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Simhypo-sand: a simple hypoplastic model for granular materials and SPH implementation 模拟砂:粒状材料的简单次塑性模型和 SPH 实现
IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-05-31 DOI: 10.1007/s11440-024-02350-8
Shun Wang, Hong-jie Fang, Xuan Kang, Dian-qing Li, Wei Wu

This paper introduces a new hypoplastic model characterized by a simple and elegant formulation. It requires only 7 material parameters to depict salient mechanical behaviors of granular materials. The numerical implementation employs an explicit integration method, enhanced by a best-fit stress correction algorithm in a smoothed particle hydrodynamics code. The performance of this model in capturing soil behavior across a range of scenarios is demonstrated by conducting various numerical tests, including triaxial and simple shear at low strain rates, as well as granular collapse, rigid penetration and landslide process at high strain rates.

本文介绍了一种新的次塑性模型,其特点是表述简单而优雅。它只需要 7 个材料参数就能描述颗粒材料的显著力学行为。数值实现采用了显式积分法,并通过平滑粒子流体力学代码中的最佳拟合应力校正算法进行了增强。通过进行各种数值测试,包括低应变率下的三轴剪切和简单剪切,以及高应变率下的颗粒塌陷、刚性渗透和滑坡过程,证明了该模型在各种情况下捕捉土壤行为的性能。
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引用次数: 0
Site water salinity effect on the hydro-mechanical behavior of compacted GMZ bentonite with technological void 场地水盐度对具有技术空隙的压实GMZ膨润土水力学行为的影响
IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-05-28 DOI: 10.1007/s11440-024-02338-4
Qiong Wang, Xusheng Yan, Wei Su, Weimin Ye, Fengshou Zhang

The hydromechanical behavior of compacted bentonite in near-field salinity groundwater environment is of great importance for achieving the low-permeability sealing capacity in deep geological repositories. Within this context, swelling pressure and hydraulic conductivity of compacted bentonites with technological voids were evaluated under simulated site water salinity conditions. Water content, dry density and pore size distribution were measured after hydration. Results showed that the swelling pressure shows a trend of rapid rise and reach the peak value, then drop sharply and stabilized. The rapid decrease in the hydraulic conductivity for all salinity is the salient features, and then, it reduces slowly. The above evolution behavior is dominated by the swelling mechanisms and the self-sealing of technological void under different salinity conditions. Adequate water and space provided by technological void lead to gradient evolution of geotechnical properties, such as water content, dry density and pore size distribution. The density increase mechanism derived from salinity fails to compete with the density decrease mechanism derived from sufficient space sourced from technological void. Therefore, the dry density at the external sampling site decreases with increasing salinity. At high salinity, the compressed diffuse double layer not only increases the inter-aggregate pores but also widens the water flow channels. As a result, hydraulic conductivity increases with increasing salinity. Considering the influence from groundwater salinity, it is necessary to improve basic properties and technological void dimensions of bentonite blocks for the safety of long-term operation of deep geological repository.

压实膨润土在近场含盐地下水环境中的水力学行为对于实现深层地质储藏库的低渗透密封能力非常重要。在此背景下,我们在模拟现场水盐度条件下评估了具有技术空隙的压实膨润土的膨胀压力和水力传导性。对水化后的含水量、干密度和孔径分布进行了测量。结果表明,膨胀压力呈快速上升趋势,达到峰值后急剧下降并趋于稳定。所有盐度下水力传导率的显著特点是快速下降,然后缓慢降低。在不同盐度条件下,上述演化行为主要受膨胀机制和技术空隙自封的影响。技术空隙提供的充足水分和空间导致岩土特性的梯度演化,如含水量、干密度和孔径分布。盐度导致的密度增加机制无法与技术空隙提供的充足空间导致的密度降低机制相抗衡。因此,外部取样点的干密度随着盐度的增加而降低。在高盐度条件下,压缩扩散双层不仅增加了聚集间孔隙,还拓宽了水流通道。因此,水力传导率随盐度的增加而增大。考虑到地下水盐度的影响,有必要改善膨润土砌块的基本特性和技术空隙尺寸,以确保深层地质储藏库长期运行的安全性。
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引用次数: 0
Calcium ions and calcium carbonate: key regulators of the enzymatic mineralization for soil dispersivity control 钙离子和碳酸钙:控制土壤分散性的酶矿化关键调节剂
IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-05-24 DOI: 10.1007/s11440-024-02304-0
Guanzhou Ren, Minqiang Meng, Henghui Fan, Jixiang Wen, Jianwei Zhang, Gaowen Zhao, Xiujuan Yang, Zengchun Sun, Xiang He

