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本文提出了一类计算饱和土层中震动孔隙水压力增长与消散的解析解.文中首先将大沙基因结理论与不排水条件下震动孔压增长模式相耦合,给出了描述自然排水条件下震动孔压长消的微分方程式;其次针对具有水平自由界面的饱和土层以及工业与民用建筑中大量存在的浅基础条件,并考虑到孔压增长模式的多样性以及起始孔压场的影响,采用了Sturm-Liouville系统以及Duhamel积分与多重Fourier展开,定出了分域表示的一类一般性解析解.进而考虑到地震波形态及其作用强度以及动孔压长消过程中土渗透特性与体积应变特性的变化,试图提出一个既能反映土材料特性又简单易用的半解析迭代算法,以期对饱和砂层震动孔压长消与液化分析能有所裨益.
In this paper, a class of analytical solutions to calculate the growth and dissipation of water pressure in a viscous pore in a saturated soil layer is presented. First, the genetic theory of large sands is coupled with the model of the growth of pore water pressure under undrained conditions, and the description of natural drainage is given. Differential equations for vibratory pore pressure and long-term elimination; secondly for shallow ground conditions in saturated soil layers with horizontal free interfaces and in industrial and civil buildings, taking into account the diversity of pore pressure growth patterns and the influence of initial pore pressure field Using the Sturm-Liouville system and the Duhamel and multiple Fourier expansions, a general analytical solution for the subdomain representations is devised. Considering the seismic wave morphology, its effect strength, and the soil permeation characteristics during the process of dynamic pore pressure reduction, The change of the volumetric strain characteristics attempts to propose a semi-analytical iterative algorithm that can reflect the characteristics of soil materials and is easy to use, so as to benefit the analysis of long-term vibration and saturation of saturated sand pores.