Robert L. Schiffman

A finite difference method for analyzing the compression of poro-viscoelastic media

SummaryThe progress of compression of a water saturated porous medium is derivable from the equation of continuity,Darcys law, and an appropriate effective stressdilation relationship. Theories of secondary consolidation assume that the effective stress-dilatation relationship is time-dependent. One form of this type of characterization is a system of linear viscoelastic models. The system chosen consists of an elastic element in series with an arbitrary number ofKelvin units. The formulation of this system is a differential-integral equation. The integral portions of the equation are a series of convolution integrals. A finite difference scheme is developed in which the single governing differential-integral equation is broken up into a system of equations of the heat conduction andEuler types. A stability theorem is proved.ZusammenfassungDas Zunehmen der Kompression von wassergesättigten, porösen Medien läßt sich aus der Kontinuitätsgleichung, demDarcyschen Gesetz und einer passenden Druck-Ausdehnungsbeziehung herleiten. Theorien einer sekundären Verdichtung nehmen an, daß die tatsächliche Druck-Ausdehnungsbeziehung zeitabhängig ist. Eine Form dieser Charakterisierungsart ist ein System von linearen, viscoelastischen Modellen. Das ausgewählte Model besteht aus einem elastischen Element in Serie mit einer beliebigen Anzahl vonKelvin-Einheiten. Formuliert wird dieses System als Differential-Integral-Gleichung. Es wird ein endliches Differenzenschema entwickelt, in dem die beherrschende gewöhnliche Differential-Integralgleichung in ein Gleichungssystem übergeführt wird, das aus WärmeleitungsundEuler-Gleichungen besteht. Ein Stabilitätstheorem wird bewiesen.

The Theory of One-Dimensional Consolidation of Saturated Clays: III. Existing Testing Procedures and Analyses

The successful calculation of the progress of consolidation requires that both the theory used to model the field problem and the material properties used by the theory must be appropriate and suitable. Thus the testing procedure must provide reliable and consistent information on the material behavior. Further, the test procedure must be accompanied by methods of analysis that will produce values of the material properties that are appropriate to the theory. This paper presents a summary of the existing laboratory methods that are used to determine the consolidation properties of soils. Emphasis is placed on the analysis of the test data. It is shown that all the methods that are currently used contain inherent simplifying assumptions. These methods are restricted in their applicability to problems where linear or constant material properties or both are good approximations to real behavior.

The consolidation of soft marine sediments

This paper outlines the governing relationships of nonlinear finite strain consolidation. A short review of current literature is presented. Nonlinear finite strain consolidation theory is applied to the analysis of the slow deposition of Gulf of Mexico Holocene sediments. It is shown that the conventional means of calculating rates of sediment accumulation are highly inaccurate. It is further shown that the state of effective stress and excess pore-water pressure, as calculated by nonlinear finite strain theory, is substantially different than when calculated by conventional Terzaghi-Frohlich theory.

A Bibliography of Consolidation

This is a citation bibliography of works dealing with the quasi-static theory of consolidation of soil, and rock, as at 1982.

Non-linear Finite Strain Consolidation of Soft' Marine Sediments

This paper presents an analytical procedure for hindcasting the genesis of a soft marine sediment which is consolidating under its own weight. The procedure is based upon the use of non-linear finite strain consolidation. This theory is reviewed. A formulation is developed which permits the computation of the progress of consolidation during the accumulation of a sediment column. A numerical procedure for solving the governing equation by the method of lines is outlined. The procedure is applied to the development of the geotechnical stratigraphy of Mississippi delta sediments. It is shown that an accurate calculation can be made of the present state of effective stresses and pore-water pressures. It is further shown that an accurate assessment of the present void ratio profile can be obtained.