Joint Beamforming Design for Dual-Functional Radar-Communication Systems Under Beampattern Gain Constraints

The joint beamforming design challenge for dual-functional radar-communication systems is addressed in this paper.The base station in these systems is tasked with simultaneously sending shared signals for both multi-user communication and target sensing.The primary objective is to maximize the sum rate of multi-user communication,while also ensuring sufficient beampattern gain at particular angles that are of interest for sensing,all within the constraints of the transmit power budget.To tackle this complex non-convex problem,an effective algorithm that iteratively optimizes the joint beamformers is developed.This algorithm leverages the techniques of fractional programming and semidefinite relaxation to achieve its goals.The numerical results confirm the effectiveness of the proposed algorithm.

Cyclic shear behavior of en-echelon joints under constant normal stiffness conditions

To reveal the mechanism of shear failure of en-echelon joints under cyclic loading,such as during earthquakes,we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness(CNS)conditions.We analyzed the evolution of shear stress,normal stress,stress path,dilatancy characteristics,and friction coefficient and revealed the failure mechanisms of en-echelon joints at different angles.The results show that the cyclic shear behavior of the en-echelon joints is closely related to the joint angle,with the shear strength at a positive angle exceeding that at a negative angle during shear cycles.As the number of cycles increases,the shear strength decreases rapidly,and the difference between the varying angles gradually decreases.Dilation occurs in the early shear cycles(1 and 2),while contraction is the main feature in later cycles(310).The friction coefficient decreases with the number of cycles and exhibits a more significant sensitivity to joint angles than shear cycles.The joint angle determines the asperities on the rupture surfaces and the block size,and thus determines the subsequent shear failure mode(block crushing and asperity degradation).At positive angles,block size is more greater and asperities on the rupture surface are smaller than at nonpositive angles.Therefore,the cyclic shear behavior is controlled by block crushing at positive angles and asperity degradation at negative angles.

Analysis of the joint detection capability of the SMILE satellite and EISCAT-3D radar

The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)satellite is a small magnetosphere–ionosphere link explorer developed cooperatively between China and Europe.It pioneers the use of X-ray imaging technology to perform large-scale imaging of the Earth’s magnetosheath and polar cusp regions.It uses a high-precision ultraviolet imager to image the overall configuration of the aurora and monitor changes in the source of solar wind in real time,using in situ detection instruments to improve human understanding of the relationship between solar activity and changes in the Earth’s magnetic field.The SMILE satellite is scheduled to launch in 2025.The European Incoherent Scatter Sciences Association(EISCAT)-3D radar is a new generation of European incoherent scatter radar constructed by EISCAT and is the most advanced ground-based ionospheric experimental device in the high-latitude polar region.It has multibeam and multidirectional quasi-real-time three-dimensional(3D)imaging capabilities,continuous monitoring and operation capabilities,and multiple-baseline interferometry capabilities.Joint detection by the SMILE satellite and the EISCAT-3D radar is of great significance for revealing the coupling process of the solar wind–magnetosphere–ionosphere.Therefore,we performed an analysis of the joint detection capability of the SMILE satellite and EISCAT-3D,analyzed the period during which the two can perform joint detection,and defined the key scientific problems that can be solved by joint detection.In addition,we developed Web-based software to search for and visualize the joint detection period of the SMILE satellite and EISCAT-3D radar,which lays the foundation for subsequent joint detection experiments and scientific research.

A photogrammetric approach for quantifying the evolution of rock joint void geometry under varying contact states

Accurate measurement of the evolution of rock joint void geometry is essential for comprehending the distribution characteristics of asperities responsible for shear and seepage behaviors.However,existing techniques often require specialized equipment and skilled operators,posing practical challenges.In this study,a cost-effective photogrammetric approach is proposed.Particularly,local coordinate systems are established to facilitate the alignment and precise quantification of the relative position between two halves of a rock joint.Push/pull tests are conducted on rock joints with varying roughness levels to induce different contact states.A high-precision laser scanner serves as a benchmark for evaluating the photogrammetry method.Despite certain deviations exist,the measured evolution of void geometry is generally consistent with the qualitative findings of previous studies.The photogrammetric measurements yield comparable accuracy to laser scanning,with maximum errors of 13.2%for aperture and 14.4%for void volume.Most joint matching coefficient(JMC)measurement errors are below 20%.Larger measurement errors occur primarily in highly mismatched rock joints with JMC values below 0.2,but even in cases where measurement errors exceed 80%,the maximum JMC error is only 0.0434.Thus,the proposed photogrammetric approach holds promise for widespread application in void geometry measurements in rock joints.

