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Physics-guided symbolic neural network reveals optimal functional forms describing ground motions 物理引导的符号神经网络揭示了描述地面运动的最佳函数形式
IF 4.2 2区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-11-21 DOI: 10.1016/j.soildyn.2024.109100
Xianwei Liu , Su Chen , Lei Fu , Xiaojun Li , Fabrice Cotton
This study presents a novel framework for ground motion modelling utilizing Physics-Guided Symbolic Neural Networks (PGSNN). Symbolic neural networks offer a new method for knowledge discovery, providing a unique perspective for automatically uncovering predictive functional forms from data. This approach differs from traditional methods as it does not rely on predefined equations. Instead, it employs symbolic operators to freely combine input parameters in a high-dimensional space. This method addresses the problem of data imbalance by incorporating physical guidance to ensure that the model produces results that are consistent with established physical principles. The resulting equations align with the expectations of the engineering seismology community, particularly within the magnitude-distance ranges, where classical equations are well calibrated. The prediction performance of the PGSNN, evaluated across different intensity measures (PGA, PGV, and PSA), was assessed by calculating the residuals between measured and predicted values and their standard deviations. The predictive capability of this model was verified using new event records. The results indicate that the prediction performance of the PGSNN is comparable to those of traditional methods.
本研究提出了一种利用物理引导的符号神经网络(PGSNN)进行地面运动建模的新框架。符号神经网络为知识发现提供了一种新方法,为从数据中自动发现预测功能形式提供了一个独特的视角。这种方法与传统方法不同,它不依赖于预定义方程。相反,它采用符号运算符在高维空间中自由组合输入参数。这种方法通过结合物理指导来解决数据不平衡的问题,以确保模型产生的结果符合既定的物理原理。由此产生的方程符合工程地震学界的期望,特别是在震级-距离范围内,经典方程已得到很好的校准。通过计算测量值和预测值之间的残差及其标准偏差,评估了 PGSNN 在不同烈度测量(PGA、PGV 和 PSA)中的预测性能。使用新的事件记录对该模型的预测能力进行了验证。结果表明,PGSNN 的预测性能与传统方法相当。
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引用次数: 0
Characteristics and predictions of accumulative deformation of structured soft soil under long-term cyclic loading 长期循环荷载下结构软土累积变形的特征与预测
IF 4.2 2区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-11-21 DOI: 10.1016/j.soildyn.2024.109088
Weizheng Liu , Jiming Tan , Weihua Lv , Cheng Chen , Shuai Qu
To address the long-term settlement of embankments over structured soft soil during the in-service stage, artificial structured soils with different interparticle bonding strengths and initial void ratios were prepared, and repeated triaxial loading tests were conducted to investigate the effects of bonding strength, initial void ratio, stress amplitude and cycle number on the accumulative deformation characteristics. The results show that the relationship between the accumulative plastic strain and cycle number can be classified into stable, critical and destructive types, and an empirical relationship between the stress sensitivity and dynamic stress ratio is established. Furthermore, two different empirical models for accumulative plastic strain are presented that incorporate soil structure. Reasonable agreement between the model predictions and the experimental results for different natural soft soils demonstrate that the proposed models can accurately capture the accumulative deformation behaviour of structured soils. In addition, considering the accumulated plastic deformation of soil subjected to cyclic loading as static creep, a simplified method for calculating three-dimensional cyclic accumulative deformation is proposed by implementing the proposed model in a finite-element simulation utilizing an implicit stress integration algorithm. Finally, the effects of the dynamic stress level and structural strength on the accumulative deformation are analyzed. This has important implications in controlling the long-term settlement of embankment in soft soil area.
