Particle morphology is critical in affecting the crushing behavior of rockfill materials.In contrast,most current single particle simulations lack satisfactory morphology accuracy,and the resulting crushing modes devi...Particle morphology is critical in affecting the crushing behavior of rockfill materials.In contrast,most current single particle simulations lack satisfactory morphology accuracy,and the resulting crushing modes deviate from observations to some extent.Therefore,we reconstruct the real particle morphology with the spherical harmonic(SH)method and employ the finite-discrete element method(FDEM)to simulate the one-dimensional(1D)compressive crushing process of basalt particles commonly used in rockfill.The influences of four main morphological parameters,i.e.sphericity,aspect ratio,roundness,and convexity,on the single particle strength and the crushing modes are discussed.The results show that with the SH degree set to 15 and a mesh number of 20,480,the FDEM models of reconstructed particles achieve sufficient morphology accuracy and high computational efficiency.Based on the model,the simulation results demonstrate that the aspect ratio has the most significant impact on single particle strength,followed by sphericity.In contrast,roundness and convexity have a weaker effect than the above two parameters.Also,it is revealed that single particle strength decreases with increasing aspect ratio and sphericity,while it increases with higher roundness and convexity.Furthermore,aspect ratio significantly changes the initial crushing position,sphericity dominates post-crushing fragment size and quantity,and roundness mainly affects post-crushing morphology.The model results have been employed in establishing a support vector regression(SVR)-based predicted model,exhibiting good predictive performance and advantages for the optimization of rockfill particles in engineering.展开更多
Particle morphology has great influence on mechanical behaviour and hydro/thermal/electrical conductivities of granular materials.Surface reconstruction and mesh generation are critical to consider realistic particle ...Particle morphology has great influence on mechanical behaviour and hydro/thermal/electrical conductivities of granular materials.Surface reconstruction and mesh generation are critical to consider realistic particle shapes in various computational simulations.This study adopts the combined finitediscrete element method(FDEM)to investigate single particle crushing behaviour.Particle shapes were reconstructed with spherical harmonic(SH)in both spherical and Cartesian coordinate systems.Furthermore,the reconstructed surface mesh qualities in two coordinate systems are investigated and compared.Although the efficiency of the two SH systems in reconstructing star-like shapes is nearly identical,SH in Cartesian coordinate system can reconstruct non-star-like shapes with the help of surface parameterisation.Meanwhile,a higher triangular mesh quality is generated with spherical coordinate.In single particle crushing tests,the low mesh quality produces more fluctuations on load-displacement curves.The particles with more surficial mesh elements tend to have a lower contact stiffness due to more contact stress concentrations induced by complexity of morphology features and more volumetric tetrahedral elements.The fracture patterns are also influenced by mesh quality and density,e.g.a particle with fewer mesh elements has a simpler fragmentation pattern.This study serves as an essential step towards modelling particle breakage using FDEM with surface mesh directly from SH reconstruction.展开更多
Considering the effects of particle crushing and intermediate principal stress on material yielding strength, the spatial mobilization plane(SMP) yielding criterion and state parameter model including a general critic...Considering the effects of particle crushing and intermediate principal stress on material yielding strength, the spatial mobilization plane(SMP) yielding criterion and state parameter model including a general critical state line are selected in the analysis of cylindrical cavity expansion.Meanwhile, combining Rowe s flow rule and Bolton s simplification to stress-dilatancy relationship to reflect soil shear dilatancy and softening behavior, this paper analyzes the problem of cylindrical cavity expansion i...展开更多
As a typical solid waste from the iron and steel,the mechanical properties of steel slag are regarded as the core basis for realizing its resource recycling.To explore the influence of shape and external loading speed...As a typical solid waste from the iron and steel,the mechanical properties of steel slag are regarded as the core basis for realizing its resource recycling.To explore the influence of shape and external loading speed on the crushing characteristics of steel slag,single particle crushing tests were carried out.The research focuses on the correlation between parameters such as the load−displacement relationship of single particles,crushing mode,crushing energy,and Weibull modulus,as well as external loading rate and quantified morphological parameters.The results show that the single particle crushing modes of steel slag mainly consist of three modes:through-splitting,complete fragmentation and local cutting;Compared with natural aggregates or recycled materials,steel slag particles are found to potentially exhibit higher compressive strength and the increase in loading rate further accelerates the occurrence of particle crushing behavior;Significant impacts on the crushing mode and characteristic stress of steel slag particles are exerted by their shape differences,and the energy release mode is jointly regulated by shape and loading rate.This research provides theoretical guidance and technical support for the diversified utilization of steel slag single particles,a new type of solid waste resource.展开更多
