Force Chains Research Articles

Study on the influence of temperature on the damage evolution of hot dry rock in the development of geothermal resources

In order to more accurately understand the rock mechanics properties of hot dry rock (HDR) reservoirs under high-temperature conditions and further guide the drilling and construction of HDR wells, conducting research on rock damage evolution under high-temperature conditions plays a guiding role in the efficient development of geothermal resources. To reveal the evolution law of fracture damage of HDR under temperature influence, taking marble as an example, the thermo-mechanical damage and failure mechanism under the conditions of 30 °C, 60 °C, 90 °C, 120 °C and 150 °C were studied using a rock high-temperature rheometer and an acoustic emission (AE) testing system. The numerical simulation results were compared with the indoor experimental results by combining the particulate flow program Particle Flow Code 3D (PFC3D) to verify the effectiveness of the simulation analysis model of thermo-coupled particulate flow at the micro scale. The results show that under high temperature, the marble three-axis compression failure passes through the compaction and elastic deformation stage, plastic deformation stage, ductile failure stage and instability failure stage, and the peak strength and elastic modulus of the marble decrease with the increase of temperature, and the acoustic emission b-value of the sample can judge the damage evolution process of the marble. At the micro scale, high temperature accelerates the force chain transmission between particles, the contact force between marble particles gradually decreases during the heating process, and the number of particle bonding failures increases steadily; the bearing capacity and elastic modulus attenuation of the rock are the result of microcrack evolution, and the force chain void zone and particle displacement field inside the sample are consistent with its macroscopic failure form. The development of microcracks in marble under different test loading conditions is different, and with the increase of test temperature, the total number of cracks inside the sample increases, but the proportion of shear cracks decreases, the activity of particle displacement increases, and the “plastic extension” characteristic of marble becomes more significant. The thermal damage evolution of marble was quantitatively analyzed based on the elastic modulus method and the peak stress method, and the damage evolution law of marble under different temperatures was obtained.

Identification of force chains in wet coal dust layer and the effect of porosity on three-body contact stiffness

Aiming at the three-body contact problem of mechanical rough surface containing wet coal dust interface, the three-body contact model of rough surface containing wet coal dust interface is constructed by comprehensively considering the contact deformation of rough surface and contact characteristics of wet coal dust, and based on the crushing theory. By analysing the contact force, load-bearing particle size and adjacent contact angle thresholds of the wet coal dust layer, the force chain identification criterion is formulated. Finally, quantitative calculations of the force chain characteristics are performed to reveal the effect of different initial porosities on the three-body contact stiffness, which is verified experimentally. The results of the study show that the average contact force of the wet coal dust layer can be used as the force chain contact force threshold, the average particle size can be used as the force chain particle size threshold, and the force chain angle threshold is determined by the particle coordination number. As the initial porosity decreases, the number, length and stiffness of force chains in the wet coal dust layer increase significantly, and the stiffness reaches a maximum value of 2.007 × 108 pa/m at the moment of downward pressure to stabilisation, while the trend of force chain bending varies in the opposite direction, and its minimum bending degree decreases to 20°. The maximum relative error between the simulation and experimental results of three-body contact stiffness is 9.64%, which proves the accuracy of the force chain identification criterion and the quantitative calculation of three-body contact stiffness by force chain.

Study on the mechanical behavior of microcapsules during the mixing process of asphalt mixture

To enhance the survival rate of microcapsules during the mixing process of asphalt mixture, the mechanical behavior of microcapsules during this process was investigated through simulation. Initially, the asphalt mixture containing microcapsules was divided into mesoscopic and microscopic scales. Utilizing composite material models, the stepwise inclusion method and high-temperature tensile tests, the equivalent mechanical parameters for the microcapsules, asphalt mastic and asphalt mortar at mixing temperature were estimated. Following this, the mixing process of the asphalt mixture incorporating microcapsules was simulated employing the discrete element method (DEM) coupled with multi-body dynamics (MBD). This simulation was instrumental in identifying optimal mixing parameters and enabled the analysis of force chain transmission across the multi-scale model. Furthermore, the finite element method (FEM) was employed to develop a monomer model of the microcapsules, facilitating the assessment of their mechanical behavior under optimal mixing conditions. Finally, a detailed sensitivity analysis was performed to investigate the influence of various parameters on the mechanical behavior of microcapsules. The results indicated that, at the mixing temperature, the equivalent Young’s modulus and Poisson's ratio for urea-formaldehyde (UF) resin microcapsules, asphalt mastic, and asphalt mortar were determined to be 0.22 GPa and 0.478, 19.87 GPa and 0.4986, and 88.77 GPa and 0.468, respectively. The optimal mixing parameters for AC-16 asphalt mixture including mixing speed, filling rate and mixing duration were identified as 49 rpm, 50 % and 53 s, under which the most adverse load on the microcapsule is 80 mN. Under the most adverse load, microcapsules might rupture from the inside out, and their survival rate was not less than 68.9 %. Increasing the particle size of microcapsules and reducing the relative radius of the microcapsule core could potentially enhance the crack resistance of microcapsules during mixing.

