基于OpenSees的地震动对软土震陷影响研究

软土具有高灵敏度、低强度等特性,在地震过程中极易产生震陷。基于OpenSees数值模拟方法对软土场地的震陷反应进行非线性动力有限元分析,通过改变地震动峰值加速度、频谱特性、输入方式来研究其对软土震陷的影响。结果表明,地震动峰值加速度对地基土的不均匀震陷有显著影响,地震动峰值加速度越大,震陷量显著增大,震陷影响深度更大,对水平地表造成的破坏范围也更大;地震动频谱特性对软土震陷有重要影响,当地震动卓越频率与场地自振频率相近时,其幅值越大,产生的震陷越严重;水平、竖向同时输入地震动的方式能更好地反映土体的振动及震陷响应。该研究成果对探索软土震陷的机理有一定的指导意义。     

A frequency‐dependent and intensity‐dependent macroelement for reduced order seismic analysis of soil‐structure interacting systems

The computational demand of the soil‐structure interaction analysis for the design and assessment of structures, as well as for the evaluation of their life‐cycle cost and risk exposure, has led the civil engineering community to the development of a variety of methods toward the model order reduction of the coupled soil‐structure dynamic system in earthquake regions. Different approaches have been proposed in the past as computationally efficient alternatives to the conventional finite element model simulation of the complete soil‐structure domain, such as the nonlinear lumped spring, the macroelement method, and the substructure partition method. Yet no approach was capable of capturing simultaneously the frequency‐dependent dynamic properties along with the nonlinear behavior of the condensed segment of the overall soil‐structure system under strong earthquake ground motion, thus generating an imbalance between the modeling refinement achieved for the soil and the structure. To this end, a dual frequency‐dependent and intensity‐dependent expansion of the lumped parameter modeling method is proposed in the current paper, materialized through a multiobjective algorithm, capable of closely approximating the behavior of the nonlinear dynamic system of the condensed segment. This is essentially the extension of an established methodology, also developed by the authors, in the inelastic domain. The efficiency of the proposed methodology is validated for the case of a bridge foundation system, wherein the seismic response is comparatively assessed for both the proposed method and the detailed finite element model. The above expansion is deemed a computationally efficient and reliable method for simultaneously considering the frequency and amplitude dependence of soil‐foundation systems in the framework of nonlinear seismic analysis of soil‐structure interaction systems.     

考虑SSI效应储油罐的子结构实验方法与数值模拟

提出了应用振动台子结构试验方法来研究考虑土-结构相互作用（SSI）效应储罐的抗震性能,该方法将土体简化为双自由度八参量集总参数模型进行模拟,储罐作为试验子结构应用振动台加载,两部分联机完成振动台子结构试验。该方法能完成大比例尺储罐试验,具有传统试验方法难以比拟的优势。然后,通过数值模拟分析了SSI效应对储罐动力响应的影响。分别研究了不同储液高度和不同地基刚度对储罐位移和加速度响应的影响。研究结果表明：考虑SSI效应时,罐体位移响应和加速度响应均有所减小,土质越软,效果越明显;随着储液高度的增高,位移、加速度反应呈现减小趋势。     

Complex response analysis of shells of revolution including uniform base translation and rocking

A complex response algorithm for the dynamic analysis of axisymmetric thin shells supported on an interactive foundation is developed. The substructure deletion method is employed through the utilization of a dynamic boundary system at the contact area between the superstructure and the substructure. A new mathematical formulation in conjunction with the shell behaviour is developed to deal with rigid body motions due to the negation of the fixed base assumption. Four foundation conditions, that is, a fixed base, two pile foundation cases and a flexible base, are to examine the effect of base flexibility on the seismic response of cooling towers. Also, excellent comparative results between the frequency domain solution and a time domain solution are obtained.     

Effects of the dynamic cross-interaction in the seismic analysis of multiple embedded foundations

A boundary element formulation of the substructure deletion method is presented for the seismic analysis of the dynamic cross-interaction between multiple embedded foundations. This approach is particularly suitable for three-dimensional foundations of any arbitrary geometrical shape and spatial location, since it requires only the discretization of the foundations’ surfaces. The surrounding soil is represented by a homogeneous viscoelastic half-space while the foundations are assumed to be rigid and subjected to incoming SH-, P-, and SV-waves arbitrarily inclined in both the horizontal and vertical planes. The proposed methodology is tested for the case of two identical embedded square foundations for different values of the foundations’ embedment and distance. The effects of the cross-interaction are outlined in the components of the impedance matrix and of the foundation input motion. © 1997 John Wiley & Sons, Ltd.     

