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Mathematical Reconstruction Analysis of a Natural Fracture Network in Rock Based on a Modified Fisher Model and Its Numerical Realization 基于修正Fisher模型的岩石天然裂缝网络数学重构分析及其数值实现
IF 4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL Pub Date : 2025-12-13 DOI: 10.1002/nag.70205
Qingci Qin, Chaoquan Luo, Kegang Li, Fa Dong, Naeem Abbas
Fractures are one of the most critical factors influencing the mechanical properties of rocks. To explore the quantitative description method of fracture networks in natural rock masses and achieve precise mathematical reconstruction of the stochastic distribution characteristics of natural fractures, the apparent fracture distribution characteristics of 499 fractures in 12 standard specimens were investigated. The results show that there is a significant correlation among the density, length, and dip angle of fractures in different directions. Based on this, a quantitative description method for fracture networks that considers the relationship between fracture density and orientation is proposed. Combined with the Fisher model, the probability density distribution function of natural fracture orientation density was established. Using this method, the equivalent numerical analysis model of rock specimens containing natural fractures was reconstructed on the RFPA platform, and numerical experiments of triaxial loading and unloading were performed on the reconstructed equivalent fractured rock numerical model. This method can quantitatively describe the geometric distribution characteristics of fractures in natural rocks. The modified Fisher model enables the visual reconstruction of natural fracture networks, offering an effective technical approach for building equivalent numerical analysis models of rocks with natural fractures. It is highly valuable for studying the coupled mechanical behavior of multi‐physical fields in natural fractured rocks and provides an equivalent analysis method for visualizing and analyzing the damage process of natural fractured rocks.
裂缝是影响岩石力学性能最关键的因素之一。为探索天然岩体中裂缝网络的定量描述方法,实现天然裂缝随机分布特征的精确数学重构,对12个标准试样中499条裂缝的表观裂缝分布特征进行了研究。结果表明,不同方向裂缝的密度、长度和倾角之间存在显著的相关性。在此基础上,提出了一种考虑裂缝密度与方位关系的裂缝网络定量描述方法。结合Fisher模型,建立了天然裂缝定向密度的概率密度分布函数。利用该方法,在RFPA平台上重构了含天然裂缝岩石试件的等效数值分析模型,并在重构的等效裂隙岩石数值模型上进行了三轴加载和卸载数值试验。该方法可以定量描述天然岩石裂缝的几何分布特征。修正后的Fisher模型实现了天然裂缝网络的可视化重建,为建立含天然裂缝岩石等效数值分析模型提供了有效的技术途径。研究天然裂隙岩体中多物理场的耦合力学行为,为可视化分析天然裂隙岩体损伤过程提供了一种等效分析方法,具有重要的应用价值。
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引用次数: 0
Extended Kelvin–Voigt Model for Simulating Thermally Accelerated Creep in Fine‐Grained Soils 模拟细粒土热加速蠕变的扩展Kelvin-Voigt模型
IF 4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL Pub Date : 2025-12-13 DOI: 10.1002/nag.70190
Giulia Capati, Diana Salciarini, Alessandro F. Rotta Loria
The subsurface undergoes temperature variations in many situations due to anthropogenic and natural causes, which strongly influence the long‐term behavior of soils. These phenomena can involve temperature anomalies in the ground across distances of a few meters, as in the case of nuclear waste repositories, to distances encompassing entire cities, as in the case of subsurface urban heat islands. To date, a number of constitutive models have been proposed to capture the mechanics of soils under non‐isothermal conditions, with particular attention to fine‐grained soils due to their renowned sensitivity to temperature variations. However, most of the available models suffer from many constitutive parameters that hinder their applicability to the analysis of large and complex problems involving thermally induced deformations of fine‐grained soils. This study extends the classical Kelvin–Voigt model with a temperature‐dependent formulation for capturing the reversible or irreversible thermally induced deformations of fine‐grained soils, interpreted through the theory of thermally accelerated creep. Implemented in a finite element software and validated against experimental data, the model shows that the thermally induced deformations of fine‐grained soils are highly sensitive to the temperature variation rate, while they are little influenced by the magnitude of the applied mechanical loads. The proposed model effectively captures the complex, time‐dependent deformations of fine‐grained soils with only a few easily calibrated parameters, making it a practical tool for the long‐term analysis of thermally induced creep in such materials.