Weak shock compaction on granular salt

This study conducted integrated experiments and computational modeling to investigate the speeds of a developing shock within granular salt and analyzed the effect of various impact velocities up to 245 m/s. Experiments were conducted on table salt utilizing a novel setup with a considerable bore length for the sample, enabling visualization of a moving shock wave. Experimental analysis using particle image velocimetry enabled the characterization of shock velocity and particle velocity histories. Mesoscale simulations further enabled advanced analysis of the shock wave’s substructure. In simulations, the shock front’s precursor was shown to have a heterogeneous nature, which is usually modeled as uniform in continuum analyses. The presence of force chains results in a spread out of the shock precursor over a greater ramp distance. With increasing impact velocity, the shock front thickness reduces, and the precursor of the shock front becomes less heterogeneous. Furthermore, mesoscale modeling suggests the formation of force chains behind the shock front, even under the conditions of weak shock. This study presents novel mesoscale simulation results on salt corroborated with data from experiments, thereby characterizing the compaction front speeds in the weak shock regime.

Quantitative analysis of grain size effect on tensile mechanical behavior of granite based on multi-level force chain networks

Quantitative analysis of grain size effect on tensile mechanical behavior of granite based on multi-level force chain networks

Discrete element analysis of the dynamic behavior of ballast track-subgrade system under train dynamic load

To study the dynamic response law of the ballast track-subgrade coupling system under the action of train dynamic load, considering the real shape of ballast particles, a refined discrete element model of the rail-sleeper-ballast bed-subgrade coupling system was established. The established model can realistically simulate the coupling mechanism between irregular ballast particles, between track panel and ballast bed, and between ballast bed and subgrade under train dynamic load. The validity of the established model is verified using on-site measurement results. This study, from a microscopic perspective, focuses on particle contact forces, vibrations, and frictional energy consumption in the rail-sleeper-ballast bed-subgrade coupling system under train dynamic load and investigates the influence of train speed and axle weight. Results show that an increase in train speed and axle weight enhances the number and probability distribution of strong force chains between ballast particles, increasing the risk of particle breakage and deterioration. The influence range and depth in the ballast bed-subgrade system increase with the train's speed and axle weight. Due to the granular nature of the ballast bed, the vibration acceleration distribution of ballast particles under train dynamic loads is relatively random. Overall, the vibration level of the ballast bed increases with train speed and axle weight. The frictional energy consumption of ballast particles rapidly grows as the train's bogie load passes, and the effect of train axle weight on the frictional energy consumption of ballast particles is more significant than the train's speed.

Inner structures of rapid free-surface granular avalanche over a small bump obstacle: Expansion fan, oblique shock wave, and contact anisotropy

This study investigates the inner flow characteristics of a rapid granular avalanche passing over a small bump obstacle fixed on an inclined chute using the discrete element method. Both the cross-sectional mean flow properties, such as free-surface height, mean flow velocity, and mean stresses, and the inner local flow properties, including granular temperature, coordination number, pressure, contact force orientation, and granular fabrics, were comprehensively investigated. Upstream of the obstacle, a wide compression region where mean stresses strengthen and exhibit anisotropy was observed. Employing the kinetic theory of granular gas, we revealed a smooth supersonic-to-subsonic transition near the obstacle, a phenomenon distinct from typical gas dynamics. These upstream flow phenomena are attributed to the generation of stream-wise-oriented contact force chains as the flow impacts the obstacle. Downstream of the obstacle, a complex non-monotonic expansion–compression–expansion process was observed. We demonstrated that this non-monotonic flow process reflects an inner gasdynamic-like phenomenon characterized by an expansion fan followed by an oblique shock wave. Moreover, the force chains and the inner shock structure were found to significantly influence the evolution of stream-wise velocity profiles. These findings underscore the significance of inner flow structures in shaping the dynamics of granular avalanche flow interacting with obstacles.

