Shear behavior and off-fault damage of saw-cut smooth and tension-induced rough joints in granite

The damage of rock joints or fractures upon shear includes the surface damage occurring at the contact asperities and the damage beneath the shear surface within the host rock.The latter is commonly known as off-fault damage and has been much less investigated than the surface damage.The main contribution of this study is to compare the results of direct shear tests conducted on saw-cut planar joints and tension-induced rough granite joints under normal stresses ranging from 1 MPa to 50 MPa.The shear-induced off-fault damages are quantified and compared with the optical microscope observation.Our results clearly show that the planar joints slip stably under all the normal stresses except under 50 MPa,where some local fractures and regular stick-slip occur towards the end of the test.Both post-peak stress drop and stick-slip occur for all the rough joints.The residual shear strength envelopes for the rough joints and the peak shear strength envelope for the planar joints almost overlap.The root mean square(RMS)of asperity height for the rough joints decreases while it increases for the planar joint after shear,and a larger normal stress usually leads to a more significant decrease or increase in RMS.Besides,the extent of off-fault damage(or damage zone)increases with normal stress for both planar and rough joints,and it is restricted to a very thin layer with limited micro-cracks beneath the planar joint surface.In comparison,the thickness of the damage zone for the rough joints is about an order of magnitude larger than that of the planar joints,and the coalesced micro-cracks are generally inclined to the shear direction with acute angles.The findings obtained in this study contribute to a better understanding on the frictional behavior and damage characteristics of rock joints or fractures with different roughness.

Experimental Study on Vortex-Induced Vibration of Rough Risers with Coupling Interference Effect Under Side-by-Side Arrangement

A vortex-induced vibration(VIV)experiment of rough risers with coupling interference effect under a side-by-side arrangement was carried out in a wave-current combined flume.The roughness of the riser was characterized by arranging different specifications of surface attachments on the surface of the riser.Rough risers with three different roughnesses were arranged side by side with smooth risers to explore the VIV response of the riser under the combined action of roughness and interference effect,and to reveal the coupling mechanism between roughness and interference effect.The experimental results show that,compared with that of a smooth riser,the VIV of a rough riser under the coupling interference effect has a wider"lock-in"region,and the displacement decreases more significantly at a high reduced velocity,which is more likely to excite higher-order modes and frequency responses.In addition,the displacement response and frequency response of the smooth riser are not significantly affected by wake interference from the rough riser,which is caused by the decrease of the wake region due to the delay of the boundary layer separation point of the rough riser.

Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

Roughness characterization and shearing dislocation failure for rock-backfill interface

Shearing dislocation is a common failure type for rock–backfill interfaces because of backfill sedimentation and rock strata movement in backfill mining goaf.This paper designed a test method for rock–backfill shearing dislocation.Using digital image techno-logy and three-dimensional(3D)laser morphology scanning techniques,a set of 3D models with rough joint surfaces was established.Further,the mechanical behavior of rock–backfill shearing dislocation was investigated using a direct shear test.The effects of interface roughness on the shear–displacement curve and failure characteristics of rock–backfill specimens were considered.The 3D fractal dimen-sion,profile line joint roughness coefficient(JRC),profile line two-dimensional fractal dimension,and the surface curvature of the frac-tures were obtained.The correlation characterization of surface roughness was then analyzed,and the shear strength could be measured and calculated using JRC.The results showed the following:there were three failure threshold value points in rock–backfill shearing dis-location:30%–50%displacement before the peak,70%–90%displacement before the peak,and 100%displacement before the peak to post-peak,which could be a sign for rock–backfill shearing dislocation failure.The surface JRC could be used to judge the rock–backfill shearing dislocation failure,including post-peak sliding,uniform variations,and gradient change,corresponding to rock–backfill disloca-tion failure on the field site.The research reveals the damage mechanism for rock–backfill complexes based on the free joint surface,fills the gap of existing shearing theoretical systems for isomerism complexes,and provides a theoretical basis for the prevention and control of possible disasters in backfill mining.