由于人为和自然原因,地下温度在许多情况下都会发生变化,这对土壤的长期行为产生强烈影响。这些现象可能涉及到几米范围内的地面温度异常,比如核废料储存库,也可能涉及到覆盖整个城市的距离,比如城市地下热岛。迄今为止,已经提出了许多本构模型来捕捉非等温条件下土壤的力学,特别关注细粒土壤,因为它们对温度变化非常敏感。然而,大多数可用的模型都存在许多本构参数,这阻碍了它们对涉及细粒土热致变形的大型复杂问题的分析。本研究扩展了经典的Kelvin-Voigt模型,通过热加速蠕变理论解释了温度依赖公式,用于捕获细粒土壤的可逆或不可逆热诱导变形。该模型在有限元软件中实现,并与实验数据进行了验证,结果表明,细粒土的热致变形对温度变化率高度敏感,而受施加的机械载荷大小的影响很小。所提出的模型有效地捕获复杂的,时间依赖的变形细粒土只有几个容易校准的参数,使其成为一个实用的工具,长期分析热诱发蠕变在这种材料。
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引用次数: 0
An Efficient User‐Defined Element Framework for Joint Behavior Simulation and Transverse Deformation Analysis in Shield Tunnels 盾构隧道接缝行为模拟与横向变形分析的有效用户定义单元框架
IF 4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL Pub Date : 2025-12-13 DOI: 10.1002/nag.70206
Hanwen Ji, Ximin Hu, Yu Miao, Hongjun He
This study proposes an efficient modeling approach for shield tunnel joints based on user‐defined elements (UELs), which is applied to the analysis of transverse deformation in shield tunnels. The element stiffness matrix of longitudinal joints with irregular geometric configurations was derived under arbitrary loading conditions. The solution procedure of the stiffness matrix was then incorporated into the UEL algorithm framework. The developed element simultaneously accounts for the varying load state at longitudinal joints, geometric configurations of the joint, and material nonlinearity, as well as their coupling effect on the load‐bearing capacity of the joint. Subsequently, the feasibility and accuracy of the UEL‐based modeling approach were evaluated across multiple modeling scales. The results demonstrate that this element not only significantly simplifies the modeling process but also effectively captures the nonlinear characteristics of tunnel convergence deformation observed in practical engineering scenarios. In addition, the UEL‐based modeling approach was employed to investigate the transverse deformation of shield tunnels subjected to an extreme surcharge–unloading–grouting rehabilitation sequence. Lining displacement–subgrade reaction and in situ stress state were appropriately incorporated into the numerical model. The effects of initial soil stiffness and the coefficient of earth pressure at rest on tunnel transverse deformation were quantitatively examined, along with the relationship between tunnel convergence and joint rotation. The results reveal a flag‐shaped hysteresis in the moment‐rotation response of tunnel joints under unloading and grouting, underscoring the importance of precisely capturing the multi‐degree‐of‐freedom coupling in joint element for practical engineering applications.
