Contact Force Chains Research Articles

Effect of grain dissolution on sloping ground

The static and dynamic stability of natural or constructed slopes can be affected by dissolution or dissolution-like phenomena. Their underlying mechanisms, however, remain unclear. New experimental results and discrete element simulations provide particle-level and macroscale information on the consequences of mineral dissolution on slope behavior. At the microscale, load-carrying grain arches develop around dissolving particles, the porosity increases, and contact force chains evolve to form a honeycomb topology. At the macroscale, while vertical settlements are the prevailing deformation pattern, lateral granular movements that create mass wasting are prominent in sloping ground, even under the quasi-static granular loss. Horizontal grain displacement is maximum at the surface and decreases linearly with the distance from the slope surface to become zero at the bottom boundaries, much like vertical granular displacement along the depth. Sediments with smaller friction angles and steeper slopes experience greater displacement, both vertically and horizontally. Slopes become flatter after dissolution, with the reduction in slope angle directly related to the loss in ground elevation, ΔH/Ho. Yet, because of the porous fabric that results from dissolution, vertical shortening is less than the upper bound, estimated from the loss in the solid mass fraction, ΔH/Ho≈SF. Under water-saturated conditions, the post-dissolution fabric may lead to sudden undrained shear and slope slide.

Investigation of Volumetric Block Proportion (VBP) Effect on Excavation-Induced Ground Response of Talus-like Rock Mass Based on DEM Simulations.

Due to the complexity of the talus-like rock mass with different values of volumetric block proportion (VPB), it is thus crucial to explore the VBP effect on the excavation-induced ground responses. We conduct a series of 2D DEM (discrete element method) simulations on a common circular tunnel excavation in the talus-like rock mass with different VBPs (0%, 15%, 50%, 85% and 100%). For each VBP, two support scenarios, i.e., unsupported and supported by a rigid lining, are considered. The micro characteristics of the excavation-induced ground responses, including the contact force, force chain, coordination number and shear-slip contact, and the stress distribution and ground settlement are elaborated in detail. Accordingly, three types of talus-like rock masses are identified as soil-, hybrid- and rock-types, corresponding to VBP = 0-15%, 50%, and 85-100%, respectively. It is found that the lining support is essential for maintaining the ground stability of a tunnel excavation in the soil- and hybrid-type talus-like rock masses while the backbones formed by rock blocks in the rock-type talus-like rock mass can provide a certain support for the surrounding ground. Our findings have important implications for optimizing the construction scheme of tunnel excavation in different types of talus-like rock masses.

Effects of morphological gene decay and mutation on the micro–macro mechanical behaviours of granular soils

Particle morphology is multi-scale in nature. To investigate the effects of particle morphology at a specific length scale on the macro–micro mechanical behaviours of granular soils, morphological gene decay and mutation was incorporated into discrete-element method (DEM) simulations through spherical harmonic-based principal component analysis. All DEM samples were subjected to axial compression and constant confining stress. The macro-scale and grain-scale behaviours of the granular assembly were investigated. It was found that particle morphology shows significant effects on macro-scale behaviours including initial stiffness, peak stress ratio, volumetric contraction and dilation, and shear band formation, as well as grain-scale behaviours including coordination number, particle rotation and granular skeleton sustaining the major contact force chains. Among the different length scales, local roundness contributes the most to stress ratio, volumetric strain and particle coordination number, while general form contributes the most to shear strain, particle rotation and fabric structure. Another interesting finding was that the particle morphological effects are well reflected in the granular skeleton sustaining the major contact force chains, which is featured with a strong variation of the degree of particle shape irregularity among different kinds of gene-mutated samples.

Microscopic investigation of the influence of complex stress states on internal erosion and its impacts on critical hydraulic gradients

AbstractInternal erosion involves the loss of fine particles within the matrix of coarse particles under seepage flow, posing a severe threat to hydraulic structures. This paper focuses on internal erosion considering anisotropic stress conditions. The influence of the anisotropic stress state, represented by vertical stress equal to, bigger than, or smaller than horizontal stress, was investigated using coupled computational fluid dynamics (CFD) and the discrete element method (DEM). Results show that the loss of fine particle specimens under anisotropic stress conditions is greater than that for samples under isotropic stress states, as the loss of fine particles leads to an evolution of anisotropy into isotropy, with local contact force chains gradually forming spatially isotropic structures. The strong force chains of specimens under triaxial compression were also found to develop a dominant orientation in the vertical direction, leading to clogging in the upward migration of fine particles and increasing the critical hydraulic gradient. In addition, the evolution of void ratio, hydraulic drag force, connectivity, and coordination number has also been analyzed to exhibit the influence of stress anisotropy on internal erosion.