针对结构软土上路堤在使用阶段的长期沉降问题,制备了不同颗粒间粘结强度和初始空隙率的人工结构土,并进行了反复三轴加载试验,研究了粘结强度、初始空隙率、应力幅值和循环次数对累积变形特性的影响。结果表明,累积塑性应变与循环次数之间的关系可分为稳定型、临界型和破坏型,并建立了应力敏感性与动态应力比之间的经验关系。此外,还提出了结合土壤结构的两种不同的累积塑性应变经验模型。模型预测结果与不同天然软土的实验结果之间的合理一致性表明,所提出的模型能够准确捕捉结构土的累积变形行为。此外,考虑到土壤在循环荷载作用下的累积塑性变形为静态蠕变,通过在有限元模拟中利用隐式应力积分算法实施所提出的模型,提出了计算三维循环累积变形的简化方法。最后,分析了动态应力水平和结构强度对累积变形的影响。这对控制软土地区路堤的长期沉降具有重要意义。
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引用次数: 0
Ultimate bearing capacity of sand under lateral movement of buried pipelines 埋设管道横向移动时沙子的极限承载力
IF 4.2 2区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-11-21 DOI: 10.1016/j.soildyn.2024.109104
Zilan Zhong , Lingyue Xu , Chuntang Han , Junyan Han , M. Hesham El Naggar , Jinqiang Li , Xin Zhao , Huiquan Miao
Permanent ground deformation hazards, such as fault displacement, liquefaction-induced settlement, and landslides, pose a severe threat to the integrity of buried pipelines. In this study, three-dimensional numerical simulations are performed to investigate the horizontal lateral soil-pipeline interaction in medium-dense sand and to identify the failure mechanisms of the surrounding sand for different pipeline depth-diameter ratios. The ultimate bearing capacity of sand around the pipeline is evaluated for different soil failure mechanisms. Moreover, a simplified analytical model of the soil-pipeline under lateral movement is proposed based on the identified soil failure mechanisms. Consequently, an analytical solution for the ultimate bearing capacity of the soil under lateral motion of the buried pipeline is derived based on the limit-state equilibrium. The results obtained from the analytical solution indicate that at the limit state, the soil around a shallowly buried pipeline forms a ruptured surface extending to the ground surface with a logarithmic spiral failure surface. The lateral ultimate bearing capacity increases as the pipeline burial depth-diameter ratio increases until it reaches a constant value at a certain critical depth-diameter ratio. As the pipeline depth-diameter ratio increases, the pipeline displacement that causes shear failure of the soil also gradually increases. It is demonstrated that the proposed analytical solution well predicts the soil ultimate lateral bearing capacity for pipelines installed shallowly in medium and dense sand. Furthermore, the ultimate bearing capacity of pipelines in sand is evaluated by Chinese and some international codes. The disparity between results from different codes is attributed to the variation in empirical lateral bearing capacity coefficients used in the respective codes.
断层位移、液化引起的沉降和滑坡等永久性地面变形危害对埋地管道的完整性构成严重威胁。本研究进行了三维数值模拟,以研究中密砂中土壤与管道的水平横向相互作用,并确定不同管道深度-直径比下周围砂的破坏机制。针对不同的土壤破坏机制,对管道周围砂土的极限承载力进行了评估。此外,根据确定的土壤破坏机制,提出了横向移动下土壤-管道的简化分析模型。因此,根据极限状态平衡推导出了埋设管道横向运动下土壤极限承载力的解析解。分析求解结果表明,在极限状态下,浅埋管道周围的土壤会形成一个延伸至地表的破裂面,破裂面呈对数螺旋形。横向极限承载力随着管道埋深-直径比的增大而增大,直至达到某一临界埋深-直径比时的恒定值。随着管道埋深-直径比的增大,导致土壤剪切破坏的管道位移也逐渐增大。结果表明,所提出的分析方案可以很好地预测浅埋于中密砂中的管道的土壤极限侧向承载力。此外,中国和一些国际规范也对砂土中管道的极限承载力进行了评估。不同规范结果之间的差异归因于各规范中使用的经验侧向承载力系数的不同。
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引用次数: 0
Investigating small-strain site response using inverse soil dynamic parameters from downhole arrays 利用井下阵列的反土壤动力参数研究小应变场地响应
IF 4.2 2区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-11-20 DOI: 10.1016/j.soildyn.2024.109091
Hongjun He , Xiaohua Ke , Yu Miao , Chenxi Miao
Previous research on site response has primarily focused on reproducing and predicting ground motions recorded by vertical seismic arrays. This study evaluated the ability to reproduce and predict small-strain site response at the Treasure Island Downhole Array and Delaney Park Downhole Array using inverse soil dynamic parameters. First, parameters such as seismic wave velocity profiles and Rayleigh damping ratios were obtained through seismic interferometry and spectral ratio methods based on the earthquake records. Subsequently, the validity and reliability of these inverse soil dynamic parameters were evaluated by comparing the simulated and observed ground responses. Finally, the inverse method was compared with other methods considering spatial variability in one-dimensional site response analysis. Quantitative comparisons show that the inverse method effectively predicts and reproduces site response and outperforms the traditional method relying on the single borehole shear wave velocity profile and damping ratio from empirical model. Moreover, the inverse method better captures spatial variability at the Delaney Park Downhole Array.
