Geomechanics for Energy and the Environment最新文献_第10页

Investigation on mechanical response and fracture behavior of initially damaged shale based on multi-level PB-GBM method 基于多级PB-GBM方法的初始损伤页岩力学响应及破裂行为研究

IF 3.7 2区工程技术 Q3 ENERGY & FUELS

Geomechanics for Energy and the Environment

Pub Date : 2025-09-08 DOI: 10.1016/j.gete.2025.100738

Jianping Zuo , Bo Lei , Genshui Wu , Haiyan Liu , Massimo Coli

Research on the failure behavior of Longmaxi shale is vital for shale reservoir reconstruction. Shale inherently contains some initial micro-cracks, which significantly affect its strength and failure behavior. In this paper, a refined boundary multi-level parallel bonded grain-based model (multi-level PB-GBM) in Particle Flow Code (PFC2D) was developed, and the effect of inherent initial damage on shale strength and failure behavior was quantitatively investigated. The results showed that inherent initial damage significantly influences the failure pattern and mechanical properties of shale. The newly generated cracks of the initially damaged samples are significantly self-organized compared with those of the undamaged samples, indicating that the inherent initial damaged cracks induce the orientation and aggregation of micro-cracks. High initially damaged samples mainly demonstrate by splitting-shear coupled fracture as a result of the co-evolution of primary and secondary micro-cracks. Generally, rock strength gradually decreases as the initial damage increases. When the inherent initial damage within the sample is low, the rock strength is greatly influenced by confining pressure, whereas when the initial damage is high enough, the initial damage contributes more to the rock strength.

研究龙马溪页岩破坏行为对页岩储层改造具有重要意义。页岩固有的初始微裂缝对其强度和破坏行为有重要影响。本文建立了颗粒流规范（PFC2D）中基于颗粒的精细边界多级平行粘结模型（多级PB-GBM），定量研究了固有初始损伤对页岩强度和破坏行为的影响。结果表明，固有初始损伤对页岩的破坏模式和力学性能有显著影响。与未损伤试样相比，初始损伤试样新生成的裂纹具有明显的自组织特征，表明固有的初始损伤裂纹诱导了微裂纹的取向和聚集。高初始损伤试样主要表现为初生微裂纹与次生微裂纹共同演化导致的劈裂-剪切耦合断裂。一般情况下，随着初始损伤的增加，岩石强度逐渐降低。当试样内部固有初始损伤较小时，围压对岩石强度的影响较大；当初始损伤足够大时，初始损伤对岩石强度的贡献较大。

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引用次数: 0

A three-dimensional fractional elastoplastic constitutive model for rocks within ductile domain 岩石塑性域三维分形弹塑性本构模型

IF 3.7 2区工程技术 Q3 ENERGY & FUELS

Geomechanics for Energy and the Environment

Pub Date : 2025-09-02 DOI: 10.1016/j.gete.2025.100736

Jiacun Liu , Junjie Xiao , Ying Xu , Xing Li , Kaiwen Xia , Gang Han

Under the influence of high three-dimensional geostress, rocks transition into the ductile domain, undergoing continuous plastic hardening and volumetric contraction. Accurately describing the three-dimensional anisotropic deformation of rocks within ductile domain is of great significance for deep underground engineering. Therefore, a three-dimensional fractional elastoplastic constitutive within ductile domain is proposed in this study, including yield function and fractional flow rule. The ductile yield function is based on the modified Mohr-Coulomb criterion and generalized Matsuoka-Nakai deviatoric function. The deviatoric stress of yield surface is negatively correlated to hydrostatic pressure, but positively correlated to Lode angle. The yield surfaces in both meridian and deviatoric planes evolve with the plastic internal variable, accurately capturing the stress state during hardening. Two different fractional orders are used to control the plastic flow direction within meridian and deviatoric planes, represented by dilation angle and plastic deflection angle, respectively. These fractional orders are determined based on the relationship between plastic shear strain and volumetric strain, and they vary with the plastic internal variable, effectively capturing the plastic flow direction throughout hardening. The proposed model is validated using green sandstone data from hydrostatic compression and true-triaxial tests. The effect of fractional orders on the dilation angle and plastic deflection angle is discussed. Under the influence of fractional orders, both dilation angle and plastic deflection angle range from

0^{\circ}

to

- 90^{\circ}

. Besides, a comparison between the non-orthogonality and orthogonality flow rules is made. These results indicate that the fractional flow rule significantly improves the applicability and accuracy of constitutive model.

