Contact Relationships Research Articles

Mechanism of Wheel-Rail Adhesion Recovery during Large Sliding processes under Water Lubrication condition

The challenge of low adhesion between the wheel and rail constrains the advancement of train braking technologies, resulting in sliding during braking, increased braking distances, and even operational safety incidents. Low adhesion arises from the contamination of the rail surface by a third body, such as water or oil, significantly reducing adhesion. However, experimental studies have found that wheel-rail adhesion coefficient under water lubrication conditions possesses a recovery capability: In scenarios characterized by low adhesion in water lubrication conditions, a secondary rise in adhesion occurs when substantial wheel-rail sliding is present. This paper focuses on numerically modeling the unique phenomenon of adhesion recovery during large-sliding processes under water lubrication conditions. Considering the notable differences in frictional heating during wheel sliding, as opposed to pure rolling conditions, we construct a wheel-rail contact model under mixed lubrication conditions that incorporates the solid-liquid coupled heat transfer effect. This model achieves stable solutions for the wheel-rail contact relationship and the temperature at the wheel-rail interface. The impacts of velocity, axle load, water temperature, and slide ratio on the adhesion recovery phenomenon are discussed, revealing the underlying mechanism of adhesion recovery during large sliding processes. Finally, brake adhesion tests under water lubrication conditions are conducted on a scaled test rig to validate the proposed theoretical model.

Digital workflow in oral splint manufacturing.

The objective of the present article is to demonstrate the digital workflow used to manufacture an adjusted oral splint in a patient case. A 25-year-old female patient presented for management of her bruxism. Therefore, an adjusted oral splint was manufactured. A computer-aided motion analysis of the patient was conducted (JMA Optic). Full-arch scans of the maxilla and mandible, a biocopy of the maxilla with a bite fork, and buccal scans of the centric jaw relation (Primescan) were performed. The jaw relation was determined beforehand by ballistic closing on a chairside-fabricated anterior jig. The digital construction of a Michigan splint took place in the dental laboratory. The design was nested and milled from a polymethyl methacrylate (PMMA)-containing blank (CLEARsplint Disc). The oral splint was inserted into the patient's mouth and checked to ensure a tension-free fit. The static and dynamic contact relationship was checked. During the follow-up visit, the patient reported an improvement in tension in the masticatory muscles. The described procedure allows for the manufacture of an adjusted oral splint through a purely digital workflow.

Constitutive relationship of soil in contact with mortar under continuous loading

Mortars will remain critical in future land wars due to their flexibility and versatility. When mortars are fired continuously, the contact soil is gradually compacted by the mortar base plate, and dynamic research into this process is the basis for innovative mortar design. However, the discontinuity and nonlinearity of soil contact absolutely necessitate the constitutive relationship of soil contact, which is difficult to study. Therefore, this study conducted experimental research and theoretical derivation to establish an accurate dynamic model of the mortar system. First, based on the nonlinear elastic–plastic theory and the stress–strain relationship of soil under cyclic loading, a theoretical analysis method for the constitutive relationship of contact soil under continuous loading was proposed. Second, an experimental and testing system was designed to simulate launch loads, and the stress–strain response of soil under continuous impact loads was obtained experimentally. Subsequently, based on theoretical analysis and experimental data, the stress–strain relationship during the gradual compaction of soil was established using the least squares method. Finally, a constitutive relationship model of the contact soil in the mortar system was established in ABAQUS using the VUMAT subroutine interface, and the calculated results were compared and analyzed with traditional calculation results. The results indicated that studying the constitutive relationship of mortar in contact with soil during continuous firing using this method can improve the accuracy of dynamically modeling mortar systems. Moreover, this study has practical value in the engineering design of mortar systems.

Research on the mechanism and measures of riding comfort deterioration in a low floor tram

With the global widespread preference for low-floor trams, the expectation for tram riding comfort has been increasingly heightened. This paper identifies an abnormal riding comfort problem (ARCP, characterized by an excessive and W-shaped distribution of riding comfort) during dynamic field tests on a low-floor tram. To address ARCP, a multi-body dynamics model of the tram was constructed and validated its accuracy through dynamic field tests. By integrating track irregularities and wheel-rail contact analysis, the riding comfort index was assessed and reproduced the ARCP phenomenon. Linearization and time-domain integration studies were conducted on the mechanisms and measures to resolve the ARCP. The research findings reveal that the primary cause of the deterioration in the mean comfort index is the large amplitude of the track irregularity and the low equivalent conicity of the wheel-rail contact relationship. The main reason for the W-shaped distribution of riding comfort is the weaker inter-vehicle constraints and the lack of lateral energy-absorbing devices. Finally, optimization measures were proposed, including reducing the lateral stiffness of the second suspension, altering the carbody structural parameters, and modifying the inter-vehicle connection devices. This research enriches the study of tram dynamic performance and offers insights that may contribute to the resolution of ARCP.

