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Coupled hydraulic-mechanical-chemical PD–FEM model for the non-uniform corrosion of reinforcement concrete under hydraulic pressure 钢筋混凝土水压不均匀腐蚀的水力-机械-化学耦合PD-FEM模型
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-07-20 DOI: 10.1007/s40571-025-01006-y
Shenhua Liu, Weizhong Chen, Jingqiang Yuan

Underwater concrete is vulnerable to the coupling erosion of water pressure and chlorides, threatening the durability of underwater concrete structures. To predict this process more realistically, a chemical-hydraulic-mechanical peridynamic-finite element method (PD–FEM) model of the chloride erosion of reinforced concrete under hydraulic pressure was developed to investigate the entire process of reinforced concrete damage caused by chloride erosion under water pressure. A multi-phase concrete model with irregular aggregates was employed to simulate the effects of aggregates and the interfacial transition zone (ITZ) on water penetration, chloride diffusion, and steel corrosion. The proposed PD–FEM model focuses both on the unsaturated transport process of water and chloride and the corrosion failure of unsaturated reinforced concrete under water pressure. The proposed PD–FEM model in simulating the mechanical effects and seepage-diffusion coupling was verified by two numerical experiments, and the entire process of corrosion expansion failure of underwater reinforced concrete is simulated by this model. The numerical results show that the proposed chemical-hydraulic-mechanical coupling PD–FEM model can simulate the penetration of water and chloride in unsaturated concrete and failure process of concrete caused by chloride corrosion under water pressure, as well as the effects of aggregates and the ITZ on water penetration, chloride diffusion, and steel corrosion. Furthermore, parameter sensitivity analysis indicated that water pressure accelerated the transport of water and chloride in concrete and softened the concrete, accelerating the durability failure of underwater concrete.

水下混凝土易受水压和氯化物的耦合侵蚀,威胁着水下混凝土结构的耐久性。为了更真实地预测这一过程,建立了水压作用下钢筋混凝土氯离子侵蚀的化学-水力-力学周动力有限元模型,研究了水压作用下氯离子侵蚀对钢筋混凝土的破坏全过程。采用不规则骨料多相混凝土模型,模拟了骨料和界面过渡区(ITZ)对水渗透、氯离子扩散和钢腐蚀的影响。提出的PD-FEM模型既关注水和氯化物的非饱和输运过程,又关注非饱和钢筋混凝土在水压作用下的腐蚀破坏。通过两个数值实验验证了所提出的PD-FEM模型在模拟力学效应和渗透扩散耦合方面的有效性,并利用该模型模拟了水下钢筋混凝土腐蚀膨胀破坏的全过程。数值结果表明,所建立的化学-水力-力学耦合PD-FEM模型能够模拟水和氯化物在非饱和混凝土中的渗透过程和水压下氯化物腐蚀引起混凝土破坏的过程,以及集料和ITZ对水渗透、氯化物扩散和钢腐蚀的影响。参数敏感性分析表明,水压加速了混凝土中水和氯离子的运移,使混凝土软化,加速了水下混凝土的耐久性破坏。
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引用次数: 0
Stability analysis of a gravelly soil slope based on energy criterion and discrete element strength reduction method 基于能量准则和离散单元强度折减法的砂质土坡稳定性分析
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-07-20 DOI: 10.1007/s40571-025-01008-w
Yuqi Li, Yiwei Ding, Yu Fang, Danda Shi, Qing Xie

Soil in slope engineering is a granular material, so it is more advantageous to study the movement of particles during slope instability by discrete element method. A three-dimensional discrete element numerical model for gravelly soil slopes was established, and a new energy-based criterion was introduced to define slope failure in this paper. The slope stability was assessed according to the principle of strength reduction method, and the slope safety factor was determined based on the energy criterion. The results show that there was a significant inflection point in the evolution of kinetic energy, elastic strain energy, and dissipation energy with strength reduction factor, and the corresponding strength reduction factor is the slope safety factor. The slope safety factor determined based on the energy criterion was 1.4, which is consistent with that obtained by the change in particle displacement and theoretical equation, verifying the correctness of the slope safety factor determined by the energy criterion in this paper. The research work in this paper provides a novel approach for the stability analysis of slopes.