在高三维地应力作用下，岩石过渡到韧性域，经历连续的塑性硬化和体积收缩。准确描述岩石在韧性域内的三维各向异性变形对深部地下工程具有重要意义。因此，本研究提出了包含屈服函数和分数流动规则的塑性域三维分数弹塑性本构。塑性屈服函数基于修正的Mohr-Coulomb准则和广义的Matsuoka-Nakai偏差函数。屈服面偏应力与静水压力呈负相关，与Lode角呈正相关。子午面和偏面屈服面随塑性内变量的变化而变化，准确地捕捉了硬化过程中的应力状态。用两个不同的分数阶来控制子午面和偏面内的塑性流动方向，分别用膨胀角和塑性挠度角表示。这些分数阶是根据塑性剪切应变和体积应变之间的关系确定的，它们随着塑性内部变量的变化而变化，有效地捕捉了整个硬化过程中的塑性流动方向。利用静水压缩和真三轴试验的绿砂岩数据验证了所提出的模型。讨论了分数阶对膨胀角和塑性挠曲角的影响。在分数阶的影响下，膨胀角和塑性挠度的范围从0°到−90°。此外，还对非正交和正交流动规律进行了比较。这些结果表明，分数流动规则显著提高了本构模型的适用性和准确性。

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引用次数: 0

MICP-enhanced wind erosion resistance of desert sand: process parameter optimization and microstructural mechanism mip增强沙漠砂抗风蚀性能：工艺参数优化及微观结构机理

IF 3.7 2区工程技术 Q3 ENERGY & FUELS

Geomechanics for Energy and the Environment

Pub Date : 2025-09-01 DOI: 10.1016/j.gete.2025.100735

Jian Xu , Liangkun Ding , Zihan Li , Jiayuan Li

This study employed the microbially induced calcium carbonate precipitation (MICP) technique to investigate the mechanism of desert sand stabilization through a multiscale approach, ranging from macro to micro levels. A multi-objective optimization model was created to enhance surface strength, CaCO₃ content, and solidified layer thickness using a comprehensive analysis of multiple factors. The solidification effect was validated with wind tunnel and water retention tests. Microstructural mechanisms were examined through XRD, SEM, and PCAS. Results indicate that the optimum parameters for MICP technology are the 1:2.12 mix ratio, the 1.895 mol/L cementation solution concentration, and 4 treatment cycles. There was also a clear correlation between the performance indexes after solidification. The parameters optimized by the response surface method were essentially the same as those obtained from the experiments, with a difference of less than 5 % between the repeated test results and the optimized results. Under conditions of high CSC (single treatment cycle) or low CSC (multiple treatment cycles), MICP-treated desert sands can achieve highly efficient sand fixation and long-lasting water retention. Microanalysis revealed that increasing CSC and T_c altered the mode of particle contact from point to surface, and a significant negative correlation was observed between pore parameters and surface strength. This proves that it improves the water retention and mechanical strength of desert sand.

本研究采用微生物诱导碳酸钙沉淀（MICP）技术，从宏观到微观的多尺度研究了沙漠沙地的稳定机理。通过多因素综合分析，建立了提高表面强度、CaCO3含量和凝固层厚度的多目标优化模型。通过风洞试验和保水性试验验证了固化效果。通过x射线衍射（XRD）、扫描电镜（SEM）和原子吸收光谱（PCAS）分析了其微观结构机理。结果表明，MICP工艺的最佳工艺参数为：混合比为1:2.12，胶结液浓度为1.895 mol/L，处理周期为4次。凝固后各项性能指标之间也存在明显的相关性。响应面法优化得到的参数与实验结果基本一致，重复试验结果与优化结果相差小于5 %。在高CSC（单次处理周期）或低CSC（多次处理周期）条件下，micp处理的沙漠砂可以实现高效的固沙和持久的保水。微观分析表明，CSC和Tc的增加改变了颗粒从点到表面的接触方式，孔隙参数与表面强度呈显著负相关。这证明它提高了沙漠砂的保水性和机械强度。

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引用次数: 0

Accelerating the Energy Transition with Energy Geotechnics: editorial 用能源岩土技术加速能源转型：社论

