The surrounding rock is prone to large-scale loosening and failure after the excavation of shallow large-span caverns because of the thin overlying strata and large cross-section span.The rational design of bolt suppo...The surrounding rock is prone to large-scale loosening and failure after the excavation of shallow large-span caverns because of the thin overlying strata and large cross-section span.The rational design of bolt support is very important to the safety control of surrounding rock as a common support means.The control mechanism and design method of bolt support for shallow-buried large-span caverns is carried out.The calculation method of bolt prestress and length based on arched failure and collapsed failure mode is established.The influence mechanism of different influencing factors on the bolt prestress and length is clarified.At the same time,the constant resistance energy-absorbing bolt with high strength and high toughness is developed,and the comparative test of mechanical properties is carried out.On this basis,the design method of high prestressed bolt support for shallow-buried large-span caverns is put forward,and the field test is carried out in Qingdao metro station in China.The monitoring results show that the maximum roof settlement is 6.8 mm after the new design method is adopted,and the effective control of the shallow-buried large-span caverns is realized.The research results can provide theoretical and technical support for the safety control of shallow-buried large-span caverns.展开更多
Toppling failure of rock mass/soil slope is an important geological and environmental problem.Clarifying its failure mechanism under different conditions has great significance in engineering.The toppling failure of a...Toppling failure of rock mass/soil slope is an important geological and environmental problem.Clarifying its failure mechanism under different conditions has great significance in engineering.The toppling failure of a cutting slope occurred in a hydropower station in Kyushu,Japan illustrates that the joint characteristic played a significant role in the occurrence of rock slope tipping failure.Thus,in order to consider the mechanical properties of jointed rock mass and the influence of geometric conditions,a simplified analytical approach based on the limit equilibrium method for modeling the flexural toppling of cut rock slopes is proposed to consider the influence of the mechanical properties and geometry condition of jointed rock mass.The theoretical solution is compared with the numerical solution taking Kyushu Hydropower Station in Japan as one case,and it is found that the theoretical solution obtained by the simplified analysis method is consistent with the numerical analytical solution,thus verifying the accuracy of the simplified method.Meanwhile,the Goodman-Bray approach conventionally used in engineering practice is improved according to the analytical results.The results show that the allowable slope angle may be obtained by the improved Goodman-Bray approach considering the joint spacing,the joint frictional angle and the tensile strength of rock mass together.展开更多
Cable-stayed bridges have been widely used in high-speed railway infrastructure.The accurate determination of cable’s representative temperatures is vital during the intricate processes of design,construction,and mai...Cable-stayed bridges have been widely used in high-speed railway infrastructure.The accurate determination of cable’s representative temperatures is vital during the intricate processes of design,construction,and maintenance of cable-stayed bridges.However,the representative temperatures of stayed cables are not specified in the existing design codes.To address this issue,this study investigates the distribution of the cable temperature and determinates its representative temperature.First,an experimental investigation,spanning over a period of one year,was carried out near the bridge site to obtain the temperature data.According to the statistical analysis of the measured data,it reveals that the temperature distribution is generally uniform along the cable cross-section without significant temperature gradient.Then,based on the limited data,the Monte Carlo,the gradient boosted regression trees(GBRT),and univariate linear regression(ULR)methods are employed to predict the cable’s representative temperature throughout the service life.These methods effectively overcome the limitations of insufficient monitoring data and accurately predict the representative temperature of the cables.However,each method has its own advantages and limitations in terms of applicability and accuracy.A comprehensive evaluation of the performance of these methods is conducted,and practical recommendations are provided for their application.The proposed methods and representative temperatures provide a good basis for the operation and maintenance of in-service long-span cable-stayed bridges.展开更多