本研究提出了一种基于用户自定义单元(UELs)的盾构隧道节点高效建模方法,并将其应用于盾构隧道横向变形分析。推导了任意载荷条件下具有不规则几何构型的纵向节理单元刚度矩阵。将刚度矩阵的求解过程纳入UEL算法框架。所开发的单元同时考虑了节点纵向荷载状态的变化、节点几何形态的变化和材料的非线性,以及它们对节点承载能力的耦合效应。随后,在多个建模尺度上评估了基于UEL的建模方法的可行性和准确性。结果表明,该单元不仅显著地简化了建模过程,而且有效地捕捉了实际工程场景中观察到的隧道收敛变形的非线性特征。此外,采用基于UEL‐的建模方法,研究了极端超载-卸载-注浆修复顺序下盾构隧道的横向变形。数值模型中适当地考虑了衬砌位移-路基反力和原位应力状态。定量分析了土体初始刚度和静土压力系数对隧道横向变形的影响,以及隧道收敛与节理旋转的关系。结果表明,在卸载和注浆作用下,隧道节理的弯矩-旋转响应存在旗形滞后,强调了在实际工程应用中精确捕捉节理单元中多自由度耦合的重要性。
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引用次数: 0
Optimizing Cutterhead Scouring Systems for Large‐Diameter Slurry Shields: A Case Study of the Qingdao Second Submarine Tunnel 大直径泥浆盾构刀盘冲刷系统优化——以青岛第二海底隧道为例
IF 4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL Pub Date : 2025-12-13 DOI: 10.1002/nag.70201
Hanbiao Zhu, Shuying Wang, Zihao Jin, Jiazheng Zhong, Xiangcou Zheng, Pengfei Liu
Frequent occurrences of shield clogging during slurry shield tunneling emphasize the necessity of optimizing cutterhead scouring systems. Conventional studies largely rely on empirical design and simplified analyses, which fail to capture complex flow–solid interactions or enable quantitative optimization. To overcome these limitations, a computational fluid dynamics (CFD) model was developed to simulate jet flow formation in shield nozzles and the flow field in the cutterhead excavation zone. It allows to systematically investigate the effects of nozzle inlet velocity, slurry chamber pressure, and cutterhead rotation speed, promoting the optimization of nozzle geometry and arrangement. The optimized configuration has been validated in the Qingdao Second Submarine Tunnel. Results show that increasing inlet velocity enhances jet strength without altering the overall velocity distribution pattern. Cutterhead rotation generates a rotating flow field that intensifies scouring but causes jet deflection, while interference between central and adjacent nozzles limits the effective scouring area. By modifying the outlet geometry and eliminating ineffective main arm nozzles, both the effective scouring area ratio and scouring efficiency index were improved. The optimized configuration ensures stable and efficient advancement when the nozzle inlet velocity exceeds 4 m/s, effectively preventing shield clogging. This work provides a validated modeling framework and practical optimization strategy for enhancing slurry shield performance in complex geological conditions.
泥浆盾构施工中盾构堵塞的频繁发生,凸显了对刀盘冲刷系统进行优化的必要性。传统的研究主要依赖于经验设计和简化的分析,无法捕捉复杂的流固相互作用或实现定量优化。为了克服这些限制,开发了计算流体动力学(CFD)模型来模拟屏蔽喷嘴内的射流形成和刀盘开挖区域的流场。它可以系统地研究喷嘴入口速度,浆室压力和刀盘转速的影响,促进喷嘴几何形状和布置的优化。优化后的结构已在青岛第二海底隧道中得到验证。结果表明,在不改变整体速度分布规律的情况下,增大进口速度可提高射流强度。刀盘旋转产生的旋转流场加剧了冲刷,但造成了射流偏转,而中心喷嘴和相邻喷嘴之间的干扰限制了有效冲刷面积。通过改进出料口几何形状和消除无效主臂喷嘴,提高了有效冲刷面积比和冲刷效率指数。优化后的结构保证了喷嘴进口速度超过4m /s时的稳定高效推进,有效防止屏蔽堵塞。为提高复杂地质条件下泥浆盾构性能提供了有效的建模框架和实用的优化策略。
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引用次数: 0
Suspended Sediment Transport in Ice‐Covered Turbulent Flow: Semi‐Analytical Solution and Parametric Sensitivity 冰覆盖湍流中的悬浮泥沙输运:半解析解和参数敏感性
IF 4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL Pub Date : 2025-12-13 DOI: 10.1002/nag.70192
Sourav Hossain, Ashok Das, Sanjib Naskar, Sweta Narayan Sahu, Koeli Ghoshal
This study presents a semi‐analytical solution for modeling suspended sediment distribution in turbulent flows within ice‐covered channels under unsteady, non‐equilibrium conditions. The solution is derived using the generalized integral transform technique (GITT). Validation was performed against the cell‐centered finite volume method and existing experimental data. The results confirm high accuracy, supported by error analysis. Optimized parameter values were obtained through a hybrid genetic and interior point algorithm. Several underlying phenomena of particle‐turbulence interactions in ice‐covered channels are explored. The focus is on the influence of key sediment transport parameters on the time‐dependent evolution of vertical concentration profiles of suspended sediment particles. Key findings indicate that increasing the settling‐velocity correction coefficient raises sediment concentration profiles over time. In contrast, greater ice‐cover roughness reduces sediment suspension. Sensitivity analysis highlights the inverse of the Schmidt number as a critical factor. This novel application of GITT and variance‐based sensitivity analysis (VBSA) provides a detailed solution library, and serves as a benchmark for numerical models.