IF 3.7 2区工程技术 Q3 ENERGY & FUELS

Geomechanics for Energy and the Environment

Pub Date : 2025-09-01 DOI: 10.1016/j.gete.2025.100706

Philip J. Vardon , Anne-Catherine Dieudonné , John. S. McCartney , Jean-Michel Pereira , David Smeulders , Guillermo Narsilio

引用次数: 0

Energy and entropy balance laws for porous media saturated by one or two non-miscible pore fluids at different temperatures 不同温度下一种或两种非混溶孔隙流体饱和多孔介质的能量和熵平衡规律

IF 3.7 2区工程技术 Q3 ENERGY & FUELS

Geomechanics for Energy and the Environment

Pub Date : 2025-08-29 DOI: 10.1016/j.gete.2025.100731

A. Gajo

The energy and entropy balance equations of porous media saturated by one or more non-miscible fluids have been investigated by many Authors leading to expressions which are based on different thermodynamic potentials and include various simplifying assumptions. Thus the various approaches often appear to be unrelated with respect to each other. In this work, two thermodynamic potentials recently proposed in the literature for porous media saturated by one or two non-miscible and compressible pore fluids are exploited for reconsidering different and perfectly equivalent expressions of the energy balance equations given in terms of internal energies, entropies and enthalpies, without simplifying assumptions. In particular, the entropy fluxes and the dissipation functions are presented for a simple case of irreversible response of the solid skeleton, involving neither irreversibility of the solid grain response, nor elastoplastic coupling nor frozen inelastic energy. Some comparisons with the formulations proposed in the literature are discussed.

许多作者研究了被一种或多种非混相流体饱和的多孔介质的能量和熵平衡方程，得出了基于不同热力学势和包含各种简化假设的表达式。因此，不同的方法往往显得彼此无关。在这项工作中，利用最近在文献中提出的两种热力学势，对由一种或两种非混溶和可压缩孔隙流体饱和的多孔介质进行重新考虑，以内能、熵和焓给出的能量平衡方程的不同和完全等价的表达式，而不简化假设。特别地，给出了固体骨架不可逆响应的简单情况下的熵通量和耗散函数，既不涉及固体颗粒响应的不可逆性，也不涉及弹塑性耦合和冻结的非弹性能量。并与文献中提出的公式进行了比较。

引用次数: 0

Influence of the strain rate on the deformation and failure of rocks with multiscale cracks 应变速率对多尺度裂纹岩石变形破坏的影响

IF 3.7 2区工程技术 Q3 ENERGY & FUELS

Geomechanics for Energy and the Environment

Pub Date : 2025-08-24 DOI: 10.1016/j.gete.2025.100734

Yan-jie Feng , Cheng-zhi Qi , Fa Zhao , Tao Li , An-sen Gao , Xiao-yu Ma

The deformation and failure of rock are affected by the strain rate. However, the effect of the strain rate on rock failure has not been well studied at the microscale level. This study focuses on this complexity by constructing a three-scale wing-shaped crack propagation model that accounts for the interactions between cracks. Based on this model, we determined the initiation and coalescence times of 3 scale levels cracks to reveal the effect of the strain rate on the propagation and failure patterns of multiscale cracks. In addition, we analyzed the critical strain rate (strain rate required for simultaneous coalescence of adjacent scale-level cracks) that leads to failure. The results show that both crack initiation and coalescence times decrease significantly with increasing strain rate and that an increase in initial crack length leads to earlier crack initiation. For the multiscale crack model, as the strain rate increases, large-scale cracks (1-st-scale level cracks) coalesce first, followed sequentially by medium- and small-scale cracks (2-nd and 3-d-scale level cracks). Furthermore, we observed that the critical strain rate initially increases and then decreases with increasing initial crack concentration. Moreover, both an increase in the initial crack length and size decrease factor (ratio of the length of a specific scale-level crack to the length of adjacent larger scale-level cracks) lead to a decrease in the critical strain rate, further confirming the influence of crack size on the failure properties of rock. A comparison with the existing theoretical model shows that the proposed theoretical model is reasonable.