An accurate long-term energy demand forecasting is essential for energy planning and policy making. However, due to the immature energy data collecting and statistical methods, the available data are usually limited i...An accurate long-term energy demand forecasting is essential for energy planning and policy making. However, due to the immature energy data collecting and statistical methods, the available data are usually limited in many regions. In this paper, on the basis of comprehensive literature review, we proposed a hybrid model based on the long-range alternative energy planning (LEAP) model to improve the accuracy of energy demand forecasting in these regions. By taking Hunan province, China as a typical case, the proposed hybrid model was applied to estimating the possible future energy demand and energy-saving potentials in different sectors. The structure of LEAP model was estimated by Sankey energy flow, and Leslie matrix and autoregressive integrated moving average (ARIMA) models were used to predict the population, industrial structure and transportation turnover, respectively. Monte-Carlo method was employed to evaluate the uncertainty of forecasted results. The results showed that the hybrid model combined with scenario analysis provided a relatively accurate forecast for the long-term energy demand in regions with limited statistical data, and the average standard error of probabilistic distribution in 2030 energy demand was as low as 0.15. The prediction results could provide supportive references to identify energy-saving potentials and energy development pathways.展开更多
The flow stress of ferrite/pearlite steel under uni-axial tension was simulated with finite element method (FEM) by applying commercial software MARC/MENTAT. Flow stress curves of ferrite/pearlite steels were calculat...The flow stress of ferrite/pearlite steel under uni-axial tension was simulated with finite element method (FEM) by applying commercial software MARC/MENTAT. Flow stress curves of ferrite/pearlite steels were calculated based on unit cell model. The effects of volume fraction, distribution and the aspect ratio of pearlite on tensile properties have been investigated.展开更多
Aiming at that the successive test data set of the strapdown inertial measurement unit is always small,a Bayesian method is used to study its statistical characteristics.Its prior and posterior distributions are set u...Aiming at that the successive test data set of the strapdown inertial measurement unit is always small,a Bayesian method is used to study its statistical characteristics.Its prior and posterior distributions are set up by the method and the pretest,sample and population information.Some statistical inferences can be made based on the posterior distribution.It can reduce the statistical analysis error in the case of small sample set.展开更多
This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor ...This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.展开更多
In the current work, to predict and improve the formability of deep drawing process for steel plate cold rolled commercial grade （SPCC） sheets, three parameters including the blanking force, the die and punch comer ...In the current work, to predict and improve the formability of deep drawing process for steel plate cold rolled commercial grade （SPCC） sheets, three parameters including the blanking force, the die and punch comer radius were considered. The experimental plan according to Taguchi＇s orthogonal array was coupled with the finite element method （FEM） simulations. Firstly, the data from the test of stress-strain and forming limit curves were used as input into ABAQUS/Explicit finite element code to predict the failure occurrence of deep drawing process. The three parameters were then validated to establish their effects on the press formability. The optimum case found via simulation was finally confirmed through an experiment. In order to obtain the complex curve profile of cup shape after deep drawing, the anisotropic behavior of earring phenomenon was modeled and implemented into FEM. After such phenomenon was correctly predicted, an error metric compared with design curve was then measured.展开更多
The pit limit optimization is discussed, which is one of the most important problems in the combined min-ing method, on the basis of the economic model of ore-blocks. A new principle of the limit optimization is put f...The pit limit optimization is discussed, which is one of the most important problems in the combined min-ing method, on the basis of the economic model of ore-blocks. A new principle of the limit optimization is put for-ward through analyzing the limitations of moving cone method under such conditions. With a view to recovering asmuch mineral resource as possible and making the maximum profit from the whole deposit, the new principle is tomaximize the sum of gain from both open-pit and underground mining. The mathematical models along the horizon-tal and vertical directions and modules for software package (DM&MCAD) have been developed and tested inTonglushan Copper Mine. It has been proved to be rather effective in the mining practice.展开更多