Particle crushing commonly occurs in granular materials and affects their structures and mechanical properties.Unlike idealized particles in experimental single particle crushing tests with two loading points,natural ...Particle crushing commonly occurs in granular materials and affects their structures and mechanical properties.Unlike idealized particles in experimental single particle crushing tests with two loading points,natural particles are crushed under multicontact loading.To date,the criteria and patterns of par-ticle crushing under multicontact conditions are not fully understood.By using the three-dimensional discrete element method,this report explores the effect of multicontact loading on the crushing criterion of a single particle,the crushing pattern,and the relationship between the particle crushing strength and loading distribution.The particles are modelled as aggregates of glued Voronoi polyhedra.The numer-ical results indicate that the logarithm of the mean principal stress has a good linear correlation with the coordination number.For a specific coordination number,the number of child particles presents a significant normal distribution.For a specific number of child particles,the volumes of child particles can be statistically described as normal or gamma distribution.Three typical models are proposed to qual-itatively analyse the relationship between the loading distribution and crushing strength.The relevant conclusions can be helpful in engineering practice and in further studies on crushable granular materials via the discrete element method.展开更多
An experimental study is presented to measure the elastic,yielding,and crushing properties of individual particles under compression using substrates made of aluminum alloy,stainless steel,and sapphire.Carefully selec...An experimental study is presented to measure the elastic,yielding,and crushing properties of individual particles under compression using substrates made of aluminum alloy,stainless steel,and sapphire.Carefully selected,highly spherical individual Ottawa sand particles of 0.75e1.1 mm in nominal diameter were compressed between two smooth substrates,and the loadedeformation curves were analyzed by Hertz elastic contact theory to derive their reduced modulus and Young’s modulus as well as yielding and crushing strengths,which vary significantly with the type of substrate materials.Further analysis of the yielding and plastic deformation at the particle-substrate contact shows that the yield strength or hardness of the substrate materials dominates the local contact behavior and hence affects the measured apparent yielding and crushing strengths.The two softer substrates(aluminum alloy and stainless steel)actually lead to underestimated apparent shear yield strengths of quartz particles by 60.4%and 54.2%,respectively,which are actually the yielding of substrates,while the true particle yielding occurs in the sapphire-particle contact.Moreover,the two softer substrates cause much overestimated crushing strengths of the quartz particles by 50.4%and 36.4%,respectively.Selection of inappropriate substrate materials and inappropriate interpretation of the particle-substrate contact can lead to significant errors in the measured yielding and crushing strengths.It is recommended that single particle compression testing uses substrates with yield strength greater than that of the tested particles and result interpretation also considers the elastic and yielding behaviors of the substrates.展开更多
The correlation between hydrogen absorption capacity(HAC)and the micro structure of Sm_(26.2)Co_(bal)Fe_(x)Cu_(4.0)Zr_(2.3)(x=23 wt%,25 wt%,27 wt%,30 wt%)ingots and cast strips was systematically investigated.As the t...The correlation between hydrogen absorption capacity(HAC)and the micro structure of Sm_(26.2)Co_(bal)Fe_(x)Cu_(4.0)Zr_(2.3)(x=23 wt%,25 wt%,27 wt%,30 wt%)ingots and cast strips was systematically investigated.As the temperature rises from 373 to 423 K,the activation time,hydrogen absorption time and HAC of the Sm_(26.2)Co_(bal)Fe_(23)Cu_(4.0)Zr_(2.3)ingot decrease by 14.4%,14.1%,and 19.3%,respectively.Dispersed 1:5phase provides more channels for hydrogen diffusion,which is the main reason that HAC increases with the x increasing.The HAC of the same compound strips increases as the particles size of the pre-crushed decreases.However,no further embrittlement behavior appears in pre-crushed strips,which reaches an equal HAC as ingots.Micro-computerized tomography reveals that ingots contain small spherical-like holes and large flake micro-cracks,whereas strips mainly contain elliptical pores.The effects of grain size and inner defects size on structure stability were invested by Abaqus.Simulation results reveal that the superior embrittlement behavior of the ingots is predominantly influenced by the presence of large flake-like micro-cracks.展开更多