以前对场地响应的研究主要集中在重现和预测垂直地震阵列记录的地面运动。本研究评估了利用反土壤动力参数再现和预测金银岛井下阵列和德莱尼公园井下阵列小应变场地响应的能力。首先,根据地震记录,通过地震干涉测量法和频谱比方法获得了地震波速度剖面和瑞利阻尼比等参数。随后,通过比较模拟和观测的地面响应,评估了这些反演土壤动力参数的有效性和可靠性。最后,在一维场地响应分析中,将反演方法与其他考虑空间变异性的方法进行了比较。定量比较结果表明,反演法有效地预测和再现了场地响应,优于依赖单孔剪切波速度曲线和经验模型阻尼比的传统方法。此外,反演法还能更好地捕捉德莱尼公园井下阵列的空间变化。
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引用次数: 0
Quantitative analysis of subway station seismic deformation under random earthquakes and uncertain soil properties using the equivalent linearization method 利用等效线性化方法对随机地震和不确定土质条件下的地铁站地震变形进行定量分析
IF 4.2 2区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-11-20 DOI: 10.1016/j.soildyn.2024.109086
Wenhao Zhang , Rui Sun , Pinghe Ni , Mi Zhao , M. Hesham El Naggar , Xiuli Du
The seismic performance of underground structures is strongly influenced by the characteristics of both the surrounding soil and the earthquake. In contrast to traditional deterministic analysis methods, this study uses a stochastic analysis approach to investigate the effect of uncertainties in nonlinear soil characteristics, shear wave velocity, density, and earthquake randomness on the response of underground stations. The equivalent linearization method is employed to approximate the nonlinear behavior of the soil. The soil was modeled using a linear elastic constitutive model combined with Rayleigh damping in the finite element model. Inter-story displacements are used to determine structural damage. Probabilistic analysis methods are used to obtain their statistical characteristics, and the probability of failure is calculated. The results show that, according to single parameter analysis, random ground motion results in the greatest probability of exceeding the threshold (PET), while ground shear wave velocity significantly affects the coefficient of variation (COV), and the effect of density is the smallest. The study also found that when soil nonlinearity, shear wave velocity, and random ground motion are considered simultaneously, the range, mean, standard deviation, and COV of interstory displacement all increase significantly, but the PET slightly decreases. In summary, the analysis results indicate that random ground motion has the greatest impact on interstory displacement, followed by shear wave velocity, with nonlinear soil characteristics having a smaller effect, and density the least. Therefore, the impact of various uncertainties should be fully considered in the analysis of underground structures, especially random ground motion and shear wave velocity.