Maximal operators of pseudo-differential operators with rough symbols

Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

RB-DEM Modeling and Simulation of Non-Persisting Rough Open Joints Based on the IFS-Enhanced Method

When the geological environment of rock masses is disturbed,numerous non-persisting open joints can appear within it.It is crucial to investigate the effect of open joints on the mechanical properties of rock mass.However,it has been challenging to generate realistic open joints in traditional experimental tests and numerical simulations.This paper presents a novel solution to solve the problem.By utilizing the stochastic distribution of joints and an enhanced-fractal interpolation system(IFS)method,rough curves with any orientation can be generated.The Douglas-Peucker algorithm is then applied to simplify these curves by removing unnecessary points while preserving their fundamental shape.Subsequently,open joints are created by connecting points that move to both sides of rough curves based on the aperture distribution.Mesh modeling is performed to construct the final mesh model.Finally,the RB-DEM method is applied to transform the mesh model into a discrete element model containing geometric information about these open joints.Furthermore,this study explores the impacts of rough open joint orientation,aperture,and number on rock fracture mechanics.This method provides a realistic and effective approach for modeling and simulating these non-persisting open joints.

High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

Mechanical properties and fracture surface roughness of thermally damaged granite under dynamic splitting

In order to understand the mechanical properties and the fracture surface roughness characteristics of thermally damaged granite under dynamic splitting,dynamic Brazilian splitting tests were conducted on granite samples after thermal treatment at 25,200,400,and 600℃.Results show that the dynamic peak splitting strength of thermally damaged granite samples increases with increasing strain rate,showing obvious strain‐rate sensitivity.With increasing temperature,thermally induced cracks in granite transform from intergranular cracks to intragranular cracks,and to a transgranular crack network.Thermally induced damages reduce the dynamic peak splitting strength and the maximum absorbed energy while increasing the peak radial strain.The fracture mode of the thermally damaged granite under dynamic loads is mode Ⅱ splitting failure.By using the axial roughness index Z2 a,the distribution ranges of the wedge‐shaped failure zones and the tensile failure zones in the fracture surfaces under dynamic Brazilian splitting can be effectively identified.The radial roughness index Z_(2)^(r)is sensitive to the strain rate and temperature.It shows a linear correlation with the peak splitting strength and the maximum absorbed energy and a linear negative correlation with the peak radial strain.Z_(2)^(r)can be used to quantitatively estimate the dynamic parameters based on the models proposed.

Boulder-induced form roughness and skin shear stresses in a gravel-bed stream

Boulder spacing in mountain rivers and near-wake flow zones within the boulder array is very useful for fish habitat and growth of aquatic organisms.The present study aims to investigate how the boulder array and spacing influence the near-bed flow structures in a gravel-bed stream.Boulders are staggered over a gravel-bed stream with three different inter-boulder spacing namely(a)large(b)medium and(c)small spacing.An acoustic Doppler velocimeter was used for flow measurements in a rectangular channel and the results were compared with those acquired from numerical simulation.The time-averaged velocity profiles at the near-wake flow zones of boulders experience maximum flow retardation which is an outcome of the boulder-induced form roughness.The ratio of velocity differences associated to form and skin roughness and its positive magnitude reveals the dominance of form roughness closest to the boulders.Form roughness computed is 1.75 to 2 times higher than the skin roughness at the near-wake flow region.In particular,the collective immobile boulders placed at different inter-boulder spacings developed high and low bed shear stresses closest to the boulders.The low bed shear stresses characterised by a secondary peak developed at the trough location of the boulders is attributed to the skin shear stress.Further,the spatial averaging of time-averaged flow quantities gives additional impetus to present an improved illustration of fluid shear stresses.The formation of form-induced shear stress is estimated to be 17%to 23%of doubleaveraged Reynolds shear stress and partially compensates for the damping of time-averaged Reynolds shear stress in the interfacial sub-layer.The quadrant analysis of spatial velocity fluctuations depicts that the form-induced shear stresses are dominant in the interfacial sub-layer and have no significance above the gravel-bed surface.

