【作者】 潘晓东；

【导师】 蔡袁强；

【作者基本信息】 浙江大学 ， 岩土工程， 2004， 博士

【摘要】 本文运用随机动力有限元法，对可液化地基与堤坝在非平稳随机地震输入下进行了动力响应的可靠度分析。本文主要完成了以下工作： 1、根据《建筑抗震设计规范》(GB 50011-2001)的地震影响系数曲线，通过时间包络函数考虑地震的非平稳特性，利用加速度峰值等效原则迭代计算得到地面的加速度功率谱密度。然后运用半无限长剪切梁上的一维波动方程，将得到的地面加速度平稳功率谱密度作为地面边界上的虚拟稳态输入，通过迭代计算反演得到非线性分层地基下基岩的加速度平稳功率谱密度曲线，并采用与地面相同的时间包络函数考虑基岩地震动的非平稳性。通过以上方法建立了与抗震规范相对应的基岩非平稳地震动输入，为随机分析提供了输入基础。 2、基于饱和多孔介质的Biot动力固结方程，建立了一套μ-p格式的二维有限元分析方法。通过Hardin-Drnevich动力本构关系的等效线性化法考虑土体的非线性特性。利用动三轴的液化试验和震陷试验数据，将振动孔压与残余应变作为初应变引入Biot动力固结方程之中。通过对Blot动力方程右端项进行分离，使动力方程分为与地震加速度项相对应的零均值振动项和与振动孔压和残余位移相对应的均值项。在第一分离中引入虚拟激励法，考虑了地震的随机性，并通过概率平均法计算单元的动力模量、阻尼比、振动孔压及残余剪应变。通过以上方法建立了一套在非平稳随机地震输入下的、同时在时域和频域内计算的、考虑土体非线性的动力响应可靠度计算方法。通过有限元求解可计算在地震历时内各种动力响应的自功率谱密度和互功率谱密度。 3、采用一种半定量半定性的方法，验证了动力有限元程序的正确性，并通过不同范围下水平地基的动力响应分析，确定了动力计算的边界条件及边界范围。计算表明，当左右边界为所要研究地基范围的5倍以上时，采用简单的截断边界可满足动力计算的精度要求。 4、利用上述动力有限元程序分别对水平地基进行了总应力、不排水有效应力和排水有效应力随机动力响应分析，并通过4种不同的方法来计算地基的等效剪切模量、阻尼比、振动孔压和残余剪应力。结果表明，采用基于概率平均法的插值方法计算所得结果与确定性分析结果的均值较为一致，因此在随机动力分析中推荐使用该方法。 5、结合钱塘江防洪堤工程项目，对防洪堤典型断面进行了随机动力响应分析，展示了本文随机动力分析方法的工程意义。更多还原

【Abstract】 In this dissertation, the probabilistic seismic response of liquefiable foundations and earth dams was carried out via stochastic finite element method under nonstationary seismic loadings. The following work was finished mainly:1. The nonstationary power spectral density (PSD) of acceleration at the ground level was obtained by an iterative approach of equivalence of peak acceleration according to the response spectrum in the Chinese seismic code (GB 50011-2001). After the stiffness and damping ratio of each soil layer were evaluated by the equivalent linearization technique and by the use of the one-dimensional wave propagation function on the semi-finite shear beam, the earthquake motion at bedrock under nonlinear layered ground was evaluated iteratively. In this frame, the nonstationary seismic model according to the seismic code was presented It provides relatively reliable and accurate earthquake motion input at the bedrock for the stochastic seismic analysis.2. Based on the Biot dynamic consolidation equation of the saturated porous medium, a set of u-p form two-dimentional finite element methods was established. Hardin-Drnevich constitutive model was applied accounting for the nonlinearity of soil. The effect of pore pressure and residual strain on dynamic response was considered as initial strain base on the data of cyclic triaxial tests and seismic settlement tests. The right members of the Biot dynamic equation was divided into two parts. The first part was zero mean value vibration corresponding to earthquake acceleration corresponding and the second part was the mean value corresponding to initial strain. The pseudo excitation algorithm was introduced to the first part accounting for the stochastic nature of earthquake. The equivalent shear modulus, damping, excess pore water pressure and residual strain induced by seismic loading were estimated by the interpolation method based on probabilistic average approach. In this frame, the nonstationary dynamic probabilistic response of soil was obtained in frequency domain and time domain under stochastic seismic loadings. The results were presented as evolution self-PSD and cross- PSD of dynamic response.3. By a half-quantitative and half-qualitative method, the exactness of the dynamic finite element was verified. The boundary condition and boundary range were determined by the compared result of dynamic response of different range of foundation. The results show that the truncated boundary can meet the precision demand of the dynamic calculation when the boundary is 5 time as the range of the foundation to study.4. The stochastic dynamic response of level ground was carried out by total stress method, undrained effective stress method and drained effective method. Also, the performance of four techniques, using different approximation to estimate the equivalent peak value of shear stress and strain were investigated for the purpose to determine the equivalent shear modulus, damping, excess pore water pressure and residual strain induced by seismic loading, in which the equivalent peak value was computed in terms of its standard deviation and the corresponding peak factor. It is found that the interpolation method based on probabilistic average approach is appropriate compared to the mean value of deterministic method.5. The stochastic dynamic response of a typical section of embankment was analyzed in the project of Qiantang River anti-flood embankment. The results indicate that the analysis method put forward in this dissertation is of great practical importance in seismic design.更多还原