Numerical simulation of the effect of internal hole defect size on the mechanical properties of limestone.

To better understand the effect of the size of hole defects on the mechanical properties of a rock mass, the two-dimensional particle flow discrete element code (PFC2D) is applied to establish rock mass models with single circular hole defects of different diameters. Uniaxial compressive strength (UCS) tests are conducted on each model by only taking the defect size (area) as a variable. This study analyzes each model’s stress-strain, contact force chain, crack evolution, meso-damage and failure, and mechanical properties. The results showed that with the size enlargement of the circular hole defects, each model’s UCS and elastic modulus gradually decrease, and the defect size is negatively correlated with the mechanical strength of the rock samples. The size of the hole defects affects the entire process of contact force chain and crack evolution. The larger the aperture dimension of the circular hole defects in each model, the greater the concentration degree of the contact force chain, the earlier the crack initiation, and the higher the degree of crack coalescence in the post-peak stage. The number of cracks decreases as the hole size increases, and the model is more prone to failure. Rock models’ strength and failure characteristics with different numbers and arrangements of hole defects are discussed under the same defect area condition.

SFG modified model and particle flow simulation

Based on the unified yield surface SFG model and combined with the unified hardening parameters, the elastoplastic constitutive model of unsaturated soil is derived. The model is capable of describing the stress–-strain characteristics of over-consolidated unsaturated soils in terms of softening and shear expansion. The model can be degraded to a uniform yield surface SFG model under normal consolidation. The theoretical values of the model were calculated by MAPLE and compared with the experimental results, and the results show that the model can simulate the relevant properties of over-consolidated unsaturated soils better. Using PFC3D to simulate unsaturated triaxial tests, the process of unsaturated soil triaxial experiments was simulated by introducing gas particles and differentiating between the effective stress of the soil and the matric suction, and it was concluded that with higher matric suction, the contact force chains between particles in the specimen become more frequent and it is more difficult to form shear zones.

Numerical simulation of mesomechanical properties of limestone containing dissolved hole and persistent joint

In order to reveal the complex mechanical properties and mesoscopic failure behavior of limestone rock mass containing both dissolved hole defect and persistent joint, numerical models are developed using the two-dimensional particle flow code (PFC2D) to carry out the uniaxial compressive strength (UCS) tests. The stress–strain, contact force chain, vertical stress field, and crack evolution characteristics of limestone samples containing circular holes and different dip angles persistent joints were analyzed. The results show that the UCS and elastic modulus of the rock samples can be reduced by the circular hole and the persistent joint, and the persistent joints with steep dip angles have a more obvious control effect on the mechanical properties of the rock samples. With the increase in loading stress level, the contact force chain in the hole-joint combination model gradually deflects slightly along the joint dip angle from the left and right sides of the hole and gradually spreads outward. Under uniaxial compression, the initiation cracks in persistent joints and rock blocks are primarily tensile cracks. The initiation positions first appear in the persistent joint, and the initiation positions in the rock block change from the upper and lower vertices of the circular hole to the junction below the joint with the increase of the joint dip angle. The crack initiation stress in the persistent joint is smaller than that in the corresponding rock block, and the control effect of the joint dip angle on the crack initiation stress of the whole rock sample is reduced.

Modelling of gas-solid-liquid flow and particle mixing in a rotary drum

Solid-liquid rotary drums have been widely practised in various industries, while the complex multiphase hydrodynamics hinders the understanding and optimisation of these apparatuses. In this work, the computational fluid dynamics-discrete element methoddata (CFD-DEM) coupled with volume of fluid (VOF) is developed to describe the gas-solid-liquid flow and mixing behaviours in a rotary drum considering inter-particle collisions, inter-phase interactions, and interface morphology. A smoothing method is used to link the quantities between the particle and computational grids, allowing the fine grids to resolve flow details such as the gas-liquid interface position and curvature. After model validations, the typical mixing behaviours of gas-solid-liquid flow in a rotary drum are studied. The effects of liquid presence and rotating speed on particle-scale behaviours (e.g., repose angle, active-passive zone depth, solid residence time and contact force chain) and the time evolved mixing performance (e.g., mixing index and dispersion) are studied. The results show a positive correlation of the active depth, mixing degree, and particle dispersion with the rotating speed. The liquid presence leads to a deeper active depth, prolonged solid residence time in the active zone, and lower contact force. The work sheds light on the design and process optimization of rotary drums.