Multi-Granularity Neighborhood Fuzzy Rough Set Model on Two Universes

The two universes multi-granularity fuzzy rough set model is an effective tool for handling uncertainty problems between two domains with the help of binary fuzzy relations. This article applies the idea of neighborhood rough sets to two universes multi-granularity fuzzy rough sets, and discusses the two-universes multi-granularity neighborhood fuzzy rough set model. Firstly, the upper and lower approximation operators are defined in the two universes multi-granularity neighborhood fuzzy rough set model. Secondly, the properties of the upper and lower approximation operators are discussed. Finally, the properties of the two universes multi-granularity neighborhood fuzzy rough set model are verified through case studies.

Attribute Reduction of Neighborhood Rough Set Based on Discernment

For neighborhood rough set attribute reduction algorithms based on dependency degree,a neighborhood computation method incorporating attribute weight values and a neighborhood rough set attribute reduction algorithm using discernment as the heuristic information was proposed.The reduction algorithm comprehensively considers the dependency degree and neighborhood granulation degree of attributes,allowing for a more accurate measurement of the importance degrees of attributes.Example analyses and experimental results demonstrate the feasibility and effectiveness of the algorithm.

Novel On-Line North-Seeking Method Based on a Three-Axis MEMS Gyroscope

A novel on-line north-seeking method based on a three-axis micro-electro-mechanical system(MEMS)gyroscope is designed.This system processes data by using a Kalman filter to calibrate the installation error of the three-axis MEMS gyroscope in complex environment.The attitude angle updating for quaternion,based on which the attitude instrument will be rotated in real-time and the true north will be found.Our experimental platform constitutes the dual-axis electric rotary table and the attitude instrument,which is developed independently by our scientific research team.The experimental results show that the accuracy of north-seeking is higher than 1°,while the maximum root mean square error and the maximum mean absolute error are 0.906 7 and 0.910 0,respectively.The accuracy of north-seeking is much higher than the traditional method.

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.

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.

Compression failure conditions of concrete-granite combined body with different roughness interface

Bedrock and concrete lining are typical composite structures in the engineering field and the stability of the geological body and engineering body is directly connected to the mechanical properties of the composite body.Under this background,the study provides the transverse isotropic equivalent model of concrete-granite double-layer composite based on the notion of strain energy equivalence.Assuming that the strength failure of concrete and granite meets the Mohr-Coulomb criterion,then the strength failure model of the combined body considering the joint roughness coefficient(JRC)is derived,and the influences of JRC,the height ratio of concrete to granite,and confining pressure on the strength failure characteristics of the combined body are emphatically analyzed.Finally,the model applicability is illustrated by the uniaxial and triaxial compression tests on concrete monomer,granite monomer and concretegranite composite samples(CGCSs)with different JRCs.The results revealed that the compressive strength of the composite is closer to the concrete with lower strength in the combined body under different confining pressures.Adding interface roughness causes to raise the compressive strength of the composite due to interfacial adhesion between concrete and granite,and a slowing growth trend is observed in compressive strength as roughness.The model can provide a certain reference for the stability design and evaluation of engineering rock mass.

Effect of Surface Roughness on Lubrication Performance of Bump-Type Gas Foil Bearings

Taking bump-type gas foil bearings as the research object,a deformation model of bump foil and a thin-plate finite element model of top foil were proposed.By solving Reynolds equation and energy equation,the pressure distribution and the temperature distribution of gas films in foil bearings were obtained.Further,a numerical method for calculating the lubrication performance of gas foil bearings with considering the surface roughness was proposed.With a specific example,effects of the surface roughness on the bearing lubrication performance were parametrically studied.The results indicate that rougher journal surface can lead to larger fluctuation of the lubrication performance,while surface roughness of top foil has few effects on the fluctuation.Moreover,the mean values of performance parameters almost remain constant at different values of surface roughness.

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.