地下结构的抗震性能受周围土壤特性和地震的影响很大。与传统的确定性分析方法不同,本研究采用随机分析方法来研究非线性土壤特性、剪切波速度、密度和地震随机性等不确定性因素对地下车站响应的影响。采用等效线性化方法来近似分析土壤的非线性行为。在有限元模型中使用线性弹性构成模型结合瑞利阻尼对土壤进行建模。层间位移用于确定结构损伤。采用概率分析方法获得其统计特征,并计算出破坏概率。结果表明,根据单参数分析,随机地面运动导致超过临界值的概率(PET)最大,而地面剪切波速度对变异系数(COV)有显著影响,密度的影响最小。研究还发现,当同时考虑土壤非线性、剪切波速度和随机地面运动时,层间位移的范围、平均值、标准偏差和 COV 都会显著增加,但 PET 会略有下降。总之,分析结果表明,随机地面运动对层间位移的影响最大,其次是剪切波速,非线性土壤特性的影响较小,而密度的影响最小。因此,在地下结构分析中应充分考虑各种不确定因素的影响,尤其是随机地面运动和剪切波速。
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引用次数: 0
Subsurface S-wave velocity structure inversion using particle swarm optimization based on horizontal site response extracted using generalized inversion technique 基于使用广义反演技术提取的水平站点响应,使用粒子群优化技术反演地下 S 波速度结构
IF 4.2 2区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-11-19 DOI: 10.1016/j.soildyn.2024.109093
Ziqian Wang , Kenichi Nakano , Jikai Sun , Eri Ito , Hiroshi Kawase
A new methodology, including a mature algorithm with adjustments and a new target for the subsurface sedimentary inversion problem was introduced. This study adopted the particle swarm optimization (PSO) algorithm as a global optimization algorithm. PSO incorporates the patterns embedded in natural bird foraging behaviors to invert the subsurface S-wave velocity structure. Using the concept of particle velocity, PSO involves particle individual inertia, individual experience, and social experience of the swarm, pursuing the global optimum solution in a multidimensional abstract space. The inversion target was the horizontal site amplification factor (HSAF), which was extracted using the generalized inversion technique for the observed strong ground motions. HSAF is an appropriate target in the S-wave velocity structure inversion problem as it directly represents the site response to the incident S-wave at the seismological bedrock. We validated the convergence ability of the PSO and applied it to three field earthquake observation stations. From the perspective of the misfit between the target and estimation velocity profile, improvements exceeding 95 % and 70 % can be confirmed in the validation case and practical applications, respectively. The use of HSAF as the target and PSO as the algorithm is currently limited but is demonstrably effective. This study introduces a methodology that has significant potential for solving velocity structure inversion problems at subsurface levels.
针对地下沉积反演问题引入了一种新方法,包括对成熟算法进行调整和新目标。本研究采用粒子群优化算法(PSO)作为全局优化算法。PSO 结合了自然界鸟类觅食行为中蕴含的模式来反演地下 S 波速度结构。PSO 利用粒子速度的概念,将粒子群的个体惯性、个体经验和社会经验结合起来,在多维抽象空间中追求全局最优解。反演目标是水平场地放大系数(HSAF),它是利用观测到的强地面运动的广义反演技术提取的。在 S 波速度结构反演问题中,HSAF 是一个合适的目标,因为它直接代表了地震基岩对入射 S 波的场地响应。我们验证了 PSO 的收敛能力,并将其应用于三个现场地震观测站。从目标速度剖面与估计速度剖面之间的误差角度来看,验证案例和实际应用中的改进分别超过了 95% 和 70%。使用 HSAF 作为目标和 PSO 作为算法目前还很有限,但已证明是有效的。本研究介绍了一种在解决地下速度结构反演问题方面具有巨大潜力的方法。
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引用次数: 0
Study on the mechanism of EPWP dissipation at the joints of shield tunnel in liquefiable strata during seismic events 地震事件中可液化地层中盾构隧道接缝处 EPWP 消散机理研究
IF 4.2 2区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-11-19 DOI: 10.1016/j.soildyn.2024.109089
Jun Shen , Xiaohua Bao , Junhong Li , Xiangsheng Chen , Hongzhi Cui
The segment joints of a shield tunnel are susceptible to deformation and leakage during seismic events. In liquefiable strata, opened joints can form seepage channels, which accelerate the dissipation of pore pressure. This study explores the interaction mechanism between tunnel structure with significant segment joints deformation and liquefiable strata under earthquakes, considering the multi-joint characteristics of a shield tunnel. First, shaking table tests were conducted to examine the dynamic characteristics of a tunnel structure with multiple joints in liquefiable strata. Based on the measured data from these tests, an optimal marginal distribution was selected from four different distribution types based on the measured values of the test results. Subsequently, a two-dimensional probability distribution model of dynamic response factors was established using Copula theory to analyse the relationship between excess pore water pressure (EPWP) dissipation and tunnel radial deformation. The correlation between EPWP dissipation and tunnel radial deformation with joints opening in the liquefiable strata was clarified. The results reveal significant differences in EPWP dissipation across different positions of the tunnel. The Gaussian Copula method effectively fits the EPWP distribution and tunnel radial deformation, indicating a positive correlation between EPWP dissipation and joints deformation. The formation of new seepage channels at the tunnel joints exacerbates EPWP dissipation. The developed probability distribution model provides a new approach for studying the dynamic response between tunnel and liquefiable soil.