边坡工程中土体为粒状物质,采用离散元法更有利于研究边坡失稳过程中土体颗粒的运动。建立了含砾土边坡的三维离散元数值模型,引入了基于能量的边坡破坏定义准则。根据强度折减法原理对边坡进行稳定性评价,根据能量准则确定边坡安全系数。结果表明:边坡动能、弹性应变能和耗散能随强度折减系数的演化存在一个显著拐点,对应的强度折减系数即为边坡安全系数;根据能量准则确定的边坡安全系数为1.4,与颗粒位移变化及理论方程的结果一致,验证了本文能量准则确定的边坡安全系数的正确性。本文的研究工作为边坡稳定性分析提供了一种新的思路。
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引用次数: 0
A numerical model for the electrode calendering process considering the cohesive behavior between damageable particles and metal foil 考虑损伤颗粒与金属箔黏结行为的电极压延过程数值模型
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-07-19 DOI: 10.1007/s40571-025-01011-1
Chuanqi Liu, Min Ru, Zonghan Li, Jinding Liang

Calendering is a critical step in the manufacturing process of lithium-ion batteries, but simulating this process presents challenges due to the binder, which bonds discrete particles to the continuous metal foil. In this study, we propose a numerical model to simulate the calendering process effectively. The model treats the metal foil as a continuum using the finite element method (FEM) and represents the active particles as discrete entities using the discrete element method (DEM). To account for the binder’s effect on the metal foil, a set of ghost particles is embedded within a narrow zone of the continuum, enabling volume coupling. A damage variable is introduced at the level of individual particles to assess the effects of the calendering process. Additionally, we present a comprehensive approach for calibrating material parameters through physical experiments. The model’s effectiveness is demonstrated through two examples, highlighting its ability to analyze key manufacturing parameters such as roller compression and curvature. This study provides a valuable tool for simulating the calendering process, capturing the essential role of the binder, and guiding the optimization of electrode manufacturing.

压延是锂离子电池制造过程中的关键步骤,但由于粘合剂将离散颗粒粘合到连续金属箔上,因此模拟这一过程存在挑战。在本研究中,我们提出了一个数值模型来有效地模拟压延过程。该模型采用有限元法将金属箔视为连续体,采用离散元法将活性粒子表示为离散实体。为了解释粘合剂对金属箔的影响,在连续体的狭窄区域内嵌入了一组鬼粒子,从而实现了体积耦合。在单个颗粒的水平上引入损伤变量来评估压延过程的影响。此外,我们提出了一种通过物理实验校准材料参数的综合方法。通过两个实例验证了该模型的有效性,突出了其分析关键制造参数(如辊压和曲率)的能力。该研究为模拟压延过程、捕捉粘结剂的重要作用以及指导电极制造的优化提供了有价值的工具。
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引用次数: 0
Investigating the frost cracking of offshore wind power concrete piles using an improved meshless numerical method 采用改进的无网格数值方法研究海上风电混凝土桩的冻裂问题
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-07-19 DOI: 10.1007/s40571-025-01032-w
Cong Hu, Taicheng Li, Haiying Mao, Jianfeng Xue, Haotian Chang, Zhaoqing Fu, Wenbing Zhang, Shuyang Yu

Offshore wind power plays a crucial role in the global development of clean energy. However, the concrete piles of offshore wind turbines face the problem of frost heave cracking in cold sea areas. In this study, the meso-scale frost heave cracking mechanisms of concrete is investigated. Traditional smoothed particle hydrodynamics (SPH) method is improved. A fracture marker is introduced to simulate the progressive failure processes of particles, and a method for generating the meso-structures of concrete is proposed. By embedding the temperature equation and combining with the equivalent thermal expansion method, the frost heave cracking process of concrete is simulated. Simulation schemes with different aggregate percentages, aggregate sizes, pore percentages, and prefabricated fissure angles are set up to study the influence of various factors on the frost heave cracking of concrete. The results show that different factors have a significant impact on the frost heave cracking of concrete. The improved SPH method can effectively simulate the frost heave cracking process of concrete. Compared with traditional numerical methods, it has more obvious advantages in dealing with particle failure and complex meso-structures. This study reveals the laws of concrete frost heave cracking under different meso-structure factors, providing a solid theoretical basis for the anti-frost heave design of concrete piles in offshore wind farms.

