场地非线性地震反应分析方法及其应用研究
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摘要
地震是全人类共同面临的一个灾害问题。中国和意大利都是地震多发国家,同时也是受地震灾害影响较为严重的国家。场地地震反应分析是震害估计和抗震工程领域中的重要内容,在工程场地地震安全性评价中有着举足轻重的地位。20世纪60年代后,在大量试验数据和强震观测资料的基础上,研究学者发现了强震作用下土体会产生大应变从而导致非线性。于是,强震作用下土体的非线性特征开始逐渐引起国际岩土地震工程领域的关注。如何描述土体在地震荷载作用下的应力-应变关系一直是学术界关注的研究课题,土体动力本构模型的建立也成为土动力学中的前沿课题之一。然而,大多数非线性本构模型中的参数较多,参数的确定也较为繁琐,需要占用大量的计算机内存,不利于计算机实现。而在现有地震反应分析程序的实际应用中,相关参数的正确选取却缺乏依据,特别是对于程序的初学者以及缺乏经验的工程人员更是缺乏相对比较完善的参考资料和正确的指导,通过不同地震分析程序得到的地震反应的正确性和精确度值得商榷。此外,在工程实践中,剪切波速度呈逆向分布的特殊场地的研究没有得到较好的发展,这种独特的地层特征能够确定土层随着深度影响的复杂动力反应,会显著地影响土的表面运动和内部运动。在土壤的液化,桩基础设计和埋入式结构等许多岩土地震工程问题中有着实际意义。
针对以上问题,通过重庆大学与罗马大学的国际合作项目,作者在罗马大学联合培养学习期间,基于Giuseppe Lanzo教授等的研究基础,围绕场地非线性地震反应,主要做了以下几个方面的研究工作:
①场地地震反应分析的理论研究。论述了场地非线性研究方法、分析模型和非线性特性方面的研究现状,总结了场地地震反应分析中土体动力本构模型,反应分析方法和数值程序实际应用中存在的主要问题和不足。总结国内外学者在场地非线性特性方面的研究,场地非线性反应分析的模型和分析方法,针对土层对地震波的放大作用,重新推导了地震作用下的土层放大函数。介绍了场地地震反应的现行分析方法,即频域分析和时域分析中的等效线性化方法和非线性方法,阐述了各自的原理,并对实际应用中的优缺点进行评述和对比。
②提出了基于双曲正切函数的土动力非线性本构模型。主要针对已有本构模型参数较多,各参数确定比较繁琐,不利于实际应用,且有时模型出现的不合理情况,从土体本构模型的一般构造原则出发,基于简单的双曲正切函数,根据其函数图像性质和具有双渐近线特征,通过函数的平移和缩放原则推导了土体非线性本构模型的骨架曲线和滞回曲线的双曲正切表达式,构造出基于双曲正切函数的土体动力本构模型,并把通过该模型得出的结果与现场实测数据进行拟合。同时,基于该非线性本构模型,采用直接积分的数值算法,编制了场地非线性地震反应分析程序,并将该程序应用于场地地震反应分析中,进行可行性论证。
③应用频域和时域分析方法对场地地震反应进行计算分析。采用粘滞阻尼假定,详细探讨了时域分析中的几种Rayleigh阻尼矩阵形式。并通过国际岩土工程界广泛使用的五种数值分析程序,研究了怎样由Rayleigh阻尼表达式中由粘滞阻尼系数,即控制频率形成阻尼矩阵的问题,并以频域分析的结果作为精确解,对各程序的分析结果进行对比,对实际应用中不同程序相关参数的合理选取进行了归纳总结,提出相关建议。
④实际中的土层都是置于弹性基岩之上,但是在数值计算中又常常假定基岩为刚性的。为了检验地震波的两种输入方式在不同计算软件中的精度和准确性,对半空间不同基底类型上的均质粘土层进行地震反应分析,讨论了不同数值计算程序中采用不同基岩假定的合理性,及所求出地震反应的准确性。
⑤针对意大利中南部地区许多历史古迹中心具有剪切波速度逆向分布土层的特殊古迹场地,建立理想分析模型,并从意大利强震数据记录库SISMA中精选6组实测地震加速度记录作为输入地震动,结合不同土层剖面组合,通过改变不同土层的几何及力学参数,分析了该类型场地的地震反应。分析结果表明,土层的剪切波速度是确定土层地震反应的首要影响因素,两种不同性质土层的其接触面是薄弱面,在地震动作用下会产生很大的剪切应变。
通过本文的研究,形成了新的场地地震非线性反应分析方法,同时对已有数值程序的特征及相应参数选取进行了深入探讨,提出了相关的建议,这对于促进抗震工程的发展具有重要的学术指导意义。
Ground response analysis are used to predict ground surface motions for development of design response spectra and determine the earthquake-induced forces that can lead to instability of earth and earth-retaining structures. Evaluation of ground response is typically important and also one of the most commonly encountered problems in geotechnical earthquake engineering. The nonlinear soil characteristics have received much attention since the soil nonlinearity under strong motions was found. Construction of soil constitutive models uses basic principles of mechanics to reproduce the soil behavior under general initial stress conditions. The penalty for this increased versatility comes in the form of increased complexity, and increased computational efforts and computational instability, even increased number of model parameters, some of which are difficult to determine when incorporated into seismic ground response analyses and the computation is expensive. As a result, attempts have been made to derive a simple, straightforward and feasible new model to describe the nonlinear stress strain relationship. In addition, with dramatic development of computer technology, numerical studies with computer codes is playing increasingly significant roles in various fields of geotechnical earthquake engineering to understand the basic concepts and