Embedded foundation in layered soil under dynamic excitations

The critical step in the substructure approach for the soil–structure interaction (SSI) problem is to determine the impedance functions (dynamic-stiffness coefficients) of the foundations. In the present study, a computational tool is developed to determine the impedance functions of foundation in layered soil medium. Cone frustums are used to model the foundation soil system. Cone frustums are developed based on wave propagation principles and force-equilibrium approach. The model is validated for its ability to represent the embedded foundation in layered medium by comparing the results with the rigorous analysis results. Various degrees of freedom, such as, horizontal, vertical and rocking are considered for this study.     

基于动力子结构方法的场地地震反应分析方法

本文验证了将约束子结构法引入到复杂场地地震反应分析的可行性,并在此基础上提出了两种进一步提高计算效率的简化措施。结合土层有限元模型的自身特点,提出了标准子结构的概念,通过设置标准子结构,可减少相同子结构的重复计算。基于约束子结构本身的性质,假定土层计算区域为局部非线性,可简化等效线性化分析过程,通过数值试验给出了局部非线性区域的取值范围。算例表明,上述简化措施在提高大规模复杂场地地震反应分析计算效率方面具有显著的优势。     

分层土-基础-高层框架结构相互作用体系振动台模型试验研究

本文设计实现了分层土－基础－高层框架结构相互作用体系的振动台模型试验，再现了地震动激励下上部结构和基础的震害现象和砂质粉土的液化现象。通过试验，研究了相互作用体系地震动反应的主要规律：由于动力相互作用的影响，软土地基中相互作用体系的频率小于不考虑结构－地基相互作用的结构频率，而阻尼比则大于结构材料阻尼比；体系的振型曲线与刚性地基上结构的振型曲线明显不同，基础处存在平动和转动。土层传递振动的放大或减振作用与土层性质、激励大小等因素有关，砂土层一般起放大作用，砂质粉土层一般起减振隔振作用；由于土体的隔震作用，上部结构接受的振动能量较小，各层反应均较小。上部结构顶层加速度反应组成取决于基础转动刚度、平动刚度和上部结构刚度的相对大小。     

考虑SSI效应的层间隔震结构自振特性及随机响应分析

基于水平摇摆阻尼系统模型,建立土-层间隔震结构简化分析模型,将地基土等效到上部结构,推导得到简化模型动力特性参数表达式,并通过对结构周期比及振型参与位移进行分析,讨论质量比及土体剪切波速对层间隔震结构自振特性的影响规律。利用虚拟激励法及均匀调制非平稳随机响应分析方法,分别从时域和频域角度分析不同场地条件下SSI效应对层间隔震结构的振动响应影响。结果表明：在刚性地基下,结构质量比对结构周期比及振型参与位移的影响较小,SSI效应放大了各子结构响应,尤其对下部子结构响应影响最大,各子结构在场地土差异下变化明显,软土场地下各子结构响应变大。     

Real-time dynamic hybrid testing for soil–structure interaction analysis

Simulating dynamic soil–structure interaction (SSI) problems is a challenge when using a shaking table because of the semi-infinity of soil foundations. This paper develops real-time dynamic hybrid testing (RTDHT) for SSI problems in order to consider the radiation damping effect of the semi-infinite soil foundation using a shaking table. Based on the substructure concept, the superstructure is physically tested and the semi-infinite foundation is numerically simulated. Thus, the response of the entire system considering the dynamic SSI is obtained by coupling the numerical calculation of the soil and the physical test of the superstructure. A two-story shear frame on a rigid foundation was first tested to verify the developed RTDHT system, in which the top story was modeled as the physical substructure and the bottom story was the numerical substructure. The RTDHT for a two-story structure mounted on soil foundation was then carried out on a shaking table while the foundation was numerically simulated using a lumped parameter model. The dynamic responses, including acceleration and shear force, were obtained under soft and hard soil conditions. The results show that the soil–structure interaction should be reasonably taken into account in the shaking table testing for structures.     

