Using cemented paste backfill to tackle the phosphogypsum stockpile in China:A down-to-earth technology with new vitalities in pollutant retention and CO_(2) abatement

Phosphogypsum(PG),a hard-to-dissipate by-product of the phosphorus fertilizer production industry,places strain on the biogeochemical cycles and ecosystem functions of storage sites.This pervasive problem is already widespread worldwide and requires careful stewardship.In this study,we review the presence of potentially toxic elements(PTEs)in PG and describe their associations with soil properties,anthropogenic activities,and surrounding organisms.Then,we review different ex-/in-situ solutions for promoting the sustainable management of PG,with an emphasis on in-situ cemented paste backfill,which offers a cost-effective and highly scalable opportunity to advance the value-added recovery of PG.However,concerns related to the PTEs'retention capacity and long-term effectiveness limit the implementation of this strategy.Furthermore,given that the large-scale demand for ordinary Portland cement from this conventional option has resulted in significant CO_(2) emissions,the technology has recently undergone additional scrutiny to meet the climate mitigation ambition of the Paris Agreement and China's Carbon Neutrality Economy.Therefore,we discuss the ways by which we can integrate innovative strategies,including supplementary cementitious materials,alternative binder solutions,CO_(2) mineralization,CO_(2) curing,and optimization of the supply chain for the profitability and sustainability of PG remediation.However,to maximize the co-benefits in environmental,social,and economic,future research must bridge the gap between the feasibility of expanding these advanced pathways and the multidisciplinary needs.

Investigation of the block toppling evolution of a layered model slope by centrifuge test and discrete element modeling

Primary toppling usually occurs in layered rock slopes with large anti-dip angles.In this paper,the block toppling evolution was explored using a large-scale centrifuge system.Each block column in the layered model slope was made of cement mortar.Some artificial cracks perpendicular to the block column were prefabricated.Strain gages,displacement gages,and high-speed camera measurements were employed to monitor the deformation and failure processes of the model slope.The centrifuge test results show that the block toppling evolution can be divided into seven stages,i.e.layer compression,formation of major tensile crack,reverse bending of the block column,closure of major tensile crack,strong bending of the block column,formation of failure zone,and complete failure.Block toppling is characterized by sudden large deformation and occurs in stages.The wedge-shaped cracks in the model incline towards the slope.Experimental observations show that block toppling is mainly caused by bending failure rather than by shear failure.The tensile strength also plays a key factor in the evolution of block toppling.The simulation results from discrete element method(DEM)is in line with the testing results.Tensile stress exists at the backside of rock column during toppling deformation.Stress concentration results in the fragmented rock column and its degree is the most significant at the slope toe.

An MPI parallel DEM-IMB-LBM framework for simulating fluid-solid interaction problems

The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive computational costs.To overcome this limitation,a message passing interface(MPI)parallel DEM-IMB-LBM framework is proposed aimed at enhancing computation efficiency.This framework utilises a static domain decomposition scheme,with the entire computation domain being decomposed into multiple subdomains according to predefined processors.A detailed parallel strategy is employed for both contact detection and hydrodynamic force calculation.In particular,a particle ID re-numbering scheme is proposed to handle particle transitions across sub-domain interfaces.Two benchmarks are conducted to validate the accuracy and overall performance of the proposed framework.Subsequently,the framework is applied to simulate scenarios involving multi-particle sedimentation and submarine landslides.The numerical examples effectively demonstrate the robustness and applicability of the MPI parallel DEM-IMB-LBM framework.

