مروری بر تحلیل دینامیکی خطی محیط های متخلخل اشباع

در این مقاله، به مرور اهمّ مطالعات موجود پیرامون تحلیل دینامیکی محیط های متخلخل اشباع پرداخته شده است. ابتدا ضمن ارائه مختصر مبانی نظری و برخی معادلات اساسی حاکم در تئوری محیط های مزبور، ادبیات موضوع مبتنی بر رویکردهای مختلف تحلیل در دو دسته روش تحلیلی/نیمه تحلیلی و عددی تقسیم بندی شده است. سپس، پژوهش های در دسترس در هر دسته بر اساس سال ارائه طبقه بندی و گزارش شده است. با توجه به جامعه ی آماری گسترده ی روش های عددی در تحلیل محیط های متخلخل اشباع، این دسته روش ها به‌طور ویژه در دو حوزه ی حجمی و مرزی تفکیک شده است. در این راستا تحقیقات حاضر پیرامون روش های اجزای محدود و تفاضل محدود برای حوزه ی حجمی و روش های معادله انتگرال مرزی و اجزای مرزی برای حوزه ی مرزی ارائه شده است. همچنین، به لحاظ اهمیت دو چندان روش های مرزی در تحلیل این محیط ها، تسهیم مطالعات این حوزه با جزئیات بیشتر و با در نظر گرفتن ارکان اصلی آن انجام گرفته است. از جمع‌بندی ادبیات فنی می توان اذعان داشت روش اجزای مرزی همواره از رویکردهای محاسباتی مناسب برای تحلیل محیط‌ های متخلخل اشباع محسوب شده و استفاده ی کاربردی از آن به‌ویژه در مدل‌سازی عوارض توپوگرافی سطحی/زیرسطحی از چالش های موجود در حوزه ی ژئوتکنیک لرزه ای پیرامون تدقیق آیین‌نامه‌های طراحی به شمار می رود.

a review on dynamic analysis of linear saturated porous media

in this paper, the most important existing studies were reviewed on the dynamic analysis of the saturated porous media. first, a brief evaluation of theoretical expressions, essential equations, and the most important solutions was illustrated for the mentioned problem. then, by dividing the literature based on various analysis approaches into two categories of analytical/semi-analytical and numerical methods, the available researches were classified in each category to report according to the publication year. in recent decades, by increasing the power of computers besides the development of numerical approaches, researchers were eager to use them for analyzing wave propagation problems as well as predicting the real response of topographic features more than ever. in this regard, modeling of the porous soil media was generally done for the quasi-static analysis of the consolidation phenomenon. however, due to the complexity of the dynamic formulation of porous media, it is very difficult to solve this kind of problem analytically with traditional approaches. therefore, most of the studies to analyze the elastic porous media based on modern dynamic formulations were done with the help of numerical approaches, in which it became possible to perform the dynamic analysis of wave propagation models in saturated porous media derived from poro-elastodynamic theory. according to the formulation, the numerical methods can be usually divided into two general categories known as the domain and boundary methods. in the common domain methods, such as the finite element method (fem) and finite difference method (fdm), it was required to discretize the whole body including internal parts of the model, the surrounding boundaries, and defining absorbing boundaries. although the simplicity of domain methods makes them favorable for analyzing the seismic finite media, the models are complicated because of discretize the whole body and its boundaries at a considerable distance from the desired zone. this issue causes the number of elements as well as the required computational efforts to increase to reach accurate results, especially in a half-space soil medium. on the other side, in boundary methods which are mostly known today as the boundary element method (bem), by concentrating the meshes only around the boundary of the desired features, the automatic satisfaction of wave radiation conditions at infinity, reducing the volume of input data, and analysis time was remarkably achieved as well. also, the high accuracy of the obtained results was guaranteed due to the large contribution of analytical processes in solving various problems by bem. one main feature that made the bem very interesting for analyzing the poro-elastodynamic problems was its capability to obtain the half-space fundamental solutions by eliminating the meshes of far-field boundaries. this issue made it very comfortable to solve problems related to semi-infinite space. therefore, the bem presented a better manner for analyzing infinite/semi-infinite problems. by considering the high importance of boundary methods in analyzing the saturated porous media, the separation of studies was done in more detail in this field concerning its main elements. by reviewing the technical literature, it can be known that boundary methods can be divided into two main categories, direct and indirect approaches. in the direct method, all unknowns of the problem were calculated directly from the boundary integral equation (bie). however, in the indirect method, it is required to define the estimator functions according to the unknowns of the problems, which results in a simplified bem formulation. by looking at the recent studies, it is clarified that the bem was always considered a suitable computational approach for analyzing the saturated porous domains, especially in investigating the seismic surface / subsurface topographies features.