Precise Time - Integral Method For Time - Domain Solution Of Near - Field Fluctuation Problem For Saturated Two - Phase Media

A new time-domain method for wave propagation of the fluid-saturated porous media is developed by introducing the precise time-integration method. Some conclusions are obtained by analyzing the relevant characteristics of the method:1. On the basis of the precise time-integration method, a time-domain method for the wave propagation of the fluid-saturated porous media is proposed to describe the dynamic response of the fluid-saturated porous media with the formulation of solid phase displacement u and pore pressure p. The solid phase displacement u is computed by precise time-integration method and fluid pressure p is computed by backward difference method. The proposed method is verified by a standard example. Moreover, the proposed method is compared with Newmark algorithm that is proposed by Zienkiewicz. The verifications indicate that the proposed method with high computational precision and efficiency. Therefore, the method is capable of analyzing the dynamic response of the fluid-saturated porous media, reasonably.2. By analyzing the dynamic response of free field under seismic loading, the functions of proposed method were validated by elastic wave theory of two-phase medium. It indicates that this method is suitable for the complex wave problems of saturated two-phase medium. Thus, it is an efficient tool on wave propagation of the fluid-saturated porous media.3. On the basis of the precise time-integration method for wave problems of saturated two-phase medium, the trapezoidal integration, Guass integration and Simpson integration are used to calculate the integral term. And the calculations have no differences between various integrations, which indicate that the proposed method has higher calculation precision. Moreover, the precision deficiency of numerical integration(e.g. trapezoidal integration) can be made up in proposed precise time-integration method. When the Guass integration is utilized to calculate the integral term, the numbers of integral points have no influence on the calculated results. Therefore, the number of Guass integral points can be set as two in order to reduce calculation amount. The various numerical algorithm are used to calculate the pore pressure, such as Wilson-? method, Newmark-? method and backward difference method. The calculated results show almost same precise. In order to improve the calculated efficient, the backward difference method is adopted.4. The calculation results of the algorithm presented in this article can be convergent stably when the permeability coefficient is relative large(31.0 10 cm / s?? ?). This illustrates the validity of the presented algorithm. The larger the permeability coefficient is, the faster the calculation results converge. This is consist with the phenomenon in the dynamic consolidation that the larger the permeability coefficient is, the faster the pore fluid pressure dissipates and the less the consolidation time is needed. When the permeability coefficient is relative small(45.0 10 cm / s?? ?), the time needed to be convergent of the presented algorithm increases and the calculation results may even shakes violently. Strictly speaking, the calculation is not convergent in this case and the algorithm is no longer applicable. A large number of calculation results show that the algorithm is applicable when the permeability coefficient 4k5.0 10 cm / s?? ?. Therefore, the presented algorithm can be applied to solve the Near-field fluctuations and dynamic consolidation problem of gravel, sand and saturated silt with a large permeability coefficient.The researches in this paper indicate that the proposed time-domain method has higher calculated precision and efficient. The method can be used to calculate the wave problems of the fluid-saturated porous media. Furthermore, it is an efficient method to solve the wave problems of the fluid-saturated porous media.