Discrete Element Simulation of the Macro-Meso Mechanical Behaviors of Gas-Hydrate-Bearing Sediments under Dynamic Loading

Under the action of dynamic loadings such as earthquakes and volcanic activities, the mechanical properties of gas-hydrate-bearing sediments will deteriorate, leading to a decrease in the stability of hydrate reservoirs and even inducing geological disasters such as submarine landslides. In order to study the effect of dynamic loading on the mechanical properties of hydrate sediments, triaxial compression tests of numerical specimens were carried out by using particle flow code (PFC2D), and the macro-meso mechanical behaviors of specimens were investigated. The results show that the loading frequency has a small effect on the stiffness of the hydrate sediment, while it has a large effect on the peak strength. The peak strength increases and then decreases with the increase in loading frequency. Under the same loading frequency, the peak strength of the hydrate sediment increases with the increase in loading amplitude, and the stiffness of the specimen decreases with the increase in loading amplitude. The maximum shear expansion of the specimen changes with the movement of the phase change point and the rearrangement of the particles. The maximum shear expansion of the specimen changes with the movement of the phase change point and the change of the bearing capacity of the particles after the rearrangement, and the more forward the phase change point is, the stronger the bearing capacity of the specimen in the plastic stage. The shear dilatancy angle and the shear dilatancy amount both increase linearly with the increase in loading amplitude. The influence of loading frequency and amplitude on the contact force chain, displacement, crack expansion, and the number of cementation damage inside the sediment is mainly related to the average axial stress to which the specimen is subjected, and the number of cracks and cementation damage of the sediment specimen increases with the increase in the average axial stress to which the sediment specimen is subjected. As the rate of cementation damage increases, the distribution of shear zones becomes more obvious.

Research on the Macro-Mesoscopic Response Mechanism of Multisphere Approximated Heteromorphic Tailing Particles

Abstract The shape of tailing particles is essential factors of their macroscopic mechanical properties. Scholars have studied the effects of controllable factors, such as loading method, confining pressure, and strain rate, on the strength of tailing sand. However, research on the tailing particle structure and shape through laboratory tests has proved to be difficult due to the uncertain and discrete tailing particle distribution. Thus, the macro-mesoscopic response of heteromorphic tailing particles is rarely investigated. In this paper, the macro-mesoscopic response of heteromorphic tailing particles is studied using multisphere approximation, and numerical simulation of triaxial tests on the particles is conducted. Nonlinear evolution patterns of porosity, internal friction angle, and cohesion of heteromorphic tailing particles with the variation of angularity were investigated using the flexible boundary program developed in this study, which revealed the intrinsic relationship between the mesostructure evolution mechanism and the macroscopic engineering characteristics of heteromorphic tailing particles. The research results showed that (1) changes in angularity led to tailing particle rearrangements and, in turn, porosity changes. With increased angularity and confining pressure, particle sphericity decreased, and the deviatoric and peak stress increased accordingly. In the meantime, the softening was more significant as the peak stress was exceeded, while the cohesive force generally increased. (2) With fixed particle shape and angularity, the internal friction angle decreased slightly as the effective confining pressure increased. (3) In the shearing process, the simulated contact force chain evolution of tailing particles with different shapes was similar. The disordered contact force chains gradually undergo directional connection, i.e., the increased confining pressure reduced the number of free tailing particles and increased the number of stressed particles. (4) The triaxial stress-strain and peak stress in rigid boundary simulations under different confining pressures were slightly lower than those in the flexible boundary simulations. However, the difference was insignificant, indicating the good feasibility and reasonability of rigid boundary simulations for the macroscopic mechanical behaviors in triaxial tests. The research results could offer more direct insights into the macro-mesoscopic response and mechanical mechanisms of nonspherical particles and provide references for the simulation of tailings at the microscopic levels.