Extension Mechanism of Water-Conducting Cracks in the Thick and Hard Overlying Strata of Coal Mining Face

It is of great significance for coal safety production and water resource protection in the Yuheng mining area to master the evolution law of water-conducting fractures under the condition of thick and hard overburden. This research focuses on the 2102 fully mechanized mining face in the Balasu Coal Mine as the research background. The fracture evolution and strata movement characteristics in thick and hard overlying strata are simulated and analyzed by combining numerical simulation with physical simulation, and the formation mechanism of a water-conducting fracture in the overlying strata is revealed and verified by field measurements of the development height of “two zones”. The results show that the anisotropy of fracture propagation in low-position overlying strata is high, and the fracture propagation in high-position overlying strata is mainly vertical, which indicates characteristics of leapfrog development. The number and development height of fractures undergo the change–growth process of “slow–rapid–uniform”. Multiple rock strata together form a complex force chain network with multiple strong chain arches. The local stress concentration leads to the initiation of micro-cracks in contact fractures, and the cracks gradually penetrate from bottom to top and then the strong chain arches are broken. The water-conducting cracks in overlying strata show a dynamic expansion process of “local micro-cracks–jumping cracks–through cracks–water-conducting cracks”. The fracture between the caving zone and fracture zone presents obvious layered characteristics, the overall shape of the water-conducting fracture zone is “saddle-shaped”, and the maximum development height lags behind the coal mining face by about 180 m. Through the observation of water injection leakage and borehole TV observation of three boreholes under underground construction, combined with the results of water pressure tests, it is comprehensively determined that the height of the water-conducting fracture zone is 103.68~107.58, and the fracture–production ratio is 31.42~32.60, which is basically consistent with the results of numerical simulation and physical simulation. This research provides theoretical guidance and a scientific basis for coal mine water disaster prevention under similar geological conditions.

Repacking in Compacting Mushes at Intermediate Melt Fractions: Constraints From Numerical Modeling and Phase Separation Experiments on Granular Media

AbstractBefore large volumes of crystal poor rhyolites are mobilized as melt, they are extracted through the reduction of pore space within their corresponding crystal matrix (compaction). Petrological and mechanical models suggest that a significant fraction of this process occurs at intermediate melt fractions (ca. 0.3–0.6). The timescales associated with such extraction processes have important ramifications for volcanic hazards. However, it remains unclear how melt is redistributed at the grain‐scale and whether using continuum scale models for compaction is suitable to estimate extraction timescales at these melt fractions. To explore these issues, we develop and apply a two‐phase continuum model of compaction to two suites of analog phase separation experiments—one conducted at low and the other at high temperatures, T, and pressures, P. We characterize the ability of the crystal matrix to resist porosity change using parameterizations of granular phenomena and find that repacking explains both data sets well. A transition between compaction by repacking to melt‐enhanced grain boundary diffusion‐controlled creep near the maximum packing fraction of the mush may explain the difference in compaction rates inferred from high T + P experiments and measured in previous deformation experiments. When upscaling results to magmatic systems at intermediate melt fractions, repacking may provide an efficient mechanism to redistribute melt. Finally, outside nearly instantaneous force chain disruption events occasionally recorded in the low T + P experiments, melt loss is continuous, and two‐phase dynamics can be solved at the continuum scale with an effective matrix viscosity.

