粘弹性层状地基的动态反分析
摘要
本文分析了层状地基的动态响应求解与岩土工程反分析现状，针对粘
弹性层状地基的动态材料识别这一目的，首先对粘弹性层状地基的动力响
应问题进行了较为系统的研究。在此基础上，利用系统识别方法进行了相
应的动力反分析研究。主要研究内容及研究成果概括如下：
1 针对粘弹性层状地基的动态响应研究现状，在国内外学者研究成
果的基础上，对粘弹性层状地基在动态荷载作用下的轴对称问题的响应进
行了系统研究。从基本方程出发，在频域推导了粘弹性层状地基的轴对称
问题的动态响应表达式，给出了动态荷载作用下的地表位移的解析解。并
进一步对该解的数值积分技术进行了研究，使被积式的双重振荡问题得到
了较好的解决。通过与相关文献结果进行对比而使本文方法与结果的正确
性及有效性得以验证。本文工作证明，频域求解方法是解决动力问题的行
之有效的途径，应用解析法求解粘弹性动力问题思路明确，表达清晰，简
洁有效。
2 时域分析采用有限元方法对动荷载作用下的粘弹性层状地基的轴
对称问题进行了求解与考证。由基本理论出发，推导了粘弹性地基的动力
平衡方程，采用Wilson-θ法对Burgers模型下的有限元动力方程进行了
求解。与相关文献的结果对比表明，利用本文方法对粘弹性层状地基进行
动态响应分析行之有效，计算过程稳定，精度较高。有限元方法适用性强，
是进行时域粘弹性动力问题求解的有效方法，尤其对于作用时间较短的
FWD荷载，边界范围的效应较小，易得到令人满意的结果。
3 对落锤式弯沉仪（FWD）的实测时程数据-荷载脉冲及位移脉
冲曲线进行了特征分析。对60毫秒采样区间末端处的位移通常为非零值
进行讨论、分析，提出了截断误差的校正方法，并对误差来源（如随机干
扰等）进行了分析讨论。在此基础上对大量的FWD实测脉冲时程曲线进
行了分析。根据FWD提供的地基系统的输入与输出双方面的时程数据，
通过Fourier积分变换将时域脉冲数据转换到频域，并求出路表频率响应
函数，为路面结构的频域反分析提供实际标准响应。
4 采用系统识别方法，分别在频域和时域对粘弹性层状地基的结构
层参数进行了较为深入的动态问题位移反演分析理论研究，并对方法与程
序的正确性进行了考证。本文反分析研究所用方法稳定性较好，收敛精度
较高，适用性也较强，能够较好地解诀材料性能识别问题。
5 面层采用与沥青材料较为接近的二参数蠕变柔量公式，基层及土
基采用复阻尼理论，对柔性路面结构的粘弹性性质进行描述。以FWD实
测结果作为系统的标准响应，采用系统识别方法对实际的路面工程结构进
行动态参数反演，取得了较为合理的结果。在实际路面工程中的应用算例
表明，本文方法正问题精度较高，反问题结果满足工程要求，为进一步研
究路面结构使用性能和承载能力评价提供了一种有效、实用的方法。
The research methods and engineering applications about the dynamic response of the multi-layered soil as well as the inverse-analysis of the soil structure both in domestic and abroad are discussed in this paper. Aimed at the identification problem of the material properties of the viscoelastic multi-layered soil under dynamical load, the problem of dynamic response of the viscoelastic multi-layered soil is studied systematically. Then, the system identification method is used to study the related dynamic inverse analysis. The major contents and research results are as follows:
1 Considering the state-of-the-art of dynamic response of the viscoelastic multi-layered soil, the response of the symmetric problem of the viscoelastic multi-layered soil due to dynamical load is studied systematically. The expression of dynamic response is derived from the fundamental equation in the frequency domain. An analytical solution of the surface displacement of the problem is given. Further more, the numerical integration technique is investigated to solve the problem of the double oscillation of the integrated equations. The computational results are verified by using the previous survey data.
2 Using the finite element method, the response of the symmetric problem of the viscoelastic multi-layered soil due to dynamical load is studied in time domain. The dynamic equation of the viscoelastic soil is derived and the Wilson - 6 method is used to solve the equation of Burgers model. The results are verified by comparing with the results in references. Numerical results show that the method is of high validity and precision. It can easily obtain a satisfactory result, especially for the short-time loads.
3 By a FFT (Fast Fourier Transformation), the falling weight deflectometer (FWD) data, namely, the load pulse and displacement pulse of the tested curve, is transformed from the time domain to the frequency domain. Then, dynamic analysis is performed to obtain the characters of the tested soil. It is discussed and analyzed why usually, in the end of 60 millisecond sampling area, the data of the displacement is not zero. After discussed and analyzed, a new method is suggested to correct the truncation error. Then, a number of FWD data are analyzed.
4 Using the system identification method, a displacement depended inverse analysis of the parameters of the viscoelastic multi-layered soil has been done in the time
domain and the frequency domain, respectively. The validity of the method is verified by several examples. Numerical result shows the method is of good stability and high accuracy, and reliable to identify the material properties.
5 A two-parameter creep compliance formulation is utilized to characterize the viscoelastic behavior of the asphalt pavement surface layer. And the properties of the base and the subgrade adopted the complex damping theory. Based on the FWD data, the system identification method figures out the dynamic parameters of a real pavement structure. The computational parameters are reasonable to the engineering expectation. It shows that the dynamic analytical model here is suitable to the pavement structure and the method is of validity to the pavement identification problems.