Accurately simulating the crushing process of ore particles in a semi-autogenous grinding mill (SAG mill) is quite challenging. This study utilizes the discrete element method (DEM) to construct a breakage model for o...Accurately simulating the crushing process of ore particles in a semi-autogenous grinding mill (SAG mill) is quite challenging. This study utilizes the discrete element method (DEM) to construct a breakage model for ore particles. Calibration of the discrete element basic parameters and Tavares breakage model parameters is conducted based on angle of repose (AoR) tests and single-particle impact tests. 3D scanning is employed to capture the morphology of the ore for particle modeling. On this basis, a discrete element breakage model for ore particles is built for single-particle impact simulations and validated through testing to determine the calibrated model parameters. The results indicate that the AoR angles and stacking shapes from the simulation and tests are highly similar, with a relative error of about 0.19%. The similarity in crushing outcomes and quantitative values between single-particle impact simulations and tests preliminary validates the reliability of the calibration method and the applicability of the Tavares breakage model, successfully determining a group of model parameters suitable for simulating ore particle crushing processes. This study lays the groundwork for utilizing DEM to simulate the visualization of ore particle crushing.展开更多
In this paper,the densely arrayed bonded particle model is proposed for simulation of granular materials with discrete element method(DEM)considering particle crushing.This model can solve the problem of pore calculat...In this paper,the densely arrayed bonded particle model is proposed for simulation of granular materials with discrete element method(DEM)considering particle crushing.This model can solve the problem of pore calculation after the grains are crushed,and reduce the producing time of specimen.In this work,several one-dimensional compressing simulations are carried out to investigate the effect of particle crushing on mechanical properties of granular materials under a wide range of stress.The results show that the crushing process of granular materials can be divided into four different stages according to er-logσy curves.At the end of the second stage,there exists a yield point,after which the physical and mechanical properties of specimens will change significantly.Under extremely high stress,particle crushing will wipe some initial information of specimens,and specimens with different initial gradings and void ratios present some similar characteristics.Particle crushing has great influence on grading,lateral pressure coefficient and compressibility of granular materials,and introduce extra irreversible volume deformation,which is necessary to be considered in modelling of granular materials in wide stress range.展开更多
In order to better understand the mechanical properties of graded crushed rocks （GCRs） and to optimize the relevant design, a numerical test method based on the particle flow modeling technique PFC2D is developed fo...In order to better understand the mechanical properties of graded crushed rocks （GCRs） and to optimize the relevant design, a numerical test method based on the particle flow modeling technique PFC2D is developed for the California bearing ratio （CBR） test on GGRs. The effects of different testing conditions and micro-mechanical parameters used in the model on the CBR numerical results have been systematically studied. The reliability of the numerical technique is verified. The numerical results suggest that the influences of the loading rate and Poisson＇s ratio on the CBR numerical test results are not significant. As such, a loading rate of 1.0-3.0 mm/min, a piston diameter of 5 cm, a specimen height of 15 cm and a specimen diameter of 15 cm are adopted for the CBR numerical test. The numerical results reveal that the GBR values increase with the friction coefficient at the contact and shear modulus of the rocks, while the influence of Poisson＇s ratio on the GBR values is insignificant. The close agreement between the CBR numerical results and experimental results suggests that the numerical simulation of the CBR values is promising to help assess the mechanical properties of GGRs and to optimize the grading design. Be- sides, the numerical study can provide useful insights on the mesoscopic mechanism.展开更多
A simple constitutive model is presented to describe the mechanical behaviors of granular soils in a large stress range. A novel normal compression line(NCL) is first expressed by introducing a limit void ratio(e_L) i...A simple constitutive model is presented to describe the mechanical behaviors of granular soils in a large stress range. A novel normal compression line(NCL) is first expressed by introducing a limit void ratio(e_L) in the double logarithmic scale.Subsequently, a state parameter(ξ) is defined to quantify the current state of granular soils, and a unified hardening parameter(H)that is a function of the state parameter(ξ) is developed to govern the hardening process of the drop-shaped yield surface.Combining with flow rule, a constitutive model for granular soils is proposed. Finally, the comparison between the predictions and the test results of Cambria sand and Coarse-grained material indicates that the model is able to describe the mechanical behaviors of granular soils in a large stress range.展开更多
基金financial support to this study from the National Natural Science Foundation of China,NSFC(Grant No.52278367).