Field Compaction Characteristics of Ultra-Thin Porous Friction Course Based on Laboratory Simulation

As a preventive maintenance treatment, the ultra-thin porous friction course (UPFC) has been widely recognized and used in road maintenance because of its excellent performance and cost effectiveness. The Marshall compaction method (MCM) has been adopted to design UPFC mixtures worldwide, particularly in China. However, there are few studies concerning the field compaction properties of MCM-designed UPFCs. The laboratory test results of this study from simulating on-site compaction showed that all UPFC specimens with thicknesses of less than 20 mm barely achieved the target compaction thickness, and all UPFC specimens with different thicknesses failed to meet the air void (AV) requirements of UPFC mixes designed using the MCM. According to the results of a virtual compaction test, and using the discrete element method, the strong force chains were strengthened as the UPFC thickness decreased inside the specimen, making it difficult to evenly diffuse and transfer inside the specimen and resulting in insufficient compaction of the UPFC. Furthermore, it was demonstrated that the MCM-designed UPFC specimens showed significant differences in the AV distributions along the vertical and lateral directions from those of the UPFC specimens that simulated field compaction. The UPFCs designed using the MCM had a poor correlation with field compaction.

Transport behavior of particles and evolution of plugging zones in rough fractures: Insights from a novel coupled CFD-DEM model

The meso-mechanism of particle bridging and plugging in rough fractures remains unclear. Therefore, this study explores a novel meso-model for simulating particle transport in rough fractures by combining Computational Fluid Dynamics and Discrete Element Method (CFD-DEM). The dynamic behavior of particles and the corresponding evolution mechanism of plugging zones are investigated. The simulation innovatively uses particle boundaries to correct fluid flow, greatly simplifying the fluid mesh partitioning while ensuring accuracy. The results reveal the connection between particles’ transport and bridging behavior in rough fracture spaces, the distribution characteristics of plugging zones, and fluid flow characteristics. The distribution of bridging favorable zones determines the position and pattern of the front edge of subsequent plugging zones. The stress accumulated by particles has little effect on the strong force chain of the front edge. The force chain strength of the double-particle bridging structure is greater than that of the single-particle bridging structure. Due to weak shear planes, the double-particle bridging structure is more prone to shear failure and instability under external loads. Improving the particle size distribution range can reduce bridging blind zones and achieve better sealing performance. The results provide theoretical help for the design of field operation processes.

Experimental and DEM analysis for the shear characteristics of interface between sand and irregular concrete under dynamic normal loading

To explore the dynamic shear property of sand–irregular concrete interface, a series of direct shear tests were conducted under dynamic normal loading. These tests were designed with various joint roughness coefficients (JRC), amplitudes and frequencies of dynamic normal loading. DEM models were established to analyze the microscopic mechanical behavior. The research results indicate that a larger amplitude and frequency of the dynamic normal loading would lead to a decrease in the interface shear stress and dilation. As the JRC increased, the interface shear strength first increased and then decreased, and the dilation increased. A rougher surface would reduce the phase shift between peak shear and normal stress. The phase shift between normal stress and friction coefficient was always half a normal loading cycle. A greater JRC would activate a more violent particle motion and a thicker shear band. The increase in effective roughness would lead to an increase in the deviation angle of the anisotropic direction. The evolution of force chains was observed in three-dimensional space. Weak force chains were screened out during the shearing process. As the shearing developed, the number of force chains decreased, the average length and strength of force chains continued to increase.

Study of the mechanical properties and propagation mechanisms of non-coplanar and discontinuous joints via numerical simulation experiments

Non-coplanar and discontinuously jointed rock masses are more complex than coplanar and discontinuously jointed rock masses. The mechanical properties and propagation mechanisms of non-coplanar and discontinuous joints were studied via direct shear tests with microscopic numerical simulation experiments. The numerical simulation tests were performed under different normal stresses, joint inclination angles, and shear rates. The numerical experimental results show that the microscale failure of non-coplanar and discontinuously jointed rock masses is mainly caused by tensile cracks. Additionally, when the peak shear stress is reached, the growth rate of cracks increases rapidly, and the number of cracks increases with increasing normal stress. The shear strength of non-coplanar and discontinuously jointed rock masses increases with increasing normal stress. Under the same normal stress, the variation curves of the shear strength of non-coplanar and discontinuously jointed rock masses with respect to the dip angle exhibit an “S”-shaped nonlinear pattern. Rock masses with joint inclination angles of approximately 15° and 65° have minimum and maximum shear strengths, respectively. The joint dip angle has a significant impact on the final failure mode of rock bridges in the rock mass. As the joint dip angle increases, the final failure modes of rock bridges change from “end-to-end” connection to a combination of “head-to-head” and “tail-to-tail” connections. The shear rate has a certain impact on the peak shear stress, but the impact is not significant. The spatial distribution of the tensile force chains changes as shearing progresses, and stress concentration occurs at the tips of the original joints, which is the reason for the development of long tensile cracks in the deeper parts.

