空间网格结构土—结构相互作用模型与地震反应研究
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摘要
目前大跨空间网格结构抗震研究主要把屋盖结构作为分析对象，有关抗震分析理论比较成熟。实际的空间网格结构是由屋盖结构、支承结构、下部基础以及地基组成。大跨空间网格结构的支承结构一般由柱子或框架结构组成。基础一般为独立基础，条形基础，筏板基础以及桩基础。土-结构相互作用的一般作用机理为如果地表存在建筑物，地震将迫使地基与上部结构一起振动。由于地震产生的上部结构振动在建筑物内部经过多次折射后将有一部分再次传入地基引起基础地基新的振动后再作用于上部结构，如此反复的这种现象称为地震作用下的结构-地基动力相互作用，简称为土-结构相互作用。地震作用下考虑结构-地基相互作用与刚性地基假定相比较可归纳为两方面：结构动力特性改变，包括自振频率降低、振型改变；结构的整体阻尼增加。本文主要以带支承的平板网架和带支承的单层网壳结构为分析模型，研究空间结构屋盖-支承结构-地基耦合效应，以及土-结构相互作用对空间结构地震响应的影响。主要研究内容如下：
（1）适合于空间网格结构土-结构相互作用分析模型研究
在Gazatas半无限空间模型的基础上，提出在强震作用下的浅基础与土分离的改进分析模型。在群桩基础模型中，提出考虑竖向桩-土相互作用的空间网格结构三维非耦合分析模型。并以一个空间桁架结构为例，通过本文所提出的非耦合分析模型与完全耦合模型的桩基础以及上部结构地震反应的对比，验证所提空间网格结构非耦合桩-土相互作用模型的正确性。并且通过对比也验证所提强震作用下浅基础与土分离的改进分析模型的正确性。
（2）地震动特性和土-结构相互作用双重因素对平板网架地震反应影响研究
在提出强震作用下浅基础与土分离的改进分析模型基础上，研究地震动特性和土-结构相互作用双重因素对结构地震反应的影响。考虑土-结构相互作用后，结构的周期将会变长。近场地震动具有长周期的速度大脉冲，远场地震动也具有长周期分量。研究近场地震动与远场地震动对于考虑土-结构相互作用的平板网架的地震反应的影响。
（3）土-结构相互作用对平板网架地震反应影响中辐射阻尼的影响研究
在上述平板网架结构的浅基础土-结构相互作用研究中，一是延长了结构的周期，二是通过上部结构与下部结构的相互作用增加了结构的整体阻尼比。在本文的研究中，主要基于平板网架第一阶模态求出土-结构相互作用对于结构整体阻尼比的增加。分析考虑辐射阻尼对于空间结构土-结构相互作用的影响。
（4）以柱支承的空间桁架结构为分析模型，研究完全耦合的桩-土相互作用对上部桁架结构地震反应的影响以及参数化分析。
在建模中主要应用动力非线性p-y弹簧模拟水平桩-土相互作用、动力非线性t-z弹簧模拟桩-土相互作用的摩擦力、以及用动力非线性q-z弹簧模拟桩端的非线性力-位移关系来描述桩-土非线性相互作用关系。主要研究不排水抗剪强度，极限主应力为一半时的应变值以及最大桩侧横向磨阻力与承载力比值对上部结构地震反应影响并进行参数化研究。
（5）以单层网壳结构为研究对象，非线性桩-土相互作用对单层网壳结构的地震反应影响研究。
运用非线性弹簧单元模型分别模拟三维动力非线性桩土相互作用中的p-y曲线，t-z曲线以及q-z曲线，使得非线性弹簧的骨架曲线与上述非线性p-y曲线，t-z曲线以及q-z非线性曲线近似并且假设上述三种非线性弹簧单元的非线性滞回规律。在此基础上，研究三维非线性桩-土相互作用对单层网壳结构的地震反应影响规律。
（6）在空间网格结构桩-土相互作用研究的基础上，以三维动力非线性桩-土相互作用模型在地震作用下的地震反应为对比标准，选取嵌固法模型，阻抗函数法模型以及“m值”模型三种桩-土相互作用简化模型，对比三种桩-土相互作用简化模型在地震输入下的地震反应的对比，找到了适合于单层网壳结构的桩基础抗震设计简化模型。
The roof structure is chosen as the analysis model in the current seismic researchof the long-span latticed spatial structure and the relevant seismic theory is mature.The real latticed spatial structure includes the roof structure, the supporting structureand the soil medium. The supporting structure in the long-span latticed spatialstructure is the column or the frame. In most cases, the foundation includes theindependent foundation, the strip foundation, the raft foundation and the pilefoundation. When the structure is on the soil medium, the soil medium and thesuperstructure will vibrate simultaneously under the earthquake. At the same time,some of the energy from the vibration of superstructure will be transmitted to thesurrounding soil medium, and then the vibration in the soil medium will acted uponthe superstructure. This phenomenon is called the soil structure interaction under theseismic actions. Compared with the rigid foundation assumption, the effect of the soilstructure interaction under the seismic actions could be categorized as the followingtwo aspects: the change of the dynamic characteristic which including the decrease ofthe frequency and the change of the mode shape, the increase of the damping ratio.This paper, where the reticulated space structure and the sphere shell with supportingstructure is the analysis model, mainly analyze the interactions between the roof, thesupporting structure and the soil medium and the effect of the interaction on theseismic response of the roof. The main research in this paper is as follows:
(1) Suitable soil structure interaction model for the latticed spatial structure.