A transient model integrating the nanoconfinement effect and pore structure characteristics of oil transport through nanopores

Understanding the integrated transport behavior of oil in shale nanopores is critical to efficient shale oil development. In this paper, based on the time-dependent Poiseuille flow momentum equation, we present a novel transient model to describe oil transport in unsteady and steady states. The model incorporates the effect of the critical shift density, apparent viscosity, slip length, and alkane property, as well as pore tortuosity and surface roughness. We evaluated our model through a comparison with other models, experiments, and molecular dynamics simulations. The results show that the development rates of the volume flows of C_(6)–C_(12) alkane confined in inorganic nanopores and C_(12) alkane confined in organic nanopores were faster than that of the corresponding bulk alkane. In addition, the critical drift density positively promoted the volume flow development rate in the unsteady state and negatively inhibited the mass flow rate in the steady state. This effect was clearest in pores with a smaller radius and lower-energy wall and in alkane with shorter chain lengths. Furthermore, both the nanoconfinement effect and pore structure determined whether the volume flow enhancement rate was greater than or less than 1. The rate increased or decreased with time and was controlled mainly by the nanoconfinement effect. Moreover, as the wall energy increased, the flow inhibition effect increased;as the carbon number of alkane increased, the flow promotion effect increased. The results indicate that the proposed model can accurately describe oil transport in shale nanopores.

Influence of surface roughness on the development of moss-dominated biocrusts on mountainous rock-cut slopes in West Sichuan, China

Since natural restoration combined with artificial auxiliary measures may achieve a relatively rapid restoration effect at a lower cost, it has become an essential measure for the ecological restoration of rock slopes. Previous studies have focused heavily on the relationship between substrate nutrients and water conditions and the development of mosses on the rock surface, but quantitative characterization of substantial effect of rock surface texture(e.g., microrelief) on moss growth is absent. The undulating microrelief on the rock surface can increase the heterogeneity of the microhabitat, which may be an important factor affecting the development of mossdominated biocrusts. In this study, the roughness of rock surfaces, moss coverage and biomass, weight and major nutrient contents of soils within the biocrusts were measured in the western mountainous area of Sichuan Province, Southwest China to further examine the role of rock surface microrelief in the biocrusts. The results showed that three main factors affecting the development of the biocrusts were bryophyte emergence, soil accumulation, and lithology. The presence of moss accelerates soil formation on rock surfaces and lead to the accumulation of nutrients so that all parts of the moss-dominated biocrusts system can develop synergistically. It was found that a microrelief structure with a roughness between 1.5 and 2.5 could gather soil and bryophyte propagules effectively, which may have a strong relationship with the angle of repose. When the roughness is 1.5, the corresponding undulation angle is very close to the theoretical minimum value of the undulation angle calculated according to the relationships between the undulation angle of the protrusion, slope and angle of repose.

Improved Microwave Ocean Emissivity and Reflectivity Models Derived from Two-Scale Roughness Theory

The Geometrical Optics(GO)approach and the FAST Emissivity Model(FASTEM)are widely used to estimate the surface radiative components in atmospheric radiative transfer simulations,but their applications are limited in specific conditions.In this study,a two-scale reflectivity model(TSRM)and a two-scale emissivity model(TSEM)are developed from the two-scale roughness theory.Unlike GO which only computes six non-zero elements in the reflectivity matrix,The TSRM includes 16 elements of Stokes reflectivity matrix which are important for improving radiative transfer simulation accuracy in a scattering atmosphere.It covers the frequency range from L-to W-bands.The dependences of all TSRM elements on zenith angle,wind speed,and frequency are derived and analyzed in details.For a set of downwelling radiances in microwave frequencies,the reflected upwelling brightness temperature(BTs)are calculated from both TSRM and GO and compared for analyzing their discrepancies.The TSRM not only includes the effects of GO but also accounts for the small-scale Bragg scattering effect in an order of several degrees in Kelvins in brightness temperature.Also,the third and fourth components of the Stokes vector can only be produced from the TSRM.For the emitted radiation,BT differences in vertical polarization between a TSEM and FASTEM are generally less than 5 K when the satellite zenith angle is less than 40°,whereas those for the horizontal component can be quite significant,greater than 20 K.