岩石的变形和破坏受应变速率的影响。然而，在微观尺度上，应变速率对岩石破坏的影响还没有得到很好的研究。本研究通过构建一个考虑裂纹间相互作用的三尺度翼形裂纹扩展模型来关注这一复杂性。基于该模型，确定了3个尺度裂纹的起裂时间和聚结时间，揭示了应变速率对多尺度裂纹扩展和破坏模式的影响。此外，我们分析了导致破坏的临界应变速率（相邻尺度级裂纹同时合并所需的应变速率）。结果表明：随着应变速率的增加，裂纹起裂次数和合并次数均显著减少，且初始裂纹长度的增加使裂纹起裂时间提前；对于多尺度裂纹模型，随着应变速率的增大，大尺度裂纹（1-st级裂纹）首先合并，其次是中、小尺度裂纹（2- d级和3-d级裂纹）。随着初始裂纹浓度的增加，临界应变速率先增大后减小。初始裂纹长度和尺寸减小系数（特定尺度裂纹长度与相邻较大尺度裂纹长度之比）的增大均导致临界应变速率的减小，进一步证实了裂纹尺寸对岩石破坏特性的影响。与现有理论模型的比较表明，本文提出的理论模型是合理的。

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引用次数: 0

Numerical comparison between square and circular plate anchors in clay 粘土中方形与圆形板锚的数值比较

IF 3.7 2区工程技术 Q3 ENERGY & FUELS

Geomechanics for Energy and the Environment

Pub Date : 2025-08-23 DOI: 10.1016/j.gete.2025.100733

Mohammadreza Jahanshahinowkandeh, Marina Miranda, Jorge Castro

This paper presents a numerical comparison of the vertical pull-out capacity of square and circular anchors in purely cohesive soils (i.e. clays in undrained conditions). For simplicity, ultrathin, infinitely rigid anchors are considered and to isolate the effect of anchor shape, comparisons are made between anchors of equal area and embedment depth. Finite Element Limit Analyses (FELA) are used to compute upper and lower bound values of the break-out factor over the full range of embedment ratios, and the associated failure mechanisms are identified. The results show for the first time (to the best of the authors’ knowledge) that square anchors exhibit slightly higher efficiency at shallow embedment ratios due to their larger perimeter, while at greater depths, circular anchors become more efficient as a result of the different failure mechanisms involved. The study also investigates the influence of anchor inclination and shows that inclined anchors have a higher pull-out capacity in vented conditions due to elongated failure mechanisms. Under attached conditions, the deep failure mechanism is obtained in most cases with the corresponding constant break-out factor. In addition, the paper analyses the influence of anchor spacing in anchor groups, identifying optimal spacing to avoid capacity reduction due to interaction effects. For shallow depths, a spacing of about two times the anchor width is sufficient, while deeper installations require larger spacings due to the extended failure zone. Once the deep failure mechanism is reached, spacing requirements decrease again, less than two times the anchor width. Overall, the presented numerical simulations offer insights for the design of plate anchors in cohesive soils, contributing to the advancement of offshore foundation technologies.

本文提出了在纯粘性土（即不排水条件下的粘土）中方形和圆形锚杆的垂直拔拔能力的数值比较。为简单起见，我们考虑了超薄的无限刚性锚杆，为了隔离锚杆形状的影响，我们对等面积和埋深的锚杆进行了比较。采用有限元极限分析（FELA）计算了全埋置比范围内破坏因子的上限和下限，并确定了相关的破坏机制。结果首次表明（据作者所知），由于方形锚的周长较大，在浅埋比下，方形锚的效率略高，而在更深的深度下，圆形锚由于不同的破坏机制而效率更高。该研究还探讨了锚杆倾角的影响，结果表明，由于锚杆的破坏机制拉长，在通风条件下，倾斜锚杆具有更高的拔出能力。在附加条件下，大多数情况下均可得到深部破坏机理，并具有相应的恒定破裂因子。此外，本文还分析了锚群中锚间距的影响，确定了最优的锚间距，以避免因相互作用而导致的承载力下降。对于较浅的深度，大约两倍锚固宽度的间距就足够了，而较深的安装需要更大的间距，因为破坏区域会扩大。一旦达到深部破坏机制，间距要求再次降低，小于锚固宽度的两倍。总的来说，所提出的数值模拟为粘性土壤中板锚的设计提供了见解，有助于海洋基础技术的进步。

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引用次数: 0

Coupled SPH–FEM modeling of waterjet-assisted coal cutting: Numerical simulation and experimental validation 水射流辅助采煤SPH-FEM耦合建模：数值模拟与实验验证