Based on the half-space model by Gazatas, a new model, which considers thecrack between the foundation and the soil under strong earthquake, is put forward. Inthe pile group model, the3-D non-coupling model considering vertical soil-pileinteraction is put forward. With one spatial truss as one example, the new shallowfoundation and the pile group model is verified by the comparison between thecoupling model and the un-uncoupling model.
(2) The effect of the dynamic characteristics of the ground motion and soilstructure interaction on the seismic response of spatial structure.
Based on the shallow foundation model considering the crack between thefoundation and soil, the effect of two factors including the ground motion characterand the soil structure interaction on the seismic response of spatial structure is studied.When the soil structure interaction is considered, the period of the structurewill be increased. The near field ground motion has the characteristic of the velocitypulse with long period and the high frequency in the far field ground motion will befiltered during the propagation, so both kinds of the ground motions have thecharacteristic of the long period. The effect of the two kinds of the ground motions onthe response of the reticulated spatial structure incorporating the soil structureinteraction is studied.
(3) Effect of the radiation damping on the seismic response of the reticulatedspatial structure incorporating the soil structure interaction
There are two main effects in the study of the soil structure interaction on theseismic response of the latticed space structure with shallow foundation. One is theelongation of the period of the structure, second is the increase of the overall radiationdamping ratio. In this paper, the increase of the overall radiation damping is mainlybased on the elongation of period of the first mode shape. The effect of the radiationdamping on the seismic response of the roof structure is mainly considered in the soilstructure interaction analysis.
(4) Effect of fully coupling soil pile interaction on the seismic response of thespatial truss supported by the column and the parametric analysis by the softwareopensees.
In the analysis model, the nonlinear p-y spring is to model the horizontal soil-pileinteraction; the nonlinear t-z spring is to model the vertical soil–pile frictionsinteraction; the nonlinear q-z spring is to model the soil–pile interactions between thesoil and the force at the end of the pile.
(5) Effect of the nonlinear soil pile interaction on the seismic response of thelatticed shell by the software SAP2000.
In the analysis model, the skeleton curve of the nonlinear spring in the SAP2000is equal to the skeleton curve of the p-y curve, the t-z curve and the q-z curverespectively. The hysteretic models are assumed for the three springs respectively.Based on the above, the3D soil pile interaction on the seismic response ofsingle-layer shell is studied. Some important conclusions are drawn.
（6）Simplified pile analysis model in the seismic design of the single-layerlatticed shell.
On the basis of the seismic response of the single-layer latticed shellincorporating the3D nonlinear soil-pile interaction, the seismic response of the single –layer latticed shell incorating the nD rigid model, the impedence function model andthe m model are compared. By the comparison, the simplified soil-pile interactionmodel in the seismic response of spatial model is found.
（1）适合于空间网格结构土-结构相互作用分析模型研究
在Gazatas半无限空间模型的基础上，提出在强震作用下的浅基础与土分离的改进分析模型。在群桩基础模型中，提出考虑竖向桩-土相互作用的空间网格结构三维非耦合分析模型。并以一个空间桁架结构为例，通过本文所提出的非耦合分析模型与完全耦合模型的桩基础以及上部结构地震反应的对比，验证所提空间网格结构非耦合桩-土相互作用模型的正确性。并且通过对比也验证所提强震作用下浅基础与土分离的改进分析模型的正确性。
（2）地震动特性和土-结构相互作用双重因素对平板网架地震反应影响研究
在提出强震作用下浅基础与土分离的改进分析模型基础上，研究地震动特性和土-结构相互作用双重因素对结构地震反应的影响。考虑土-结构相互作用后，结构的周期将会变长。近场地震动具有长周期的速度大脉冲，远场地震动也具有长周期分量。研究近场地震动与远场地震动对于考虑土-结构相互作用的平板网架的地震反应的影响。
（3）土-结构相互作用对平板网架地震反应影响中辐射阻尼的影响研究
在上述平板网架结构的浅基础土-结构相互作用研究中，一是延长了结构的周期，二是通过上部结构与下部结构的相互作用增加了结构的整体阻尼比。在本文的研究中，主要基于平板网架第一阶模态求出土-结构相互作用对于结构整体阻尼比的增加。分析考虑辐射阻尼对于空间结构土-结构相互作用的影响。
（4）以柱支承的空间桁架结构为分析模型，研究完全耦合的桩-土相互作用对上部桁架结构地震反应的影响以及参数化分析。
在建模中主要应用动力非线性p-y弹簧模拟水平桩-土相互作用、动力非线性t-z弹簧模拟桩-土相互作用的摩擦力、以及用动力非线性q-z弹簧模拟桩端的非线性力-位移关系来描述桩-土非线性相互作用关系。主要研究不排水抗剪强度，极限主应力为一半时的应变值以及最大桩侧横向磨阻力与承载力比值对上部结构地震反应影响并进行参数化研究。
（5）以单层网壳结构为研究对象，非线性桩-土相互作用对单层网壳结构的地震反应影响研究。
运用非线性弹簧单元模型分别模拟三维动力非线性桩土相互作用中的p-y曲线，t-z曲线以及q-z曲线，使得非线性弹簧的骨架曲线与上述非线性p-y曲线，t-z曲线以及q-z非线性曲线近似并且假设上述三种非线性弹簧单元的非线性滞回规律。在此基础上，研究三维非线性桩-土相互作用对单层网壳结构的地震反应影响规律。
（6）在空间网格结构桩-土相互作用研究的基础上，以三维动力非线性桩-土相互作用模型在地震作用下的地震反应为对比标准，选取嵌固法模型，阻抗函数法模型以及“m值”模型三种桩-土相互作用简化模型，对比三种桩-土相互作用简化模型在地震输入下的地震反应的对比，找到了适合于单层网壳结构的桩基础抗震设计简化模型。