Mineral effects on methane hydrate formation and distribution in sand sediments

Methane hydrate is a promising energy resource widely occurring in the world, but the formation and distribution of methane hydrate in marine sediments with complex minerals remains unclear. Due to the small pore space and fine-grained size of clay minerals, the contact relationship between methane hydrate and clay mineral surface under excess water has not been characterized fully, which is required to investigate the mineral effect on methane hydrate formation. In this study, cryo-SEM was applied to observe the distribution of methane hydrate synthesized in pure quartz sands and the quartz sands mixed with montmorillonite or illite separately. According to the results of the research, methane hydrate dispersedly forms in the pore space away from and on the surface of quartz under a local excess water condition. In addition, methane hydrate occurs away from montmorillonite in pores with excess water and contacts the edge of montmorillonite under a local excess-gas condition. Moreover, methane hydrate was only observed to form away from illite aggregates in the pore with residual water. Montmorillonite and illite influence the preferable distribution of methane hydrate to occur away from mineral surface in excess water condition. In the sediments composed of different minerals, methane hydrate forms stochastically in the pore space and grows up individually. As a result, the findings of this study significantly expand the understanding of the formation and distribution of methane hydrate in marine sediments and the prediction of physical properties of hydrate-bearing sediments, and provide insights into natural gas hydrate exploration and production.

Nonlinear characteristics in the cylindrical roller bearing with raceway defects

Cylindrical roller bearings (CRBs) are subjected to significant cyclic stress under extreme operating conditions. This leads to the formation of localized wave defects on the raceway surface, such as burn. Thus, a new mathematical model is proposed to consider the local wave defects on the raceway caused by burns in this paper. Further, a dynamic model of CRB incorporating raceway defects is developed based on the contact relationships between components, and the proposed model is verified by measured acceleration responses. The effects of local wave defects on the nonlinear vibration characteristics of the bearings are studied and the results show that an increase in the number of defect waves reduces the additional displacement of rollers passing through the defect area, obscuring signal characteristics induced by the defect. Moreover, the presence of the defect influences the nonlinear interaction between the roller and raceway, which subsequently affects the cage whirling motion. This study of bearing dynamic behavior in this paper can contribute to the condition monitoring of bearings.

A continuous-discontinuous coupling computational method for multi-material mixtures

Considering the important role of particle-reinforced composites (PRCs), and to accurately assess the mechanical properties of PRC with arbitrarily complex internal structures, this paper proposes a new continuous-discontinuous coupled computational method, i.e., the multi-material integrated analysis (MIA) method, by combining the advantages of the discontinuous deformation analysis (DDA) method, the numerical manifold method (NMM), and the meshless method, for the continuous-discontinuous dual state of this kind of materials when they are subjected to forces. The core idea of this method is by establishing a single physical cover (PC) on each particle and defining a unified and piecewise approximation function over it to achieve displacement coordination between the particles and the matrix. In this model, the particles can maintain the contact and separation characteristics like the blocks, while the matrix is able to achieve the bonding function by overlapping different covers. Two numerical integration schemes, namely single-point Gaussian integration and Monte Carlo integration, are proposed to address the integration issues in stiffness matrix calculations. Meanwhile by considering the similarity between NMM and meshless method interpolation function construction, this paper combines circular coverage and 0th-order moving least squares to construct the interpolation function to form the displacement approximation function for the whole solution space. Moreover, the method of lattice retrieval (also Nearest Neighbor Search, NNS) is invoked for particle contact determination to improve the efficiency of contact and coverage relationship determination. The validity of the model is verified by taking asphalt mixture, a typical PRC, as a demonstrative case study. The results show that the MIA method solves the one-sided problem that the existing algorithms usually only consider the continuous or discontinuous properties of PRC, and provides a new method for comprehensively analyzing the micromechanical response of PRC and solving its large deformation problem.