to model the real situations under earthquake loadings. But nonlinear seismic ground response analysis is seldom used in practice by non-expert users because parameter selection and code usage protocols are often unclear and poorly documented, the effects of parametric variability on the analysis results are unknown, and the benefits of nonlinear analyses relative to equivalent-linear analyses are often un-quantified. Thus, the development of reliable and dependable documented parameter selection for the numerical simulation is needed in practice. Moreover, it should be considered that in the Italian territory, especially in central and southern Italy, many historical centres are founded on site characterised by shear wave velocity inversion. This shear wave velocity inversion can determine a complex dynamic response of the soil column significantly affecting the in-depth and at surface ground motion. This response may be of practical interest in many geotechnical earthquake engineering problems such as the design of pile foundations and of critical buried structures.
Based on the research carried out by Prof. Giuseppe Lanzo and Dr. Alessandro Pagliaroli, some further work has been accomplished with respect to nonlinear seismic ground response analysis and implications for seismic codes implementation. The main work involved in this thesis is:
Firstly, Literature review, previous research on nonlinear seismic ground response analysis and the main methods to estimating ground response are summarized. Theory of wave propagation is also presented again, then the equation of motion of three dimensional wave propagation is re-derived.
Secondly, the thesis focuses on the seismic ground response analysis. Relative contents are including: specification of input motion which describe how the control motion is applied as the outcrop motion or within motion correspond to the rigid base and elastic base; soil amplification, which represents the characteristics of the soil itself, and it is independent of any earthquake; time domain and frequency domain analysis in company with the nonlinear and equivalent linear method; viscous Rayleigh damping ratio which consisting of three type of formulations.
Thirdly, stable numerical integration techniques and realistic constitutive models of soil are the two important and necessary components of nonlinear seismic ground response analyses. Study in this thesis is only involved in nonlinear constitutive models of soil. NHT model is new and first attempt to model nonlinear stress-strain behavior of soil based on the hyperbolic tangent function. The backbone (stress-strain) curve and unloading, reloading curves are all conducted according to the basic standard hyperbolic tangent function. It is indicated that the NHT model can exhibit the soil dynamics. Moreover, NHT model is expressed in the simple form, in which the physical meaning is clear and straightforward. The unloading and reloading can start at the point even without standing in the backbone curve, and the only thing need to do for obtaining hysteresis loop is determination of shear strain and shear stress values at the beginning of unloading and reloading.