海上风电在全球清洁能源发展中发挥着至关重要的作用。然而,在寒冷海域,海上风电机组混凝土桩面临着冻胀开裂的问题。本文对混凝土的中尺度冻胀开裂机理进行了研究。对传统的光滑颗粒流体力学方法进行了改进。引入断裂标志来模拟颗粒的渐进破坏过程,提出了一种生成混凝土细观结构的方法。通过嵌入温度方程,结合等效热膨胀法,对混凝土冻胀开裂过程进行了模拟。建立不同骨料含量、骨料粒径、孔隙率和预制裂缝角的模拟方案,研究各种因素对混凝土冻胀开裂的影响。结果表明,不同因素对混凝土冻胀开裂有显著影响。改进的SPH方法可以有效地模拟混凝土的冻胀开裂过程。与传统数值方法相比,该方法在处理颗粒破坏和复杂细观结构方面具有更明显的优势。本研究揭示了不同细观结构因素下混凝土冻胀开裂规律,为海上风电场混凝土桩抗冻胀设计提供了坚实的理论依据。
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引用次数: 0
Reduction of stress oscillations in the material point method based on the random grid-shift technique 基于随机格移技术的质点法应力振荡减小
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-07-19 DOI: 10.1007/s40571-025-01026-8
M. Koßler, S. Maassen, R. Niekamp, J. Schröder

The material point method (MPM) is a particle method, suitable for large-deformation analysis. Bodies are represented by particles, the so-called material points. These carry all information such as mass, velocity, position and deformation state, to name just a few. With this in hand, the Lagrangian representation of the body is combined with a computational background grid in an Eulerian sense in order to solve the differential equations of interest. Since the grid does not keep track of history data it is reset at the beginning of each time step using the same geometry throughout the simulation. As a result, mesh distortion is diminished, enabling large deformations throughout the simulation. While using (C^0)-continuous shape functions, stress oscillations are likely to occur. One way of solving this issue is the application of higher-order shape functions. In this contribution, focus is on (C^0)-continuous shape functions in combination with the grid-shift technique in order to reduce stress oscillations. Here, the initial placement of the grid nodes is altered, i.e., the grid is translated in space at the beginning of each time step. This method is realized by randomly shifting the origin of the grid, resulting in no computational overhead and a straightforward implementation. Comparisons of four numerical examples are analyzed using the standard fixed grid approach and the grid-shift technique with respect to oscillations in the stress field, alternative application of boundary conditions and energy conservation.

材料点法(MPM)是一种适用于大变形分析的颗粒法。物体由粒子表示,即所谓的物质点。它们携带所有信息,如质量,速度,位置和变形状态,仅举几例。有了这个,身体的拉格朗日表示与欧拉意义上的计算背景网格相结合,以解决感兴趣的微分方程。由于网格不跟踪历史数据,因此在整个模拟过程中使用相同的几何图形在每个时间步的开始处重置。因此,网格失真减少,在整个模拟过程中实现大变形。当使用(C^0) -连续形状函数时,应力振荡很可能发生。解决这一问题的一种方法是应用高阶形状函数。在此贡献中,重点是(C^0) -连续形状函数与网格移位技术相结合,以减少应力振荡。在这里,网格节点的初始位置被改变,即在每个时间步的开始,网格在空间上被平移。该方法通过随机移动网格原点来实现,没有计算开销,实现简单。采用标准固定网格法和栅格移法对应力场振荡、边界条件的替代应用和能量守恒等问题进行了比较分析。
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引用次数: 0
Analysis of elbow erosion in natural gas–hydrogen pipelines under dense and pseudo-dense phase flow: a CFD-DEM (gas–solid flow) study 致密相流和拟致密相流条件下天然气-氢气管道弯头侵蚀分析:CFD-DEM(气固流动)研究
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-07-18 DOI: 10.1007/s40571-025-01017-9
Moslem Abrofarakh