Sedimentary Reservoir Characteristics of Fuyu Oil Formation in the Middle of Fuxin Uplift, Southern Songliao Basin

Currently, the Fuyu reservoir in the middle of the Fuxin uplift, located in the southern Songliao Basin, is in a high water cut development stage. The understanding of this reservoir is limited, and the distribution of favorable reservoirs remains unclear, necessitating detailed reservoir characterization. This study employs a combination of well and seismic technologies to accurately depict the sedimentary and reservoir characteristics of the Fuyu oil reservoir. By conducting detailed correlations of oil zones, a regional high-resolution isochronous stratigraphic framework is established. The division of sedimentary microfacies enables fine characterization of single sand bodies, identifying channel boundaries, clarifying lateral connectivity, and detailing the vertical contact relationships of sand bodies across different deposition periods. The results demonstrate that root-mean-square amplitude and total energy metrics effectively correspond to sand bodies in the study area and can be used to analyze sand body distribution. Provenance is primarily from the southwest to the northeast, with shallow deltas predominantly developed. Delta plain subfacies are found in zones 4-12, while delta front subfacies are in zones 1-3. Microfacies types mainly include the main distributary channel, distributary channel sides, crevasse splay, overbank sand, and underwater distributary channels. The main distributary channel reservoirs exhibit the best physical properties, with porosity ranging from 20-25%, while sand bodies at the sides of distributary channels reach 15-20%. Predicted favorable areas are mainly located at the intersections of distributary channels and structural highs, where drilling is likely to yield high oil flow.

Sliding-attention transformer neural architecture for predicting T cell receptor–antigen–human leucocyte antigen binding

Neoantigens are promising targets for immunotherapy by eliciting immune response and removing cancer cells with high specificity, low toxicity and ease of personalization. However, identifying effective neoantigens remains difficult because of the complex interactions among T cell receptors, antigens and human leucocyte antigen sequences. In this study, we integrate important physical and biological priors with the Transformer model and propose the physics-inspired sliding transformer (PISTE). In PISTE, the conventional, data-driven attention mechanism is replaced with physics-driven dynamics that steers the positioning of amino acid residues along the gradient field of their interactions. This allows navigating the intricate landscape of biosequence interactions intelligently, leading to improved accuracy in T cell receptor–antigen–human leucocyte antigen binding prediction and robust generalization to rare sequences. Furthermore, PISTE effectively recovers residue-level contact relationships even in the absence of three-dimensional structure training data. We applied PISTE in a multitude of immunogenic tumour types to pinpoint neoantigens and discern neoantigen-reactive T cells. In a prospective study of prostate cancer, 75% of the patients elicited immune responses through PISTE-predicted neoantigens.

Parent-child relationship quality and older parents’ cognitive trajectories

This study assesses the bidirectional link between parent-child relationship quality and older parents’ cognitive trajectories over time, with particular attention to potential variations by parents’ gender. Methods: Using a longitudinal, nationally representative sample of parents aged 50 and older from the Health and Retirement Study 2006–2016, the analysis examines three dimensions of the relationship quality between parents and children—contact, support, and strain—in relation to parents’ cognitive function. Parallel latent growth curve models (LGCMs) estimate how baseline relationship quality relates to subsequent change in parents’ cognition and how parents’ baseline cognitive function relates to subsequent change in relationship quality over time. Results: Higher initial levels of relationship strain with children predicts a faster cognitive decline for older parents. Neither initial contact frequency nor initial relationship support is associated with subsequent change in a parent’s cognition, however, good cognitive function predicts a more rapid increase or a slower decline in contact frequency and relationship support over time. No gender difference was found. Conclusion: The results highlight the importance of the “linked lives” of aging parents and their children as well as the potential for bidirectional associations between cognition and family relationships.

A Late-Pleistocene confined volcanic debris avalanche promoted by hydrothermal alteration at the Tinguiririca volcano (Andes of Central Chile)

