithmic function was developed between the soil surface roughness and Manning＇s roughness coefficient, and an exponential function was derived to describe the relationship between the soil surface roughness and Reynolds number. On the slope with a gradient of 15°, a significant power function was developed to reflect the relationship between the soil surface roughness and Manning＇s roughness coefficient, and a linear function was derived to relate the soil surface roughness to the Reynolds number. These findings can provide alternative ways to estimate the hydraulic roughness coefficient for different types of soil surface roughness.

A roughness parameter considering joint material properties and peak shear strength model for rock joints

This study aims at proposing a reasonable roughness parameter that can reflect the peak shear strength(PSS)of rock joints.Firstly,the contribution of the asperities with different apparent dip angles to shear strength is studied.Then the shear strength of the entire joint asperities is derived.The results showed that the PSS of the entire joint asperities is proportional to a key parameter hs,which is related to the geometric character of the joint surface and the joint material properties.The parameter hsis taken as the new roughness parameter,and it is reasonable to associate the PSS with the geometric characteristics of the joint surface.Based on the new roughness parameter and shear test results of 20 sets of joint specimens,a new PSS model for rock joints is proposed.The new model is validated with the artificial joints in this paper and real rock joints in published studies.Results showed that it is suitable for different types of rock joints except for gneiss joints.The new model has the form of the Mohr-Coulomb model,which can directly reflect the relationship between the 3 D roughness parameters and the peak dilation angle.

Roughness coefficient and its uncertainty in gravel-bed river

Manning＇s roughness coefficient was estimated for a gravel-bed river reach using field measurements of water level and discharge, and the applicability of various methods used for estimation of the roughness coefficient was evaluated. Results show that the roughness coefficient tends to decrease with increasing discharge and water depth, and over a certain range it appears to remain constant. Comparison of roughness coefficients calculated by field measurement data with those estimated by other methods shows that, although the field-measured values provide approximate roughness coefficients for relatively large discharge, there seems to be rather high uncertainty due to the difference in resultant values. For this reason, uncertainty related to the roughness coefficient was analyzed in terms of change in computed variables. On average, a 20% increase of the roughness coefficient causes a 7% increase in the water depth and an 8% decrease in velocity, but there may be about a 15% increase in the water depth and an equivalent decrease in velocity for certain cross-sections in the study reach. Finally, the validity of estimated roughness coefficient based on field measurements was examined. A 10% error in discharge measurement may lead to more than 10% uncertainty in roughness coefficient estimation, but corresponding uncertainty in computed water depth and velocity is reduced to approximately 5%. Conversely, the necessity for roughness coefficient estimation by field measurement is confirmed.

Determination of Water Diffusion Coefficients and Dynamics in Adhesive/Carbon Fiber Reinforced Epoxy Resin Composite Joints

To determinate the water diffusion coefficients and dynamics in adhesive/carben fiber reinforced epoxy resin composite joints, energy dispersive X-ray spectroscopy analysis（EDX） is used to establish the content change of oxy- gen in the adhesive in adhesive/carbon fther reinforced epoxy resin composite joints. As water is made up of oxygen and hydrogen, the water diffusion coefficients and dynamics in adhesive/carben fiber reinforced epoxy resin composite joints can be obtained from the change in the content of oxygen in the adhesive during humidity aging, via EDX analy-sis. The authors have calculated the water diffusion coefficients and dynamics in the adhesive/carbon fiber reinforced epoxy resin composite joints with the aid of beth energy dispersive X-ray spectroscopy and elemental analysis. The de- termined results with EDX analysis are almost the same as those determined with elemental analysis and the results al- so show that the durability of the adhesive/carbon fther reinforced epoxy resin composite joints subjected to silane cou- pling agent treatment is better than those subjected to sand paper burnishing treatment and chemical oxidation treat- ment.

Hydraulic model with roughness coefficient updating method based on Kalman filter for channel flood forecast

A real-time channel flood forecast model was developed to simulate channel flow in plain rivers based on the dynamic wave theory. Taking into consideration channel shape differences along the channel, a roughness updating technique was developed using the Kalman filter method to update Manning＇s roughness coefficient at each time step of the calculation processes. Channel shapes were simplified as rectangles, triangles, and parabolas, and the relationships between hydraulic radius and water depth were developed for plain rivers. Based on the relationship between the Froude number and the inertia terms of the momentum equation in the Saint-Venant equations, the relationship between Manning＇s roughness coefficient and water depth was obtained. Using the channel of the Huaihe River from Wangjiaba to Lutaizi stations as a case, to test the performance and rationality of the present flood routing model, the original hydraulic model was compared with the developed model. Results show that the stage hydrographs calculated by the developed flood routing model with the updated Manning＇s roughness coefficient have a good agreement with the observed stage hydrographs. This model performs better than the original hydraulic model.

