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学者姓名：赵密
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Abstract ：
Due to the complex nature of site conditions and the influence of deposition conditions, aging, environmental exposure, and characterization techniques, the calibration of geotechnical parameters is significantly uncertain. The present study introduces a Bayesian updating method for geotechnical parameters to address the issues of parameter uncertainty and incomplete parameter information. Developed by combining a high-fidelity Polynomial Chaos Kriging (PC-Kriging) model with the Gibbs sampling method, this approach uses Least Angle Regression (LAR) to construct the Polynomial Chaos Expansion (PCE) coefficients, incorporating PCE as the trend function in the Kriging method to build the PC-Kriging model. The proposed method can avoid the computational challenges involved in Bayesian inference using dense numerical models, effectively reducing computational costs while obtaining the posterior distribution and statistical information of the model. This study primarily applies the proposed PC-Kriging-Gibbs (PCK-Gibbs) method to geotechnical engineering issues. The method is validated on two critical dynamic soil problems: Horizontal-to-vertical spectral ratio (HVSR) inversion and equivalent linearization in site response analysis. Meanwhile, the Kriging method and PCE were also used to verify the feasibility and computational efficiency of the proposed method. The posterior distribution samples of the model parameters obtained show good consistency between the sample means and actual values, significantly reducing the uncertainty of shear wave velocity. Compared to Bayesian inference analysis using only the Gibbs method, the proposed method dramatically decreases computation time while maintaining satisfactory results, providing a powerful computational tool for parameter updating in geotechnical engineering.
Keyword ：
PC-Kriging PC-Kriging Bayesian Inference Bayesian Inference HVSR HVSR Site response analyses Site response analyses Gibbs sampling Gibbs sampling Geotechnical parameters Geotechnical parameters
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| GB/T 7714 | Zhang, Wenhao , El Naggar, M. Hesham , Ni, Pinghe et al. Bayesian updating of geotechnical parameters with polynomial chaos Kriging model and Gibbs sampling [J]. | COMPUTERS AND GEOTECHNICS , 2025 , 180 . |
| MLA | Zhang, Wenhao et al. "Bayesian updating of geotechnical parameters with polynomial chaos Kriging model and Gibbs sampling" . | COMPUTERS AND GEOTECHNICS 180 (2025) . |
| APA | Zhang, Wenhao , El Naggar, M. Hesham , Ni, Pinghe , Zhao, Mi , Du, Xiuli . Bayesian updating of geotechnical parameters with polynomial chaos Kriging model and Gibbs sampling . | COMPUTERS AND GEOTECHNICS , 2025 , 180 . |
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Abstract ：
With the development of the Chinese economy and society, the height and density of urban buildings are increasing, and large underground transportation hubs have been constructed in many places to alleviate the pressure of transportation. Commercial buildings are usually developed above the large underground transportation hubs, so the underground structures may have very shallow depths or no soil cover. The seismic response and damage mechanisms of such underground structures still need to be studied. In this paper, an example of a project in China is taken as an object to analyze the seismic response and damage mechanism of the structure after simplification. The spatial distribution of deformations and internal forces of such structures and the location of the maximum internal forces are obtained, and the effect of the frequency of seismic motions on the structural response is obtained. Finally, an elastoplastic analysis of such structures is carried out to assess the damage location and the damage evolution process.