The objective of the paper is to compute the optimal burn-out conditions and control requirements that would result in maximum down-range/cross-range performance of a waverider type hypersonic boost-glide(HBG) vehicle...The objective of the paper is to compute the optimal burn-out conditions and control requirements that would result in maximum down-range/cross-range performance of a waverider type hypersonic boost-glide(HBG) vehicle within the medium and intermediate ranges,and compare its performance with the performances of wing-body and lifting-body vehicles vis-a-vis the g-load and the integrated heat load experienced by vehicles for the medium-sized launch vehicle under study.Trajectory optimization studies were carried out by considering the heat rate and dynamic pressure constraints.The trajectory optimization problem is modeled as a nonlinear,multiphase,constraint optimal control problem and is solved using a hp-adaptive pseudospectral method.Detail modeling aspects of mass,aerodynamics and aerothermodynamics for the launch and glide vehicles have been discussed.It was found that the optimal burn-out angles for waverider and wing-body configurations are approximately 5° and 14.8°,respectively,for maximum down-range performance under the constraint heat rate environment.The down-range and cross-range performance of HBG waverider configuration is nearly 1.3 and 2 times that of wing-body configuration respectively.The integrated heat load experienced by the HBG waverider was found to be approximately an order of magnitude higher than that of a lifting-body configuration and 5 times that of a wing-body configuration.The footprints and corresponding heat loads and control requirements for the three types of glide vehicles are discussed for the medium range launch vehicle under consideration.展开更多
In the process of shield tunneling through soft soil layers,the presence of confined water ahead poses a significant threat to the stability of the tunnel face.Therefore,it is crucial to consider the impact of confine...In the process of shield tunneling through soft soil layers,the presence of confined water ahead poses a significant threat to the stability of the tunnel face.Therefore,it is crucial to consider the impact of confined water on the limit support pressure of the tunnel face.This study employed the finite element method(FEM)to analyze the limit support pressure of shield tunnel face instability within a pressurized water-containing layer.Subsequently,a multiple linear regression approach was applied to derive a concise solution formula for the limit support pressure,incorporating various influencing factors.The analysis yields the following conclusions:1)The influence of confined water on the instability mode of the tunnel face in soft soil layers makes the displacement response of the strata not significant when the face is unstable;2)The limit support pressure increases approximately linearly with the pressure head,shield tunnel diameter,and tunnel burial depth.And inversely proportional to the thickness of the impermeable layer,soil cohesion and internal friction angle;3)Through an engineering case study analysis,the results align well with those obtained from traditional theoretical methods,thereby validating the rationality of the equations proposed in this paper.Furthermore,the proposed equations overcome the limitation of traditional theoretical approaches considering the influence of changes in impermeable layer thickness.It can accurately depict the dynamic variation in the required limit support pressure to maintain the stability of the tunnel face during shield tunneling,thus better reflecting engineering reality.展开更多
Due to rainfall infiltration,groundwater activity,geological processes,and natural erosion,soil often exhibits heterogeneity and unsaturation.Additionally,seismic events can compromise slope stability.Existing analyti...Due to rainfall infiltration,groundwater activity,geological processes,and natural erosion,soil often exhibits heterogeneity and unsaturation.Additionally,seismic events can compromise slope stability.Existing analytical solutions typically consider a single failure mode,leading to inaccurate slope stability assessments.This study analyzes the impact of matric suction through three nonlinear shear strength models and adopts a heterogeneous soil model where cohesion linearly increases with depth.An improved pseudo-dynamic method is used to account for seismic effects.Based on a three-dimensional(3D)trumpet-shaped rotational failure mechanism,a new framework is established to analyze the stability of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects.The internal energy dissipation rate and external power at failure are calculated,and the gravity increase method is introduced to derive an explicit expression for the safety factor(F_(s)).The results are compared with previously published results,demonstrating the effectiveness of the proposed method.Sensitivity analyses on different parameters are conducted,discussing the influence of various factors on F s.This study proposes a new formula for calculating the F_(s) of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects,providing a practical application for slope engineering.展开更多