本研究提出了一种半解析解,用于模拟非稳定、非平衡条件下冰覆盖通道内湍流中悬浮沉积物的分布。利用广义积分变换技术(GITT)推导了该问题的解。根据细胞中心有限体积法和现有实验数据进行验证。结果表明,该方法具有较高的精度,并得到了误差分析的支持。通过遗传和内点混合算法得到优化参数值。探讨了冰覆盖通道中粒子-湍流相互作用的几种潜在现象。重点研究了关键输沙参数对悬沙颗粒垂直浓度曲线随时间变化的影响。主要发现表明,随着时间的推移,沉降速度修正系数的增加会提高泥沙浓度曲线。相反,更大的冰盖粗糙度减少了沉积物悬浮。敏感性分析强调了施密特数的逆作为一个关键因素。这种基于方差的敏感性分析(VBSA)的新应用提供了一个详细的解决方案库,并作为数值模型的基准。
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引用次数: 0
A Novel Approach to Analyzing the Mechanical Response of Pipe Umbrella Support in Shallow Buried Tunnels Considering Construction Characteristics 考虑施工特点的浅埋隧道管伞支护力学响应分析新方法
IF 4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL Pub Date : 2025-12-10 DOI: 10.1002/nag.70196
Yazhen Sun, Lifan Yuan, Jinchang Wang, Longyan Wang, Youlin Ye
A novel analytical approach based on the state‐space method (SSM) is proposed to facilitate the rapid and accurate analysis of the mechanical behavior of pipe umbrellas in shallow‐buried tunnels. First, a mechanical analysis model and its governing equations are developed based on the Winkler elastic foundation beam theory, incorporating key construction‐related factors such as the lag effect of primary support, differential stress release in the surrounding rock, and the elasto‐plastic behavior of the stratum. The governing equations are then transformed into a concise matrix form using the SSM and solved based on matrix theory and the continuity conditions between adjacent beam segments. Analytical solutions for deformation and internal forces at any cross‐section of the pipe umbrella are derived under the nonlinear interactions among the pipe umbrella, surrounding rock, and primary support. The accuracy and applicability of the proposed method are verified through comparisons with existing field monitoring data, analytical solutions, and numerical simulation results from other researchers. On this basis, taking the Aketepu Tunnel as a case study, the influences of the surrounding rock stiffness ahead of the tunnel face, excavation footage, steel pipe diameter, and other factors on the deformation and internal forces of the pipe umbrella were investigated, and a recommended design scheme was proposed accordingly. The scheme was subsequently applied in the field, and monitoring results showed that the maximum deformations at two sections were 26.1 and 22.3 mm, respectively, both within the acceptable limits for surrounding rock deformation control.