Dispersive soil is a widely distributed problematic soil in arid or semiarid areas of the world and can cause pipe erosion, gully damage and other seepage failures. This study analyzed the effect of environmentally friendly enzyme-induced carbonate precipitation (EICP) on the dispersivity of dispersive soils. This methodology was tested for the stabilization of three dispersive soil types (two high-sodium soils, two low-clay-content soils, and two soils with both high sodium and low clay contents) to examine the impact on dispersivity based on the results of pinhole tests and mud ball tests. Physical, chemical, mechanical, and microscopic tests were also conducted to investigate the effects of the components in the EICP reaction solution on dispersive soil modification. The experiments showed that the concentration of the reaction solution and the curing time required to limit the dispersivity decreased with increasing clay content in the soil. Ca2+ limited the dispersivities of dispersive soils via four distinct mechanisms. The first mechanism was ion exchange; Ca2+ decreased the percentage of exchangeable sodium ions to less than 7% while reducing the thickness of the diffuse double layer such that the spacings between soil particles were reduced and the chemical dispersivity was limited. Second, Ca2+ increased the viscosity of the solution by salting out the organic matter present in the soybean urease. Subsequently, the D1-class physically dispersive soil was converted into an ND2-class nondispersive soil. Third, Ca2+ decreased the soil pH by reducing the CO32− content, which could hydrolyze to increase the soil alkalinity. Finally, the presence of Ca2+ led to the generation of cementitious minerals through the precipitation of CaCO3 crystals that continuously generated CO32−, filling and cementing soil particles and thereby limiting their physical dispersivity. These results indicated that a low-concentration EICP reaction solution efficiently controlled the dispersivities of the three dispersive soils.

分散性土壤是世界上干旱或半干旱地区广泛分布的问题土壤,可造成管道侵蚀、沟渠破坏和其他渗流故障。本研究分析了环保型酶诱碳酸盐沉淀法(EICP)对分散性土壤分散性的影响。根据针孔试验和泥球试验的结果,该方法对三种分散性土壤类型(两种高钠土壤、两种低粘土含量土壤和两种高钠低粘土含量土壤)进行了稳定化试验,以考察其对分散性的影响。此外,还进行了物理、化学、机械和显微测试,以研究 EICP 反应溶液中的成分对分散性土壤改性的影响。实验表明,随着土壤中粘土含量的增加,限制分散性所需的反应溶液浓度和固化时间也随之减少。Ca2+ 通过四种不同的机制限制了分散性土壤的分散性。第一种机制是离子交换;Ca2+ 将可交换钠离子的百分比降至 7% 以下,同时减少了扩散双层的厚度,从而减少了土壤颗粒之间的间距,限制了化学分散性。其次,Ca2+ 盐化了大豆脲酶中的有机物,从而增加了溶液的粘度。随后,D1 级物理分散性土壤转化为 ND2 级非分散性土壤。第三,Ca2+ 通过减少 CO32- 的含量来降低土壤 pH 值,而 CO32- 可以水解来增加土壤碱度。最后,Ca2+ 的存在通过 CaCO3 晶体的沉淀产生了胶结矿物,这些晶体不断生成 CO32-,填充和胶结土壤颗粒,从而限制了它们的物理分散性。这些结果表明,低浓度 EICP 反应溶液可有效控制三种分散性土壤的分散性。
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引用次数: 0
Lateral load-carrying mechanism of driven battered minipiles 驱动式撞击微型桩的侧向承载机制
IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-05-24 DOI: 10.1007/s11440-024-02250-x
Sanchari Mondal, Mahdi M. Disfani