Rock joint coefficients and their computerized classification

A computerized method for determining rock joint coefficients is presented.Two relative similarity indicators are introduced to classify surface morphology of rock joints.The classification enables to compare investigated and database rock joints.Such a comparison aims at finding the couple of surfaces that are distinguished by the highest dynamical conformity.The first absolute indicator results from the Fourier matrix and evaluates wavy shapes of surfaces.The second absolute indicator quantifies the heights of surface reliefs and is defined as the root mean square height of the surface outline.Numerical reliability of these indicators is tested within the surface analysis of a series of limestone specimens.Besides the computerized assessment,25 people have performed visual assessment of these limestone specimens.The results of visual assessments have been statistically processed and compared to the results received from the computerized procedure.The newly introduced absolute indicators have proved to be prospective numerical tools for evaluating joint rock coefficients.

New criterion for rock joints based on three-dimensional roughness parameters

The shear behavior of rock joints is important in solving practical problems of rock mechanics. Three group rock joints with different morphologies are made by cement mortar material and a series of CNL(constant normal loading) shear tests are performed. The influences of the applied normal stress and joint morphology to its shear strength are analyzed. According to the experimental results, the peak dilatancy angle of rock joint decreases with increasing normal stress, but increases with increasing roughness. The shear strength increases with the increasing normal stress and the roughness of rock joint. It is observed that the modes of failure of asperities are tensile, pure shear, or a combination of both. It is suggested that the three-dimensional roughness parameters and the tensile strength are the appropriate parameter for describing the shear strength criterion. A new peak shear criterion is proposed which can be used to predict peak shear strength of rock joints. All the used parameters can be easily obtained by performing tests.

Shear behaviours and roughness degeneration based on a quantified rock joint surface description

The asperity wear of rock joints significantly affects their shear behaviour.This study discusses the wear damage of the asperities on the joint surface,highlighting the roughness degradation characteristics during the shear process.The direct shear experiment of artificial specimens containing rock joints was conducted under different normal stresses based on three-dimensional scanning technology.These experimental results showed the contribution of joint wear to roughness degeneration,such as the height,zone,and volume of asperity degeneration.The wear coefficient of the rock joint was obtained based on the volume wear of asperities in the laboratory experiment.The functional relationship between the friction coefficient and wear coefficient is subsequently determined.To quantitatively analyse the wear damage of a joint surface,a calculation method for determining the wear depth of the rock joint after shearing was proposed based on wear theory.The relationship between the ultimate dilation and wear depth was analysed.A coefficient m,which can describe the damage degree of the joint surface,and a prediction method of joint surface roughness after shearing are established.Good agreement between analytical predictions and measured values demonstrates the capability of the developed model.Lastly,the sensitivity factors on the wear depth are explored.

STUDY ON FLUXES OF MOMENTUM AND SENSIBLE HEAT, THE DRAG COEFFICIENT C_D AND ROUGHNESS Z_0

In this paper, fluxes of momentum and sensible heat are discussed with the data collected by tethered balloon sounding system over the Philippine Sea during the cruise of the R/V SCIENCE 1 from September through October in 1987. These fluxes were calculated using the semiempirical flux-profile relationships of Monin-Obkhov similarity theory with observed data. The friction velocity U. was determined by the observed data's least-square fit with the similarity formulae under stable, neutral and unstable conditions. The roughness Z0 was determined by Z0 = a1 (U./g), then substituted into the similarity formulae to compute V. again. The final values of U. and Z0 could be determined through this iteration. The flux temperature θ, was calculated from the temperature profile with Z0 determined above. Finally the fluxes of momentum and sensible heat, and the drag coefficient CD, were obtained by computation with U., θ. and the wind speed (U_10) at 10 meters above the sea surface.

The role of hardness and roughness on the wear of different CoCrMo counterfaces on UHMWPE for artificial joints

Wear tests were carried out to study the effect of the hardness and roughness with various counterface materials on UHMWPE wear behaviour. The materials used as counterfaces were based on varieties of CoCrMo: 1) forged (hand-polished) CoCrMo, 2) forged (mass-finished) CoCrMo, and 3) cast (mass-finished) CoCrMo. Additionally, two coatings were proposed: 1) a CoCrMo coating applied to the forged CoCrMo alloy by means of physical vapour deposition (PVD), and 2) a ZrO2 coating applied to the forged CoCrMo alloy by means of plasma-assisted chemical vapour deposition (PACVD). The reciprocating pin-on-flat (RPOF) device for pin-on-disk wear testing was used for this study. The worn surfaces were observed using optical, atomic force and scanning electron microscopes.

Calibration of Pipe Roughness Coefficient Based on Manning Formula and Genetic Algorithm

This paper presents a method to calibrate pipe roughness coefficient (i.e., Manning n-factor) with genetic algorithm (GA) under multiple loading conditions. Due to the old pipe age as well as deleting valves and blends in the skeleton of distribution network, most of the pipes in hydraulic model of practical water distribution system (WDS) are rough. The commonly used Hazen-Williams C-factor is therefore replaced by Manning n-factor in calibrating WDS hydraulic model. Adjustment to GA is designed, and the program efficiency is improved. A case study shows that the adjustment can save 60% of the total runtime. About 90% of the relative differences between simulated and observed pressures at monitoring locations are lower than 3%, which suggests that the proposed adjustment to the calibration is efficient and effective.