在地震事件中,盾构隧道的节段接缝容易发生变形和渗漏。在可液化地层中,打开的接缝会形成渗流通道,从而加速孔隙压力的消散。本研究考虑到盾构隧道的多接缝特性,探讨了地震时具有明显分段接缝变形的隧道结构与可液化地层之间的相互作用机理。首先,进行了振动台试验,以研究在可液化地层中具有多个接缝的隧道结构的动态特性。根据这些试验的测量数据,从四种不同的分布类型中选择了一种基于试验结果测量值的最优边际分布。随后,利用 Copula 理论建立了动态响应因子的二维概率分布模型,以分析过剩孔隙水压力(EPWP)耗散与隧道径向变形之间的关系。明确了过剩孔隙水压力(EPWP)消散与隧道径向变形之间的相关性,以及在可液化地层中接缝打开的情况。结果表明,隧道不同位置的 EPWP 消散存在显著差异。高斯Copula方法有效拟合了EPWP分布和隧道径向变形,表明EPWP耗散与节理变形之间存在正相关。隧道接缝处新渗流通道的形成加剧了 EPWP 消散。所开发的概率分布模型为研究隧道与可液化土壤之间的动态响应提供了一种新方法。
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引用次数: 0
Quantitative benefits of geocells in controlling liquefaction in sands 土工格室在控制砂土液化方面的量化效益
IF 4.2 2区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-11-19 DOI: 10.1016/j.soildyn.2024.109098
Prerana Krishnaraj, Gali Madhavi Latha
Geocells have become an integral part of many geosystems like road and railway embankments, retaining walls and foundations, attributed to their multiple merits in terms of stability and strength, but their contributions towards liquefaction mitigation are unknown. The present study aims to understand the role of geocell reinforcement on the liquefaction and post-liquefaction shear response of saturated sands through monotonic and cyclic triaxial tests. Low-strength geocells of required physical and mechanical properties were fabricated through ultrasonic welding of 3D printed polypropylene (PP) sheets. The liquefaction benefits of including a single geocell in sand were quantified in terms of the reduction in pore water pressure, retardation in stiffness degradation and delay in the retardation of effective stress. In general, the inclusion of geocells delayed liquefaction, with higher beneficial effects at lower initial confining pressure, higher cyclic strain amplitude and higher cyclic loading frequency. The maximum benefit measured in terms of percentage rise in the number of cycles needed to liquefy was calculated to be about 230 %. Geocell reinforcement also helped in the quick regain of post-liquefaction shear strength and stiffness.
