Search

Copyright of Geotechnik is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The paper presents a comparative analysis of three systems of dynamic equations for fluid‐saturated solids: the exact equations and two simplified versions known as the u‐p approximations obtained by neglecting certain acceleration terms in the exact equations. The constitutive relations for the solid skeleton are written in the general anisotropic incrementally linear form without considering any specific constitutive model or a particular type of anisotropy. The dynamic equations are compared in relation to the existence of solutions in the form of plane harmonic waves. Emphasis is placed on finding conditions for the non‐existence or existence of growing waves whose amplitude increases in time or space as the wave propagates. The conditions are formulated in terms of the acoustic tensor of the skeleton and the compressibility of the pore fluid. In particular, it is shown that for a hyperelastic skeleton, the exact equations and one of the u‐p approximations do not have growing wave solutions, whereas the other u‐p approximation may have such solutions even if the skeleton is hyperelastic. [ABSTRACT FROM AUTHOR]

The numerical solution of dynamic problems for porous fluid‐saturated solids is often performed with the use of simplified equations known as the u‐p approximation. The simplification of the equations consists in neglecting some acceleration terms, which is justified for a certain class of problems related, in particular, to geomechanics and earthquake engineering. There exist two u‐p approximations depending on how many acceleration terms are neglected. All comparative studies of the exact and u‐p formulations are focused on the question of how well the u‐p solutions approximate those obtained with the exact equations. In this paper, the equations are compared from a different point of view, addressing the question of well‐posedness of boundary value problems. The exact equations must be hyperbolic and satisfy the corresponding hyperbolicity conditions for the boundary value problems to be well posed. The u‐p equations are not of the form to which the conventional definition of hyperbolicity applies. A slight extension of the approach makes it possible to derive hyperbolicity conditions as necessary conditions for well‐posedness for the u‐p approximations. The hyperbolicity conditions derived in this paper for the u‐p approximations are formulated in terms of the acoustic tensor of the skeleton. They differ essentially from the hyperbolicity conditions for the exact equations. [ABSTRACT FROM AUTHOR]