Keyword ：
damage mechanisms damage mechanisms seismic structure-soil structure interaction seismic structure-soil structure interaction large underground frame structures large underground frame structures dynamic analysis dynamic analysis finite element simulation finite element simulation
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| GB/T 7714 | Ding, Qingpeng , Zhao, Mi , Shen, Jiaxu . Seismic Response and Damage Analysis of Large Underground Frame Structures without Overburden [J]. | APPLIED SCIENCES-BASEL , 2024 , 14 (11) . |
| MLA | Ding, Qingpeng et al. "Seismic Response and Damage Analysis of Large Underground Frame Structures without Overburden" . | APPLIED SCIENCES-BASEL 14 . 11 (2024) . |
| APA | Ding, Qingpeng , Zhao, Mi , Shen, Jiaxu . Seismic Response and Damage Analysis of Large Underground Frame Structures without Overburden . | APPLIED SCIENCES-BASEL , 2024 , 14 (11) . |
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Abstract ：
The development of multifunctional, multipurpose small modular next generation nuclear reactors has become a trend in designing small-scale nuclear power stations. In this study, taking a new next-generation buried nuclear power structure as the target structure, a 3D finite element model of the site-nuclear power plant structure system was established, and its response at different sites was studied. Using the internal substructure method, this study initially explored the impact of earthquake input and artificial boundary locations on the structural response. The results indicate that the internal substructure method enhances computational efficiency without compromising accuracy. For this model, it is recommended to input earthquake motion close to the structure, set the lateral boundary location to three times the width of the structure, and set the bottom boundary location to two times the depth of the structure. Subsequently, an investigation into the response of the structure at varying site wave velocities is conducted. The results show that as the wave velocity increases, the acceleration response intensifies, while the displacement response diminishes. However, the relationship is nonlinear; the response exhibits less variation with increasing site wave velocity. The seismic response of a structure is profoundly influenced by site conditions, emphasizing the imperative need for careful consideration of specific site characteristics in seismic analyses. In addition, the response pattern of the overall structure is significantly different from that of conventional large surface-sited nuclear power plants, and further research should be conducted on the seismic response characteristics of buried nuclear power plants.
Keyword ：
Dynamic soil-structure interaction Dynamic soil-structure interaction Internal substructure method Internal substructure method Nuclear structure Nuclear structure Structural seismic response Structural seismic response
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| GB/T 7714 | Wang, Xin , Zhao, Mi , Guan, Jiacheng et al. Site effect on seismic response of buried nuclear power plant structure [J]. | SOIL DYNAMICS AND EARTHQUAKE ENGINEERING , 2024 , 183 . |
| MLA | Wang, Xin et al. "Site effect on seismic response of buried nuclear power plant structure" . | SOIL DYNAMICS AND EARTHQUAKE ENGINEERING 183 (2024) . |
| APA | Wang, Xin , Zhao, Mi , Guan, Jiacheng , Yang, Jie , Du, Xiuli , Zhao, Xu . Site effect on seismic response of buried nuclear power plant structure . | SOIL DYNAMICS AND EARTHQUAKE ENGINEERING , 2024 , 183 . |
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Abstract ：
The Winkler foundation modulus is key to evaluating the response of underground structures using the elastic foundation beam model. In this paper, an improved formula of the Winkler foundation modulus for a beam embedded in a full space is proposed to overcome the limitation of inconsistent assumptions in previous studies. To achieve this goal, the bending responses of the beam are obtained using the elastic foundation beam model and three-dimensional elastic continuum model, respectively, wherein a consistent assumption is proposed that tangential interactions at the beam-ground interface are ignored in the two models. In addition, as deformation of the site is an important source of the underground structure response, the beam is applied to standard soil displacement of the free field on the Winkler foundation to improve the accuracy of the Winkler modulus obtained by fitting solutions based on the concentrated force on the beam. The formula for the Winkler foundation is obtained by equating the first zero of the bending moment in the two models. The Winkler foundation modulus is verified by comparing the results with numerical solutions and previous studies.
Keyword ：
full space full space underground structures underground structures elastic foundation beam model elastic foundation beam model Winkler foundation modulus Winkler foundation modulus
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| GB/T 7714 | Xu, Lihui , Zhao, Mi , Huang, Jingqi et al. An Improved Winkler Foundation Modulus for a Beam in a Full Space [J]. | APPLIED SCIENCES-BASEL , 2024 , 14 (6) . |
| MLA | Xu, Lihui et al. "An Improved Winkler Foundation Modulus for a Beam in a Full Space" . | APPLIED SCIENCES-BASEL 14 . 6 (2024) . |
| APA | Xu, Lihui , Zhao, Mi , Huang, Jingqi , Li, Huifang , Du, Xiuli , Zhao, Xu et al. An Improved Winkler Foundation Modulus for a Beam in a Full Space . | APPLIED SCIENCES-BASEL , 2024 , 14 (6) . |
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Abstract ：
The physics-informed neural network (PINN) is an effective alternative method for solving differential equations that do not require grid partitioning, making it easy to implement. In this study, using automatic differentiation techniques, the PINN method is employed to solve differential equations by embedding prior physical information, such as boundary and initial conditions, into the loss function. The differential equation solution is obtained by minimizing the loss function. The PINN method is trained using the Adam algorithm, taking the differential equations of motion in structural dynamics as an example. The time sample set generated by the Sobol sequence is used as the input, while the displacement is considered the output. The initial conditions are incorporated into the loss function as penalty terms using automatic differentiation techniques. The effectiveness of the proposed method is validated through the numerical analysis of a two-degree-of-freedom system, a four-story frame structure, and a cantilever beam. The study also explores the impact of the input samples, the activation functions, the weight coefficients of the loss function, and the width and depth of the neural network on the PINN predictions. The results demonstrate that the PINN method effectively solves the differential equations of motion of damped systems. It is a general approach for solving differential equations of motion.