In addition, the implications for seismic codes implementation are presented. Application of five leading common used computer codes in ground seismic response is handled by creating simple homogeneous soil model. Exact solutions for body wave propagation through soil medium are carried out. The major emphasis of the research is to reduce confusions in the usage of procedures in practice and create relative clear guidelines so that the numerical analysis problem can be handled for those even non-expert users at currently available common used computer facilities. Furthermore,shear wave velocity inversion can determine a complex dynamic response of the soil column significantly affecting the in-depth and at surface ground motion. This response may be of practical interest in many geotechnical earthquake engineering problems such as the design of pile foundations and of critical buried structures. Considering the fact that in the Italian territory, especially in central and southern Italy, many historical centres are founded on large soft rock slabs overlying more deformable clay deposits, a two-layer system was established for seismic response of soil columns characterised by shear wave velocity inversion.
Last but not least, the recommendations and some further efforts which can be considered in the future research are summarized.
针对以上问题,通过重庆大学与罗马大学的国际合作项目,作者在罗马大学联合培养学习期间,基于Giuseppe Lanzo教授等的研究基础,围绕场地非线性地震反应,主要做了以下几个方面的研究工作:
①场地地震反应分析的理论研究。论述了场地非线性研究方法、分析模型和非线性特性方面的研究现状,总结了场地地震反应分析中土体动力本构模型,反应分析方法和数值程序实际应用中存在的主要问题和不足。总结国内外学者在场地非线性特性方面的研究,场地非线性反应分析的模型和分析方法,针对土层对地震波的放大作用,重新推导了地震作用下的土层放大函数。介绍了场地地震反应的现行分析方法,即频域分析和时域分析中的等效线性化方法和非线性方法,阐述了各自的原理,并对实际应用中的优缺点进行评述和对比。
②提出了基于双曲正切函数的土动力非线性本构模型。主要针对已有本构模型参数较多,各参数确定比较繁琐,不利于实际应用,且有时模型出现的不合理情况,从土体本构模型的一般构造原则出发,基于简单的双曲正切函数,根据其函数图像性质和具有双渐近线特征,通过函数的平移和缩放原则推导了土体非线性本构模型的骨架曲线和滞回曲线的双曲正切表达式,构造出基于双曲正切函数的土体动力本构模型,并把通过该模型得出的结果与现场实测数据进行拟合。同时,基于该非线性本构模型,采用直接积分的数值算法,编制了场地非线性地震反应分析程序,并将该程序应用于场地地震反应分析中,进行可行性论证。
③应用频域和时域分析方法对场地地震反应进行计算分析。采用粘滞阻尼假定,详细探讨了时域分析中的几种Rayleigh阻尼矩阵形式。并通过国际岩土工程界广泛使用的五种数值分析程序,研究了怎样由Rayleigh阻尼表达式中由粘滞阻尼系数,即控制频率形成阻尼矩阵的问题,并以频域分析的结果作为精确解,对各程序的分析结果进行对比,对实际应用中不同程序相关参数的合理选取进行了归纳总结,提出相关建议。
④实际中的土层都是置于弹性基岩之上,但是在数值计算中又常常假定基岩为刚性的。为了检验地震波的两种输入方式在不同计算软件中的精度和准确性,对半空间不同基底类型上的均质粘土层进行地震反应分析,讨论了不同数值计算程序中采用不同基岩假定的合理性,及所求出地震反应的准确性。
⑤针对意大利中南部地区许多历史古迹中心具有剪切波速度逆向分布土层的特殊古迹场地,建立理想分析模型,并从意大利强震数据记录库SISMA中精选6组实测地震加速度记录作为输入地震动,结合不同土层剖面组合,通过改变不同土层的几何及力学参数,分析了该类型场地的地震反应。分析结果表明,土层的剪切波速度是确定土层地震反应的首要影响因素,两种不同性质土层的其接触面是薄弱面,在地震动作用下会产生很大的剪切应变。
通过本文的研究,形成了新的场地地震非线性反应分析方法,同时对已有数值程序的特征及相应参数选取进行了深入探讨,提出了相关的建议,这对于促进抗震工程的发展具有重要的学术指导意义。
Ground response analysis are used to predict ground surface motions for development of design response spectra and determine the earthquake-induced forces that can lead to instability of earth and earth-retaining structures. Evaluation of ground response is typically important and also one of the most commonly encountered problems in geotechnical earthquake engineering. The nonlinear soil characteristics have received much attention since the soil nonlinearity under strong motions was found. Construction of soil constitutive models uses basic principles of mechanics to reproduce the soil behavior under general initial stress conditions. The penalty for this increased versatility comes in the form of increased complexity, and increased computational efforts and computational instability, even increased number of model parameters, some of which are difficult to determine when incorporated into seismic ground response analyses and the computation is expensive. As a result, attempts have been made to derive a simple, straightforward and feasible new model to describe the nonlinear stress strain relationship. In addition, with dramatic development of computer technology, numerical studies with computer codes is playing increasingly significant roles in various fields of geotechnical earthquake engineering to understand the basic concepts and to model the real situations under earthquake loadings. But nonlinear seismic ground response analysis is seldom used in practice by non-expert users because parameter selection and code usage protocols are often unclear and poorly documented, the effects of parametric variability on the analysis results are unknown, and the benefits