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.

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.

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.

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.

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.

Measurement of Joint Roughness Coefficient by Using Profilograph and Roughness Ruler

Joint roughness coefficient（JRC） is the key parameter for the empirical estimation of joint shear strength by using the JRC-JCS（joint wall compressive strength） model.Because JRC has such characteristics as nonuniformity,anisotropy,and unhomogeneity,directional statistical measurement of JRC is the precondition for ensuring the reliability of the empirical estimation method.However,the directional statistical measurement of JRC is time-consuming.In order to present an ideal measurement method of JRC,new profilographs and roughness rulers were developed according to the properties of rock joint undulating shape based on the review of measurement methods of JRC.Operation methods of the profilographs and roughness rulers were also introduced.A case study shows that the instruments and operation methods produce an effective means for the statistical measurement of JRC.

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.

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.

Determination of the Drag Coefficient over the Tibetan Plateau

In this paper,a preliminary study is given on the drag (i.e.bulk transfer for momentum) coefficient,on the basis of data from four sets of AWS in Tibet during the first observational year from July 1993 to July 1994 according to China Japan Asian Monsoon Cooperative Research Program.The results show that the drag coefficient over the Tibetan Plateau is 3.3 to 4.4×103.In addition,monthly and diurnal variations of drag coefficient and the relationship among the drag coefficients and the bulk Richardson number,surface roughness length and wind speed at 10 m height are discussed in detail.

Developments and Applications of Neutrosophic Theory in Civil Engineering Fields:A Review

Neutrosophic theory can effectively and reasonably express indeterminate,inconsistent,and incomplete information.Since Smarandache proposed the neutrosophic theory in 1998,neutrosophic theory and related research have been developed and applied to many important fields.Indeterminacy and fuzziness are one of the main research issues in the field of civil engineering.Therefore,the neutrosophic theory is very suitable for modeling and applications of civil engineering fields.This review paper mainly describes the recent developments and applications of neutrosophic theory in four important research areas of civil engineering:the neutrosophic decision-making theory and applied methods,the neutrosophic evaluation methods and applications of slope stability,the neutrosophic expressions and analyses of rock joint roughness coefficient,and the neutrosophic structural optimization methods and applications.In terms of these research achievements in the four areas of civil engineering,the neutrosophic theory demonstrates its advantages in dealing with the indeterminate and inconsistent issues in civil engineering and the effectiveness and practicability of existing applied methods.In the future work,the existing research results will be further improved and extended in civil engineering problems.In addition,the neutrosophic theory will also have better application prospects in other fields of civil engineering.

Study on the Characteristics of the Gas Switch Electrode Erosion

Gas spark switch is one of the key parts in pulsed power technology.Electrode erosion has great influence on the switch performance and lifetime.In this paper,a field distortion gas switch is selected for the experiment and a great deal of discharging experiments have been conducted in different test conditions.The forming process of etch pit as well as its influencing factors is discussed briefly and surface roughness coefficient(SRC) of the electrode is put forward to evaluate the state of electrode erosion.Experimental results show that current peak plays an important role in electrode erosion when waveforms of discharge current are the same,and electric charge and oscillation frequency of discharge current also have great effect on the electrode erosion when waveforms of discharge current are different.With the increase of discharge times,SRC decreases slowly at first and then decreases quickly after three thousand of discharge times.

Numerical modeling of flow in continuous bends from Daliushu to Shapotou in Yellow River

The upper reach of the Yellow River from Daliushu to Shapotou consists of five bends and has complex topography. A two-dimensional Re-Normalisation Group （RNG） k-ε model was developed to simulate the flow in the reach. In order to take the circulation currents in the bends into account, the momentum equations were improved by adding an additional source term. Comparison of the numerical simulation with field measurements indicates that the improved two-dimensional depth-averaged RNG k-e model can improve the accuracy of the numerical simulation. A rapid adaptive algorithm was constructed, which can automatically adjust Manning＇s roughness coefficient in different parts of the study river reach. As a result, not only can the trial computation time be significantly shortened, but the accuracy of the numerical simulation can also be greatly improved. Comparison of the simulated and measured water surface slopes for four typical cases shows that the longitudinal and transverse slopes of the water surface increase with the average velocity upstream. In addition, comparison was made between the positions of the talweg and the main streamline, which coincide for most of the study river reach. However, deviations between the positions of the talweg and the main streamline were found at the junction of two bends, at the position where the river width suddenly decreases or increases.

Macro and meso characteristics evolution on shear behavior of rock joints

Direct shear tests were conducted on the rock joints under constant normal load(CNL), while the acoustic emission(AE) signals generated during shear tests were monitored with PAC Micro-II system. Before and after shearing, the surfaces of rock joints were measured by the Talysurf CLI 2000. By correlating the AE events with the shear stress-shear displacement curve, one can observe four periods of the whole course of shearing of rock joints. By the contrast of AE location and actual damage zone, it is elucidated that the AE event is related to the morphology of the joint. With the increase of shearing times, the shear behavior of rock joints gradually presents from the response of brittle behavior to that of ductile behavior. By combining the results of topography measurement, four morphological parameters of joint surface, S p(the maximum height of joint surface), N(number of islands), A(projection area) and V(volume of joint) were introduced, which decrease with shearing. Both the joint roughness coefficient(JRC) and joint matching coefficient(JMC) drop with shearing, and the shear strength of rock joints can be predicted by the JRC-JMC model. It establishes the relationship between micro-topography and macroscopic strength, which have the same change rule with shearing.