基金Project(2023YFC3805700) supported by the National Key Research and Development Program of ChinaProjects(42477166,42277174) supported by the National Natural Science Foundation of China+2 种基金Project(2024JCCXSB01) supported by the Fundamental Research Funds for the Central Universities,ChinaProject(KFJJ24-01M) supported by the State Key Laboratory of Explosion Science and Safety Protection,Beijing Institute of Technology,ChinaProject(HLCX-2024-04) supported by the Open Foundation of Collaborative Innovation Center of Green Development and Ecological Restoration of Mineral Resources,China。
文摘The surrounding rock is prone to large-scale loosening and failure after the excavation of shallow large-span caverns because of the thin overlying strata and large cross-section span.The rational design of bolt support is very important to the safety control of surrounding rock as a common support means.The control mechanism and design method of bolt support for shallow-buried large-span caverns is carried out.The calculation method of bolt prestress and length based on arched failure and collapsed failure mode is established.The influence mechanism of different influencing factors on the bolt prestress and length is clarified.At the same time,the constant resistance energy-absorbing bolt with high strength and high toughness is developed,and the comparative test of mechanical properties is carried out.On this basis,the design method of high prestressed bolt support for shallow-buried large-span caverns is put forward,and the field test is carried out in Qingdao metro station in China.The monitoring results show that the maximum roof settlement is 6.8 mm after the new design method is adopted,and the effective control of the shallow-buried large-span caverns is realized.The research results can provide theoretical and technical support for the safety control of shallow-buried large-span caverns.
基金Project(52109132)supported by the National Natural Science Foundation of ChinaProject(ZR2020QE270)supported by the Natural Science Foundation of Shandong Province,China+1 种基金Project(JMDPC202204)supported by State Key Laboratory of Strata Intelligent Control,Green Mining Co-founded by Shandong Province and the Ministry of Science and TechnologyShandong University of Science and Technology,China。
文摘Toppling failure of rock mass/soil slope is an important geological and environmental problem.Clarifying its failure mechanism under different conditions has great significance in engineering.The toppling failure of a cutting slope occurred in a hydropower station in Kyushu,Japan illustrates that the joint characteristic played a significant role in the occurrence of rock slope tipping failure.Thus,in order to consider the mechanical properties of jointed rock mass and the influence of geometric conditions,a simplified analytical approach based on the limit equilibrium method for modeling the flexural toppling of cut rock slopes is proposed to consider the influence of the mechanical properties and geometry condition of jointed rock mass.The theoretical solution is compared with the numerical solution taking Kyushu Hydropower Station in Japan as one case,and it is found that the theoretical solution obtained by the simplified analysis method is consistent with the numerical analytical solution,thus verifying the accuracy of the simplified method.Meanwhile,the Goodman-Bray approach conventionally used in engineering practice is improved according to the analytical results.The results show that the allowable slope angle may be obtained by the improved Goodman-Bray approach considering the joint spacing,the joint frictional angle and the tensile strength of rock mass together.
基金Project(2017G006-N)supported by the Project of Science and Technology Research and Development Program of China Railway Corporation。
文摘Cable-stayed bridges have been widely used in high-speed railway infrastructure.The accurate determination of cable’s representative temperatures is vital during the intricate processes of design,construction,and maintenance of cable-stayed bridges.However,the representative temperatures of stayed cables are not specified in the existing design codes.To address this issue,this study investigates the distribution of the cable temperature and determinates its representative temperature.First,an experimental investigation,spanning over a period of one year,was carried out near the bridge site to obtain the temperature data.According to the statistical analysis of the measured data,it reveals that the temperature distribution is generally uniform along the cable cross-section without significant temperature gradient.Then,based on the limited data,the Monte Carlo,the gradient boosted regression trees(GBRT),and univariate linear regression(ULR)methods are employed to predict the cable’s representative temperature throughout the service life.These methods effectively overcome the limitations of insufficient monitoring data and accurately predict the representative temperature of the cables.However,each method has its own advantages and limitations in terms of applicability and accuracy.A comprehensive evaluation of the performance of these methods is conducted,and practical recommendations are provided for their application.The proposed methods and representative temperatures provide a good basis for the operation and maintenance of in-service long-span cable-stayed bridges.