Genesis of the Nuri Cu-W-Mo Deposit,Tibet,China:Constraints from in situ Trace Elements and Sr Isotopic Analysis of Scheelite

The Nuri deposit is the only Cu-W-Mo polymetallic deposit with large-scale WO3 resources in the eastern section of the Gangdese metallogenic belt,Tibet,China.However,the genetic type of this deposit has been controversial since its discovery.Based on a study of the geological characteristics of the deposit,this study presents mineralization stages,focusing on the oxide stage and the quartz-sulfide stage where scheelite is mainly formed,referred to as Sch-A and Sch-B,respectively.Through LA-ICP-MS trace element and Sr isotope analyses,the origin,evolutionary process of the oreforming fluid and genesis of the ore deposit are investigated.Scanning Electron Microscope-Cathodoluminescence(SEMCL)observations reveal that Sch-A consists of three generations,with dark gray homogenous Sch-A1 being replaced by relatively lighter and homogeneous Sch-A2 and Sch-A3,with Sch-A2 displaying a gray CL image color with vague and uneven growth bands and Sch-A3 has a light gray CL image color with hardly any growth band.In contrast,Sch-B exhibits a‘core-rim’structure,with the core part(Sch-B1)being dark gray and displaying a uniform growth band,while the rim part(Sch-B2)is light gray and homogeneous.The normalized distribution pattern of rare earth elements in scheelite and Sr isotope data suggest that the early ore-forming fluid in the Nuri deposit originated from granodiorite porphyry and,later on,some country rock material was mixed in,due to strong water-rock interaction.Combining the O-H isotope data further indicates that the ore-forming fluid in the Nuri deposit originated from magmatic-hydrothermal sources,with contributions from metamorphic water caused by water-rock interaction during the mineralization process,as well as later meteoric water.The intense water-rock interaction likely played a crucial role in the precipitation of scheelite,leading to varying Eu anomalies in different generations of scheelite from the oxide stage to the quartz-sulfide stage,while also causing a gradual decrease in oxygen fugacity(fO2)and a slow rise in pH value.Additionally,the high Mo and low Sr contents in the scheelite are consistent with typical characteristics of magmatic-hydrothermal scheelite.Therefore,considering the geological features of the deposit,the geochemical characteristics of scheelite and the O-H isotope data published previously,it can be concluded that the genesis of the Nuri deposit belongs to porphyry-skarn deposit.

Multi-layer perceptron-based data-driven multiscale modelling of granular materials with a novel Frobenius norm-based internal variable

One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural networks(RNNs)have been extensively applied to capture history-dependent constitutive responses of granular materials,but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method(FEM).Single-step-based neural networks like the multi-layer perceptron(MLP)are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories.In this work,one novel Frobenius norm-based internal variable,together with the Fourier layer and residual architectureenhanced MLP model,is crafted to replicate the history-dependent constitutive features of representative volume element(RVE)for granular materials.The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case.The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency.The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.

Biomedical rare-earth magnesium alloy:Current status and future prospects

Biomedical magnesium(Mg)alloys have garnered significant attention because of their unique biodegradability,favorable biocompatibility,and suitable mechanical properties.The incorporation of rare earth(RE)elements,with their distinct physical and chemical properties,has greatly contributed to enhancing the mechanical performance,degradation behavior,and biological performance of biomedical Mg alloys.Currently,a series of RE-Mg alloys are being designed and investigated for orthopedic implants and cardiovascular stents,achieving substantial and encouraging research progress.In this work,a comprehensive summary of the state-of-the-art in biomedical RE-Mg alloys is provided.The physiological effects and design standards of RE elements in biomedical Mg alloys are discussed.Particularly,the degradation behavior and mechanical properties,including their underlying action are studied in-depth.Furthermore,the preparation techniques and current application status of RE-Mg alloys are reviewed.Finally,we address the ongoing challenges and propose future prospects to guide the development of high-performance biomedical Mg-RE alloys.

Method to measure tree-ring width,density,elemental composition,and stable carbon and oxygen isotopes using one sample