土工格室因其在稳定性和强度方面的多重优点,已成为公路和铁路路堤、挡土墙和地基等许多土工系统不可或缺的组成部分,但其对缓解液化的贡献却不为人知。本研究旨在通过单调和循环三轴试验了解土工格室加固对饱和砂土液化和液化后剪切响应的作用。通过超声波焊接三维打印聚丙烯(PP)板材,制造出了具有所需物理和机械性能的低强度土工格室。从孔隙水压力的降低、刚度退化的延缓和有效应力延缓的角度,量化了在砂中加入单个土工格室的液化效益。一般来说,加入土工格室可延缓液化,在初始约束压力较低、循环应变振幅较大和循环加载频率较高的情况下,土工格室的益处更大。根据计算,以液化所需循环次数的上升百分比计算,最大效益约为 230%。土工格室加固还有助于快速恢复液化后的抗剪强度和刚度。
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引用次数: 0
Synthesis of the time-frequency non-stationary stochastic near-fault fling-step ground motion based on time-frequency non-stationary ground motion model and stochastic pulse model 基于时频非稳态地动模型和随机脉冲模型的时频非稳态随机近断层撺阶地动合成
IF 4.2 2区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-11-18 DOI: 10.1016/j.soildyn.2024.109094
Qingfei Luo, Jingru An, Zhengzheng Wang
Near-fault fling-step ground motions (NFFS-GMs) are known to cause significant permanent ground displacements, resulting in greater structural damage for long-period flexible structures compared to far-field ground motions. Furthermore, even during the same seismic event, the pulse parameters—such as permanent ground displacements Dsite and pulse period Tp—can vary considerably. Despite their importance, research on stochastic NFFS-GMs remains limited. To address this gap, this paper proposes a method for synthesizing the time-frequency non-stationary stochastic near-fault fling-step ground motion for a specific seismic scenario. Firstly, we employ the discrete wavelet transform (DWT) method, utilizing five mother wavelet functions (MWFs) to analyze 210 Chi-Chi ground motions. This analysis identifies 41 valid NFFS-GMs. The effectiveness of the identification method is validated by comparing the displacement time histories of the original ground motion. Pulse parameters are subsequently derived using the fling-step (FS) pulse model proposed by Abrahamson, in conjunction with the nonlinear least-squares method. A regression model correlating pulse parameters with the seismological parameter of the fault distance R is then developed through Pearson correlation analysis and the nonlinear least-squares method. The residuals of the regression model σlnDsite and Tp are treated as random variables, and their probability distributions are determined. After that, a new stochastic pulse model is introduced to simulate low-frequency ground motions, while a time-frequency non-stationary model is used to simulate high-frequency ground motions. These components are synthesized in the frequency domain to obtain the time-frequency non-stationary stochastic near-fault fling-step ground motion (TFNS-SNFFS-GM) via inverse Fourier transform. Finally, the effectiveness of the proposed method is confirmed by comparing the response spectrum of the synthesized ground motion with that of actual NFFS-GMs.
众所周知,近断层跃层地面运动(NFFS-GMs)会造成巨大的永久地面位移,与远场地面运动相比,会对长周期柔性结构造成更大的结构破坏。此外,即使在同一地震事件中,脉冲参数(如永久地表位移 Dsite 和脉冲周期 Tp)也会有很大不同。尽管随机 NFFS-GM 非常重要,但对其的研究仍然有限。针对这一空白,本文提出了一种针对特定地震场景的时频非稳态随机近断层跃层地面运动的合成方法。首先,我们采用离散小波变换(DWT)方法,利用五个母小波函数(MWF)对 210 个 Chi-Chi 地面运动进行分析。该分析确定了 41 个有效的 NFFS-GM。通过比较原始地面运动的位移时间历程,验证了识别方法的有效性。随后,利用亚伯拉罕森提出的平步(FS)脉冲模型,结合非线性最小二乘法,得出了脉冲参数。然后,通过皮尔逊相关分析和非线性最小二乘法,建立脉冲参数与断层距离 R 的地震学参数相关的回归模型。回归模型的残差 σlnDsite 和 Tp 被视为随机变量,并确定其概率分布。之后,引入一个新的随机脉冲模型来模拟低频地面运动,同时使用一个时频非稳态模型来模拟高频地面运动。通过反傅里叶变换,在频域合成这些分量,从而得到时频非稳态随机近断层跃层地面运动(TFNS-SNFFS-GM)。最后,通过比较合成地面运动与实际 NFFS-GM 的响应谱,证实了所提方法的有效性。