Distinguishing volcanic debris avalanche deposits from other epiclastic breccia could be complex. For more than 60 years, the Tinguiririca deposit (sourced from the homonymous volcano) in the Andes of Central Chile has been described by different authors as glacial moraines, a lahar, a volcanic debris avalanche, and even a debris flow deposit. To decipher its obscured origin and emplacement dynamics, we have carried out a detailed investigation of its distribution, contact relationships, sedimentology, and facies. Our findings unravel that the 57 km-long deposit is 5 to 300 m thick, totalling a reconstructed volume of 3.64 ± 0.05 km3. It is composed of unsorted heterometric breccias formed by clasts and blocks arranged in mixed and matrix facies characterised by distinctive lithological domains. In general, three clasts lithologies are dominant, consisting of black and grey andesites and hydrothermally altered clasts with jigsaw cracks and fractures. The deposit overlies terraced colluvium along the valleys and forms hummocks and ridges. Emplacement velocities estimates range from 39.6 m/s to 108.4 m/s. Therefore, the Tinguiririca deposit should represent a massive volcanic debris avalanche that formed after a lateral collapse that affected the ancient Tinguiririca Volcanic Complex, during the Late Pleistocene (between 45 ± 18 and c. 19.2 ± 1.2 ka). The abundance of hydrothermal minerals within the deposit's matrix and clasts (i.e., illite, phengite, epidote, tridymite, chlorite, hematite, jarosite, and alunite) all represent the volcano's hydrothermal system that likely favoured rock weakness and edifice collapse. Finally, the new interpretation is valuable for evaluating volcanic hazards and requires further mapping and research efforts.

Every intrusion has its time: New zircon U-Pb ages from the Greater Antilles Arc in the Cordillera Central, Dominican Republic

The Cordillera Central on the island of Hispaniola comprises a section through the crust of the Late Cretaceous phase of the Greater Antilles Arc. The gabbroic-tonalitic batholiths of the Cordillera Central are widely considered to represent the temporal main axis of this island arc. Although they have been studied extensively, the timing of batholith emplacement is not well constrained. We present new LA-ICP-MS U-Pb zircon ages and whole-rock geochemical data from diorites, tonalites, and granites of the El Río, El Bao, Jumunuco, and Loma de Cabrera batholiths, and from tonalite boulders deposited in the Eocene-Oligocene Velázquitos Formation. The sample ages range from 97 to 80 Ma with small differences between the intrusive bodies. Samples from the El Río, Jumunuco, and Loma de Cabrera batholiths cover most of the above age range, while the rocks of the El Bao pluton yield a well-defined maximum around 87 Ma. In the El Río batholith, U-Pb ages are in good agreement with the exposed contact relationships. Based on their composition and existing geochronological data, we divide the intrusive history of the Cordillera Central into four stages reflecting different magma compositions: ultramafic to dioritic magmatism lasted from 105 to 87 Ma, tonalite units formed between 96 and 84 Ma, felsic tonalites and granites intruded from 87 to 80 Ma overlapping with a younger phase of dioritic magmatism between 84 and 78 Ma.The geochemical signatures of the felsic tonalites of the Jumunuco batholith and the granites of the El Río batholith are similar to the rhyolitic and dacitic island-arc volcanics from the Restauración Formation of the Tireo Group, thus confirming the relationship between the volcanic and plutonic units of the Greater Antilles Arc. Based on petrographical, geochemical, and geochronological data of the tonalite samples from the Velázquitos Formation, we interpret these boulders as being eroded from the Jumunuco batholith or the related Buena Vista pluton.

Peridynamic study on thermomechanical damage of the rail during wheel idling

Wheel idling is an extreme sliding contact scenario that accelerates rail failure. Using temperature-dependent elastoplastic materials, a peridynamic (PD) model for wheel-rail contact was developed to investigate the thermomechanical damage behavior of rails during wheel idling. Numerical simulations of loading and unloading during wheel idling under different loads were performed, and the results of contact stress, temperature, plastic deformation, and material damage were obtained and analyzed. During loading, the temperature of the rail surface increases rapidly to over 1200 °C, which is well above the austenitization temperature. The intense thermal softening caused by high temperatures deteriorates the wheel-rail contact relationship and leads to a surge in plastic deformation. The softened surface material was continuously removed by the contact load, leading to severe wear damage, and the wear depth increased significantly with the load and idling time. The wear coefficients for the Archard wear model were derived using the wear results from the PD model. During unloading, the surface material cools rapidly at a rate of 1400°C/s through heat transfer into the rail, undergoing martensitic transformation and forming a brittle and hard white etching layer. The thickness of the WEL decreases as the wear depth increases.