In this study, the erosion behavior of elbows in natural gas–hydrogen pipelines was investigated using CFD-DEM under dense phase (DP), pseudo-dense phase (PDP), and vapor phase (VP) conditions. Three pipeline models were analyzed: model 1 with 0% hydrogen, model 2 with 2%, and model 3 with 4%. The simulations explored the effects of Reynolds numbers (2,000,000–5,000,000), particle diameters (100–300 μm), and particle mass flow rates (100–300 kg/h) on the erosion rate. The results showed that across all models, the erosion rate increased with Reynolds number, particle mass flow rate, and particle diameter. At Reynolds number 2,000,000, the erosion rate in DP was about 60% lower than in VP for model 1, 64% lower for model 2, and 60% lower for model 3. As hydrogen mole fraction increased, the erosion rate slightly decreased: in DP at Reynolds 2,000,000, the erosion for model 3 was 5% lower than model 2 and 2.5% lower than model 1. Across all particle diameters, the maximum erosion rate in DP was 63% lower than in VP and 20% lower than in PDP. At 100 μm, the DP erosion rate for model 1 was 67% and 31% lower than VP and PDP; for model 2, 70% and 19% lower; and for model 3, 65% and 16% lower. The Reynolds number had a stronger effect on erosion than particle mass flow rate or diameter. High hydrogen content slightly reduces erosion but requires higher pressure.

在本研究中,利用CFD-DEM研究了天然气-氢气管道中弯头在致密相(DP)、伪致密相(PDP)和气相(VP)条件下的侵蚀行为。分析了三种管道模型:模型1含0%氢,模型2含2%氢,模型3含4%氢。模拟研究了雷诺数(200万~ 500万)、颗粒直径(100 ~ 300 μm)和颗粒质量流量(100 ~ 300 kg/h)对侵蚀速率的影响。结果表明,在所有模型中,侵蚀速率随雷诺数、颗粒质量流量和颗粒直径的增加而增加。在雷诺数为200万时,模型1中DP的侵蚀速率比VP低约60%,模型2低64%,模型3低60%。随着氢摩尔分数的增加,侵蚀速率略有下降,DP在雷诺数为200万时,模型3的侵蚀速率比模型2低5%,比模型1低2.5%。在所有粒径范围内,DP的最大侵蚀速率比VP低63%,比PDP低20%。在100 μm下,模型1的DP侵蚀速率比VP和PDP分别低67%和31%;对于模型2,降低70%和19%;对于模型3,分别降低了65%和16%。雷诺数对冲蚀的影响大于颗粒质量、流速和直径。高氢含量稍微减少侵蚀,但需要更高的压力。
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引用次数: 0
The effect of particle shape on the reflux performance of the lifting pump 颗粒形状对提升泵回流性能的影响
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-07-16 DOI: 10.1007/s40571-025-01021-z
Minggao Tan, Yaohan Jiang, Xianfang Wu, Houlin Liu, Denghao Wu, Runan Hua

In order to explore the influence of particle shape on the reflux performance in mining lifting pump, the CFD-DEM coupling method was used to numerically simulate the solid–liquid two-phase flow in the mining lifting pump, and the effects of spherical particles, square particles and cylindrical particles on the reflux characteristics in the pump were compared and analyzed. The research results show that when the reflux occurs in the pump, the high-speed particles are mainly distributed at the inlet of the first-stage and second-stage impellers and the outlet of the first-stage guide vane. The accumulation phenomenon mainly occurs on the pressure surface of the guide vane blade and the junction between the impeller and the guide vane. When particles of different shapes reflux in the pump, the distribution area of the spherical particles in the first-stage and second-stage impellers is the smallest, followed by the cylindrical particles, and the largest is the square particles. The accumulation phenomenon of the spherical, cylindrical, and square particles in the pump gradually extends toward the impeller passage in turn. In addition, the average velocity of the particles decreases in the order of spherical, cylindrical, and square particles, and the total number of collisions of the particles increases in the order of spherical, cylindrical, and square particles. The time required for the spherical particles to reflux through the pump is the shortest, and the time required for the non-spherical particles to pass through the pump is similar, with the square particles having the lowest passage rate of 43.98%. These factors cause the reflux performance of the spherical, cylindrical, and square particles to decrease in order.