文摘Particle morphology is critical in affecting the crushing behavior of rockfill materials.In contrast,most current single particle simulations lack satisfactory morphology accuracy,and the resulting crushing modes deviate from observations to some extent.Therefore,we reconstruct the real particle morphology with the spherical harmonic(SH)method and employ the finite-discrete element method(FDEM)to simulate the one-dimensional(1D)compressive crushing process of basalt particles commonly used in rockfill.The influences of four main morphological parameters,i.e.sphericity,aspect ratio,roundness,and convexity,on the single particle strength and the crushing modes are discussed.The results show that with the SH degree set to 15 and a mesh number of 20,480,the FDEM models of reconstructed particles achieve sufficient morphology accuracy and high computational efficiency.Based on the model,the simulation results demonstrate that the aspect ratio has the most significant impact on single particle strength,followed by sphericity.In contrast,roundness and convexity have a weaker effect than the above two parameters.Also,it is revealed that single particle strength decreases with increasing aspect ratio and sphericity,while it increases with higher roundness and convexity.Furthermore,aspect ratio significantly changes the initial crushing position,sphericity dominates post-crushing fragment size and quantity,and roundness mainly affects post-crushing morphology.The model results have been employed in establishing a support vector regression(SVR)-based predicted model,exhibiting good predictive performance and advantages for the optimization of rockfill particles in engineering.
基金financially supported by Australian Research Council(Projects DP170102886)The University of Sydney via SOAR(Sydney Research Accelerator)Fellowship。
文摘Particle morphology has great influence on mechanical behaviour and hydro/thermal/electrical conductivities of granular materials.Surface reconstruction and mesh generation are critical to consider realistic particle shapes in various computational simulations.This study adopts the combined finitediscrete element method(FDEM)to investigate single particle crushing behaviour.Particle shapes were reconstructed with spherical harmonic(SH)in both spherical and Cartesian coordinate systems.Furthermore,the reconstructed surface mesh qualities in two coordinate systems are investigated and compared.Although the efficiency of the two SH systems in reconstructing star-like shapes is nearly identical,SH in Cartesian coordinate system can reconstruct non-star-like shapes with the help of surface parameterisation.Meanwhile,a higher triangular mesh quality is generated with spherical coordinate.In single particle crushing tests,the low mesh quality produces more fluctuations on load-displacement curves.The particles with more surficial mesh elements tend to have a lower contact stiffness due to more contact stress concentrations induced by complexity of morphology features and more volumetric tetrahedral elements.The fracture patterns are also influenced by mesh quality and density,e.g.a particle with fewer mesh elements has a simpler fragmentation pattern.This study serves as an essential step towards modelling particle breakage using FDEM with surface mesh directly from SH reconstruction.
基金Supported by National Natural Science Foundation of China (No. 50639010)PhD Start-up Research Fund of Northeast Dianli University (2010)
文摘Considering the effects of particle crushing and intermediate principal stress on material yielding strength, the spatial mobilization plane(SMP) yielding criterion and state parameter model including a general critical state line are selected in the analysis of cylindrical cavity expansion.Meanwhile, combining Rowe s flow rule and Bolton s simplification to stress-dilatancy relationship to reflect soil shear dilatancy and softening behavior, this paper analyzes the problem of cylindrical cavity expansion i...
基金Project(52025085)supported by the National Science Foundation for Distinguished Young Scholars of ChinaProjects(52208421,52408394)supported by the National Natural Science Foundation of China+2 种基金Project(2023JJ40050)supported by the Hunan Provincial Natural Science Foundation,ChinaProject(2024JJ1001)supported by the Science Fund for Creative Research Groups of Hunan Provincial Natural Science Foundation,ChinaProject(kfj210201)supported by the Open Fund of the Key Laboratory of Highway Engineering of Ministry of Education(Changsha University of Science&Technology),China。
文摘As a typical solid waste from the iron and steel,the mechanical properties of steel slag are regarded as the core basis for realizing its resource recycling.To explore the influence of shape and external loading speed on the crushing characteristics of steel slag,single particle crushing tests were carried out.The research focuses on the correlation between parameters such as the load−displacement relationship of single particles,crushing mode,crushing energy,and Weibull modulus,as well as external loading rate and quantified morphological parameters.The results show that the single particle crushing modes of steel slag mainly consist of three modes:through-splitting,complete fragmentation and local cutting;Compared with natural aggregates or recycled materials,steel slag particles are found to potentially exhibit higher compressive strength and the increase in loading rate further accelerates the occurrence of particle crushing behavior;Significant impacts on the crushing mode and characteristic stress of steel slag particles are exerted by their shape differences,and the energy release mode is jointly regulated by shape and loading rate.This research provides theoretical guidance and technical support for the diversified utilization of steel slag single particles,a new type of solid waste resource.