Tree-ring width(RW),density,elemental com-position,and stable carbon and oxygen isotope(δ^(13)C,δ^(18)O)are widely used as proxies to assess climate change,ecology,and environmental pollution;however,a specific pretreat-ment has been needed for each proxy.Here,we developed a method by which each proxy can be measured in the same sample.First,the sample is polished for ring width meas-urement.After obtaining the ring width data,the sample is cut to form a 1-mm-thick wood plate.The sample is then mounted in a vertical sample holder,and gradually scanned by an X-ray beam.Simultaneously,the count rates of the fluorescent photons of elements(for chemical characteriza-tion)and a radiographic grayscale image(for wood density)are obtained,i.e.the density and the element content are obtained.Then,cellulose is isolated from the 1-mm wood plate by removal of lignin,and hemicellulose.After producing this cellulose plate,cellulose subsamples are separated by knife under the microscope for inter-annual and intra-annual stable carbon and oxygen isotope(δ^(13)C,δ^(18)O)analysis.Based on this method,RW,density,elemental composition,δ^(13)C,and δ^(18)O can be measured from the same sample,which reduces sample amount and treatment time,and is helpful for multi-proxy comparison and combination research.

Effect of Ti and Ta content on the oxidation resistance of Co-Ni-based superalloys

Co-Ni-based superalloys are known for their capability to function at elevated temperatures and superior hot corrosion and thermal fatigue resistance.Therefore,these alloys show potential as crucial high-temperature structural materials for aeroengine and gas turbine hot-end components.Our previous work elucidated the influence of Ti and Ta on the high-temperature mechanical properties of alloys.However,the intricate interaction among elements considerably affects the oxidation resistance of alloys.In this paper,Co-35Ni-10Al-2W-5Cr-2Mo-1Nb-xTi-(5−x)Ta alloys(x=1,2,3,4)with varying Ti and Ta contents were designed and compounded,and their oxidation resistance was investigated at the temperature range from 800 to 1000℃.After oxidation at three test conditions,namely,800℃for 200 h,900℃for 200 h,and 1000℃for 50 h,the main structure of the oxide layer of the alloy consisted of spinel,Cr_(2)O_(3),and Al_(2)O_(3)from outside to inside.Oxides consisting of Ta,W,and Mo formed below the Cr_(2)O_(3)layer.The interaction of Ti and Ta imparted the highest oxidation resistance to 3Ti2Ta alloy.Conversely,an excessive amount of Ti or Ta resulted in an adverse effect on the oxidation resistance of the alloys.This study reports the volatilization of W and Mo oxides during the oxidation process of Co-Ni-based cast superalloys with a high Al content for the first time and explains the formation mechanism of holes in the oxide layer.The results provide a basis for gaining insights into the effects of the interaction of alloying elements on the oxidation resistance of the alloys they form.

A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

Analysis of mesoscopic mechanical dynamic characteristics of ballast bed with under sleeper pads

The meso-dynamical behaviour of a high-speed rail ballast bed with under sleeper pads(USPs)was studied.The geometrically irregular refined discrete element model of the ballast particles was constructed using 3D scanning techniques,and the 3D dynamic model of the rail-sleeper-ballast bed was constructed using the coupled discrete element method-multiflexible-body dynamics(DEM-MFBD)approach.We analyse the meso-mechanical dynamics of the ballast bed with USPs under dynamic load on a train and verify the correctness of the model in laboratory tests.It is shown that the deformation of the USPs increases the contact area between the sleeper and the ballast particles,and subsequently the number of contacts between them.As the depth of the granular ballast bed increases,the contact area becomes larger,and the contact force between the ballast particles gradually decreases.Under the action of the elastic USPs,the contact forces between ballast particles are reduced and the overall vibration level of the ballast bed can be reduced.The settlement of the granular ballast bed occurs mainly at the shallow position of the sleeper bottom,and the installation of the elastic USPs can be effective in reducing the stress on the ballast particles and the settlement of the ballast bed.

Computer vision-aided DEM study on the compaction characteristics of graded subgrade filler considering realistic coarse particle shapes