为了探索颗粒形状对矿用提升泵内回流性能的影响,采用CFD-DEM耦合方法对矿用提升泵内固液两相流动进行数值模拟,对比分析了球形颗粒、方形颗粒和圆柱形颗粒对矿用提升泵内回流特性的影响。研究结果表明,当泵内发生回流时,高速颗粒主要分布在一级和二级叶轮入口处和一级导叶出口处。堆积现象主要发生在导叶叶片的压力面以及叶轮与导叶的结合处。不同形状的颗粒在泵内回流时,球形颗粒在一级和二级叶轮中的分布面积最小,其次是圆柱形颗粒,最大的是方形颗粒。泵内球形、圆柱形和方形颗粒的堆积现象依次逐渐向叶轮通道延伸。此外,粒子的平均速度按照球形、圆柱形和方形粒子的顺序减小,粒子的总碰撞次数按照球形、圆柱形和方形粒子的顺序增加。球形颗粒回流通过泵所需时间最短,非球形颗粒通过泵所需时间相似,方形颗粒的通过率最低,为43.98%。这些因素导致球形、圆柱形和方形颗粒的回流性能依次降低。
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引用次数: 0
Comparison of ‘rigid body motion’ of a particulate bed and a liquid pool under linear acceleration through computational simulation 线性加速度作用下颗粒床与液池“刚体运动”的比较
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-07-15 DOI: 10.1007/s40571-025-01020-0
Abhinesh Kumar, Prasanta Kumar Das

Using discrete element modeling, the unique characteristics of a bed of grains contained in a translating rectangular box with or without acceleration on a straight horizontal path have been studied. The inclined free surface shape has apparent similarities to its hydrodynamic equivalent at constant acceleration; nevertheless, due to the particle nature of the medium, there are some distinct differences. One of the notable differences is the nonlinear free surface of the granular bed. The effective slope of the accelerating granular bed is much higher compared to that of the liquid pool for the same dynamic condition. In the accelerating granular bed, the free surface profile is not affected by the particle density, but the particle size and inter-particular friction weakly influence it. Meanwhile, acceleration has an impact on the local gradient of the free surface. Nonetheless, the simulation results clearly imply that although typically, bed behavior is similar to solid body motion, locally, the discrete nature of the medium influences the distribution and motion of the particles. Contrary to the hydrodynamics case, a translation without acceleration also results in a slope in the free surface of the granular bed.

利用离散元模型,研究了在水平直线路径上有或没有加速度的平移矩形箱中颗粒床的独特特性。倾斜自由面形状与其在恒定加速度下的流体动力等效面有明显的相似之处;然而,由于介质的粒子性质,存在一些明显的差异。其中一个显著的区别是颗粒床的非线性自由表面。在相同动力条件下,加速颗粒床的有效斜率比液池的有效斜率大得多。在加速颗粒床中,自由表面轮廓不受颗粒密度的影响,但颗粒大小和种间摩擦对其影响较小。同时,加速度对自由表面的局部梯度也有影响。尽管如此,模拟结果清楚地表明,尽管通常情况下,床的行为与固体运动相似,但在局部,介质的离散性影响了颗粒的分布和运动。与流体力学的情况相反,没有加速度的平移也会导致颗粒床的自由表面出现斜率。
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引用次数: 0
Analysis of asphalt rutting simulation test considering initial defects 考虑初始缺陷的沥青车辙模拟试验分析
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-07-15 DOI: 10.1007/s40571-025-01009-9
Xiangyang Lv, Zichen Chang, Xiaoyong Wu, Zhanyou Yan, Guofang Zhao