基金supported by the National Natural Science Foundation of China(grant Nos.51809292 and 51978531).
文摘Particle crushing commonly occurs in granular materials and affects their structures and mechanical properties.Unlike idealized particles in experimental single particle crushing tests with two loading points,natural particles are crushed under multicontact loading.To date,the criteria and patterns of par-ticle crushing under multicontact conditions are not fully understood.By using the three-dimensional discrete element method,this report explores the effect of multicontact loading on the crushing criterion of a single particle,the crushing pattern,and the relationship between the particle crushing strength and loading distribution.The particles are modelled as aggregates of glued Voronoi polyhedra.The numer-ical results indicate that the logarithm of the mean principal stress has a good linear correlation with the coordination number.For a specific coordination number,the number of child particles presents a significant normal distribution.For a specific number of child particles,the volumes of child particles can be statistically described as normal or gamma distribution.Three typical models are proposed to qual-itatively analyse the relationship between the loading distribution and crushing strength.The relevant conclusions can be helpful in engineering practice and in further studies on crushable granular materials via the discrete element method.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.41372304 and 51679198),and China Scholarship Council Fellowship awarded to the first author.The authors are grateful to Dr.Yibing Deng of the University of Massachusetts Amherst for acquiring the optical images of sand particles.
文摘An experimental study is presented to measure the elastic,yielding,and crushing properties of individual particles under compression using substrates made of aluminum alloy,stainless steel,and sapphire.Carefully selected,highly spherical individual Ottawa sand particles of 0.75e1.1 mm in nominal diameter were compressed between two smooth substrates,and the loadedeformation curves were analyzed by Hertz elastic contact theory to derive their reduced modulus and Young’s modulus as well as yielding and crushing strengths,which vary significantly with the type of substrate materials.Further analysis of the yielding and plastic deformation at the particle-substrate contact shows that the yield strength or hardness of the substrate materials dominates the local contact behavior and hence affects the measured apparent yielding and crushing strengths.The two softer substrates(aluminum alloy and stainless steel)actually lead to underestimated apparent shear yield strengths of quartz particles by 60.4%and 54.2%,respectively,which are actually the yielding of substrates,while the true particle yielding occurs in the sapphire-particle contact.Moreover,the two softer substrates cause much overestimated crushing strengths of the quartz particles by 50.4%and 36.4%,respectively.Selection of inappropriate substrate materials and inappropriate interpretation of the particle-substrate contact can lead to significant errors in the measured yielding and crushing strengths.It is recommended that single particle compression testing uses substrates with yield strength greater than that of the tested particles and result interpretation also considers the elastic and yielding behaviors of the substrates.
基金Project supported by the National Key Research and Development Program of China(2022YFB3505303,2021YFB3503100,2021YFB3501500)the Major Projects in Inner Mongolia Autonomous Region of China(2021ZD0035)。
文摘The correlation between hydrogen absorption capacity(HAC)and the micro structure of Sm_(26.2)Co_(bal)Fe_(x)Cu_(4.0)Zr_(2.3)(x=23 wt%,25 wt%,27 wt%,30 wt%)ingots and cast strips was systematically investigated.As the temperature rises from 373 to 423 K,the activation time,hydrogen absorption time and HAC of the Sm_(26.2)Co_(bal)Fe_(23)Cu_(4.0)Zr_(2.3)ingot decrease by 14.4%,14.1%,and 19.3%,respectively.Dispersed 1:5phase provides more channels for hydrogen diffusion,which is the main reason that HAC increases with the x increasing.The HAC of the same compound strips increases as the particles size of the pre-crushed decreases.However,no further embrittlement behavior appears in pre-crushed strips,which reaches an equal HAC as ingots.Micro-computerized tomography reveals that ingots contain small spherical-like holes and large flake micro-cracks,whereas strips mainly contain elliptical pores.The effects of grain size and inner defects size on structure stability were invested by Abaqus.Simulation results reveal that the superior embrittlement behavior of the ingots is predominantly influenced by the presence of large flake-like micro-cracks.
