二维弹塑性土层的波动数值模拟研究

STUDY ON NUMERICAL SIMULATION FOR WAVE MOTION IN TWO-DIMENSIONAL ELASTOPLASTIC SOIL LAYER

详细分析边界面模型,采用自适应多步积分、局部迭代和射线回退相结合的积分方法,给出边界面本构关系的数值实现过程。考虑土体的边界面本构模型,采用集中质量有限元法并结合中心差分与单边差分相结合的显式积分格式,编制求解二维弹塑性土层动力反应程序WSDP,利用该程序分别进行波源问题和散射问题的算例分析。讨论土体本构关系、土层应力历史状态、人工边界的设置以及为消除人工边界高频振荡而采用的黏性阻尼等因素对土层动力反应的影响。数值模拟结果表明:(1)与采用弹性本构相比,考虑土体塑性本构时,其位移反应幅值明显增大,且位移反应持续时间延长;(2)随着土体侧压力系数K的减小,位移响应延迟,傅氏谱增大,高频成分减少;(3)采用所设置的人工边界对土层进行弹塑性动力反应分析时,结果满足精度要求;(4)在一定范围内改变消除高频振荡的阻尼比对土层的弹塑性动力反应影响不大,如所取黏性阻尼过大将影响数值计算精度。

The bounding surface plasticity constitutive model of soil is introduced.An self-adaptive multistep integration procedure in conjunction with local iteration and radial return is employed in numerical implementation of the bounding surface model.The dynamic differential equations of the saturated-porous media are discretized in spatial and temporal using the lumped-mass finite element model and explicit integral method.Considering the bounding surface plasticity constitutive model of soil,the program,named as WSDP,is coded to analyse the dynamic elastoplastic responses of two-dimensional soil layer.The influences of the constitutive models of soil,the stress history states of soil,the artificial boundary and viscous damping are considered when the dynamic elastoplastic responses of soil layer are computed using the coded program.The following conclusions can be drawn.（1） The amplitude of elastoplastic displacement becomes larger than that of elastic case;and the duration of elastoplastic response becomes longer than that of elastic case;（2） The results for the cases of different coefficients of lateral earth pressure K are computed,respectively.The comparison of the results shows that the displacement response is delayed;the amplitude of Fourier spectrum is increased,and the component of high frequency is decreased with the decrease of K.（3） The computing accuracy satisfies the requirement when the dynamic elastoplastic responses of soil layer are analyzed by the artificial boundary.（4） The influence of damping ratio that eliminates the high-frequency oscillation on the dynamic elastoplastic responses of soil layer is not obvious if the damping ratio is confined to a limited range.It will be effected by the accuracy of result if the value of damping ratio is not proper.