The lateral load-carrying mechanism of vertically installed and battered minipiles is evaluated using 1g-physical and numerical modelling. Single minipiles with batter angles of 0°, ± 25° and ± 45° are tested under lateral load in medium dense and dense sand. The minipiles are instrumented with fibre Bragg grated optic fibres to obtain a strain profile (two-dimensional) along the minipile shaft. A calibrated numerical model is further adopted to produce p–y curves for battered minipiles at various node deflections. The ratio of soil reaction of battered minipiles to vertically installed minipiles is observed to change with both deflection and depth of the minipile. An analytical solution is developed based on the decomposition of lateral load into skin friction and passive pressure for battered minipiles. A reduction factor is proposed that considers a decrease in passive pressure when the minipile is loaded in the opposite direction of the batter. The analytical solution is capable of accounting for soil properties, pile rigidity and the angle of inclination of battered minipiles. The analytical method is subsequently verified for cohesive soils using full-scale field results. The ratio of the ultimate lateral load of battered minipiles to vertical minipiles presented in the literature corroborated the findings of this study.

采用 1g 物理和数值模型评估了垂直安装和撞击式微型桩的横向承载机制。在中密度和高密度砂中,对撞击角为 0°、± 25°和± 45°的单个微型桩进行了横向荷载测试。微型桩上安装了布拉格光栅光纤仪器,以获得沿微型桩轴的应变曲线(二维)。此外,还采用了一个经过校准的数值模型,以生成不同节点挠度下撞击微型桩的 p-y 曲线。据观察,撞击式微型桩与垂直安装的微型桩的土壤反力比会随着微型桩的挠度和深度而变化。根据将侧向荷载分解为表面摩擦力和被动压力的方法,为撞击式微型桩制定了一个分析解决方案。还提出了一个折减系数,该系数考虑了当微型桩受到与撞击方向相反的荷载时被动压力的减小。分析解决方案能够考虑土壤特性、桩的刚度和撞击式微型桩的倾斜角度。分析方法随后利用全尺寸现场结果对粘性土进行了验证。文献中介绍的撞击式微型桩与垂直式微型桩的极限侧向荷载比证实了本研究的结果。
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引用次数: 0
Temperature effects on adsorption and capillarity water retention mechanisms in constrained unsaturated soils 温度对约束非饱和土壤中吸附和毛细管保水机制的影响
IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-05-20 DOI: 10.1007/s11440-024-02341-9
Yu Lu, John S. McCartney

This paper focuses on the impact of elevated temperatures on the adsorptive and capillarity water retention mechanisms of unsaturated soils under constrained (constant volume) conditions. This topic is critical for simulating the thermo-hydraulic behavior of soils in hydrogeological or geotechnical applications, including climate change effects on near surface soils, energy piles or soil borehole thermal energy storage systems in unsaturated soil layers, and buffers for geological nuclear waste repositories. A nonisothermal soil water retention curve (SWRC) that separately considers the temperature-dependency of the key parameters governing adsorptive and capillarity water retention mechanisms and soil physical parameters (e.g., surface tension, contact angle, adsorption capacity, cation exchange capacity, mean cavitation suction, air entry value and equilibrium film thickness) was developed to provide insights into the impact of temperature on water retention over the full suction range. The nonisothermal SWRC was validated using experimental data on high plasticity clays, with a good prediction of temperature effects on adsorption and capillarity water retention mechanisms in constrained unsaturated soils.

本文重点研究在受限(恒定体积)条件下,温度升高对非饱和土壤吸附和毛细管保水机制的影响。该课题对于模拟水文地质或岩土工程应用中的土壤热-水力行为至关重要,包括气候变化对近地表土壤、非饱和土层中的能源桩或土壤钻孔热能存储系统以及核废料地质处置库缓冲区的影响。开发的非等温土壤保水曲线(SWRC)分别考虑了吸附和毛细管保水机制的关键参数与土壤物理参数(如表面张力、接触角、吸附能力、阳离子交换能力、平均空化吸力、空气进入值和平衡膜厚度)的温度依赖性,以便深入了解温度在整个吸力范围内对保水的影响。利用高塑性粘土的实验数据验证了非等温 SWRC,并很好地预测了温度对受约束非饱和土壤中吸附和毛细管保水机制的影响。
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引用次数: 0
Controllable hydrophobization of sands with self-healing polymeric microcapsules 利用自修复聚合物微胶囊对泥沙进行可控憎水处理
IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-05-18 DOI: 10.1007/s11440-024-02294-z
Rui Qi, Ke Chen, Hongjie Lin, Sérgio D. N. Lourenço, Antonios Kanellopoulos

