The behaviour of saturated, porous media under dynamic or quasi-static loads was first formulated by Biot (1941, 1960). For dynamic problems a simplification was recently proposed by one of the Authors. As the two formulations must coincide over a range of problems and as for slow transients both must be adequately represented by pure consolidation theory, this Paper examines the respective ranges of validity by an analytical study of a soil layer subject to a periodic surface force. The analysis also indicates under what conditions such extremes as undrained or quasi-static assumptions can be safely used. Results of the analysis are given in a non-dimensional, generally valid, form and should find practical application in assessing the the type of approximation that is applicable in new problems. Le comportement des milieux poreux saturés soumis à des charges dynamiques ou quasi statiques a été analysé pour la première fois par Boit (1941, 1960). Pour les problèmes dynamiques, une simplification a été récemment proposée par l'un des Auteurs. Comme les deux formulations doivent coincider pour une certaine gamme de problèmes et que, dans le cas de phénomènes transitoires lents, elles doivent toutes deux être représentées d'une manière correct par une théorie de consolidation pure, cet Article examine les zones respectives de validité en étudiant analytiquement une couche de sol soumise à une force supercielle péiodique. L'analyse indique également dans quelles conditions les hypothèses extrêmes de charges non drainées ou quasi statiques, peuvent être utilisés sans risque d'erreur. Les résultats de l'analyse sont donnés sous une forme non dimensionnelle, généralement valable, et devraient trouver leur application pratique dans l'évaluation du type d'approximation applicable à de nouveaux problèmes.

SUMMARYA series of shape functions analogous to Lagrange polynomials, but including an exponential decay term, are suggested as appropriate for elements which extend to infinity. The shape functions are applied to a number of examples, mainly of viscous flow, where the domain extends to infinity. Both explicitly integrated and numerically integrated elements are described. The technique is applicable to many problems where the domain is supposed to extend to infinity.

SUMMARYThe finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems-structural mechanics being only one of these. Boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits. In this survey of the field we show how such procedures can be utilized in conventional FEM context.

SUMMARYThe wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined. Appropriate boundary conditions are described, for finite and infinite boundaries. These equations are then presented in a variational form, which is used as a basis for finite and infinite elements. The elements are used to solve a wide range of unbounded surface wave problems. Comparisons are given with other methods. It is concluded that infinite elements are a competitive method for the solution of such problems.