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.

Three‑dimensional numerical simulation of dynamic strength and failure mode of a rock mass with cross joints

To study the dynamic mechanical properties and failure characteristics of intersecting jointed rock masses with different joint distributions under confining pressure,considering the cross angleαand joint persistence ratioη,a numerical model of the biaxial Hopkinson bar test system was established using the finite element method–discrete-element model coupling method.The validity of the model was verified by comparing and analyzing it in conjunction with laboratory test results.Dynamics-static combined impact tests were conducted on specimens under various conditions to investigate the strength characteristics and patterns of crack initiation and expansion.The study revealed the predominant factors influencing intersecting joints with different angles and penetrations under impact loading.The results show that the peak stress of the specimens decreases first and then increases with the increase of the cross angle.Whenα<60°,regardless of the value ofη,the dynamic stress of the specimens is controlled by the main joint.Whenα≥60°,the peak stress borne by the specimens decreases with increasingη.Whenα<60°,the initiation and propagation of cracks in the cross-jointed specimens are mainly controlled by the main joint,and the final failure surface of the specimens is composed of the main joint and wing cracks.Whenα≥60°orη≥0.67,the secondary joint guides the expansion of the wing cracks,and multiple failure surfaces composed of main and secondary joints,wing cracks,and co-planar cracks are formed.Increasing lateral confinement significantly increases the dynamic peak stress able to be borne by the specimens.Under triaxial conditions,the degree of failure of the intersecting jointed specimens is much lower than that under uniaxial and biaxial conditions.

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.

Subsequent total joint arthroplasty: Are we learning from the first stage?

BACKGROUND With the increasing incidence of total joint arthroplasty(TJA),there is a desire to reduce peri-operative complications and resource utilization.As degenerative conditions progress in multiple joints,many patients undergo multiple proce-dures.AIM To determine if both physicians and patients learn from the patient’s initial arth-roplasty,resulting in improved outcomes following the second procedure.METHODS The institutional database was retrospectively queried for primary total hip arth-roplasty(THA)and total knee arthroplasty(TKA).Patients with only unilateral THA or TKA,and patients undergoing same-day bilateral TJA,were excluded.Patient demographics,comorbidities,and implant sizes were collected at the time of each procedure and patients were stratified by first vs second surgery.Outcome metrics evaluated included operative time,length of stay(LOS),disposition,90-d readmissions and emergency department(ED)visits.RESULTS A total of 642 patients,including 364 undergoing staged bilateral TKA and 278 undergoing bilateral THA,were analyzed.There was no significant difference in demographics or comorbidities between the first and second procedure,which were separated by a mean of 285 d.For THA and TKA,LOS was significantly less for the second surgery,with 66%of patients having a shorter hospitalization(P<0.001).THA patients had significantly decreased operative time only when the same sized implant was utilized(P=0.025).The vast majority(93.3%)of patients were discharged to the same type of location following their second surgery.However,when a change in disposition was present from the first surgery,patients were significantly more likely to be discharged to home after the second procedure(P=0.033).There was no difference between procedures for post-operative readmissions(P=0.438)or ED visits(P=0.915).CONCLUSION After gaining valuable experience recovering from the initial surgery,a patient’s perioperative outcomes are improved for their second TJA.This may be the result of increased confidence and decreased anxiety,and it supports the theory that enhanced patient education pre-operatively may improve outcomes.For the surgical team,the second procedure of a staged THA is more efficient,although this finding did not hold for TKA.

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.

Effect of cold-working on corrosion induced damage in lug joints

Lug joints are preferred joineries for transferring heavy loads to parent components in aerospace vehicles.They experience corrosion due to environmental conditions,improper surface finishes and rubbing displacement between the pin and lug-hole.This causes damage of different sizes and shapes near the lug-hole.Stiffness degradation due to corrosion-induced damage is modelled as a through-pit at one of the identified critical locations through stress analysis.The effect of this pit on fatigue crack initiation life is estimated.Lug-hole is pre-stressed by cold-working and the benefits of inducing plastic wake on the intended performance of the lug joint during the damages due to corrosion are brought out and compared with non-cold-worked lug-hole.Numerical analysis is performed on this lug joint with pressfit.The results obtained highlight the benefits of cold-working and the methodology can be extended to damage growth and analyse the effect of surface treatments for better structural integrity of components of aerospace vehicles.