of nonlinear analyses relative to equivalent-linear analyses are often un-quantified. Thus, the development of reliable and dependable documented parameter selection for the numerical simulation is needed in practice. Moreover, it should be considered that in the Italian territory, especially in central and southern Italy, many historical centres are founded on site characterised by shear wave velocity inversion. This shear wave velocity inversion can determine a complex dynamic response of the soil column significantly affecting the in-depth and at surface ground motion. This response may be of practical interest in many geotechnical earthquake engineering problems such as the design of pile foundations and of critical buried structures.
Based on the research carried out by Prof. Giuseppe Lanzo and Dr. Alessandro Pagliaroli, some further work has been accomplished with respect to nonlinear seismic ground response analysis and implications for seismic codes implementation. The main work involved in this thesis is:
Firstly, Literature review, previous research on nonlinear seismic ground response analysis and the main methods to estimating ground response are summarized. Theory of wave propagation is also presented again, then the equation of motion of three dimensional wave propagation is re-derived.
Secondly, the thesis focuses on the seismic ground response analysis. Relative contents are including: specification of input motion which describe how the control motion is applied as the outcrop motion or within motion correspond to the rigid base and elastic base; soil amplification, which represents the characteristics of the soil itself, and it is independent of any earthquake; time domain and frequency domain analysis in company with the nonlinear and equivalent linear method; viscous Rayleigh damping ratio which consisting of three type of formulations.
Thirdly, stable numerical integration techniques and realistic constitutive models of soil are the two important and necessary components of nonlinear seismic ground response analyses. Study in this thesis is only involved in nonlinear constitutive models of soil. NHT model is new and first attempt to model nonlinear stress-strain behavior of soil based on the hyperbolic tangent function. The backbone (stress-strain) curve and unloading, reloading curves are all conducted according to the basic standard hyperbolic tangent function. It is indicated that the NHT model can exhibit the soil dynamics. Moreover, NHT model is expressed in the simple form, in which the physical meaning is clear and straightforward. The unloading and reloading can start at the point even without standing in the backbone curve, and the only thing need to do for obtaining hysteresis loop is determination of shear strain and shear stress values at the beginning of unloading and reloading.
In addition, the implications for seismic codes implementation are presented. Application of five leading common used computer codes in ground seismic response is handled by creating simple homogeneous soil model. Exact solutions for body wave propagation through soil medium are carried out. The major emphasis of the research is to reduce confusions in the usage of procedures in practice and create relative clear guidelines so that the numerical analysis problem can be handled for those even non-expert users at currently available common used computer facilities. Furthermore,shear wave velocity inversion can determine a complex dynamic response of the soil column significantly affecting the in-depth and at surface ground motion. This response may be of practical interest in many geotechnical earthquake engineering problems such as the design of pile foundations and of critical buried structures. Considering the fact that in the Italian territory, especially in central and southern Italy, many historical centres are founded on large soft rock slabs overlying more deformable clay deposits, a two-layer system was established for seismic response of soil columns characterised by shear wave velocity inversion.
Last but not least, the recommendations and some further efforts which can be considered in the future research are summarized.
引文
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