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引用次数: 0
Modal modification based analysis of seismic performance of the Jiufeng Temple Ancient Masonry Pagoda 基于模态修正的九峰寺古砖石塔抗震性能分析
IF 4.2 2区 工程技术 Q1 ENGINEERING, GEOLOGICAL Pub Date : 2024-11-18 DOI: 10.1016/j.soildyn.2024.109087
Zhongwei Gao , Xiaobing Yang , Jinfang Zhang , Hongyuan Tang , Yue Du , Shiyu Zhao
Based on detailed data collected on-site, including structural construction, cross-sectional dimensions, and material properties, this paper establishes a refined three-dimensional solid initial numerical model (INM) of the Jiufeng Temple Ancient Masonry Pagoda using the ABAQUS finite element software. On the basis of the measured modal characteristics (frequency, vibration mode, and damping ratio) of the ancient masonry pagoda, a modified numerical model (MNM) was obtained by adjusting the key parameters (damping ratio, Rayleigh damping coefficients, elastic modulus, and material density) of the initial numerical model. Based on the modified numerical model, five actual strong earthquake records were input to calculate the seismic response of the ancient masonry pagoda. The seismic failure mechanism of the ancient masonry pagoda, as well as the distribution characteristics of the principal tensile stress and seismic weak-layers were analyzed. The results indicate that the stiffness and mass distribution of the ancient masonry pagoda are consistent along its height, and the deformation at the top of the ancient masonry pagoda is significant under seismic action. The results obtained from the initial numerical model are more conservative, with the maximum storey drift being 19 %, 40 %, and 27 % larger than those of the modified numerical model under minor earthquakes (with a 63 % probability of exceedance in 50 years, also called frequently occurring earthquakes), moderate earthquakes (with a 10 % probability of exceedance in 50 years), and major earthquakes (with a 2 % probability of exceedance in 50 years, also called rarely occurring earthquakes), respectively. Under the action of major earthquakes, the upper portion of the Jiufeng Temple ancient masonry Pagoda, particularly above the 9th floor, may suffer severe damage. The 10th, 11th, and 12th floors are identified as the weak-layers of the ancient masonry pagoda, and the weak-layers determination from the modified numerical model are consistent with the results of standard calculations. The method proposed in this paper can provide technical support for the seismic protection of ancient masonry pagodas.
本文基于现场采集的结构构造、截面尺寸、材料特性等详细数据,利用ABAQUS有限元软件建立了九峰寺古塔三维实体初始数值模型(INM)。在实测古塔模态特性(频率、振型和阻尼比)的基础上,通过调整初始数值模型的关键参数(阻尼比、瑞利阻尼系数、弹性模量和材料密度),得到了修正数值模型(MNM)。在修正数值模型的基础上,输入五次实际强震记录,计算了砌体古塔的地震响应。分析了砌体古塔的地震破坏机理、主拉应力和地震弱层的分布特征。结果表明,古砌石塔的刚度和质量分布沿高度方向一致,在地震作用下,古砌石塔顶部变形显著。初始数值模型得出的结果较为保守,在小震(50 年内超过概率为 63%,也称为常发地震)、中震(50 年内超过概率为 10%)和大震(50 年内超过概率为 2%,也称为罕遇地震)作用下,最大层漂分别比修正数值模型的结果大 19%、40% 和 27%。在大地震作用下,九峰寺古砖石塔上部,特别是第 9 层以上可能遭受严重破坏。第 10 层、第 11 层和第 12 层被确定为古塔的薄弱层,修改后的数值模型确定的薄弱层与标准计算结果一致。本文提出的方法可为砌体古塔的抗震设防提供技术支持。
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Soil Dynamics and Earthquake Engineering
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