A review of extreme condition effects on solder joint reliability:Understanding failure mechanisms

Solder joint,crucial component in electronic systems,face significant challenges when exposed to extreme conditions during applications.The solder joint reliability involving microstructure and mechanical properties will be affected by extreme conditions.Understanding the behaviour of solder joints under extreme conditions is vital to determine the durability and reliability of solder joint.This review paper aims to comprehensively explore the underlying failure mechanism affecting solder joint reliability under extreme conditions.This study covers an in-depth analysis of effect extreme temperature,mechanical stress,and radiation conditions towards solder joint.Impact of each condition to the microstructure including solder matrix and intermetallic compound layer,and mechanical properties such as fatigue,shear strength,creep,and hardness was thoroughly discussed.The failure mechanisms were illustrated in graphical diagrams to ensure clarity and understanding.Furthermore,the paper highlighted mitigation strategies that enhancing solder joint reliability under challenging operating conditions.The findings offer valuable guidance for researchers,engineers,and practitioners involved in electronics,engineering,and related fields,fostering advancements in solder joint reliability and performance.

Joint Optimization of Resource Allocation and Trajectory Based on User Trajectory for UAV-Assisted Backscatter Communication System

The Backscatter communication has gained widespread attention from academia and industry in recent years. In this paper, A method of resource allocation and trajectory optimization is proposed for UAV-assisted backscatter communication based on user trajectory. This paper will establish an optimization problem of jointly optimizing the UAV trajectories, UAV transmission power and BD scheduling based on the large-scale channel state signals estimated in advance of the known user trajectories, taking into account the constraints of BD data and working energy consumption, to maximize the energy efficiency of the system. The problem is a non-convex optimization problem in fractional form, and there is nonlinear coupling between optimization variables.An iterative algorithm is proposed based on Dinkelbach algorithm, block coordinate descent method and continuous convex optimization technology. First, the objective function is converted into a non-fractional programming problem based on Dinkelbach method,and then the block coordinate descent method is used to decompose the original complex problem into three independent sub-problems. Finally, the successive convex approximation method is used to solve the trajectory optimization sub-problem. The simulation results show that the proposed scheme and algorithm have obvious energy efficiency gains compared with the comparison scheme.

Thermosphere joint observations by TM-1 constellations and Swarm-B during the April 2023 geomagnetic storm

The response of thermosphere density to geomagnetic storms is a complicated physical process.Multi-satellite joint observations at the same altitude but different local times(LTs)are important for understanding this process;however,until now such studies have hardly been done.In this report,we analyze in detail the thermosphere mass density response at 510 km during the April 23−24,2023 geomagnetic storm using data derived from the TM-1(TianMu-1)satellite constellation and Swarm-B satellites.The observations show that there were significant LT differences in the hemispheric asymmetry of the thermosphere mass density during the geomagnetic storm.Densities observed by satellite TM02 at nearly 11.3 and 23.3 LTs were larger in the northern hemisphere than in the southern.The TM04 dayside density observations appear to be almost symmetrical with respect to the equator,though southern hemisphere densities on the nightside were higher.Swarm-B data exhibit near-symmetry between the hemispheres.In addition,the mass density ratio results show that TM04 nightside observations,TM02 data,and Swarm-B data all clearly show stronger effects in the southern hemisphere,except for TM04 on the dayside,which suggest hemispheric near-symmetry.The South-North density enhancement differences in TM02 and TM04 on dayside can reach 130%,and Swarm-B data even achieve 180%difference.From the observations of all three satellites,large-scale traveling atmospheric disturbances(TADs)first appear at high latitudes and propagate to low latitudes,thereby disturbing the atmosphere above the equator and even into the opposite hemisphere.NRLMSISE00 model simulations were also performed on this geomagnetic storm.TADs are absent in the NRLMSISE00 simulations.The satellite data suggest that NRLMSISE00 significantly underestimates the magnitude of the density response of the thermosphere during geomagnetic storms,especially at high latitudes in both hemispheres.Therefore,use of the density simulation of NRLMSISE00 may lead to large errors in satellite drag calculations and orbit predictions.We suggest that the high temporal and spatial resolution of direct density observations by the TM-1 constellation satellites can provide an autonomous and reliable basis for correction and improvement of atmospheric models.