IF 3.7 2区工程技术 Q3 ENERGY & FUELS

Geomechanics for Energy and the Environment

Pub Date : 2025-08-20 DOI: 10.1016/j.gete.2025.100732

Satar Mahdevari , Pedram Bakhtiari Haftlang

Coal remains a cornerstone of global energy supply, driving the need for more efficient and technologically advanced extraction methods. This study introduces a numerical framework that couples the Smoothed Particle Hydrodynamics (SPH) with the Finite Element Method (FEM) to model the dynamic response of coal under waterjet-assisted cutting—an emerging technique recognized for its applicability, minimal stress disturbance, and safe working conditions in underground mining. Implemented in LS-DYNA, the model captures two-phase fluid–solid interactions, including jet-induced fracture initiation, propagation, and material removal. A detailed parametric investigation evaluates the effects of jet velocity, nozzle diameter, impingement angle, and cutting duration on coal fragmentation behavior. Model predictions were rigorously validated through controlled laboratory experiments, achieving reliable correlation with empirical results—showing mean absolute errors of 7.2 % in Cutting Depth (CD) and 5.8 % in Cutting Volume (CV). To address the performance constraints of Pure Water Jet (PWJ) systems, extended simulations were conducted for Abrasive Water Jet (AWJ) and Ice Abrasive Water Jet (IAWJ) techniques. The AWJ configuration enhanced CD and CV by 51 % and 66 %, respectively, while IAWJ achieved up to 20 % improvement over PWJ. Stress field analysis further revealed that increased jet velocity is significantly more effective than nozzle enlargement in maximizing cutting efficiency. These findings not only validate the SPH–FEM model as a predictive tool but also offer actionable insights for optimizing next-generation waterjet systems in deep coal mining applications.

煤炭仍然是全球能源供应的基石，推动了对更高效、技术更先进的开采方法的需求。本文介绍了一种数值框架，将光滑颗粒流体动力学（SPH）与有限元法（FEM）相结合，来模拟煤在水射流辅助切割下的动态响应。水射流辅助切割是一种新兴的技术，因其适用性、应力扰动最小和在地下开采中安全的工作条件而得到认可。该模型在LS-DYNA中实现，可捕获两相流固相互作用，包括射流诱导的裂缝萌生、扩展和材料去除。详细的参数研究评估了射流速度、喷嘴直径、撞击角和切割时间对煤破碎行为的影响。模型预测通过受控的实验室实验得到了严格验证，与经验结果实现了可靠的相关性——切割深度（CD）的平均绝对误差为7.2 %，切割体积（CV）的平均绝对误差为5.8 %。为了解决纯水射流（PWJ）系统的性能限制，对磨料水射流（AWJ）和冰磨料水射流（IAWJ）技术进行了扩展模拟。AWJ配置使CD和CV分别提高了51 %和66 %，而IAWJ比PWJ提高了20 %。应力场分析进一步表明，增大射流速度比增大喷嘴更能有效地提高切削效率。这些发现不仅验证了SPH-FEM模型作为预测工具的有效性，而且为优化深煤开采应用中的下一代水射流系统提供了可行的见解。

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引用次数: 0

Damage and acoustic characteristics of water-saturated coals with different ranks under liquid nitrogen freezing and thawing treatments 不同等级水饱和煤在液氮冻融作用下的损伤及声学特性

IF 3.7 2区工程技术 Q3 ENERGY & FUELS

Geomechanics for Energy and the Environment

Pub Date : 2025-08-05 DOI: 10.1016/j.gete.2025.100730

Lei Qin , Jiawei Li , Haifei Lin , Shugang Li , Miao Mu , Shiyin Lv , Niandong Chen