基础类型对框架结构及场地土地震响应影响试验研究

本文设计独立基础框架和整体箱型基础框架结构模型,基于试验数据的对比分析,探讨基础类型与地震动特性对场地土以及结构自身地震响应的影响。试验结果及分析表明:地表结构的存在总体上是放大了地表加速度响应,放大最大幅度达到了40%,影响范围可达3倍的结构跨度,且具有一定埋深的箱型基础的影响大于浅埋独立基础。由于土体对独立基础的约束相对较弱,导致独立基础结构模型的加速度响应总体上大于箱型基础的;独立基础结构模型可能发生摇摆运动导致结构基础竖向响应的频谱特性含有较多的高频成分。另外,地震动特性对结构响应也较显著,其中脉冲地震动NR波的影响最为显著。     

Real-time dynamic hybrid testing for soil–structure interaction analysis

Simulating dynamic soil–structure interaction (SSI) problems is a challenge when using a shaking table because of the semi-infinity of soil foundations. This paper develops real-time dynamic hybrid testing (RTDHT) for SSI problems in order to consider the radiation damping effect of the semi-infinite soil foundation using a shaking table. Based on the substructure concept, the superstructure is physically tested and the semi-infinite foundation is numerically simulated. Thus, the response of the entire system considering the dynamic SSI is obtained by coupling the numerical calculation of the soil and the physical test of the superstructure. A two-story shear frame on a rigid foundation was first tested to verify the developed RTDHT system, in which the top story was modeled as the physical substructure and the bottom story was the numerical substructure. The RTDHT for a two-story structure mounted on soil foundation was then carried out on a shaking table while the foundation was numerically simulated using a lumped parameter model. The dynamic responses, including acceleration and shear force, were obtained under soft and hard soil conditions. The results show that the soil–structure interaction should be reasonably taken into account in the shaking table testing for structures.     

平面P-SV波入射时非均匀饱和土 自由场地的响应

基于Biot多孔介质波动模型,研究了非均匀饱和土层对平面P-SV波入射时的动力响应.考虑饱和土地基的物理力学特性沿厚度方向连续变化,利用亥姆霍兹矢量分解原理和动力刚度法,分析了平面入射P-SV波在非均匀饱和土层中的反射和透射,并给出了基岩表面和自由表面处反射系数和透射系数的计算表达式.基于理论推导结果,数值分析了平面SV波入射下非均匀饱和土自由场地的动力响应,其中假设饱和土地基的物理力学性质沿土层深度按幂律梯度变化.数值结果表明,平面SV波入射所引起的地面位移与基岩位移之比均随土层厚度和土体的非均匀程度、波的入射角和入射频率的增加而减小,且其竖向位移比的减小更为显著,厚土层对地震波的耗散作用尤为明显.      

Seismic response of a bridge–soil–foundation system under the combined effect of vertical and horizontal ground motions

Different levels of model sophistication have recently emerged to support seismic risk assessment of bridges, but mostly at the expense of neglecting the influence of vertical ground motions (VGMs). In this paper, the influence of VGMs on bridge seismic response is presented and the results are compared with the case of horizontal‐only excitations. An advanced finite element model that accounts for VGMs is first developed. Then, to investigate the effect of soil–structure interaction (SSI) including liquefaction potential, the same bridge with soil‐foundation and fixed boundary conditions is also analyzed. Results show that the inclusion of the VGMs has a significant influence on the seismic response, especially for the axial force in columns, normal force of bearings, and the vertical deck bending moments. However, VGMs do not have as much influence on the seismic demand of the pile cap displacements or pile maximum axial forces. Also, the significant fluctuation of the column axial force can reduce its shear and flexural capacity, and a heightened reversal of flexural effects may induce damage in the deck. In addition, relative to the fixed base case, SSI effects tend to reduce response quantities for certain ground motions while increasing demands for others. This phenomenon is explained as a function of the frequency content of the ground motions, the shift in natural vertical periods, and the VGM spectral accelerations at higher modes. Moreover, the mechanisms of liquefaction are isolated relative to SSI effects in nonliquefiable soils, revealing the influence of liquefaction on bridge response under VGMs. Copyright © 2012 John Wiley & Sons, Ltd.     

