挡土墙地震反应的波动模拟分析
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摘要
本文论述了该课题的理论意义和实际意义,总结了该研究的发展状况。基于解耦的近场波动的数值模拟技术和人们对土体本构关系、接触面特性等研究,对挡土墙—土体系(墙土体系)的线弹性和非线性地震反应做了平面内波动(P-SV)模拟分析。
在研究中,本文运用解耦的近场波动的数值模拟技术的研究成果,建立墙土体系的二维平面应变计算分析模型。为反映墙土体系在地震作用下的永久位移,引入了Desai薄层单元模拟挡土墙和土体接触面,并根据挡土墙位移的特点,提出用等效的单向双折线模拟接触单元的非线性特征;引入双线性本构关系作为土体的非线性模型,在此基础上给出了集中质量二维非线性显式有限元时域递推公式和具体的实现步骤和方法,并编制了计算程序2DNWAV。在数值模拟计算中,讨论了波场分离技术和自由波场的计算方法,运用已有的消除高频振荡失稳和低频漂移失稳的方法和研究成果,实现了长持时(60秒)的非线性体系时域波动模拟,取得了较好的效果和经验。
针对线弹性墙土体系模型,对刚性和透射两种底边界情形分别以P波、SV波和P、SV波同时输入的近似δ脉冲进行了时域和频域分析,模拟了波在墙土体系传播的过程,得到了传递函数幅值谱、相位谱、地面运动放大系数和最大幅值比例系数,说明了线弹性墙土体系反应的特点。四条实际地震波输入时,不仅求得了墙土体系各节点的反应,还重点分析了墙背、墙趾的动土压力和动土剪力的大小、合力作用点的位置和各单元的三分量应力分布规律,以及墙土体系内部节点的三分量应力时程和分布,这为改进挡土墙的抗震设计提供了有益的基础。
对非线性墙土体系模型,以输入El Centro波为例,利用2DNWAV程序计算分析了回填土为正常固结粘性土时,墙土体系的动位移和各节点的永久位移、挡土墙的最终状态、地面的沉降和不同土层的沉降等,结果较合理,说明在分析挡土墙地震位移时,同时考虑挡土墙与土体接触面以及土体非线性的必要性。
为验证本文方法和程序的可靠性和适用范围,与Madabhushi S.P.G.和Zeng X.等的离心机实验和数值模拟结果进行对比,结果表明:回填土为疏松干砂的墙土体系加速度、速度、位移的反应、永久位移和墙体倾角等同离心机试验模拟的结果吻合较好,同弹塑性数值模拟的结果相似。
挡土墙的基频有一定工程意义,本文提出一种能稳定和方便地估计挡土墙基频的实用方法。
对于P波输入和人工边界区介质特性对体系反应的影响等做了初步探讨,发现P波输入时,非线性影响小,这可能是土体非线性本构关系不够完善造成的。通过实际计算发现,对非线性体系和强地震输入而言,人工边界区应当按非线性体系处理。
最后,对本文的主要结果和进一步的工作进行了简要总结,并提出墙土体系研究工作的几点想法。
2DNWAV程序不仅可用于线弹性体系的计算,还可用于复杂场地的地震反应分析,用于堤坝、护坡、边坡稳定、桥台码头等岩土工程的地震性能分析。
In this thesis, the author has expounded theoretical and practical significance of this study, summarized the current research in this field. Based on the decoupled method of numerical simulating wave propagation of near field and on the research of soil constitutive relations and characteristic of interface, In-plane (P-SV) wave propagation of linear elastic or nonlinear Retaining Wall—Soil System (RWSS) is simulated.
In this paper, research achievements of the decoupled method of numerical simulating wave propagation of near field are applied. Two-dimensional plane-strain computing models are established. In order to analyze seismic permanent displacement of RWSS, Desai thin-layer elements imitating interface of retaining wall and backfill are inducted. According to the feature of permanent displacement of retaining wall, equivalent unidirectional broken line model is applied to simulate the nonlinear characteristic of interface elements.
At the same time, bi-linear constitutive relations are introduced as nonlinear constitutive relations of soil. Based on these models, lumped-mass nonlinear explicit finite element formula and concrete calculation methods in time domain are brought forth. For realization of this analysis, a 2-D nonlinear wave propagation program-2DNWAV is developed. Wave field separated technique and computing method of free field are discussed. Adopting the present research achievements of eliminating high-frequent instability and low-frequent drift, calculation of long duration (60 s.) of nonlinear system in time-domain is carried out successfully. It is useful for further study.