基金Project(51606225) supported by the National Natural Science Foundation of ChinaProject(2016JJ2144) supported by Hunan Provincial Natural Science Foundation of ChinaProject(502221703) supported by Graduate Independent Explorative Innovation Foundation of Central South University,China
文摘An accurate long-term energy demand forecasting is essential for energy planning and policy making. However, due to the immature energy data collecting and statistical methods, the available data are usually limited in many regions. In this paper, on the basis of comprehensive literature review, we proposed a hybrid model based on the long-range alternative energy planning (LEAP) model to improve the accuracy of energy demand forecasting in these regions. By taking Hunan province, China as a typical case, the proposed hybrid model was applied to estimating the possible future energy demand and energy-saving potentials in different sectors. The structure of LEAP model was estimated by Sankey energy flow, and Leslie matrix and autoregressive integrated moving average (ARIMA) models were used to predict the population, industrial structure and transportation turnover, respectively. Monte-Carlo method was employed to evaluate the uncertainty of forecasted results. The results showed that the hybrid model combined with scenario analysis provided a relatively accurate forecast for the long-term energy demand in regions with limited statistical data, and the average standard error of probabilistic distribution in 2030 energy demand was as low as 0.15. The prediction results could provide supportive references to identify energy-saving potentials and energy development pathways.
文摘The flow stress of ferrite/pearlite steel under uni-axial tension was simulated with finite element method (FEM) by applying commercial software MARC/MENTAT. Flow stress curves of ferrite/pearlite steels were calculated based on unit cell model. The effects of volume fraction, distribution and the aspect ratio of pearlite on tensile properties have been investigated.
文摘Aiming at that the successive test data set of the strapdown inertial measurement unit is always small,a Bayesian method is used to study its statistical characteristics.Its prior and posterior distributions are set up by the method and the pretest,sample and population information.Some statistical inferences can be made based on the posterior distribution.It can reduce the statistical analysis error in the case of small sample set.
基金Project(52278380)supported by the National Natural Science Foundation of ChinaProject(2023JJ30670)supported by the National Science Foundation of and Technology Major Project of Hunan Province,China。
文摘This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.
基金Project(107.02-2013.01)supported by the Vietnam’s National Foundation for Science and Technology Development
文摘In the current work, to predict and improve the formability of deep drawing process for steel plate cold rolled commercial grade （SPCC） sheets, three parameters including the blanking force, the die and punch comer radius were considered. The experimental plan according to Taguchi＇s orthogonal array was coupled with the finite element method （FEM） simulations. Firstly, the data from the test of stress-strain and forming limit curves were used as input into ABAQUS/Explicit finite element code to predict the failure occurrence of deep drawing process. The three parameters were then validated to establish their effects on the press formability. The optimum case found via simulation was finally confirmed through an experiment. In order to obtain the complex curve profile of cup shape after deep drawing, the anisotropic behavior of earring phenomenon was modeled and implemented into FEM. After such phenomenon was correctly predicted, an error metric compared with design curve was then measured.
基金Project (59704004) supported by the National Natural Science Foundation of ChinaProject (2000) supported by Foundation for University Key Teacher by the Ministry of Education
文摘The pit limit optimization is discussed, which is one of the most important problems in the combined min-ing method, on the basis of the economic model of ore-blocks. A new principle of the limit optimization is put for-ward through analyzing the limitations of moving cone method under such conditions. With a view to recovering asmuch mineral resource as possible and making the maximum profit from the whole deposit, the new principle is tomaximize the sum of gain from both open-pit and underground mining. The mathematical models along the horizon-tal and vertical directions and modules for software package (DM&MCAD) have been developed and tested inTonglushan Copper Mine. It has been proved to be rather effective in the mining practice.