Synthesis of organic-inorganic 3D-nanocontainers for smart corrosion protection of friction stir welded AZ31B magnesium alloy-titanium dissimilar joints

The joining of different light metals through friction stir welding(FSW)is gaining interest as a method to decrease weight and improve fuel efficiency.However,to ensure durability,these welded metals may require surface treatments to protect against corrosion or wear.This study presents a novel approach for the simultaneous delivery of two distinct corrosion inhibitors to Ti-Mg dissimilar PEO treated joints on demand.The research focuses on the synthesis,characterization,and application of cerium@polystyrene(Ce@PS)nanocontainers,which are loaded with 8-hydroxyquinoline(8-HQ)to enhance corrosion protection.The synthesis involves several key steps,including the formation of a cerium-based outer layer around polystyrene nanospheres,the selective removal of the polystyrene core to create a porous structure,and the subsequent loading of the 8-HQ inhibitor.Structural and compositional analyses,conducted using scanning transmission electron microscopy(STEM)and energy-dispersive X-ray spectroscopy(EDS),confirmed the successful incorporation of 8-HQ within the nanocontainers.Additionally,Fourier-transform infrared spectroscopy(FTIR)provided detailed information about the chemical composition of the organic materials throughout the synthesis process.Thermal decomposition analysis verified the successful fabrication and stability of the dual-shell nanocontainers.Corrosion tests on Ti-Mg joints treated with plasma electrolytic oxidation(PEO)coatings and loaded nanocontainers demonstrated sig-nificantly improved corrosion resistance compared to untreated joints.This research highlights the potential of dual-shell nanocontainers,containing both organic and inorganic inhibitors,to offer prolonged corrosion protection,particularly against galvanic corrosion in dissimilar joints.The findings suggest that these synthesized nanocontainers hold promise for various industrial applications,particularly in the context of friction stir welded(FSW)Ti-Mg dissimilar joints,providing valuable insights for the development of advanced materials designed to mitigate corrosion.

A comprehensive review of radiation effects on solder alloys and solder joints

In the realm of military and defence applications, exposure to radiation significantly challenges the performance and reliability of solder alloys and joints in electronic systems. This comprehensive review examines radiation-induced effects on solder alloys and solder joints in terms of microstructure and mechanical properties. In this paper, we evaluate the existing literature, including experimental studies and fundamental theory, to provide a comprehensive overview of the behavior of solder materials under radiation. A review of the literature highlights key mechanisms that contribute to radiation-induced changes in the microstructure, such as the formation of intermetallic compounds, grain growth,micro-voids and micro-cracks. Radiation is explored as a factor influencing solder alloy hardness,strength, fatigue and ductility. Moreover, the review addresses the challenges and limitations inherent in studying the effects of radiation on solder materials and offers recommendations for future research. It is crucial to understand radiation-induced effects on solder performance to design robust and radiationresistant electronic systems. A review of radiation effects on solder materials and their applications in electronics serves as a valuable resource for researchers, engineers, and practitioners in that field.

Microstructure,Corrosion and Mechanical Properties of Medium-Thick 6061-T6 Alloy/T2 Pure Cu Dissimilar Joints Produced by Double Side Friction Stir Z Shape Lap-Butt Welding

A novel double side friction stir Z shape lap-butt welding(DS-FSZW)process was proposed to achieve excellent mechanical properties of Al/Cu medium-thick dissimilar joints.The influence of welding parameters on weld microstructure and properties of DS-FSZW joint were systematically investigated.It indicated that defect-free medium-thick Al/Cu DS-FSZW joint could be achieved under an optimal welding parameter.DS-FSZW joint was prone to form void defects in the bottom of the second-pass weld.The recrystallization mechanisms at the top and middle of the weld nugget zone(WNZ)were continuous dynamic recrystallization(CDRX)and geometric dynamic recrystallization(GDRX).While the major recrystallization mechanism at the bottom of the WNZ was GDRX.DS-FSZW joint of the optimal welding condition with 850 r/min-400 mm/min was produced with a continuous thin and crack-free IMCs layer at the Al/Cu interface,and the maximum tensile strength of this joint is 160.57 MPa,which is equivalent to 65.54%of pure Cu base material.Moreover,the corrosion resistance of Al/Cu DS-FSZW joints also achieved its maximum value at the optimal welding parameter of 850 r/min-400 mm/min.It demonstrates that the DS-FSZW process can simultaneously produce medium-thick Al/Cu joints with excellent mechanical performance and corrosion resistance.