Taking P, SV and P,SV Delta pulse as input separately to linear elastic RWSS, which has stiff or transmitting bottom boundary, the seismic response of RWSS are analyzed in time-domain, as well as frequency-domain. Amplitude spectrum and phase spectrum of transfer function, amplification of seismic motions, etc. are analyzed to study seismic response of RWSS. For input of actual seismic motions, dynamic earth pressure and shear force at the back and the toe of retaining wall, action point of resultant pressure and shear, distribution of each component of stress in elements and nodes of RWSS are analyzed. This study may be helpful for improvement of seismic design of retaining wall.
As an example, taking seismic record of El Centro as input, nonlinear RWSS, which backfill is normal consolidated cohesive soil, is analyzed using program 2DNWAV. Dynamic displacement and permanent displacement of each node of RWSS, settlement of ground, retaining wall and different soil layer are obtained. It shows that it is necessary to take into account nonlinearly of interface of retaining wall and soil for reasonable estimation of seismic permanent displacement of retaining wall.
To verify reliability of the method and program in this paper, results of centrifuge experiment and numerical simulation which backfill is loose dry sand, obtained by Zeng X. et al. are compared with that of this paper. Calculated acceleration, velocity, displacement response of RWSS, permanent displacement and inclination angel of the retaining wall are in good agreement with those of centrifuge test, and similar to those of elastoplastic numerical simulation.
Fundamental frequency of retaining wall is significance in earthquake engineering. A practical method, which can estimate fundamental frequency of retaining wall well, is provided in this paper. When taking P wave as input, it is found that nonlinear effect is smaller than that of SV wave input. This is because of simple nonlinear of bi-linear constitute relations of this paper is not good enough to express non-linearity of soil.
For the RWSS model of this paper, there is difference between seismic responses of wall and backfill, when consider linear and nonlinear artificial boundary region. Therefore, it is necessary to take artificial boundary region as a nonlinear, when we deal with nonlinear seismic response of RWSS.
In the end of this thesis, some suggestions are proposed for further study.
The program of 2DNWAV can be used for not only seismic response analysis of linear and nonlinear RWSS, but also other geotechnical structures, e.g. seismic response of complex site, embankment and dam, stability of slope, abutment quay etc.
在研究中,本文运用解耦的近场波动的数值模拟技术的研究成果,建立墙土体系的二维平面应变计算分析模型。为反映墙土体系在地震作用下的永久位移,引入了Desai薄层单元模拟挡土墙和土体接触面,并根据挡土墙位移的特点,提出用等效的单向双折线模拟接触单元的非线性特征;引入双线性本构关系作为土体的非线性模型,在此基础上给出了集中质量二维非线性显式有限元时域递推公式和具体的实现步骤和方法,并编制了计算程序2DNWAV。在数值模拟计算中,讨论了波场分离技术和自由波场的计算方法,运用已有的消除高频振荡失稳和低频漂移失稳的方法和研究成果,实现了长持时(60秒)的非线性体系时域波动模拟,取得了较好的效果和经验。
针对线弹性墙土体系模型,对刚性和透射两种底边界情形分别以P波、SV波和P、SV波同时输入的近似δ脉冲进行了时域和频域分析,模拟了波在墙土体系传播的过程,得到了传递函数幅值谱、相位谱、地面运动放大系数和最大幅值比例系数,说明了线弹性墙土体系反应的特点。四条实际地震波输入时,不仅求得了墙土体系各节点的反应,还重点分析了墙背、墙趾的动土压力和动土剪力的大小、合力作用点的位置和各单元的三分量应力分布规律,以及墙土体系内部节点的三分量应力时程和分布,这为改进挡土墙的抗震设计提供了有益的基础。
对非线性墙土体系模型,以输入El Centro波为例,利用2DNWAV程序计算分析了回填土为正常固结粘性土时,墙土体系的动位移和各节点的永久位移、挡土墙的最终状态、地面的沉降和不同土层的沉降等,结果较合理,说明在分析挡土墙地震位移时,同时考虑挡土墙与土体接触面以及土体非线性的必要性。
为验证本文方法和程序的可靠性和适用范围,与Madabhushi S.P.G.和Zeng X.等的离心机实验和数值模拟结果进行对比,结果表明:回填土为疏松干砂的墙土体系加速度、速度、位移的反应、永久位移和墙体倾角等同离心机试验模拟的结果吻合较好,同弹塑性数值模拟的结果相似。
挡土墙的基频有一定工程意义,本文提出一种能稳定和方便地估计挡土墙基频的实用方法。
对于P波输入和人工边界区介质特性对体系反应的影响等做了初步探讨,发现P波输入时,非线性影响小,这可能是土体非线性本构关系不够完善造成的。通过实际计算发现,对非线性体系和强地震输入而言,人工边界区应当按非线性体系处理。
最后,对本文的主要结果和进一步的工作进行了简要总结,并提出墙土体系研究工作的几点想法。
2DNWAV程序不仅可用于线弹性体系的计算,还可用于复杂场地的地震反应分析,用于堤坝、护坡、边坡稳定、桥台码头等岩土工程的地震性能分析。
In this thesis, the author has expounded theoretical and practical significance of this study, summarized the current research in this field. Based on the decoupled method of numerical simulating wave propagation of near field and on the research of soil constitutive relations and characteristic of interface, In-plane (P-SV) wave propagation of linear elastic or nonlinear Retaining Wall—Soil System (RWSS) is simulated.