为了快速准确地分析浅埋隧道管伞的受力特性,提出了一种基于状态空间法(SSM)的分析方法。首先,基于Winkler弹性地基梁理论建立了力学分析模型及其控制方程,并考虑了与施工相关的关键因素,如主支护滞后效应、围岩应力释放差异和地层弹塑性行为。然后利用SSM将控制方程转化为简洁的矩阵形式,并根据矩阵理论和相邻梁段之间的连续性条件进行求解。在管伞、围岩和主支护的非线性相互作用下,导出了管伞任意截面的变形和内力解析解。通过与现有现场监测数据、解析解和其他研究人员的数值模拟结果的比较,验证了所提方法的准确性和适用性。在此基础上,以阿克特普隧道为例,研究了巷道前方围岩刚度、开挖进尺、钢管直径等因素对管伞变形和内力的影响,并提出了推荐的设计方案。随后将该方案应用于现场,监测结果表明,两个断面的最大变形分别为26.1和22.3 mm,均在围岩变形控制的可接受范围内。
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引用次数: 0
Grouting Parameter Effects on Structural Response: Precision Modeling of Soft Soil Tunnel‐Base Grouting via Cavity Expansion Theory and Mindlin Solution 注浆参数对结构响应的影响:基于空腔膨胀理论和Mindlin解的软土隧道地基注浆精度建模
IF 4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL Pub Date : 2025-12-10 DOI: 10.1002/nag.70203
Bosong Ding, Ping Lou, You Wang, Can Huang, Rui Wang
Shield tunnels in soft clay are highly susceptible to long‐term uplift and differential settlement. To precisely control these deformations, this study develops a novel anisotropic cavity expansion model integrated with Mindlin's solution, forming a coupled 2D/3D segment–soil interaction framework. Validated against field data from Fuzhou Metro Line 4, the model demonstrates superior accuracy over traditional isotropic approaches. The results quantitatively reveal that: (1) in single‐ring grouting, increasing the grouting burial depth from 5 to 15 m reduces invert uplift by 28%; (2) in planar multi‐hole grouting, symmetric‐spacing sequences effectively control segment displacements within 5 mm; and (3) in longitudinal multi‐ring grouting, symmetric injection reduces maximum stress fluctuations by 12.5% compared to staggered grouting under a 5% grouting volume. The study concludes that the anisotropic soil–grout interaction is the primary mechanism governing deformation, and the proposed model provides a foundation for optimizing grouting parameters to ensure tunnel stability.
软粘土中的盾构隧道极易受到长期隆升和差异沉降的影响。为了精确控制这些变形,本研究开发了一种新的各向异性空洞扩展模型,并结合Mindlin解,形成了一个耦合的2D/3D段-土相互作用框架。通过福州地铁4号线的现场数据验证,该模型比传统的各向同性方法具有更高的精度。结果定量表明:(1)单环注浆时,将注浆埋深从5 m增加到15 m,可使倒隆起降低28%;(2)平面多孔注浆时,对称间距层序可有效控制管片位移在5mm以内;(3)纵向多环注浆中,在注浆量为5%的情况下,对称注浆比交错注浆最大应力波动减小了12.5%。研究认为,各向异性土-浆液相互作用是控制隧道变形的主要机制,所建立的模型为优化注浆参数以保证隧道稳定提供了依据。
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引用次数: 0
Cover Image, Volume 50, Issue 1 封面图片,第50卷,第1期
IF 3.6 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL Pub Date : 2025-12-10 DOI: 10.1002/nag.70204
Piao Miao, Fusheng Zha, Qiao Wang, Shijin Feng, Hongxin Chen, Lin Mu

The cover image is based on the article Innovative Sealing Approaches for Karst Flowing Groundwater: Numerical Analysis of Secondary Grouting Mechanism After Grout-Filled Bag Sealed by Piao Miao et al., https://doi.org/10.1002/nag.70092

封面图片来源于朴淼等(https://doi.org/10.1002/nag.70092)的文章《岩溶流动地下水的创新密封方法:充浆袋密封后二次注浆机理数值分析》
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引用次数: 0
Analytical Study of Transient Seepage Effects on Soil Responses Surrounding Deep Diversion Tunnels 瞬态渗流对深层导流隧洞周围土体响应的分析研究
IF 4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL Pub Date : 2025-12-10 DOI: 10.1002/nag.70194
An Jiang, Jun Yu, Zheng Hu, Chengwei Zhu, Zhongxuan Yang
High hydraulic gradients induced by initial water filling in diversion tunnels with permeable linings or sudden fluctuations in total head inside the tunnels trigger transient seepage in the surrounding soils. Although this transient flow helps relieve excess pore pressure, it also leads to significant ground deformation, variations in in‐situ stress, and expansions of the plastic zone around the tunnel. This effect is especially produced in deep tunnels embedded in low‐permeability soils, where the transient flow process may be prolonged and have a substantial impact on the local stress‐strain environment. This study presents an analytical solution for characterizing transient seepage around deep tunnels by employing the superposition principle and the method of separation of variables. A seepage stress potential function is introduced to analyze the variations in soil responses and plastic stress evolution under high in‐situ stress conditions based on the Mohr–Coulomb failure criterion. The results show that stress, strain, and displacement within the soil are proportionally related to the total head difference between the tunnel interior and the surrounding ground. Specifically, rheological soil behaviors accelerate the transient seepage process. The plastic zone, influenced jointly by transient seepage and in‐situ stress, undergoes significant development before stabilization. The proposal analytical solution provides a rigorous and highly efficient tool for evaluating the operational environment of diversion tunnels and supports their safe and effective designs and maintenance.