Dynamic modelling and experimental validation of a dynamic track stabiliser vehicle–track spatially coupling dynamics system

A dynamic track stabiliser vehicle is an unconventional vehicle for maintaining the quality of ballasted tracks, and its dynamic performance has a significant impact on its working efficiency. For the first time, this paper proposes a comprehensive dynamic track stabiliser vehicle–track coupled vertical and lateral multi-body dynamics model based on classical vehicle–track coupling dynamics theory. In this model, detailed attention is given to the vertical, lateral, roll, yaw, and pitch motions of the components, including the vehicle body, bogies, wheelsets and stabilisers. The Shen–Hedrick–Elkins theory is employed to describe non-linear wheel–rail contact relationships between the bogie wheelsets and the rails, and three various methodologies are adopted to address complicated wheel–rail interaction problems between the stabiliser wheelsets and the rails. This comprehensive multi-body dynamics model enables a detailed investigation of the dynamic performance of the system under complex excitations, such as the lateral excitation of the stabilisers and vertical downward pressure exerted by hydraulic cylinders, especially the dynamic response of the stabilisers in the vibration environment of the complete vehicle. The dynamics model was fully validated by comparing its results with time- and frequency-domain data obtained from field tests. The results indicate that the model is capable of being used for analysis of the dynamic performance of dynamic track stabiliser vehicles.

Speaker judgments alone cannot diagnose syllable structure

Abstract The ease and consistency with which speakers of many languages provide direct judgments about syllable structure has been taken by scholars as evidence that these judgments are accurate and sufficient argumentation for an analysis of syllable structure in descriptive works. This paper questions whether the results of direct elicitation tasks reliably indicate a prosodic domain that is meaningful in the language’s phonology and provides alternative forms of evidence for syllable structure from intonation. This is done through a case study of Budai Rukai, a Formosan language whose contact relationship with Sinitic languages affects how speakers respond to syllable judgment tasks.

Field monitoring and numerical simulation for force characteristics of pipe jacking in deep buried moderately weathered slate

Understanding the force characteristics of pipe jacking in rock formations is crucial for ensuring the stability of the structure and construction safety during construction. Yet, very little is explored about its characteristics in rock formations of pipe jacking. This paper presents a case study of constructing a deeply buried moderately weathered slate sewage pipeline using pipe jacking method in Changsha, China. To this end, we propose a novel method to combine field monitoring and numerical simulation representation in an efficacious way. Field monitoring was conducted to investigate the spatial distribution characteristics of jacking force, axial stress, and hoop stress in moderately weathered slate. Numerical simulation methods were employed to discuss the influences of several factors on pipe stress: the pipe-rock contact area, contact relationships at pipe joint interfaces, the height of the jacking force position, and the depth of pipe burial. The results show that hand shield is influenced by the excavation technology, and the distribution of jacking force exhibits a stepped or oscillating upward pattern in moderately weathered slate. The maximum axial stress occurs at the mid-span position of the arched roof of pipe at 30 MPa. Hoop stresses are dominated by compressive stresses with the maximum at-8 MPa. As the pipe burial depth increases, so does the axial stress on the pipe. Lower positioning of the jacking force heightens this stress effect. A larger pipe-rock contact area correlates with reduced axial stress levels. The weakening of the contact interface between pipe joints minimally affects axial stress, as stress primarily transmits through non-weakened areas. To ensure the reliability of the data, automatic monitoring and measuring instruments calibrated for on-site monitoring are used. The results of this study can provide beneficial guidance for the design and construction of pipe jacking.

Numerical Study of Tangential Traction Mechanism between Pattern Blocks of Agricultural Radial Tires and Soft Soil.

With the increasing requirements of agricultural machinery, the study of the contact relationship between the tire-soil interface and the improvement of traction efficiency has gradually become a main concern. In this study, the pattern on the agricultural tire was simplified into single-pitch pattern blocks. The pattern blocks were made of rubber material that was highly resistant to abrasion and bending. The experiment was carried out by pressing the three types of patterned block construction into the soil and the pure sliding under the soil. The simulation used the Coupled Eulerian-Lagrangian Method (CEL) to verify the experimental results. We found that the herringbone pattern block was subjected to the highest stress for the same depth of downward pressure. The horizontal force generated by the pure sliding was also the highest. The results showed that the numerically simulated and experimentally measured data exhibited similar trends and average values. In addition, the increase in the contact area between the tire and the soil reduced the compaction and sinking of the soil. The herringbone pattern structure not only had a large contact area but also produced the most significant shear force on the soil. Thus, it may generate greater traction in actual operations.