Joint Allocation of Computing and Connectivity Resources in Survivable Inter-Datacenter Elastic Optical Networks

Inter-datacenter elastic optical networks(EON)need to provide the service for the requests of cloud computing that require not only connectivity and computing resources but also network survivability.In this paper,to realize joint allocation of computing and connectivity resources in survivable inter-datacenter EONs,a survivable routing,modulation level,spectrum,and computing resource allocation algorithm(SRMLSCRA)algorithm and three datacenter selection strategies,i.e.Computing Resource First(CRF),Shortest Path First(SPF)and Random Destination(RD),are proposed for different scenarios.Unicast and manycast are applied to the communication of computing requests,and the routing strategies are calculated respectively.Simulation results show that SRMLCRA-CRF can serve the largest amount of protected computing tasks,and the requested calculation blocking probability is reduced by 29.2%,28.3%and 30.5%compared with SRMLSCRA-SPF,SRMLSCRA-RD and the benchmark EPS-RMSA algorithms respectively.Therefore,it is more applicable to the networks with huge calculations.Besides,SRMLSCRA-SPF consumes the least spectrum,thereby exhibiting its suitability for scenarios where the amount of calculation is small and communication resources are scarce.The results demonstrate that the proposed methods realize the joint allocation of computing and connectivity resources,and could provide efficient protection for services under single-link failure and occupy less spectrum.

Optimizing profile line interval for enhanced accuracy in rock joint morphology and shear strength assessments

2D profile lines play a critical role in cost-effectively evaluating rock joint properties and shear strength.However, the interval(ΔI_(L)) between these lines significantly impacts roughness and shear strength assessments. A detailed study of 45 joint samples using four statistical measures across 500 different ΔI_(L)values identified a clear line interval effect with two stages: stable and fluctuation-discrete.Further statistical analysis showed a linear relationship between the error bounds of four parameters,shear strength evaluation, and their corresponding maximum ΔI_(L)values, where the gradient k of this linear relationship was influenced by the basic friction angle and normal stress. Accounting for these factors,lower-limit linear models were employed to determine the optimal ΔI_(L)values that met error tolerances(1%–10%) for all metrics and shear strength. The study also explored the consistent size effect on joints regardless of ΔI_(L)changes, revealing three types of size effects based on morphological heterogeneity.Notably, larger joints required generally higher ΔI_(L)to maintain the predefined error limits, suggesting an increased interval for large joint analyses. Consequently, this research provides a basis for determining the optimal ΔI_(L), improving accuracy in 2D profile line assessments of joint characteristics.

Joint Biomedical Entity and Relation Extraction Based on Multi-Granularity Convolutional Tokens Pairs of Labeling

Extracting valuable information frombiomedical texts is one of the current research hotspots of concern to a wide range of scholars.The biomedical corpus contains numerous complex long sentences and overlapping relational triples,making most generalized domain joint modeling methods difficult to apply effectively in this field.For a complex semantic environment in biomedical texts,in this paper,we propose a novel perspective to perform joint entity and relation extraction;existing studies divide the relation triples into several steps or modules.However,the three elements in the relation triples are interdependent and inseparable,so we regard joint extraction as a tripartite classification problem.At the same time,fromthe perspective of triple classification,we design amulti-granularity 2D convolution to refine the word pair table and better utilize the dependencies between biomedical word pairs.Finally,we use a biaffine predictor to assist in predicting the labels of word pairs for relation extraction.Our model(MCTPL)Multi-granularity Convolutional Tokens Pairs of Labeling better utilizes the elements of triples and improves the ability to extract overlapping triples compared to previous approaches.Finally,we evaluated our model on two publicly accessible datasets.The experimental results show that our model’s ability to extract relation triples on the CPI dataset improves the F1 score by 2.34%compared to the current optimal model.On the DDI dataset,the F1 value improves the F1 value by 1.68%compared to the current optimal model.Our model achieved state-of-the-art performance compared to other baseline models in biomedical text entity relation extraction.

A statistical damage-based constitutive model for shearing of rock joints in brittle drop mode

Some rock joints exhibit significant brittleness,characterized by a sharp decrease in shear stress upon reaching the peak strength.However,existing models often fail to accurately represent this behavior and are encumbered by numerous parameters lacking clear mechanical significance.This study presents a new statistical damage constitutive model rooted in both damage mechanics and statistics,containing only three model parameters.The proposed model encompasses all stages of joint shearing,including the compaction stage,linear stage,plastic yielding stage,drop stage,strain softening stage,and residual strength stage.To derive the analytical expression of the constitutive model,three boundary conditions are introduced.Experimental data from both natural and artificial rock joints is utilized to validate the model,resulting in average absolute relative errors ranging from 3%to 8%.Moreover,a comparative analysis with established models illustrates that the proposed model captures stress drop and post-peak strain softening more effectively,with model parameters possessing clearer mechanical interpretations.Furthermore,parameter analysis is conducted to investigate the impacts of model parameters on the curves and unveil the relationship between these parameters and the mechanical properties of rock joints.Importantly,the proposed model is straightforward in form,and all model parameters can be obtained from direct shear tests,thus facilitating the utilization in numerical simulations.