道路结构型地层瑞利波相速度频散曲线的完整求取
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摘要
研究在实数域如何完整地求取道路结构型地层的瑞利波频散曲线。在以往研究工作的基础上采用附加层法,即假定原模型的最底层介质厚度为有限,再在其下部添加一个与表层介质物性相同的半无限空间,可使原复数域的求解问题转化到实数域进行,则利用瑞利波频散方程,用二分法可得原模型的多模式相速度频散曲线。在采用附加层法进行计算时,一般假定的层厚度较大,会出现高频数值溢出现象。为此,利用二分法的特点,当计算过程中数值趋于较大时,采用较小的有限值进行替代,并且保证不改变原计算结果的正负特性,避免传递矩阵法计算中高频数值的溢出。对2个假定的三层介质模型进行模拟计算,结果表明原模型瑞利导波曲线与附加层法的计算结果完全吻合,同时附加层法计算出了高频区域泄漏波模式的相速度频散曲线,从而验证了附加层法、高频溢出处理方法的正确性和可行性。
How to obtain the whole dispersion curves of Rayleigh waves for pavement systems in real domain was discussed.A new method,namely,appending layer method based on the past research was proposed.The last layer’s thickness of original model was supposed finite,and an infinite half space was added with the original model,and the adding layer’s characteristics were the same as the surface layer.Then,a complex domain problem was translated into a real domain problem.So,multimode dispersion curves could be obtained by Rayleigh waves’ equation and bisection method.The last layer’s thickness of original model was chosen to be very big when appending layer method was used.So,numerical overflow in high frequencies would appear.The characteristics of bisection method to avoid numerical overflow in transmission matrix approach were utilized.When an intermediate calculating value was very big,a small finite value would substitute it,and the sign of original calculating results would not be altered.The Rayleigh dispersion curves of two models were calculated.According to the modeling results,the guided wave curves of original model are consistent with the appending layer methods’.And phase velocity curves of Rayleigh leaky mode waves are also calculated in high frequency by appending layer method.All of these prove that appending layer method and disposition of numerical overflow are correct and feasible.
引文
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