The compaction quality of subgrade filler strongly affects subgrade settlement.The main objective of this research is to analyze the macro-and micro-mechanical compaction characteristics of subgrade filler based on the real shape of coarse particles.First,an improved Viola-Jones algorithm is employed to establish a digitalized 2D particle database for coarse particle shape evaluation and discrete modeling purposes of subgrade filler.Shape indexes of 2D subgrade filler are then computed and statistically analyzed.Finally,numerical simulations are performed to quantitatively investigate the effects of the aspect ratio(AR)and interparticle friction coefficient(μ)on the macro-and micro-mechanical compaction characteristics of subgrade filler based on the discrete element method(DEM).The results show that with the increasing AR,the coarse particles are narrower,leading to the increasing movement of fine particles during compaction,which indicates that it is difficult for slender coarse particles to inhibit the migration of fine particles.Moreover,the average displacement of particles is strongly influenced by the AR,indicating that their occlusion under power relies on particle shapes.The dis-placement and velocity of fine particles are much greater than those of the coarse particles,which shows that compaction is primarily a migration of fine particles.Under the cyclic load,the interparticle friction coefficientμhas little effect on the internal structure of the sample;under the quasi-static loads,however,the increase inμwill lead to a significant increase in the porosity of the sample.This study could not only provide a novel approach to investigate the compaction mechanism but also establish a new theoretical basis for the evaluation of intelligent subgrade compaction.

A particle-resolved heat-particle-fluid coupling model by DEM-IMB-LBM

Multifield coupling is frequently encountered and also an active area of research in geotechnical engineering.In this work,a particle-resolved direct numerical simulation(PR-DNS)technique is extended to simulate particle-fluid interaction problems involving heat transfer at the grain level.In this extended technique,an immersed moving boundary(IMB)scheme is used to couple the discrete element method(DEM)and lattice Boltzmann method(LBM),while a recently proposed Dirichlet-type thermal boundary condition is also adapted to account for heat transfer between fluid phase and solid particles.The resulting DEM-IBM-LBM model is robust to simulate moving curved boundaries with constant temperature in thermal flows.To facilitate the understanding and implementation of this coupled model for non-isothermal problems,a complete list is given for the conversion of relevant physical variables to lattice units.Then,benchmark tests,including a single-particle sedimentation and a two-particle drafting-kissing-tumbling(DKT)simulation with heat transfer,are carried out to validate the accuracy of our coupled technique.To further investigate the role of heat transfer in particle-laden flows,two multiple-particle problems with heat transfer are performed.Numerical examples demonstrate that the proposed coupling model is a promising high-resolution approach for simulating the heat-particle-fluid coupling at the grain level.

Mathematical modeling and simulations of stress mitigation by coating polycrystalline particles in lithium-ion batteries

A chemo-mechanical model is developed to investigate the effects on the stress development of the coating of polycrystalline Ni-rich LiNixMnyCo_(z)O_(2)(x≥0.8)(NMC)particles with poly(3,4-ethylenedioxythiophene)(PEDOT).The simulation results show that the coating of primary NMC particles significantly reduces the stress generation by efficiently accommodating the volume change associated with the lithium diffusion,and the coating layer plays roles both as a cushion against the volume change and a channel for the lithium transport,promoting the lithium distribution across the secondary particles more homogeneously.Besides,the lower stiffness,higher ionic conductivity,and larger thickness of the coating layer improve the stress mitigation.This paper provides a mathematical framework for calculating the chemo-mechanical responses of anisotropic electrode materials and fundamental insights into how the coating of NMC active particles mitigates stress levels.

Paleoenvironmental Characteristics of Paleogene Lacustrine Source Rocks in the Western Bozhong Sag,Bohai Bay Basin,China:Evidence from Biomarkers,Major and Trace Elements