Multiscale modeling of seepage-induced suffusion and slope failure using a coupled FEM–DEM approach

Suffusion refers to the detachment and migration of fine particles through voids among coarse particles and is one of the major causes of slope failure. This study investigates the seepage-induced suffusion and slope instability using a hierarchical multiscale finite–discrete element method (FEM–DEM). An erosion law with the critical hydraulic gradient for the onset of suffusion is proposed. Two examples, including one-dimensional suffusion and biaxial compression tests, are performed to verify the proposed scheme. Emphases are placed on reproducing suffusion and progressive slope failure process under seepage flow. The results indicate that a shear band is initiated from the slope toe and gradually extends to the crest. The increase of erosion rate accelerates the process of suffusion and slope failure, whereas a higher critical hydraulic gradient plays an opposite role. In addition, fines loss caused by suffusion occurs mainly on the slope surface, especially near the slope toe. Microscopic analyses on locally embedded representative volume elements (RVEs) indicate that RVEs inside the shear band experience severe deformation and microstructural changes, manifested by the rearrangement of soil skeletons and variation of contact force chains.

Effect of Ballast Degradation on Track Dynamic Behavior Using Discrete Element Modeling

Ballast degradation refers to the traffic use of in-service track when aggregate particles become smaller in size and fines are generated because of particle breakage and abrasion to cause geometry defects and influence the serviceability of ballasted track affecting train operations. To evaluate effects of ballast degradation on track substructure maintenance needs, single crosstie models were developed to simulate new and degraded ballast behavior under train loading. Particle size distributions and shape properties of the new and degraded ballast materials studied were adopted from previous laboratory tests conducted at the University of Illinois, U.S. Crosstie vibrations, ballast particle contact force distributions and particle rotations, and localized contact force chain networks were compared among different single crosstie models incorporating new and degraded ballast. The following key observations were made based on the simulation results: (1) crosstie on degraded ballast exhibits larger vibrations and more inconsistent vibration patterns; (2) degraded ballast shows a higher number of localized force chains with more particle contacts while the characteristic trend observed for new ballast is the presence of more symmetric force chain networks, which might be attributed to the new ballast layer’s uniform gradation and good interlock; (3) average normal contact forces are distributed more uniformly in new ballast in both horizontal and vertical directions as opposed to these forces concentrated more in vertical direction in degraded ballast; and (4) more ballast particles experience large rotations in degraded ballast and the related impact zone, which encloses all particles with large rotations, is also broader and deeper.

Structural analysis and parametric study ballasted track in sandy regions

The sand intrusion in railway tracks in sandy regions can significantly change the mechanical behaviour of tracks and thus threaten the safety of train operation. This paper presents substantial field tests on both sandy and clean railway tracks to study the effect of sand intrusion on the longitudinal resistance of ballast bed and the vibration behaviour of track structures. After that, a 3D multi-scale the discrete element model is developed to study the micro-contact between ballast particles and the vibration behaviour of sandy tracks during train passing in detail. Also, the effect of train speeds and axle loads on the mechanical behaviour of sandy tracks is discussed. The results show that the sand intrusion increases the vibration acceleration amplitude of rail and sleeper by 11.3% and 50.3%, while ballast bed decreases by 44.9%. Besides, the sand intrusion significantly changes the energy distribution in the track, wherein the frequencies of the highest energy of rail and sleeper are increased while that of the ballast bed is decreased. The parametric study shows the high train speed can cause the increase in overall acceleration of the ballast bed and high axle load can cause an increase in the micro-contact forces between ballast particles, diffusion angle of the contact force chain, displacements of ballast particles, acceleration of ballast particles, and sleeper displacements.

Discrete Element Modeling of Instability Mechanisms of Unbound Permeable Aggregate Base Materials in Triaxial Compression.