Hydrophobized soils have functional hydrophobic coatings to delay or restrict water infiltration and thus prevent infrastructure failure and long-term degradation. Over time, hydrophobized soils will be subjected to degradation under the action of external stresses, leading to the loss of its functional properties. Microencapsulation approaches, initially developed for self-healing applications emerge as a potential solution to enhance, switch (from hydrophilic) or prolong the longevity of hydrophobized soils. The aim of this study is to produce and investigate the effectiveness of microencapsulation to impart hydrophobicity in granular materials in response to external stimuli. In this research, polydimethylsiloxane (PDMS), with hydrophobic properties, is encapsulated in calcium alginate microcapsules with the ionic gelation method. The effectiveness of the microcapsules to induce hydrophobicity is investigated by mixing sand with microcapsules and quantifying the change of the contact angle and water drop penetration time (measures of hydrophobicity) under an external trigger, i.e., under drying and consecutive wetting–drying cycles. The results show that microcapsules release the hydrophobic cargo (PDMS) during shrinkage. After drying, the PDMS content in sand increased to 0.1–0.8% by mass of sand. The released hydrophobic cargo (PDMS) induced hydrophobicity in sands, reflected by a contact angle increase from 29.7° to at least 87.7°. The amount of polydimethylsiloxane encapsulated is a key parameter controlling the release of hydrophobic cargo. In addition, 4% capsule content in sands is identified as an effective microcapsule content in inducing hydrophobicity.

疏水土具有疏水功能涂层,可延缓或限制水的渗透,从而防止基础设施失效和长期退化。随着时间的推移,疏水土会在外部压力的作用下发生降解,导致其功能特性丧失。最初为自愈应用而开发的微胶囊方法成为一种潜在的解决方案,可增强、转换(从亲水性)或延长疏水土的寿命。本研究的目的是生产和调查微胶囊技术在颗粒材料中对外界刺激赋予疏水性的有效性。在这项研究中,利用离子凝胶法将具有疏水特性的聚二甲基硅氧烷(PDMS)封装在海藻酸钙微胶囊中。通过将沙子与微胶囊混合,并量化接触角和水滴渗透时间(衡量疏水性的指标)在外部触发(即干燥和连续润湿-干燥循环)下的变化,研究了微胶囊诱导疏水性的效果。结果表明,微胶囊在收缩过程中会释放疏水性物质(PDMS)。干燥后,按沙子质量计算,沙子中的 PDMS 含量增加到 0.1-0.8%。释放出的疏水性物质(PDMS)使沙子具有疏水性,接触角从 29.7°增加到至少 87.7°。聚二甲基硅氧烷的封装量是控制疏水货物释放的关键参数。此外,金沙中 4% 的胶囊含量被认为是诱导疏水性的有效微胶囊含量。
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引用次数: 0
Frozen enzyme EICP method for more effective soil improvement 冷冻酶 EICP 法更有效地改良土壤
IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-05-14 DOI: 10.1007/s11440-024-02348-2
Samuel Ng, Jian Chu

Enzyme-induced calcite precipitation (EICP) is one of the emerging soil improvement methods. However, when plant-based enzyme is used, the urease enzyme harvested from plants cannot be stored long. This affects large-scale applications of this method. This paper presents a new method that not only enables urease enzyme to be stored for a long duration, but also improves significantly the effectiveness and efficiency of EICP for soil improvement. In this method, the storage duration of soybean derived urease enzyme is prolonged by storing it at negative 20 degrees. The experimental results indicated that the frozen-stored urease enzyme had an activity of 326% higher than that of fresh enzyme. The shear strength of a fine sand treated using the frozen-stored enzyme is 238.8% higher than that using a normal EICP method. Thus, the frozen method not only overcomes the enzyme storage problem, but also offers a much-improved EICP method. The reasons for the higher urease activity and improved strength enhancement are also explained in this paper.