文摘Accurately simulating the crushing process of ore particles in a semi-autogenous grinding mill (SAG mill) is quite challenging. This study utilizes the discrete element method (DEM) to construct a breakage model for ore particles. Calibration of the discrete element basic parameters and Tavares breakage model parameters is conducted based on angle of repose (AoR) tests and single-particle impact tests. 3D scanning is employed to capture the morphology of the ore for particle modeling. On this basis, a discrete element breakage model for ore particles is built for single-particle impact simulations and validated through testing to determine the calibrated model parameters. The results indicate that the AoR angles and stacking shapes from the simulation and tests are highly similar, with a relative error of about 0.19%. The similarity in crushing outcomes and quantitative values between single-particle impact simulations and tests preliminary validates the reliability of the calibration method and the applicability of the Tavares breakage model, successfully determining a group of model parameters suitable for simulating ore particle crushing processes. This study lays the groundwork for utilizing DEM to simulate the visualization of ore particle crushing.
基金The authors wish to thank the National Natural Science Foundation of China(No.11772117)the Fundamental Research Funds for the Central Universities(No.2015B37414)+1 种基金Henan Scientific and Technical Project under Grant(No.192102310480)Key Scientific Research Project of Colleges and Universities in Henan Province(CN)(21B560015)for financial support.
文摘In this paper,the densely arrayed bonded particle model is proposed for simulation of granular materials with discrete element method(DEM)considering particle crushing.This model can solve the problem of pore calculation after the grains are crushed,and reduce the producing time of specimen.In this work,several one-dimensional compressing simulations are carried out to investigate the effect of particle crushing on mechanical properties of granular materials under a wide range of stress.The results show that the crushing process of granular materials can be divided into four different stages according to er-logσy curves.At the end of the second stage,there exists a yield point,after which the physical and mechanical properties of specimens will change significantly.Under extremely high stress,particle crushing will wipe some initial information of specimens,and specimens with different initial gradings and void ratios present some similar characteristics.Particle crushing has great influence on grading,lateral pressure coefficient and compressibility of granular materials,and introduce extra irreversible volume deformation,which is necessary to be considered in modelling of granular materials in wide stress range.
基金supported by the Program for New Century Excellent Talents in University (NCET-08-0749)Fundamental Research Funds for the Central Universities (CHD2012JC054)
文摘In order to better understand the mechanical properties of graded crushed rocks （GCRs） and to optimize the relevant design, a numerical test method based on the particle flow modeling technique PFC2D is developed for the California bearing ratio （CBR） test on GGRs. The effects of different testing conditions and micro-mechanical parameters used in the model on the CBR numerical results have been systematically studied. The reliability of the numerical technique is verified. The numerical results suggest that the influences of the loading rate and Poisson＇s ratio on the CBR numerical test results are not significant. As such, a loading rate of 1.0-3.0 mm/min, a piston diameter of 5 cm, a specimen height of 15 cm and a specimen diameter of 15 cm are adopted for the CBR numerical test. The numerical results reveal that the GBR values increase with the friction coefficient at the contact and shear modulus of the rocks, while the influence of Poisson＇s ratio on the GBR values is insignificant. The close agreement between the CBR numerical results and experimental results suggests that the numerical simulation of the CBR values is promising to help assess the mechanical properties of GGRs and to optimize the grading design. Be- sides, the numerical study can provide useful insights on the mesoscopic mechanism.
基金supported by the National Basic Research Program of China(Grant No.2014CB47006)the National Natural Science Foundation of China(Grant Nos.51579005&11672015)
文摘A simple constitutive model is presented to describe the mechanical behaviors of granular soils in a large stress range. A novel normal compression line(NCL) is first expressed by introducing a limit void ratio(e_L) in the double logarithmic scale.Subsequently, a state parameter(ξ) is defined to quantify the current state of granular soils, and a unified hardening parameter(H)that is a function of the state parameter(ξ) is developed to govern the hardening process of the drop-shaped yield surface.Combining with flow rule, a constitutive model for granular soils is proposed. Finally, the comparison between the predictions and the test results of Cambria sand and Coarse-grained material indicates that the model is able to describe the mechanical behaviors of granular soils in a large stress range.