In this paper, research achievements of the decoupled method of numerical simulating wave propagation of near field are applied. Two-dimensional plane-strain computing models are established. In order to analyze seismic permanent displacement of RWSS, Desai thin-layer elements imitating interface of retaining wall and backfill are inducted. According to the feature of permanent displacement of retaining wall, equivalent unidirectional broken line model is applied to simulate the nonlinear characteristic of interface elements.
At the same time, bi-linear constitutive relations are introduced as nonlinear constitutive relations of soil. Based on these models, lumped-mass nonlinear explicit finite element formula and concrete calculation methods in time domain are brought forth. For realization of this analysis, a 2-D nonlinear wave propagation program-2DNWAV is developed. Wave field separated technique and computing method of free field are discussed. Adopting the present research achievements of eliminating high-frequent instability and low-frequent drift, calculation of long duration (60 s.) of nonlinear system in time-domain is carried out successfully. It is useful for further study.
Taking P, SV and P,SV Delta pulse as input separately to linear elastic RWSS, which has stiff or transmitting bottom boundary, the seismic response of RWSS are analyzed in time-domain, as well as frequency-domain. Amplitude spectrum and phase spectrum of transfer function, amplification of seismic motions, etc. are analyzed to study seismic response of RWSS. For input of actual seismic motions, dynamic earth pressure and shear force at the back and the toe of retaining wall, action point of resultant pressure and shear, distribution of each component of stress in elements and nodes of RWSS are analyzed. This study may be helpful for improvement of seismic design of retaining wall.
As an example, taking seismic record of El Centro as input, nonlinear RWSS, which backfill is normal consolidated cohesive soil, is analyzed using program 2DNWAV. Dynamic displacement and permanent displacement of each node of RWSS, settlement of ground, retaining wall and different soil layer are obtained. It shows that it is necessary to take into account nonlinearly of interface of retaining wall and soil for reasonable estimation of seismic permanent displacement of retaining wall.
To verify reliability of the method and program in this paper, results of centrifuge experiment and numerical simulation which backfill is loose dry sand, obtained by Zeng X. et al. are compared with that of this paper. Calculated acceleration, velocity, displacement response of RWSS, permanent displacement and inclination angel of the retaining wall are in good agreement with those of centrifuge test, and similar to those of elastoplastic numerical simulation.
Fundamental frequency of retaining wall is significance in earthquake engineering. A practical method, which can estimate fundamental frequency of retaining wall well, is provided in this paper. When taking P wave as input, it is found that nonlinear effect is smaller than that of SV wave input. This is because of simple nonlinear of bi-linear constitute relations of this paper is not good enough to express non-linearity of soil.
For the RWSS model of this paper, there is difference between seismic responses of wall and backfill, when consider linear and nonlinear artificial boundary region. Therefore, it is necessary to take artificial boundary region as a nonlinear, when we deal with nonlinear seismic response of RWSS.
In the end of this thesis, some suggestions are proposed for further study.
The program of 2DNWAV can be used for not only seismic response analysis of linear and nonlinear RWSS, but also other geotechnical structures, e.g. seismic response of complex site, embankment and dam, stability of slope, abutment quay etc.
引文
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