A virtual rutting experimental model was established based on the discrete element method (DEM) to investigate the influence of microscopic initial defects on the mechanical properties of asphalt materials. The data from the model, which determines the mesoscopic parameters by parameter inversion, were compared with the data from the actual rutting test. To ensure the accuracy of the model data, the discrete fracture network (DFN) was used to characterize the microscopic initial defects of the material. It indicated that the virtual rutting experiment results were consistent with the actual experimental results. The effect of incipient defects on asphalt mixtures could be well characterized by a virtual rutting test model. Microscopic defects had a significant effect on the mechanical properties of materials. The overall structural strength of the material decreased significantly. When the length of the micro-crack was greater than 4 mm and the width (dist) was between 0.15 mm and 0.45 mm, the reduction in material strength was most significant. During construction, the length and width of cracks were controlled by effective means, which was beneficial for improving the crack resistance of materials.

基于离散元法(DEM)建立了虚拟车辙试验模型,研究了微观初始缺陷对沥青材料力学性能的影响。通过参数反演确定细观参数的模型数据与实际车辙试验数据进行了对比。为了保证模型数据的准确性,采用离散断裂网络(DFN)表征材料微观初始缺陷。结果表明,虚拟车辙试验结果与实际试验结果吻合较好。虚拟车辙试验模型可以很好地表征沥青混合料初期缺陷的影响。微观缺陷对材料的力学性能有显著影响。材料的整体结构强度明显下降。当微裂纹长度大于4 mm,宽度(dist)在0.15 ~ 0.45 mm之间时,材料强度降低最为显著。在施工过程中,通过有效手段控制裂缝的长度和宽度,有利于提高材料的抗裂性。
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引用次数: 0
Exploration of relative density in discrete element simulations: implications for strength and deformation characteristics 离散单元模拟中相对密度的探索:强度和变形特征的含义
IF 2.8 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-07-13 DOI: 10.1007/s40571-025-01013-z
Miao Yang, Ning Zhang, Xinmiao Zhang, Qinghao Li

The relative density is a key indicator of the mechanical properties of coarse-grained soil. To better explain the shear behaviors such as dilatancy–contractancy and softening–hardening in simulations based on Discrete Element Method (DEM), the definitions of the maximum void ratio, minimum void ratio, and relative density were generalized to consider the impact of the confining pressure during the shear process. Comprehensive tests were conducted based on direct shear tests through the DEM. Preparation methods were presented to obtain specimens with the maximum void ratio, minimum void ratio, and target relative density. The direct shear tests show that the shear behavior of coarse-grained soil significantly varies with changes in relative density. Specifically, under high relative density conditions, soils tend to exhibit dilatancy behavior accompanied by softening characteristics. Conversely, under low relative density conditions, soils are more prone to contractancy and display hardening behavior. The peak shear strength increases with increasing relative density, indicating enhanced resistance to deformation. Additionally, compared with the void ratio, the relative density provides a more accurate description of the variation of shear strength parameters with the degree of compactness. These findings suggest that the interactions between soil particles, influenced by confining pressure and relative density, play a crucial role in determining the macroscopic shear behavior of these materials. This study provides a theoretical basis for density control and strength evaluation of coarse-grained soil.

相对密度是反映粗粒土力学性质的重要指标。为了更好地解释基于离散元法(DEM)模拟中的剪胀收缩和软化硬化等剪切行为,对最大空隙比、最小空隙比和相对密度的定义进行了推广,考虑了剪切过程中围压的影响。在直剪试验的基础上,通过DEM进行综合试验。提出了最大空隙比、最小空隙比和靶相对密度的制备方法。直剪试验表明,粗粒土的抗剪性能随相对密度的变化而显著变化。在高相对密度条件下,土体表现出膨胀特性和软化特性。相反,在低相对密度条件下,土壤更容易收缩并表现出硬化行为。峰值抗剪强度随相对密度的增加而增加,表明抗变形能力增强。相对于孔隙率,相对密度能更准确地描述抗剪强度参数随密实度的变化。这些发现表明,受围压和相对密度影响的土颗粒之间的相互作用在决定这些材料的宏观剪切行为中起着至关重要的作用。该研究为粗粒土的密度控制和强度评价提供了理论依据。
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引用次数: 0
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Computational Particle Mechanics
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