Study on shear surface morphology and failure mechanism of soil-rock mixture under wet-dry cycle action

The present study investigates the failure modes and formation mechanisms of shear surfaces in soil-rock mixtures from various perspectives. Firstly, through in-situ direct shear tests, two main shear failure modes, namely planar and non-planar, are identified. Subsequently, using PFC 2D numerical simulation, an in-depth exploration of the characteristics and causes of these two typical failure modes is conducted. The findings reveal that in the natural state, the material is relatively dry, and the matrix suction within the soil-rock mixture is significant. During shearing, the inter-particle force chains are prone to rupture, exhibiting characteristics akin to brittle failure. This leads to nearly planar shear surfaces, with force chain ruptures primarily localized near the planar regions adjacent to the shear surface. However, after multiple dry-wet cycles, the plastic enhancement of the soil-rock mixture reduces the matrix suction to almost zero. The continuous rupture and reorganization of force chains deepen the shear band under their influence, resulting in non-planar shear surfaces. It is noteworthy that the characteristic point fitting curve of non-planar shear surfaces exhibits a nonlinear trend. In summary, our study elucidates the evolution process and causes of shear surface morphology in soil-rock mixtures, which holds significant implications for understanding their mechanical properties and engineering behavior.

Experimental and numerical study on the damage evolution and acoustic emission multi-parameter responses of single flaw sandstone under uniaxial compression

Cracks are generally the weakest position in engineering rock mass. It is of great practical significance to study the influence of cracks on the fracture process of rock mass and the precursor criterion of failure for disaster prevention and mitigation projects. In this paper, particle flow program (PFC2D) is used to analyze the mechanical strength and damage evolution of fractured rock. The multi-parameter stage characteristics of acoustic emission (AE) and the difference of fracture precursor information of fractured rock mass under uniaxial compression (UC) are explored. The results are as follows: (1) The strength and modulus of elasticity of fractured rock samples are smaller than that of intact rock mass, and increase in quadratic function with the increase of fracture angle, and the strength of B-90 sample is closest to intact rock samples; (2) The PFC analysis shows that the cracks in the defective rock samples all originate from the tip of the prefabricated crack, and the crack initiation angle is basically in the range of 60°∼90°. The loading process mainly produces tensile damage, and the number of tensile cracks are far more than that of shear cracks. Compressive stress and tensile stress increase with the increase of load, but the force chain of failure surface is the smallest after complete failure of rock; (3) The acoustic emission ringing number, RA/AF value, b value and entropy value of sandstone have obvious stage characteristics, the main frequency signal is mainly low frequency signal, and large-scale cracks are mainly produced in the failure process. The sudden increase point of AE ringing times and RA/AF value accumulation curve can be used as critical failure point. The fluctuation of B value and entropy value reflects the instability of fracture development, and “cliff-like” descending point and ascending point can be regarded as the precursor of critical failure of rock; (4) The failure precursor of acoustic emission parameters of sandstone appears in the peak load period of 85 %–98 %. The order of response time of different parameters is: cumulative RA/AF value, cumulative event number, entropy value, B value. The response time of B-45 and B-15 is earlier, while that of B-60 and B-30 is later. The research results are expected to deepen the understanding of the relevant standards of damage evolution and failure precursors of defective rocks in engineering applications.