酶诱导方解石沉淀法(EICP)是一种新兴的土壤改良方法。然而,在使用植物酶时,从植物中提取的脲酶不能长期储存。这影响了这种方法的大规模应用。本文提出了一种新方法,它不仅能使脲酶长时间储存,还能显著提高 EICP 在土壤改良中的效果和效率。在这种方法中,大豆提取的脲酶通过在负 20 度的环境中储存,延长了脲酶的储存时间。实验结果表明,冷冻储存的脲酶活性比新鲜酶高出 326%。使用冷冻储存酶处理的细砂的剪切强度比使用普通 EICP 方法处理的细砂高 238.8%。因此,冷冻法不仅克服了酶的储存问题,还大大改进了 EICP 方法。本文还解释了脲酶活性提高和强度增强改善的原因。
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引用次数: 0
Progressive yielding/softening of soil–cement columns under embankment loading: a case study 路堤荷载下土灰柱的渐进屈服/软化:案例研究
IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-05-13 DOI: 10.1007/s11440-024-02346-4
Jin-chun Chai, Takenori Hino, Yafei Qiao, Wenqi Ding

An embankment with a fill thickness of 7.5 m was built on a soil–cement column-slab system improved about 15.8 m thick soft subsoil. The embankment was stable for about 5 months after construction, and then, its settlement rate increased rapidly. To avoid the failure of the embankment, 1.0 m thick fill was removed and the embankment was stabilized again. The results of field investigation using all-core boring through a cement deep mixing (CDM) column under the central of the embankment and 3D finite element analysis (FEA) indicate that the most likely mechanism for the observed field behavior is progressive yielding/softening of the upper part of the columns. In FEA, the yielding/softening of the upper part of columns was simulated using strength reduction option and the start of the softening was triggered manually at the time of observed rapid increase in the settlement rate. This case history indicates that in field quality control of CDM columns, identifying local weak part(s) by continuous measuring the strength of the column samples retrieved from all-core boring is important. It is suggested that combination of unconfined compression test as well as needle penetration tests for the cores retrieved can be an economic and practical way to do this.

在土-水泥柱-板系统上修建了填土厚度为 7.5 米的堤坝,改良了约 15.8 米厚的软基土。堤坝在建成后约 5 个月内保持稳定,随后沉降速度迅速加快。为了避免路堤坍塌,我们清除了 1.0 米厚的填土,并重新稳固了路堤。通过对堤坝中央下方的水泥深层搅拌(CDM)柱进行全芯钻孔实地调查和三维有限元分析(FEA)的结果表明,实地观察到的行为最可能的机制是柱子上部的逐渐屈服/软化。在有限元分析中,使用强度降低选项模拟了支柱上部的屈服/软化,并在观察到沉降速度快速增加时手动触发软化开始。这一案例表明,在对 CDM 柱进行现场质量控制时,通过连续测量从全岩心钻孔取回的柱样本的强度来识别局部薄弱部分非常重要。建议对取回的岩心结合进行无约束压缩试验和针入度试验,这是一种经济实用的方法。
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引用次数: 0
Morphology characterization of unsaturated soils under drying-wetting cycles: crack opening and closure 干燥-湿润循环条件下非饱和土壤的形态特征:裂缝开合
IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-05-12 DOI: 10.1007/s11440-024-02347-3
Zhuang Zhuo, Weiling Cai, Cheng Zhu, Chao-Sheng Tang, Kaniz Roksana

The volumetric and hydrological responses of clayey soils subjected to drying-wetting (D-W) cycles are of paramount importance for the integrity of geoenvironmental infrastructures. The study aimed to investigate the cracking behavior of clayey soils under D-W cycles by using advanced 2D imaging and 3D scanning techniques to capture the initiation and propagation of desiccation cracks within a soil specimen. The temporal variation in the soil water content and the corresponding 2D digital photography and 3D morphology of cracks were simultaneously monitored, and the cracking characteristics were interpreted. It was found that the time-dependent evaporation process was independent of the D-W cycles. Both 2D and 3D characterization showed the cracking hysteresis phenomenon in the unsaturated soil, which indicates the dependency of the crack opening and closure on the degree of saturation. D-W cycles led to the formation of subcracks and the increase in the total crack length, reflecting the soil degradation. Additionally, it was demonstrated that the 3D characterization exhibited the advantage of capturing the volumetric change and the subtle change in the macroporosity of the cracked soil over the 2D visualization. The current study provides a perspective of combining 2D and 3D characterization for interpreting the volumetric change of cracked soils and enhancing the understanding of the hydromechanical responses and the soil-atmosphere interactions.