具有透水衬砌的导流隧洞初始充水产生的高水力梯度或隧洞内总水头的突然波动会引发周围土体的瞬态渗流。虽然这种瞬态流动有助于缓解超孔隙压力,但它也会导致显著的地面变形、地应力变化和隧道周围塑性区的扩展。这种效应在深埋于低渗透土壤中的隧道中尤其明显,隧道瞬态流动过程可能会延长,并对局部应力应变环境产生重大影响。本文利用叠加原理和分离变量法,提出了一种表征深埋隧洞周围瞬态渗流的解析解。基于Mohr-Coulomb破坏准则,引入渗流应力势函数,分析了高地应力条件下土体响应变化和塑性应力演化。结果表明,土体内部的应力、应变和位移与隧道内部与周围地面的总水头差成正比关系。具体而言,土体流变特性加速了瞬态渗流过程。塑性区受瞬态渗流和地应力的共同影响,在稳定前会经历较大的发展。该方案为导流隧洞运行环境评估提供了严谨、高效的工具,为导流隧洞安全有效的设计和维护提供了依据。
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引用次数: 0
A Submodel Based Numerical Investigation of the Segment Uplift During Tunnel Construction 基于子模型的隧道施工中管片上拔数值研究
IF 4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL Pub Date : 2025-12-10 DOI: 10.1002/nag.70200
Bin Wang, Chenyu Fu, Jiahao Yang, Yili Zhang, Chenyang Zhao
Shield tunneling involves complex soil‐structure interactions, thereby leading to a normally time‐consuming and labor‐intensive finite element calculation. A submodel based method for predicting segment uplift during tunnel construction is proposed in this study, which can effectively reduce the computational cost. It initially focuses on determination of the submodel boundary, where plastic dissipation energy and its associated coefficient of variation are selected as criteria. Compared to traditional boundary determination methods based on soil disturbance degree, the proposed approach demonstrates great advantages in accuracy. Finite element simulations of tunnel excavation are thereafter performed for both homogeneous and composite geological strata models, where the applicability of the submodeling technique as well as the rationality of plastic dissipation energy criteria are verified. Building upon the computationally enhanced segment uplift dataset (optimized via submodel‐driven temporal efficiency framework), a rigorous benchmarking of machine learning architectures is finally implemented, among which the LSTM shows the best prediction performance, with an R 2 value of 0.9 and RMSE of 0.02, fully demonstrating the superiority of the proposed method in predicting tunnel segment uplift.
盾构隧道施工涉及复杂的土-结构相互作用,因此通常需要耗费大量时间和人力进行有限元计算。本文提出了一种基于子模型的隧道施工中管段隆起预测方法,可有效降低计算成本。首先着重于子模型边界的确定,选取塑性耗散能及其相关变异系数作为判据。与传统的基于土壤扰动程度的边界确定方法相比,该方法在精度上有很大的优势。在此基础上,分别对均匀地层模型和复合地层模型进行了隧道开挖有限元模拟,验证了子模型技术的适用性和塑性耗散能准则的合理性。基于计算增强的分段隆起数据集(通过子模型驱动的时间效率框架进行优化),最终对机器学习架构进行了严格的基准测试,其中LSTM的预测性能最好,r2值为0.9,RMSE为0.02,充分显示了本文方法在预测隧道分段隆起方面的优势。
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引用次数: 0
期刊
International Journal for Numerical and Analytical Methods in Geomechanics
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