Influence of Mesoscopic Defects on the Mechanical Behaviour of Granites Based on a Three-Dimensional Multilevel Force Chain Network

Influence of Mesoscopic Defects on the Mechanical Behaviour of Granites Based on a Three-Dimensional Multilevel Force Chain Network

DEM Research on Stress and Force Chains during Warm Compaction of Intricate Parts

DEM Research on Stress and Force Chains during Warm Compaction of Intricate Parts

DEM simulation of effects of particle size distribution on meso-mechanical properties of slip zone soil

Particle Size Distribution (PSD) exerts a substantial influence on the mechanical properties of geological materials such as rocks and soils, which can be viewed at a microscale as an assembly of discrete particles. An exploration into the effects of particle gradation on the properties of these materials provides valuable insights into their nature. In the study, the Discrete Element Method (DEM) was used to conduct numerical shear tests on eight distinct groups of slip zone soil, each characterized by a different particle gradation. The aim was to examine the meso-mechanical properties and shear evolution laws of slip zone soil numerical samples with both optimal and sub-optimal PSDs. Findings underscore the pivotal role that PSD plays in various aspects, including dilatancy, the evolution of the displacement field, the network of contact force chains, the principal stress, and the distribution of normal and tangential contact forces within the slip zone soil. It was observed that the network of contact force chains in the numerical samples with an optimal PSD was more complex than in those samples with a sub-optimal PSD. Additionally, the distribution of principal stresses before and after shear was more uniformly balanced. This particle size-based study offers significant reference value for future investigations into the impact of PSD on the macroscopic and meso-mechanical properties of slip zone soil. By augmenting this knowledge, a more comprehensive understanding of the fundamental behavior of these materials can be attained, leading to improved prediction and management of geological risks.

Micromechanical analysis of contact erosion under cyclic loads using the coupled CFD‒DEM method

Different layers of soil often have distinct particle sizes. When exposed to the natural environment, soil is easily affected by natural rainfall, rising groundwater levels, and human activities, leading to particle contact erosion, which reduces the safety and service performance of the soil structure. In this paper, a coupled computational fluid dynamics–discrete element method (CFD–DEM) model was employed to investigate the particle migration phenomena, mechanical response of contact interfaces, variations in flow fields, and macroscopic deformation during the contact erosion process under cyclic loads at different frequencies and amplitudes. The conclusions are presented as follows: (1) Within one cycle of cyclic loading, both compression during loading and stress relaxation during unloading are the main factors triggering the migration of fine particles. (2) The migration and loss of fine particles mainly occur in the early stages of cyclic loading, where strong contact force chains are formed within the fine particle layer, leading to significant plastic deformation of the soil at the macroscopic level. (3) Under cyclic loading, changes in the soil pore structure cause an upwards hydraulic gradient in the initial quiescent water flow field. This hydraulic gradient can rupture weak contact force chains and cause particle pumping. (4) Increasing the frequency and amplitude of cyclic loading intensifies the erosion of fine particles, causing greater axial deformation of the soil. Compared to cyclic loading frequency, the amplitude of cyclic loading has a greater impact on contact erosion.

Study on the force chain characteristics with coal dust layer and the three-body contact stiffness

To explore the influence of the meso-mechanical behaviors of the wet coal dust layers on the contact stiffness of mechanical bonding surfaces, a three-body contact model incorporating an interface with wet coal dust was constructed based on breakage theory. The model considered the mechanical surface morphology and contact characteristics of the wet coal dust. The force chain evolution laws of the wet coal dust layer were elucidated under the effects of gap filling and the cover layer, and the bearing characteristics of the three-body contact bonding surfaces were revealed by quantitative analyses of the number, length, collimation coefficient, and coordination number of the force chains within the wet coal dust layer. Finally, the three-body normal contact stiffness under various preload forces was computed and experimentally validated. The results demonstrate that the external load transfer path of the three-body contact bonding surfaces was from mechanical surface (macroscopic stress) to wet coal dust layer (mesoscopic force chains) and then to mechanical surface (peaks and valleys). The interactions among these three elements contributed to transforming the distributions of the macroscopic stresses and mesoscopic force chains to the locations at the peaks and valleys of the mechanical surface. Among them, the proportion of short force chains in the wet coal dust layer increased from approximately 0.8%–91%, while the proportion of long force chains exhibited an opposite changing trend. The force chain collimation coefficient initially increased and subsequently stabilized, reaching a maximum value of 0.93. A large number of broken, small particles in the wet coal dust layer mainly served to fill the gaps among large particles. The maximum relative error between the experimental and simulated values on the three-body contact stiffness is 7.26%, indicating that the simulation results can be an approximate substitute for the experimental results with a certain degree of accuracy and practicality. The research results are of great significance for understanding the contact characteristics of mechanical surfaces containing particulate media.