粘性土在干燥-湿润(D-W)循环下的体积和水文响应对地质环境基础设施的完整性至关重要。本研究旨在利用先进的二维成像和三维扫描技术,捕捉土壤试样中干燥裂缝的产生和扩展过程,从而研究粘性土壤在干湿循环条件下的开裂行为。同时监测了土壤含水量的时间变化以及相应的二维数字摄影和三维裂缝形态,并对裂缝特征进行了解释。研究发现,与时间相关的蒸发过程与 D-W 周期无关。二维和三维表征均显示了非饱和土壤中的裂缝滞后现象,这表明裂缝的开合与饱和度有关。D-W 循环导致子裂缝的形成和总裂缝长度的增加,反映了土壤退化。此外,与二维可视化相比,三维表征在捕捉开裂土壤的体积变化和宏观孔隙度的微妙变化方面具有优势。当前的研究提供了一个结合二维和三维表征的视角,以解释开裂土壤的体积变化,并加深对水力学响应和土壤-大气相互作用的理解。
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引用次数: 0
Correlation of fabric parameters and characteristic features of granular material behaviour in DEM in constitutive modelling 构造模型中 DEM 中织物参数与颗粒材料行为特征的相关性
IF 5.6 1区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-05-11 DOI: 10.1007/s11440-024-02333-9
Farid Khayyer, Md Mizanur Rahman, Md Rajibul Karim

The anisotropic microstructure of granular materials has a profound effect on their macroscopic behaviour and can be characterised using a fabric tensor. To include of fabric in the critical state theory (CST), anisotropic critical state theory (ACST) was proposed by modifying the state parameter ((psi )) of CST to a fabric-dependent dilatancy state parameter ((upzeta )). Noteworthy that (uppsi) showed a very strong correlation with characteristic features (e.g. instability, phase transformation and characteristic state) of macroscopic behaviour and, as a result, it has been adopted in many constitutive models. While (upzeta) aided the inclusion of fabric in ACST models, the correlation between (upzeta) and characteristic features has not been evaluated in detail yet, although a large number of works are found on micromechanics and fabric only. In this study, a large number of discrete element method simulations for drained and undrained triaxial were conducted to evaluate the correlation between (upzeta) and characteristic features. To this purpose, the correlation between stress ratio and both classic and dilatancy state parameter ((psi) and (upzeta)) were studied in important characteristic features (e.g. instability, phase transformation and characteristic state). It was found that this correlation was improved using (upzeta) which might be due to the inclusion of fabric in our model. This observation is new and significant for inclusion of fabric evolution in constitutive modelling.

粒状材料的各向异性微观结构对其宏观行为有着深远的影响,可以用织物张量来表征。为了将织物纳入临界状态理论(CST),有人提出了各向异性临界状态理论(ACST),将 CST 的状态参数 ((psi))修改为依赖于织物的膨胀状态参数 ((upzeta))。值得注意的是(uppsi)与宏观行为的特征(如不稳定性、相变和特征状态)有很强的相关性,因此,它已被许多构成模型所采用。虽然(upzeta)有助于将织物纳入 ACST 模型,但(upzeta)与特征特性之间的相关性尚未得到详细评估,尽管有大量关于微观力学和织物的研究。在这项研究中,对排水和非排水三轴进行了大量离散元法模拟,以评估(upzeta)与特征特性之间的相关性。为此,研究了重要特征(如不稳定性、相变和特征状态)中应力比与经典参数和膨胀状态参数((psi)和(upzeta))之间的相关性。结果发现,使用 (upzeta) 时这种相关性得到了改善,这可能是由于我们的模型中包含了织物。这一观察结果是新的,对于在构造模型中纳入织物演化具有重要意义。
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引用次数: 0
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