The roof structure is chosen as the analysis model in the current seismic researchof the long-span latticed spatial structure and the relevant seismic theory is mature.The real latticed spatial structure includes the roof structure, the supporting structureand the soil medium. The supporting structure in the long-span latticed spatialstructure is the column or the frame. In most cases, the foundation includes theindependent foundation, the strip foundation, the raft foundation and the pilefoundation. When the structure is on the soil medium, the soil medium and thesuperstructure will vibrate simultaneously under the earthquake. At the same time,some of the energy from the vibration of superstructure will be transmitted to thesurrounding soil medium, and then the vibration in the soil medium will acted uponthe superstructure. This phenomenon is called the soil structure interaction under theseismic actions. Compared with the rigid foundation assumption, the effect of the soilstructure interaction under the seismic actions could be categorized as the followingtwo aspects: the change of the dynamic characteristic which including the decrease ofthe frequency and the change of the mode shape, the increase of the damping ratio.This paper, where the reticulated space structure and the sphere shell with supportingstructure is the analysis model, mainly analyze the interactions between the roof, thesupporting structure and the soil medium and the effect of the interaction on theseismic response of the roof. The main research in this paper is as follows:
(1) Suitable soil structure interaction model for the latticed spatial structure.
Based on the half-space model by Gazatas, a new model, which considers thecrack between the foundation and the soil under strong earthquake, is put forward. Inthe pile group model, the3-D non-coupling model considering vertical soil-pileinteraction is put forward. With one spatial truss as one example, the new shallowfoundation and the pile group model is verified by the comparison between thecoupling model and the un-uncoupling model.
(2) The effect of the dynamic characteristics of the ground motion and soilstructure interaction on the seismic response of spatial structure.
Based on the shallow foundation model considering the crack between thefoundation and soil, the effect of two factors including the ground motion characterand the soil structure interaction on the seismic response of spatial structure is studied.When the soil structure interaction is considered, the period of the structurewill be increased. The near field ground motion has the characteristic of the velocitypulse with long period and the high frequency in the far field ground motion will befiltered during the propagation, so both kinds of the ground motions have thecharacteristic of the long period. The effect of the two kinds of the ground motions onthe response of the reticulated spatial structure incorporating the soil structureinteraction is studied.
(3) Effect of the radiation damping on the seismic response of the reticulatedspatial structure incorporating the soil structure interaction
There are two main effects in the study of the soil structure interaction on theseismic response of the latticed space structure with shallow foundation. One is theelongation of the period of the structure, second is the increase of the overall radiationdamping ratio. In this paper, the increase of the overall radiation damping is mainlybased on the elongation of period of the first mode shape. The effect of the radiationdamping on the seismic response of the roof structure is mainly considered in the soilstructure interaction analysis.
(4) Effect of fully coupling soil pile interaction on the seismic response of thespatial truss supported by the column and the parametric analysis by the softwareopensees.
In the analysis model, the nonlinear p-y spring is to model the horizontal soil-pileinteraction; the nonlinear t-z spring is to model the vertical soil–pile frictionsinteraction; the nonlinear q-z spring is to model the soil–pile interactions between thesoil and the force at the end of the pile.
(5) Effect of the nonlinear soil pile interaction on the seismic response of thelatticed shell by the software SAP2000.
In the analysis model, the skeleton curve of the nonlinear spring in the SAP2000is equal to the skeleton curve of the p-y curve, the t-z curve and the q-z curverespectively. The hysteretic models are assumed for the three springs respectively.Based on the above, the3D soil pile interaction on the seismic response ofsingle-layer shell is studied. Some important conclusions are drawn.
（6）Simplified pile analysis model in the seismic design of the single-layerlatticed shell.
On the basis of the seismic response of the single-layer latticed shellincorporating the3D nonlinear soil-pile interaction, the seismic response of the single –layer latticed shell incorating the nD rigid model, the impedence function model andthe m model are compared. By the comparison, the simplified soil-pile interactionmodel in the seismic response of spatial model is found.
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