Geological variability results in coal seams with diverse ranks exhibiting distinct physical properties, critically influencing liquid nitrogen (LN₂) fracturing outcomes. We systematically assess the mechanical and acoustic damage induced by single LN₂ freeze-thaw (LNSFT) and repeated freeze-thaw cycles (LNCFT) in three representative coal ranks—lignite, bituminite, and anthracite—via ultrasonic measurement, uniaxial compression, and acoustic emission (AE) techniques. Results demonstrate that initially, pore water solidification enhances coal strength and acoustic integrity; subsequently, crack initiation and propagation induced by frost heave, thermal stress, and LN₂ expansion progressively weaken these properties. This balance between strengthening and weakening is primarily governed by coal pore structure, fissures, and moisture content. AE patterns under loading distinctly follow steady-state, activation, and attenuation phases, with both the freezing and thawing phases promoting shear-oriented fracture development. Damage indices (D), computed from ultrasonic P-wave velocity (v), peak strength (σ), and elastic modulus (E), reveal an inverse correlation between freeze-thaw damage severity and coal rank, indicating that higher-rank coals exhibit greater structural stability and freeze-thaw resistance. Furthermore, under equivalent cumulative freezing durations, LNCFT cause significantly greater damage than LNSFT, highlighting a cumulative damage effect. These insights provide critical guidance for optimizing LN₂ fracturing techniques aimed at enhancing coal seam permeability.

地质变异性导致不同等级的煤层具有不同的物理性质，严重影响液氮（LN 2）压裂效果。通过超声测量、单轴压缩和声发射（AE）技术，系统地评估了褐煤、烟煤和无烟煤三种代表性煤种的单次LN2冻融（LNSFT）和多次冻融循环（LNCFT）引起的力学和声学损伤。结果表明：孔隙水凝固初期增强了煤的强度和声完整性；随后，由冻胀、热应力和LN 2膨胀引起的裂纹萌生和扩展逐渐削弱了这些特性。这种强化与弱化之间的平衡主要是由煤的孔隙结构、裂隙和含水率决定的。加载作用下的声发射模式明显遵循稳态、激活和衰减阶段，冻结和融化阶段都促进了剪切导向裂缝的发育。由超声纵波速度(v)、峰值强度（σ）和弹性模量(E)计算的损伤指数(D)表明，冻融损伤程度与煤阶呈负相关，表明煤阶越高，结构稳定性和抗冻融能力越强。此外，在相同的累积冻结时间下，LNCFT造成的损伤明显大于LNSFT，突出了累积损伤效应。这些见解为优化旨在提高煤层渗透率的LN 2压裂技术提供了重要指导。

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引用次数: 0

Displacement analysis for energy pile foundations under thermomechanical loads 热力荷载作用下能量桩基础的位移分析

IF 3.7 2区工程技术 Q3 ENERGY & FUELS

Geomechanics for Energy and the Environment

Pub Date : 2025-07-30 DOI: 10.1016/j.gete.2025.100725

Jincheng Fang , Shijin Feng , Yong Zhao , Hongxin Chen

Energy piles present an innovative energy-saving technology that can fulfill two critical building needs of structural support and energy supply. In practice, developing simple but efficient methods to predict the thermomechanical response of energy pile foundations is essential for geotechnical engineers. In this study, a practical method was proposed for the thermomechanical analyses of energy pile foundations. The proposed method could effectively describe the interactions between the grouped energy piles, the surrounding soil, and the stiff soil strata underlying the pile tip. Based on this method, parametric analyses were performed to evaluate the effects of several aspects, including the foundation geometries and ground properties, on the pile displacement behavior and the pile-to-pile interaction. Further, the proposed method was used for the displacement analysis for a square pile group containing sixteen energy piles under thermomechanical loads. Comparisons with results obtained through the experimental investigations and finite-element methods prove that the proposed method is capable of capturing the displacement response of energy pile foundations with reasonable accuracy. The aim of this study is to offer a practical method and a reliable reference to geotechnical engineers during the design of energy pile foundations.

能源桩是一种创新的节能技术，能够满足建筑结构支撑和能源供应两大关键需求。在实际应用中，开发简单而有效的方法来预测能源桩基础的热力响应对岩土工程师来说是必不可少的。本文提出了一种实用的能量桩基础热力分析方法。该方法能够有效地描述成组能量桩与周围土体以及桩端下刚性土层之间的相互作用。基于该方法，进行了参数分析，以评估地基几何形状和地基性质等方面对桩位移行为和桩间相互作用的影响。并将该方法应用于包含16根能量桩的方桩群在热力荷载作用下的位移分析。通过与试验研究结果和有限元方法的比较，证明了该方法能够以合理的精度捕捉能源桩基础的位移响应。本文的研究旨在为岩土工程师在能源桩基础的设计中提供实用的方法和可靠的参考。

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引用次数: 0