基金the Chinese Scholarship Council for supporting the research
文摘The objective of the paper is to compute the optimal burn-out conditions and control requirements that would result in maximum down-range/cross-range performance of a waverider type hypersonic boost-glide(HBG) vehicle within the medium and intermediate ranges,and compare its performance with the performances of wing-body and lifting-body vehicles vis-a-vis the g-load and the integrated heat load experienced by vehicles for the medium-sized launch vehicle under study.Trajectory optimization studies were carried out by considering the heat rate and dynamic pressure constraints.The trajectory optimization problem is modeled as a nonlinear,multiphase,constraint optimal control problem and is solved using a hp-adaptive pseudospectral method.Detail modeling aspects of mass,aerodynamics and aerothermodynamics for the launch and glide vehicles have been discussed.It was found that the optimal burn-out angles for waverider and wing-body configurations are approximately 5° and 14.8°,respectively,for maximum down-range performance under the constraint heat rate environment.The down-range and cross-range performance of HBG waverider configuration is nearly 1.3 and 2 times that of wing-body configuration respectively.The integrated heat load experienced by the HBG waverider was found to be approximately an order of magnitude higher than that of a lifting-body configuration and 5 times that of a wing-body configuration.The footprints and corresponding heat loads and control requirements for the three types of glide vehicles are discussed for the medium range launch vehicle under consideration.
基金Project(ZDRW-ZS-2021-3)supported by the Key Deployment Projects of Chinese Academy of SciencesProjects(52179116,51991392)supported by the National Natural Science Foundation of China。
文摘In the process of shield tunneling through soft soil layers,the presence of confined water ahead poses a significant threat to the stability of the tunnel face.Therefore,it is crucial to consider the impact of confined water on the limit support pressure of the tunnel face.This study employed the finite element method(FEM)to analyze the limit support pressure of shield tunnel face instability within a pressurized water-containing layer.Subsequently,a multiple linear regression approach was applied to derive a concise solution formula for the limit support pressure,incorporating various influencing factors.The analysis yields the following conclusions:1)The influence of confined water on the instability mode of the tunnel face in soft soil layers makes the displacement response of the strata not significant when the face is unstable;2)The limit support pressure increases approximately linearly with the pressure head,shield tunnel diameter,and tunnel burial depth.And inversely proportional to the thickness of the impermeable layer,soil cohesion and internal friction angle;3)Through an engineering case study analysis,the results align well with those obtained from traditional theoretical methods,thereby validating the rationality of the equations proposed in this paper.Furthermore,the proposed equations overcome the limitation of traditional theoretical approaches considering the influence of changes in impermeable layer thickness.It can accurately depict the dynamic variation in the required limit support pressure to maintain the stability of the tunnel face during shield tunneling,thus better reflecting engineering reality.
基金Project(51378510)supported by the National Natural Science Foundation of China。
文摘Due to rainfall infiltration,groundwater activity,geological processes,and natural erosion,soil often exhibits heterogeneity and unsaturation.Additionally,seismic events can compromise slope stability.Existing analytical solutions typically consider a single failure mode,leading to inaccurate slope stability assessments.This study analyzes the impact of matric suction through three nonlinear shear strength models and adopts a heterogeneous soil model where cohesion linearly increases with depth.An improved pseudo-dynamic method is used to account for seismic effects.Based on a three-dimensional(3D)trumpet-shaped rotational failure mechanism,a new framework is established to analyze the stability of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects.The internal energy dissipation rate and external power at failure are calculated,and the gravity increase method is introduced to derive an explicit expression for the safety factor(F_(s)).The results are compared with previously published results,demonstrating the effectiveness of the proposed method.Sensitivity analyses on different parameters are conducted,discussing the influence of various factors on F s.This study proposes a new formula for calculating the F_(s) of 3D two-bench slopes in heterogeneous unsaturated soil under seismic effects,providing a practical application for slope engineering.