Calculation of the coefficient and dynamics of water diffusion in graphite joints

The coefficient and dynamics of water diffusion in adhesive-graphite joints were calculated in-situ with energy dispersive X-ray (EDX) analysis, a method that is significantly simpler than elemental analysis. Water diffusion coefficient and dynamics of adhesive-graphite joints treated by different surface treatment methods were also investigated. Calculation results indicated that the water diffusion rate in adhesive-graphite joints treated by sandpaper was higher than that treated by chemical oxidation or by silane couple agent. Also the durability of graphite joints treated by coupling agent is superior to that treated by chemical oxidation or sandpaper burnishing.

A method of Robust low-angle target height and compound reflection coefficient joint estimation

It is always a challenging issue for radar systems to estimate the height of a low-angle target in the multipath propagation environment.The highly deterministic maximum likelihood estimator has a high accuracy,but the errors of the ground reflection coefficient and the reflecting surface height have serious influence on the method.In this paper,a robust es-timation method with less computation burden is proposed based on the compound reflection coefficient multipath model for low-angle targets.The compound reflection coefficient is es-timated from the received data of the array and then a one-di-mension generalized steering vector is constructed to estimate the target height.The algorithm is robust to the reflecting sur-face height error and the ground reflection coefficient error.Fi-nally,the experiment and simulation results demonstrate the validity of the proposed method.

Shear mechanical properties and fracturing responses of layered rough jointed rock-like materials

This study aims to investigate mechanical properties and failure mechanisms of layered rock with rough joint surfaces under direct shear loading.Cubic layered samples with dimensions of 100 mm×100 mm×100 mm were casted using rock-like materials,with anisotropic angle(α)and joint roughness coefficient(JRC)ranging from 15°to 75°and 2-20,respectively.The direct shear tests were conducted under the application of initial normal stress(σ_(n)) ranging from 1-4 MPa.The test results indicate significant differences in mechanical properties,acoustic emission(AE)responses,maximum principal strain fields,and ultimate failure modes of layered samples under different test conditions.The peak stress increases with the increasingαand achieves a maximum value atα=60°or 75°.As σ_(n) increases,the peak stress shows an increasing trend,with correlation coefficients R² ranging from 0.918 to 0.995 for the linear least squares fitting.As JRC increases from 2-4 to 18-20,the cohesion increases by 86.32%whenα=15°,while the cohesion decreases by 27.93%whenα=75°.The differences in roughness characteristics of shear failure surface induced byαresult in anisotropic post-peak AE responses,which is characterized by active AE signals whenαis small and quiet AE signals for a largeα.For a given JRC=6-8 andσ_(n)=1 MPa,asαincreases,the accumulative AE counts increase by 224.31%(αincreased from 15°to 60°),and then decrease by 14.68%(αincreased from 60°to 75°).The shear failure surface is formed along the weak interlayer whenα=15°and penetrates the layered matrix whenα=60°.Whenα=15°,as σ_(n) increases,the adjacent weak interlayer induces a change in the direction of tensile cracks propagation,resulting in a stepped pattern of cracks distribution.The increase in JRC intensifies roughness characteristics of shear failure surface for a smallα,however,it is not pronounced for a largeα.The findings will contribute to a better understanding of the mechanical responses and failure mechanisms of the layered rocks subjected to shear loads.

On the calibration of a shear stress criterion for rock joints to represent the full stress-strain profile

Conventional numerical solutions developed to describe the geomechanical behavior of rock interfaces subjected to differential load emphasize peak and residual shear strengths.The detailed analysis of preand post-peak shear stress-displacement behavior is central to various time-dependent and dynamic rock mechanic problems such as rockbursts and structural instabilities in highly stressed conditions.The complete stress-displacement surface(CSDS)model was developed to describe analytically the pre-and post-peak behavior of rock interfaces under differential loads.Original formulations of the CSDS model required extensive curve-fitting iterations which limited its practical applicability and transparent integration into engineering tools.The present work proposes modifications to the CSDS model aimed at developing a comprehensive and modern calibration protocol to describe the complete shear stressdisplacement behavior of rock interfaces under differential loads.The proposed update to the CSDS model incorporates the concept of mobilized shear strength to enhance the post-peak formulations.Barton’s concepts of joint roughness coefficient(JRC)and joint compressive strength(JCS)are incorporated to facilitate empirical estimations for peak shear stress and normal closure relations.Triaxial/uniaxial compression test and direct shear test results are used to validate the updated model and exemplify the proposed calibration method.The results illustrate that the revised model successfully predicts the post-peak and complete axial stressestrain and shear stressedisplacement curves for rock joints.