Keyword ：
loss function loss function differential equations of motion differential equations of motion multiple degrees of freedom multiple degrees of freedom activation function activation function physics-informed neural networks physics-informed neural networks
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| GB/T 7714 | Zhang, Wenhao , Ni, Pinghe , Zhao, Mi et al. A General Method for Solving Differential Equations of Motion Using Physics-Informed Neural Networks [J]. | APPLIED SCIENCES-BASEL , 2024 , 14 (17) . |
| MLA | Zhang, Wenhao et al. "A General Method for Solving Differential Equations of Motion Using Physics-Informed Neural Networks" . | APPLIED SCIENCES-BASEL 14 . 17 (2024) . |
| APA | Zhang, Wenhao , Ni, Pinghe , Zhao, Mi , Du, Xiuli . A General Method for Solving Differential Equations of Motion Using Physics-Informed Neural Networks . | APPLIED SCIENCES-BASEL , 2024 , 14 (17) . |
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Abstract ：
Response spectrum method (RSM) has been applied in seismic analysis of underground structures. However, the RSM is computationally low efficient for processing large soil domains. In this paper, the dynamic characteristics of underground structures are first investigated through three rectangular subway station structures. The results show that only a small number of effective frequencies and modes of soil-structure interaction (SSI) system significantly affect the seismic response of underground structure. These effective frequencies and modes are related to the natural vibration characteristics of site. An effective method is then developed to obtain the effective natural frequencies and modes of the SSI system. Subsequently, the effective modal superposition response spectrum method (ERSM) for seismic analysis of underground structure is developed by only combining the effective natural frequencies and modes of the SSI system to improve efficiency. Finally, the accuracy of ERSM is investigated through seismic response analysis of subway station structures. Numerical examples show that the ERSM can be used for seismic analysis of underground structures considering 3D SSI.
Keyword ：
Underground structure Underground structure Dynamic characteristics Dynamic characteristics Response spectrum method Response spectrum method Effective frequencies and modes Effective frequencies and modes
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| GB/T 7714 | Gao, Zhidong , Zhao, Mi , Du, Xiuli et al. Effective-mode superposition response spectrum method for three dimensional seismic response analysis of underground structures [J]. | SOIL DYNAMICS AND EARTHQUAKE ENGINEERING , 2023 , 174 . |
| MLA | Gao, Zhidong et al. "Effective-mode superposition response spectrum method for three dimensional seismic response analysis of underground structures" . | SOIL DYNAMICS AND EARTHQUAKE ENGINEERING 174 (2023) . |
| APA | Gao, Zhidong , Zhao, Mi , Du, Xiuli , Wang, Jinting . Effective-mode superposition response spectrum method for three dimensional seismic response analysis of underground structures . | SOIL DYNAMICS AND EARTHQUAKE ENGINEERING , 2023 , 174 . |
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Abstract ：
A novel artificial boundary method called the scaled boundary perfectly matched layer (SBPML) is proposed for the transient analysis of elastic wave propagation in unbounded domains. This method constructs a generalized perfectly matched layer (PML) around the finite interior subdomain based on a coordinate transformation inspired by the scaled boundary finite element method (SBFEM). It can model the infinite exterior subdomains of heterogeneous materials, featuring both parallel and radial straight-line physical surfaces and interfaces. In addition, generally-shaped (even nonconvex-shape) artificial boundaries can be used to provide high flexibility in choosing the geometry of the finite interior subdomain. Two coordinate mapping technologies, namely the modified scaled boundary coordinate transformation from the SBFEM and the complex coordinate stretching from the PML, are successively utilized to construct the proposed method. By introducing the integral of stress as an auxiliary variable, the resulting SBPML subdomain is represented in the time domain using a mixed displacement-stress unsplit-field formulation. This has the added benefit of allowing for easy incorporation into standard dynamic finite element methods. The performance of the SBPML is demonstrated through several numerical examples, including P-SV and SH wave propagation problems occurring in unbounded domains with complex geometries and heterogeneous material properties. The numerical results are evaluated in comparison to both reference solution and existing artificial boundary methods, ultimately demonstrating the flexibility, robustness, accuracy, and stability of the proposed approach.