桩基础在无限层地基中的轴向地震反应分析

本文对无限层弹性地基中单桩基础通过特性分析建立了合理的软科学模型，按分层弹性地基土模型对桩进行动力分析，给出了桩基础轴向自振特性及在竖向地震载荷与动力载荷作用了强迫反应的解析解，文中的解析公式为无限层弹性地基中的单桩基础轴向地震反应分析提供了一种新的解析方法。     

基于静力子结构的多点输入拟静力位移求解

复杂场地的土层地震反应分析对结构的地震反应计算及抗震安全性评价有重要意义。采用直接有限元法对土层进行三维建模,可使系统的计算力学模型更加符合实际情况。但由此带来的计算量之大,使得传统的计算方法难以胜任。在此背景下,本文利用静力子结构方法推导了在多点输入模式下进行土层地震反应分析时拟静力位移的求解步骤,并通过均匀土层算例验证了行波输入下利用约束子结构模态综合法进行复杂场地地震反应分析的可行性。     

SOIL–PILE–BRIDGE SEISMIC INTERACTION: KINEMATIC AND INERTIAL EFFECTS. PART I: SOFT SOIL

A substructuring method has been implemented for the seismic analysis of bridge piers founded on vertical piles and pile groups in multi-layered soil. The method reproduces semi-analytically both the kinematic and inertial soil–structure interaction, in a simple realistic way. Vertical S-wave propagation and the pile-to-pile interplay are treated with sufficient rigor, within the realm of equivalent-linear soil behaviour, while a variety of support conditions of the bridge deck on the pier can be studied with the method. Analyses are performed in both frequency and time domains, with the excitation specified at the surface of the outcropping (‘elastic’) rock. A parameter study explores the role of soil–structure interaction by elucidating, for typical bridge piers founded on soft soil, the key phenomena and parameters associated with the interplay between seismic excitation, soil profile, pile–foundation, and superstructure. Results illustrate the potential errors from ignoring: (i) the radiation damping generated from the oscillating piles, and (ii) the rotational component of motion at the head of the single pile or the pile-group cap. Results are obtained for accelerations of bridge deck and foundation points, as well as for bending moments along the piles. © 1997 by John Wiley & Sons, Ltd.     

Shaking Table Test Study on Dynamic Characteristics of Bridge Foundation Reinforcement on Slopes

With the fast development of bridge construction in mountainous and seismic areas, it is necessary to conduct related research. Based on the design of a shaking table model test, here are the following test results:the filtering effect exists in soil and is affected by the dynamic constraint conditions, the amplitude is strengthened around the natural frequency and weakened in other frequency bands in the Fourier spectrum. Since the acceleration scaling effect occurred on a sloped surface, the acceleration response decreases from the outside to the inside in soil. The dynamic response is relatively strong near the slip surface in bedrock due to the reflection of seismic waves. The failure mode of landslide is decided by the slope angle and slipping mass distribution, and the test shows the front row stabilizing piles should keep a proper distance from bridge foundation so that seismic resistance can be guaranteed for the bridge foundation.     

基于子结构方法的土-结构动力相互作用半解析方法研究现状综述

寻求高效实用的力学模型和计算方法是土与基础动力相互作用效应在工程设计中得以考虑的关键。围绕3个问题对可以通过手算或自主编程解决土-基础-结构系统动力相互作用问题的半解析子结构法展开评述:（1）为何采用子结构法研究土与结构动力相互作用问题;（2）如何求解子结构法中作为关键参数的基础振动阻抗;（3）如何利用振动阻抗求解上部结构的动力响应。最后,结合实际工程问题探讨了在已有成果的基础上可进行深化和拓展的研究方向。     

Seismic soil–structure interaction in multi‐span bridges: Application to a railway bridge

The effects of soil‐structure interaction on the seismic response of multi‐span bridges are investigated by means of a modelling strategy based on the domain decomposition technique. First, the analysis methodology is presented: kinematic interaction analysis is performed in the frequency domain by means of a procedure accounting for radiation damping, soil–pile and pile‐to‐pile interaction; the seismic response of the superstructure is evaluated in the time domain by means of user‐friendly finite element programs introducing suitable lumped parameter models take into account the frequency‐dependent impedances of the soil–foundation system. Second, a real multi‐span railway bridge longitudinally restrained at one abutment is analyzed. The input motion is represented by two sets of real accelerograms: one consistent with the Italian seismic code and the other constituted by five records characterized by different frequency contents. The seismic response of the compliant‐base model is compared with that obtained from a fixed‐base model. Pile stress resultants due to kinematic and inertial interactions are also evaluated. The application demonstrates the importance of performing a comprehensive analysis of the soil–foundation–structure system in the design process, in order to capture the effects of soil‐structure interaction in each structural element that may be beneficial or detrimental. Copyright © 2011 John Wiley & Sons, Ltd.