Numerical Calculation and Application for Crushing Rate and Fracture Conductivity of Combined Proppants

Proppant is one of the key materials for hydraulic fracturing. For special situations, such as middle-deep reservoirs and closure pressures ranging from 40 MPa to 60 MPa, using a single proppant cannot solve the contradiction between performance, which means crushing rate and fracture conductivity, and cost. However, using combined proppants is an economically effective method for hydraulic fracturing of such special reservoirs. Firstly, for different types, particle sizes, and proportions of combined proppants, various contact relationships between proppant particles are considered. The random phenomenon of proppant particle arrangement is described using the Monte Carlo method, and the deterministic phenomenon of proppant particles is processed using an optimization model, achieving computer simulation of the microscopic arrangement of proppant particles. Secondly, a mathematical model for the force analysis of combined proppant particles is established, and an improved singular value decomposition method is used for numerical solution. A computational model for the crushing rate and fracture conductivity of combined proppants is proposed. Thirdly, the numerical calculation results are compared and discussed with the test values, verifying the accuracy of the computational model. Finally, the application of combined proppants is discussed, and a model for optimizing the proportion of combined proppants is proposed. The onsite construction technology is introduced, and the cost and economic benefits of combined proppants are compared with those of all ceramic particles and excessive all-quartz sand. It is proved that combined proppants can balance performance and price, and are an economically effective method for hydraulic fracturing of special reservoirs. The research results can select the optimal proppant material and optimize the combination of different proppant types, which can help achieve cost reduction and efficiency increase in oil and gas development.

Araguainha impact structure, Brazil: New insights into the geology of the central uplift

AbstractExtensive, new outcrops along the MT‐100 state road in the northern part of the central uplift of the 40‐km diameter, 252–259 Ma old Araguainha impact structure, Central Brazil, have become available for investigation. They offer new insight into the contact relationships between the different lithologies and the genesis of different types of impact‐related rocks, as well as the current level of erosion of the structure. Three types of impact melt rock (IMR) with different field relationships and compositions can now be distinguished: (1) Type‐I of granitic composition and occurring mainly as veins and dikes, besides a few larger pods, in the central alkali granite core of the central uplift; (2) Type‐II in the form of plastically deformed clasts of mainly highly silicious compositions in polymict impact breccia; and (3) Type‐III, derived from partially melted conglomerate or sandstone precursors, and that occurs at selected sites in (meta)sedimentary strata of the basement in the immediate environs of the alkali granite core. Both polymict lithic and melt‐bearing (suevitic) impact breccias are recognized in the 110‐m thick integrated section through impact breccia directly overlying the crater floor. This crater floor is composed of (meta)‐sedimentary basement strata with granite injections and, locally, sandstones of the Devonian sedimentary Furnas Formation of the Paraná Basin. Main breccia components are (meta)‐pelites and (meta)sandstones of the basement that is currently favored to be related to the regional Paraguay Belt and to the lower sequence of the Paraná Basin sedimentary strata. Locally, breccia contains clasts of IMR Type‐II, and only very rarely are granitic fragments observed. Clasts of IMR Type‐I have never been observed in the breccia deposits. These new observations preclude significant involvement of alkali granite in the formation of the polymict breccia or in the production of shock melts. They also reveal the major role of the (meta)sedimentary precursors in the production of IMR by shock melting and provide essential information for better understanding the cratering processes involved in the formation of an impact structure in a sedimentary target, of the size of the Araguainha impact structure.

Numerical Calculation Method of Key Performance Parameters of Proppant Based on 2D Computer Simulation

The key performance parameters of proppant are mainly the crushing rate and fracture conductivity, which are usually evaluated using physical experimental methods. However, the testing method for fracture conductivity has limitations, such as its long time-consumption, high testing costs, instability, and even the presence of large errors in testing results under the same conditions. The purpose of this paper is to propose a calculation method that can replace physical experiments. Firstly, we analyze the random and deterministic phenomena in the contact relationship between proppant particles from a microscopic perspective. Subsequently, we develop a physical model of the microscopic arrangement of these particles, enabling us to conduct further computer simulations of their microscopic configuration. Secondly, we conduct a microscopic mechanical analysis of the contact between proppant particles and between particles and boundaries and establish a corresponding mathematical model. Then, utilizing the simulation and mechanical analysis results of the proppant, we calculate the crushing rate. Considering the crushing rate of proppant, we improve the Kozeny–Carmen equation to determine the fracture permeability, and subsequently calculate the fracture conductivity. Finally, the calculated results are compared with the experimental results. The results show that the calculated values for the proppant crushing rate and fracture conductivity matched well with experimental data, and that the model’s calculation values were more accurate. As the number of simulations increased, the accuracy of the calculation results became higher. Research shows that the fracture conductivity is influenced by factors such as the particle size, microstructure, and crushing rate. Numerical calculation methods can replace physical experiments and provide theoretical support for engineering applications of hydraulic fracturing proppant materials.