Keyword ：
scaled boundary finite element method scaled boundary finite element method perfectly matched layer perfectly matched layer artificial boundary condition artificial boundary condition wave propagation wave propagation unbounded domain unbounded domain
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| GB/T 7714 | Zhang, Guoliang , Zhao, Mi , Du, Xiuli et al. Time-domain scaled boundary perfectly matched layer for elastic wave propagation [J]. | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING , 2023 , 124 (18) : 3906-3934 . |
| MLA | Zhang, Guoliang et al. "Time-domain scaled boundary perfectly matched layer for elastic wave propagation" . | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 124 . 18 (2023) : 3906-3934 . |
| APA | Zhang, Guoliang , Zhao, Mi , Du, Xiuli , Zhang, Junqi . Time-domain scaled boundary perfectly matched layer for elastic wave propagation . | INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING , 2023 , 124 (18) , 3906-3934 . |
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Abstract ：
Artificial boundary method is widely used in the numerical modeling of unbounded wave problem. However, the accurate modeling of truncated infinite domain with general geometry and heterogeneous materials is still a challenging task, especially for direct time-domain analysis in three dimensions (3D). In this paper, a novel 3D time-domain artificial boundary method, called Scaled Boundary Perfectly Matched Layer (SBPML), is proposed. This method is a generalization of the Perfectly Matched Layer (PML) based on a scaled boundary coordinates transformation inspired by the Scaled Boundary Finite Element Method (SBFEM), which is capable of using artificial boundary of general geometry (not necessarily convex) and considering plane physical surfaces and interfaces extending to infinity in the truncated infinite domain. Local scaled boundary coordinates are firstly introduced on the element-level into the truncated infinite domain to describe general geometry properties of the infinite domain. Then, a complex stretching function from PML is applied to radial direction of the local scaled boundary coordinates to map the physical space onto the complex space, resulting in a SBPML domain. The spatial discretization of the SBPML domain produces semi-discrete mixed displacement-stress unsplit-field formulations of third orders in time. The order of the obtained formulation can be reduced by one, enabling a seamless coupling with the standard displacementbased finite element formulation of the interior domain. The coupled system can be solved by an explicit time integration algorithm efficiently. The validation of the SBPML is demonstrated through several benchmark tests, including wave problems in unbounded domains with general geometries and heterogeneous material properties. Furthermore, the application of the SBPML in dynamic soil-structure interaction (SSI) is demonstrated using two engineering problems, including an impact analysis of soft rock-nuclear island system and a vibration analysis of soil-lined tunnel system. (c) 2022 Elsevier B.V. All rights reserved.