Unbound permeable aggregate base (UPAB) materials with strong load-transmitting skeleton yet adequate inter-connected pores are desired for use in the sponge-city initiative. However, the micro-scale fabric evolution and instability mechanism of macroscopic strength behavior of such UPAB materials still remain unclear. In this study, virtual monotonic triaxial compression tests were conducted by using the discrete element method (DEM) modeling approach on specimens with different gradations quantified by the parameter of gravel-to-sand ratio (G/S). The realistic aggregate particle shape and inter-particle contact behavior were properly considered in the DEM model. The micromechanical mechanisms of the shearing failure of such UPAB materials and their evolution characteristics with G/S values were disclosed from contact force chains, microstructures, and particle motion. It was found that the proportion of rotating particles in the specimens decreased and the proportion of relative sliding between particles increased as the content of fine particles decreased. The plastic yielding of the specimens originated from the failure of contact force chains and the occurrence of the relative motion between particles, while the final instability was manifested by the large-scale relative motion among particles along the failure plane (i.e., changes in the internal particle topology). By comparing the macroscopic strength, microstructure evolution, and particle motion characteristics of the specimens with different G/S values, it was found that the specimens with G/S value of 1.8 performed the best, and that the G/S value of 1.8 could be regarded as the threshold for separating floating dense and skeletal gap type packing structures. The variation of Euler angles of rotating particles was significantly reduced in the particle size range of 4.75 mm to 9.50 mm, indicating that this size range separates most of the particles from rolling and sliding. Since particle rolling and sliding behavior are directly related to shear strength, this validates the rationality of the parameter G/S for controlling and optimizing gradations from the perspective of particle movement. The findings could provide theoretical basis and technical guidance for the effective design and efficient utilization of UPAB materials.

Influence of aspect ratio and arrangement direction on the shear behavior of ellipsoids

This work studies the macroscopic and microscopic behaviors of ellipsoids under triaxial tests using 3D discrete element method (DEM) simulation. To avoid the boundary effect, a novel stress servo-controlled periodic boundary condition is proposed to maintain the confining pressure of samples during testing. The shape features of ellipsoids are investigated, including the aspect ratio of elongated/oblate ellipsoids and the initial arrangement directions of ellipsoids. The macroscopic properties of ellipsoidal particle samples, such as the deviatoric stress, volumetric strain, internal friction angle, as well as dilatancy angles are explored. Elongated and oblate ellipsoids with varying aspect ratios are investigated for the occurrence of stick-slips. In addition, it is demonstrated that the initial arrangement direction has a significant impact on the coordination number and contact force chains. The corresponding anisotropy coefficients of the entire contact network are analyzed to probe the microscopic roots of macroscopic behavior.

Stability Analysis of Jointed Rock Cutting Slope Based on Discrete Element Method

The joints in the rock mass are essential for the stability of rocky slopes, and the destabilization damage of the slope is often directly related to the joints. In this study, in order to reveal the instability process and mechanism of rock slopes from a microscale perspective, the DEM simulations for rocky slopes of the K88 + 400∼K88 + 540 section of Zhongkai Expressway are carried out considering the influence of joints. Based on the findings of the on‐site jointed structural surfaces, a rocky slope model containing two sets of intermittent joints was constructed, and the linear parallel bond model and the smooth joint model are used to characterize the rock body and joints, respectively. The evolution of microfracture, contact force chain, and particle displacement are analyzed to explore the micromechanism of slope instability. Finally, the triple reinforcement scheme of anchor cable frame and grass planting is proposed. The research results can provide a reference for stability analysis and reinforcement of similar rocky slope projects.

Experimental and numerical investigation on flexural and fracture performance of steel fiber reinforced shotcrete

This paper presents an experimental and numerical study on the flexural behaviour and fracture performance of steel fiber reinforced shotcrete (SFRS). Firstly, a series of full-scale tests were carried out under four-point bending test procedure to investigate the ultimate strength and failure behaviour of SFRS. Then, parameter calibration was conducted against several lab tests to obtain the accurate meso-scale parameters which could be employed in the 3D discrete element model of SFRS. Finally, a 3D discrete element model for the SFRS specimen was established based on the bond size theory in the parallel bonding model. The numerical results obtained from the proposed 3D discrete element model of SFRS showed a good agreement with the experimental results in terms of the flexural behaviour and the failure performance. By analyzing the bond failure micrograph and contact force chain distribution diagram between particles, the flexural resistance characteristics of SFRS beams were revealed, and the results showed that the random distribution of steel fibers can be well simulated by using the random function. The proposed 3D particle discrete element model and the meso-parameters of bonded granules obtained from the parameter calibration could provide good results to investigate the flexural behaviour and failure characteristics of SFRS.