The organic matter(OM)enrichment mechanisms and depositional environment characteristics of lacustrine source rocks in the western Bozhong Sag,Bohai Bay Basin in Northeast China remain controversial.To address these issues,based on Rock-Eval pyrolysis,kerogen macerals,H/C and O/C ratios,GC-MS,major and trace elements,the Dongying Formation Member(Mbr)3(E_(3)d_(3)),the Shahejie Formation mbrs 1 and 2(E_(2)s_(1+2)),and the Shahejie Mbr 3(E_(2)s_(3))source rocks in the western Bozhong Sag were studied.The above methods were used to reveal their geochemical properties,OM origins and depositional environments,all of which indicate that E_(2)s_(1+2)and E_(2)s_(3)are excellent source rocks,and that E_(3)d_(3)is of the second good quality.E_(3)d_(3)source rocks were formed under a warm and humid climate,mainly belong to fluvial/delta facies,the E_(3)d_(3)sediments formed under weakly oxidizing and freshwater conditions.Comparatively,the depositional environments of E_(2)s_(1+2)source rocks were arid and cold climate,representing saline or freshwater lacustrine facies,and the sediments of E_(2)s_(1+2)belong to anoxic or suboxic settings with large evaporation and salinity.During the period of E_(2)s_(3),the climate became warm and humid,indicating the freshwater lacustrine facies,and E_(2)s_(3)was characterized by freshwater and abundant algae.Moreover,compared with other intervals,the OM origin of E_(3)d_(3)source rocks has noticeable terrestrial input.The OM origin of the E_(2)s_(1+2)and E_(2)s_(3)are mainly plankton and bacteria.Tectonic subsidence and climate change have affected the changes of the depositional environment in the western Bozhong Sag,thus controlling the distribution of the source rocks,the geochemical characteristics in the three intervals of lacustrine source rocks have distinct differences.Overall,these factors are effective to evaluate the paleoenvironmental characteristics of source rocks by biomarkers,major and trace elements.The established models may have positive implications for research of lacustrine source rocks in offshore areas with few drillings.

The effect of abiotic stresses on plant C:N:P homeostasis and their mitigation by silicon

In crop plants, various environmental stresses affect the balance of carbon, nitrogen, and phosphorus(C:N:P), leading to biochemical and physiological alterations and reductions in yield. Silicon(Si) is a beneficial element that alleviates plant stress. Most studies involving silicon have focused on physiological responses, such as improvements in photosynthetic processes, water use efficiency, and antioxidant defense systems. But recent research suggests that stressed plants facing either limited or excessive resources(water, light, nutrients, and toxic elements), strategically employ Si to maintain C:N:P homeostasis, thereby minimizing biomass losses. Understanding the role of Si in mitigating the impact of abiotic stresses on plants by regulating C:N:P homeostasis holds great potential for advancing sustainable agricultural practices in crop production. This review presents recent advances in characterizing the influence of environmental stresses on C:N:P homeostasis, as well as the role of Si in preserving C:N:P equilibrium and attenuating biological damage associated with abiotic stress. It underscores the beneficial effects of Si in sustaining C:N:P homeostasis and increasing yield via improved nutritional efficiency and stress mitigation.

基于内聚力单元法的船舶与重叠冰碰撞数值模拟研究

The gradual increase in shipping and drilling activities in the Arctic regions has resulted in the increased importance of studying the structural safety of polar ships in various ice conditions.Rafted ice refers to a type of accumulated and overlapped sea ice;it is driven by external forces,such as wind and waves,and may exert high loads on ships and threaten their structural safety.Therefore,the properties of rafted ice and the construction of numerical models should be studied before exploring the interaction and collision between ships and rafted ice.Based on the nonlinear finite-element method,this paper introduces the cohesive element model for the simulation of rafted ice.The interaction between ships and rafted ice is studied,and the ice force of the hull is obtained.Numerical simulation results are compared with model test findings,and the effectiveness of the cohesive element method in the construction of the model of rafted ice materials is verified.On this basis,a multilayer rafted ice model is constructed,and its interaction with the ship is studied.The research unveils that rafted ice parts impede crack generation and slow down crack propagation to a certain extent.

Physics-based seismic analysis of ancient wood structure:fault-to-structure simulation

Based on the domain reduction method,this study employs an SEM-FEM hybrid workflow which integrates the advantages of the spectral element method(SEM)for flexible and highly efficient simulation of seismic wave propagation in a three-dimensional(3D)regional-scale geophysics model and the finite element method(FEM)for fine simulation of structural response including soil-structure interaction,and performs a physics-based simulation from initial fault rupture on an ancient wood structure.After verification of the hybrid workflow,a large-scale model of an ancient wood structure in the Beijing area,The Tower of Buddhist Incense,is established and its responses under the 1665 Tongxian earthquake and the 1730 Yiheyuan earthquake are simulated.The results from the simulated ground motion and seismic response of the wood structure under the two earthquakes demonstrate that this hybrid workflow can be employed to efficiently provide insight into the relationships between geophysical parameters and the structural response,and is of great significance toward accurate input for seismic simulation of structures under specific site and fault conditions.