Keyword ：
Perfectly matched layer (PML) Perfectly matched layer (PML) Unbounded domain Unbounded domain Artificial boundary method Artificial boundary method Scaled boundary finite element method (SBFEM) Scaled boundary finite element method (SBFEM) Dynamic soil-structure interaction Dynamic soil-structure interaction Explicit finite element method Explicit finite element method
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| GB/T 7714 | Zhang, Guoliang , Zhao, Mi , Zhang, Junqi et al. Scaled Boundary Perfectly Matched Layer (SBPML): A novel 3D time-domain artificial boundary method for wave problem in general-shaped and heterogeneous infinite domain [J]. | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING , 2023 , 403 . |
| MLA | Zhang, Guoliang et al. "Scaled Boundary Perfectly Matched Layer (SBPML): A novel 3D time-domain artificial boundary method for wave problem in general-shaped and heterogeneous infinite domain" . | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 403 (2023) . |
| APA | Zhang, Guoliang , Zhao, Mi , Zhang, Junqi , Du, Xiuli . Scaled Boundary Perfectly Matched Layer (SBPML): A novel 3D time-domain artificial boundary method for wave problem in general-shaped and heterogeneous infinite domain . | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING , 2023 , 403 . |
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Abstract ：
地铁车站多采用基于地下连续墙(简称:地连墙)的明挖施工方法,施工后地连墙作为永久结构与车站共同受力.在车站结构抗震分析中,考虑到地连墙可能对结构抗震的有利作用,出于安全储备考虑通常忽略地连墙的存在,但地连墙对车站结构地震响应的影响规律和机理仍有待深入研究.以某典型两层三跨地铁车站结构为对象,基于近场波动有限元方法并结合黏弹性人工边界条件,开展有无地连墙情况车站结构地震响应特性对比研究,揭示不同场地条件下地连墙对车站结构地震响应的影响规律,阐明地连墙的影响机理.研究结果表明:地连墙具有减小车站结构总体层间位移效应,有利于侧墙和底层中柱抗震,但同时放大了顶底板与侧墙连接处的弯矩和正应力;地连墙对结构顶层中柱端部及中跨中板板端的内力和正应力的影响与场地条件相关,坚硬和中硬场地条件下具有减小效应,软弱场地下略有增大作用.上述结构响应规律的原因可归结为地连墙增加了结构侧墙刚度,降低了结构整体侧向变形,但限制了侧墙的弯曲变形,导致结构顶底板与侧墙交接处的弯曲变形和内力增大.
Keyword ：
地连墙 地连墙 地震响应 地震响应 不同场地条件 不同场地条件 土-结构动力相互作用 土-结构动力相互作用 车站结构 车站结构
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| GB/T 7714 | 赵密 , 贾智富 , 昝子卉 et al. 不同场地条件下地连墙对地铁车站结构地震动力响应的影响 [J]. | 地震工程学报 , 2023 , 45 (2) : 270-278,295 . |
| MLA | 赵密 et al. "不同场地条件下地连墙对地铁车站结构地震动力响应的影响" . | 地震工程学报 45 . 2 (2023) : 270-278,295 . |
| APA | 赵密 , 贾智富 , 昝子卉 , 黄景琦 , 杜修力 . 不同场地条件下地连墙对地铁车站结构地震动力响应的影响 . | 地震工程学报 , 2023 , 45 (2) , 270-278,295 . |
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Abstract ：
近年来, 物理先验融合数据的深度学习方法求解以偏微分方程为理论基础的正反演问题已成为交叉学科热点. 针对地震工程波动数值模拟, 本文阐明了物理驱动深度学习方法PINN的数学概念及实现方式, 以无源项一维波动为例, 开展了相关理论模型构建, 并与解析解及有限差分方法进行对比, 分析了PINN方法与其他数值算法模拟波场的相对范数误差, 验证了物理驱动深度学习方法求解波动问题的可行性. 采用物理驱动深度学习方法并结合谱元法形成的稀疏初始波场数据, 开展了二维波动数值模拟, 实现了自由边界条件及起伏地表等典型工况的模拟, 并给出了时序波场分布特性. 更换不同的初始条件, 测试了神经网络的泛化精度, 提出可显著提高网络训练效率的迁移学习方法. 通过与谱元法的结果对比, 验证了本文方法模拟均质场地、空间不均匀及复杂地形场地波动问题的可靠性. 结果表明, 物理驱动深度学习方法具备无网格、精细化模拟等优势, 并可实现自由地表及侧边界波场透射等数值模拟条件.
Keyword ：
神经网络 神经网络 物理信息深度学习 物理信息深度学习 内源波动 内源波动 边界条件 边界条件 波动数值模拟 波动数值模拟
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| GB/T 7714 | 陈苏 , 丁毅 , 孙浩 et al. 物理驱动深度学习波动数值模拟方法及应用 [J]. | 力学学报 , 2023 , 55 (1) : 272-282 . |
| MLA | 陈苏 et al. "物理驱动深度学习波动数值模拟方法及应用" . | 力学学报 55 . 1 (2023) : 272-282 . |
| APA | 陈苏 , 丁毅 , 孙浩 , 赵密 , 王进廷 , 李小军 . 物理驱动深度学习波动数值模拟方法及应用 . | 力学学报 , 2023 , 55 (1) , 272-282 . |
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