Prediction of 3D contact force chains using artificial neural networks

Contact force chains (CFCs) in the heterogeneous granular materials are often considered to be structured physical systems that play a key role in their mechanical properties such as stiffness, strength, stability and flowability. In this context, quantitatively estimating the evolution of CFCs in a quasi-statically sheared granular system is essential for advancing our understanding of the mechanics of granular materials. In this paper, based on discrete element method (DEM) simulation data, an artificial neural network (ANN) is developed and applied to predict the anisotropy of the CFCs in two types of idealized granular materials with different initial relative densities undergoing triaxial shearing. Five features including particle size, coordination number and particle displacement (i.e., x-, y- and z-components of the particle displacement) at the particle-scale and the meso-scale each are used to train and test the established ANN model. The results of model prediction show that the 3D orientational distributions of the CFCs from the ANN predictions match very well the DEM simulation results during the whole shearing progress. It is found that for both dense and loose samples, the combined set of particle-scale and meso-scale features have a dominating influence on the CFC evolutions but the ANN model performs better in the CFCs estimation at the strain increment of 0–7% than at the strain increment of 7%–14%. The outcome of this study shows that machine learning is a promising tool for studying the complex mechanical behavior of granular materials.

DEM Simulation of the Load Transfer Mechanism of a GRPS Embankment with a Fixed Geogrid Technique

As a new technique, a fixed geogrid in a geogrid-reinforced and pile-supported (GRPS) embankments has been used to reduce the total and differential settlement. To investigate the load transfer mechanism of the fixed geogrid technique of a GRPS embankment, three discrete element method (DEM) models of pile-supported embankments were established, including an unreinforced embankment, a geogrid reinforced embankment, and a fixed geogrid reinforced embankment. The efficacy of the pile, the evolution law of the contact force chain and the axial force of the reinforcement, and the microscopic load-bearing structure of the soil were investigated. Numerical simulation results showed that the embankment self-weight and surcharge load were transferred to the pile through the soil arching and tensile membrane effect. The settlement could be effectively reduced via the addition of the reinforcement, and the fixed geogrid technique was more conducive to improving the load-bearing ratio of the pile than the traditional reinforcement technique. Compared with the traditional technique of a GRPS embankment, the fixed geogrid technique had a better effect on reducing the total and differential settlement. With the increase in the surcharge load and the settlement of the soft subsoil, the reinforcement transferred a greater load to the pile. The results also showed that the stress of the embankment fill was concentrated at the pile top in all three models. The GRPS embankment with a fixed geogrid technique had a lower soil stress concentration than the other two cases. The contact force chain and stress in the embankment also showed that the reformation of the microscopic load-bearing system of the embankment fill was the internal mechanism that caused the development of the soil arching and the redistribution of stress. Furthermore, the evolution of the fabric parameters in the arching area could reflect the evolution of the soil arching structure. In the fixed geogrid case, the proportion of the load transferred to the pile from the soil arching effect was reduced, and the vertical load transferred to the pile top by the tensile membrane effect accounted for 22–28% in this study. Under the combined effect of the tensile membrane and the soil arching, the efficacy of the pile could increase by 10%.

Numerical and experimental analyses for rubber-sand particle mixtures applied in high-filled cut-and-cover tunnels

With the rapid development of the automobile industry and transportation, the disposal of scrap tires has become an internationally recognized economic and environmental problem. Fortunately, high-filled cut-and-cover tunnels (first construction and then layered backfill) provide ideal solutions for waste treatment and resource reuse as mixtures of scrap tire rubber particles and sand are used as lightweight fill material (LFM) in high-fill cut-and-cover tunnels (HFCCT). Because the backfill above the cut-and-cover tunnel (CCT) requires a large quantity of material, an appropriate ratio of scrap tire rubber particles and sand should be selected as the LFM mixture. If LFM of different thicknesses is buried above the CCT, it will inevitably bring varying degrees of influence on the earth pressure around the CCT, leading to structural deformation and soil settlement above the CCT. In this paper, a method of combining numerical simulation and model test is presented to help analyze the macroscopic and micromechanical properties of LFM through the stress–strain change and the contact force chain distribution. In the model test, certain factors influencing the earth pressure, the structural deformation, and the soil settlement mentioned above are considered, including the fill height and the embedding depth of the LFM. The results show that when the rubber fraction by volume (RF) is between 30% and 45%, the deformation and load-bearing capacity of the LFM are the most stable. Moreover, a suitable rubber fraction by volume (RF = 40%) and backfill height (between 0.63 ∼ 0.83 times the height of the CCT) can eliminate the stress concentration at the top center of the CCT.