Study on the cutting plane friction law of sandstone

The friction characteristics of rock damage plane have important impact on the stability of block structure formed after the stratum is broken. The mechanics properties of rock damage plane are described by parameters such as roughness coefficient, wall compress strength and basic friction angle. These three coefficients for fine grain sandstone and medium granular sandstone and grit sandstone are test. The friction stress is researched at the condition of different normal compressive stress acting on the tension damage plane. The friction law of tension damage plane of sandstone abided by is summed up. This law will provide scientific basis for block structure stability judging in basic roof stratum and roof pressure intensity calculating.

Morphology characteristics of joint surface in rock mass

In order to quantify the characteristics of the surface of jointed rock mass,new equipment,the three-dimensional laser surface topography instrument,was used to accurately measure surface morphology of joints.Scan pictures and parameters were obtained to describe the rock joint surface characteristics,for example,the height frequency of surface,and mean square roughness.Using the method of fractal dimension,the values of joint roughness coefficient(JRC) were calculated based on the above parameters.It could access to the joint surface rock sample morphology of the main parameters of characteristic.The maximum peak height is 2.692 mm in the test joint plane.The maximum profile height is 4.408 mm.JRC value is 6.38 by fractal dimension computing.It belongs to the smooth joint surface.The results show that it is a kind of the effective method to quantitatively evaluate the surface topography by the three-dimensional laser surface topography instrument and the fractal dimension method.According to the results,during the process of underground large-scale mining,safe measures to prevent slip failure of the joint plane by controlling surface tension and shear mechanical response were proposed.

OPTIMAL CONTROL FOR MULTISCALE ELLIPTIC EQUATIONS WITH ROUGH COEFFICIENTS

This paper concerns the convex optimal control problem governed by multiscale elliptic equations with arbitrarily rough L∞coefficients,which has not only complex coupling between nonseparable scales and nonlinearity,but also important applications in composite materials and geophysics.We use one of the recently developed numerical homogenization techniques,the so-called Rough Polyharmonic Splines(RPS)and its generalization(GRPS)for the efficient resolution of the elliptic operator on the coarse scale.Those methods have optimal convergence rate which do not rely on the regularity of the coefficients nor the concepts of scale-separation or periodicity.As the iterative solution of the nonlinearly coupled OCP-OPT formulation for the optimal control problem requires solving the corresponding(state and co-state)multiscale elliptic equations many times with different right hand sides,numerical homogenization approach only requires one-time pre-computation on the fine scale and the following iterations can be done with computational cost proportional to coarse degrees of freedom.Numerical experiments are presented to validate the theoretical analysis.

Probabilistic prediction on three-dimensional roughness of discontinuity based on two-dimensional traces under rock tunnel excavation based on Bayesian theory

Three-dimensional(3D)roughness of discontinuity affects the quality of the rock mass,but 3D roughness is hard to be measured due to that the discontinuity is invisible in the engineering.Two-dimensional(2D)roughness can be calculated from the visible traces,but it is difficult to obtain enough quantity of the traces to directly derive 3D roughness during the tunnel excavation.In this study,a new method using Bayesian theory is proposed to derive 3D roughness from the low quantity of 2D roughness samples.For more accurately calculating 3D roughness,a new regression formula of 2D roughness is established firstly based on wavelet analysis.The new JRC3D prediction model based on Bayesian theory is then developed,and Markov chain Monte Carlo(MCMC)sampling is adopted to process JRC3D prediction model.The discontinuity sample collected from the literature is used to verify the proposed method.Twenty groups with the sampling size of 2,3,4,and 5 of each group are randomly sampled from JRC2D values of 170 profiles of the discontinuity,respectively.The research results indicate that 100%,90%,85%,and 60%predicting JRC3D of the sample groups corresponding to the sampling size of 5,4,3,and 2 fall into the tolerance interval[JRC_(true)–1,JRC_(true)+1].It is validated that the sampling size of 5 is enough for predicting JRC3D.The sensitivities of sampling results are then analyzed on the influencing factors,which are the correlation function,the prior distribution,and the prior information.The discontinuity across the excavation face at ZK78+67.5 of Daxiagu tunnel is taken as the tunnel engineering application,and the results further verify that the predicting JRC3D with the sampling size of 5 is generally in good agreement with JRC3D true values.

CHARACTERISTICS OF FLOW RESISTANCE IN OPEN CHANNELS WITH NON-SUBMERGED RIGID VEGETATION

The flow resistance factors of non-submerged rigid vegetation in open channels were analyzed. The formulas of drag coefficient CD and equivalent Manning＇s roughness coefficient na were derived by analyzing the force of the flow of non-submerged rigid vegetation in open channel. The flow characteristics and mechanism of non-submerged rigid vegetation in open channel were studied through flume experiments.