弹性层状地基的动态材料识别这一目的，首先对粘弹性层状地基的动力响
应问题进行了较为系统的研究。在此基础上，利用系统识别方法进行了相
应的动力反分析研究。主要研究内容及研究成果概括如下：
1 针对粘弹性层状地基的动态响应研究现状，在国内外学者研究成
果的基础上，对粘弹性层状地基在动态荷载作用下的轴对称问题的响应进
行了系统研究。从基本方程出发，在频域推导了粘弹性层状地基的轴对称
问题的动态响应表达式，给出了动态荷载作用下的地表位移的解析解。并
进一步对该解的数值积分技术进行了研究，使被积式的双重振荡问题得到
了较好的解决。通过与相关文献结果进行对比而使本文方法与结果的正确
性及有效性得以验证。本文工作证明，频域求解方法是解决动力问题的行
之有效的途径，应用解析法求解粘弹性动力问题思路明确，表达清晰，简
洁有效。
2 时域分析采用有限元方法对动荷载作用下的粘弹性层状地基的轴
对称问题进行了求解与考证。由基本理论出发，推导了粘弹性地基的动力
平衡方程，采用Wilson-θ法对Burgers模型下的有限元动力方程进行了
求解。与相关文献的结果对比表明，利用本文方法对粘弹性层状地基进行
动态响应分析行之有效，计算过程稳定，精度较高。有限元方法适用性强，
是进行时域粘弹性动力问题求解的有效方法，尤其对于作用时间较短的
FWD荷载，边界范围的效应较小，易得到令人满意的结果。
3 对落锤式弯沉仪（FWD）的实测时程数据-荷载脉冲及位移脉
冲曲线进行了特征分析。对60毫秒采样区间末端处的位移通常为非零值
进行讨论、分析，提出了截断误差的校正方法，并对误差来源（如随机干
扰等）进行了分析讨论。在此基础上对大量的FWD实测脉冲时程曲线进
行了分析。根据FWD提供的地基系统的输入与输出双方面的时程数据，
通过Fourier积分变换将时域脉冲数据转换到频域，并求出路表频率响应
函数，为路面结构的频域反分析提供实际标准响应。
4 采用系统识别方法，分别在频域和时域对粘弹性层状地基的结构
层参数进行了较为深入的动态问题位移反演分析理论研究，并对方法与程
序的正确性进行了考证。本文反分析研究所用方法稳定性较好，收敛精度
较高，适用性也较强，能够较好地解诀材料性能识别问题。
5 面层采用与沥青材料较为接近的二参数蠕变柔量公式，基层及土
基采用复阻尼理论，对柔性路面结构的粘弹性性质进行描述。以FWD实
测结果作为系统的标准响应，采用系统识别方法对实际的路面工程结构进
行动态参数反演，取得了较为合理的结果。在实际路面工程中的应用算例
表明，本文方法正问题精度较高，反问题结果满足工程要求，为进一步研
究路面结构使用性能和承载能力评价提供了一种有效、实用的方法。
The research methods and engineering applications about the dynamic response of the multi-layered soil as well as the inverse-analysis of the soil structure both in domestic and abroad are discussed in this paper. Aimed at the identification problem of the material properties of the viscoelastic multi-layered soil under dynamical load, the problem of dynamic response of the viscoelastic multi-layered soil is studied systematically. Then, the system identification method is used to study the related dynamic inverse analysis. The major contents and research results are as follows:
1 Considering the state-of-the-art of dynamic response of the viscoelastic multi-layered soil, the response of the symmetric problem of the viscoelastic multi-layered soil due to dynamical load is studied systematically. The expression of dynamic response is derived from the fundamental equation in the frequency domain. An analytical solution of the surface displacement of the problem is given. Further more, the numerical integration technique is investigated to solve the problem of the double oscillation of the integrated equations. The computational results are verified by using the previous survey data.
2 Using the finite element method, the response of the symmetric problem of the viscoelastic multi-layered soil due to dynamical load is studied in time domain. The dynamic equation of the viscoelastic soil is derived and the Wilson - 6 method is used to solve the equation of Burgers model. The results are verified by comparing with the results in references. Numerical results show that the method is of high validity and precision. It can easily obtain a satisfactory result, especially for the short-time loads.
3 By a FFT (Fast Fourier Transformation), the falling weight deflectometer (FWD) data, namely, the load pulse and displacement pulse of the tested curve, is transformed from the time domain to the frequency domain. Then, dynamic analysis is performed to obtain the characters of the tested soil. It is discussed and analyzed why usually, in the end of 60 millisecond sampling area, the data of the displacement is not zero. After discussed and analyzed, a new method is suggested to correct the truncation error. Then, a number of FWD data are analyzed.
4 Using the system identification method, a displacement depended inverse analysis of the parameters of the viscoelastic multi-layered soil has been done in the time
domain and the frequency domain, respectively. The validity of the method is verified by several examples. Numerical result shows the method is of good stability and high accuracy, and reliable to identify the material properties.
5 A two-parameter creep compliance formulation is utilized to characterize the viscoelastic behavior of the asphalt pavement surface layer. And the properties of the base and the subgrade adopted the complex damping theory. Based on the FWD data, the system identification method figures out the dynamic parameters of a real pavement structure. The computational parameters are reasonable to the engineering expectation. It shows that the dynamic analytical model here is suitable to the pavement structure and the method is of validity to the pavement identification problems.
引文
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