Numerical modeling techniques for noise emission of free railway wheels

In this article,we consider the numerical prediction of the noise emission from a wheelset in laboratory conditions.We focus on the fluid-structure interaction leading to sound emission in the fluid domain by analyzing three different methods to account for acoustic sources.These are a discretized baffled piston using the discrete calculation method(DCM),a closed cylindrical volume using the boundary element method(BEM)and radiating elastic disks in a cubic enclosure solved with the finite element method(FEM).We provide the validation of the baffled piston and the BEM using measurements of the noise emission of a railway wheel by considering ground reflections in the numerical models.Selected space-resolved waveforms are compared with experimental results as well as with a fluid-structure interaction finite element model.The computational advantage of a discretized disk mounted on a baffle and BEM compared to FEM is highlighted,and the baffled pistons limitations caused by a lack of edge radiation effects are investigated.

Genome-wide association study of grain micronutrient concentrations in bread wheat

Bread wheat(Triticum aestivum)is a staple food crop worldwide.The genetic dissection of important nutrient traits is essential for the biofortification of wheat to meet the nutritional needs of the world's growing population.Here,45,298 single-nucleotide polymorphisms(SNPs)from 55K chip arrays were used to genotype a panel of 768 wheat cultivars,and a total of 154 quantitative trait loci(QTLs)were detected for eight traits under three environments by genome-wide association study(GWAS).Three QTLs(qMn-3B.1,qFe-3B.4,and qSe-3B.1/qFe-3B.6)detected repeatedly under different environments or traits were subjected to subsequent analyses based on linkage disequilibrium decay and the P-values of significant SNPs.Significant SNPs in the three QTL regions formed six haplotypes for qMn-3B.1,three haplotypes for qFe-3B.4,and three haplotypes for qSe-3B.1/qFe-3B.6.Phenotypic analysis revealed significant differences among haplotypes.These results indicated that the concentrations of several nutrient elements have been modified during the domestication of landraces to modern wheat.Based on the QTL regions,we identified 15 high-confidence genes,eight of which were stably expressed in different tissues and/or developmental stages.TraesCS3B02G046100 in qMn-3B.1 and TraesCS3B02G199500 in qSe-3B.1/qFe-3B.6 were both inferred to interact with metal ions according to the Gene Ontology(GO)analysis.TraesCS3B02G199000,which belongs to qSe-3B.1/qFe-3B.6,was determined to be a member of the WRKY gene family.Overall,this study provides several reliable QTLs that may significantly affect the concentrations of nutrient elements in wheat grain,and this information will facilitate the breeding of wheat cultivars with improved grain properties.

Anisotropic shearing mechanism of Kangding slate:Experimental investigation and numerical analysis

The shear mechanical behavior is regarded as an essential factor affecting the stability of the surrounding rocks in underground engineering.The shear strength and failure mechanisms of layered rock are significantly affected by the foliation angles.Direct shear tests were conducted on cubic slate samples with foliation angles of 0°,30°,45°,60°,and 90°.The effect of foliation angles on failure patterns,acoustic emission(AE)characteristics,and shear strength parameters was analyzed.Based on AE characteristics,the slate failure process could be divided into four stages:quiet period,step-like increasing period,dramatic increasing period,and remission period.A new empirical expression of cohesion for layered rock was proposed,which was compared with linear and sinusoidal cohesion expressions based on the results made by this paper and previous experiments.The comparative analysis demonstrated that the new expression has better prediction ability than other expressions.The proposed empirical equation was used for direct shear simulations with the combined finite-discrete element method(FDEM),and it was found to align well with the experimental results.Considering both computational efficiency and accuracy,it was recommended to use a shear rate of 0.01 m/s for FDEM to carry out direct shear simulations.To balance the relationship between the number of elements and the simulation results in the direct shear simulations,the recommended element size is 1 mm.