O. D. L. Strack

Modeling of Microscopic Mechanisms in Granular Material

Absract The computer program BALL has been used for the past several years to model and study the behavior of two – dimensional assemblies of discs. The main result of the study thus far, a qualitative description of the material behavior, is discussed. An attempt has been made to introduce measures that may be used in a future constitutive model. The main measures, a partitioned stress tensor, and a constraint ratio, which is related to the stability of the assembly, are introduced and illustrated for some numerical experiments with BALL.

Mean-field inelastic behavior of random arrays of identical spheres

Abstract We consider a random array of identical spheres that interact through noncentral contact forces. We assume that the displacement of a contact relative to a center may be calculated from the average strain of the aggregate. The normal component of the contact force is assumed to be Hertzian and the tangential component is assumed to be linearly elastic until frictional sliding occurs. We consider the response of the material in triaxial compression. For monotone deformations, we calculate the evolution of the contact distribution, the volume change, the stress—strain response, the plastic strain, and the strain hardening.

Analytic elements for multiaquifer flow

Abstract The objective of this paper is to present an analytic element formulation for groundwater flow in multiaquifer systems. Analytic element equations are presented for wells, line-sinks, and circular infiltration areas. Each analytic element is a solution to the governing system of differential equations, and thus simulates the leakage between aquifers exactly; the head, discharge, and leakage may be computed analytically at any point in the aquifer. Superposition of these analytic elements allows for the simulation of regional multiaquifer flow. A hypothetical example is presented of a system with three aquifers, a river network, and three pumping wells. It is demonstrated that the leakage between aquifers may vary significantly over short distances and that each aquifer has its own water divide.

Capture Zone Delineation in Two‐Dimensional Groundwater Flow Models

Procedures are presented for delineating capture zones of pumping wells. First, an algorithm is presented for determining the envelopes of the capture zones by the use of the locations of stagnation points. Second, it is discussed how the streamlines are determined that separate groundwater originating from different sources (the dividing streamlines). Third, a procedure is presented for constructing the boundary of the capture zone for any given time. The procedures are implemented in an analytic element code and are applied to groundwater flow systems that can be modeled with wells, line sinks, uniform flow, and areal infiltration.

Principles of the analytic element method

An overview of the development and current state of analytic element method, as well as a brief presentation of the principles on which the technique is based is presented in this article. Illustrations of a few representative analytic elements are also presented. A brief discussion is added of both rotational flow and transient flow. The latter two aspects of the method require further development before they are ready for implementation in computer programs and can be applied to the modeling of groundwater flow.

The superblock approach for the analytic element method

An approach, the superblock approach, is presented for increasing computational efficiency of analytic element models. The approach is based on computing the combined effect of functions using both asymptotic expansions and Taylor Series expansions. The superblocks are used to reduce both the computational effort required to determine the coefficients in the analytic element model and to reduce the effort expended in generating contour plots and streamlines. An application of flow is presented in an aquifer with one hundred thousand circular impermeable objects. The errors in the simulation are within the machine accuracy.

A multi-quadric area-sink for analytic element modeling of groundwater flow

Abstract It is shown that the approach presented by Strack (Strack, O.D.L., 1989. Groundwater Mechanics. Prentice Hall, New Jersey) for determining the discharge potential for an area-sink leads to a function that is unique except for an arbitrary constant. The approach is applied to a special area-sink, namely one with an extraction rate that varies inside a polygon as a multi-quadric interpolator (Hardy, R.L., 1971. Multiquadric equations of topography and other irregular surfaces. Journal of Geophysical Research 76, 1905–1915). The principle of over-specification presented by Jankovic and Barnes (Jankovic, I., Barnes, R., 1999a. Three-dimensional flow through large numbers of spheroidal inhomogeneities. Journal of Hydrology 226, 224–233), is used to obtain an approximate solution. Several examples are presented herewith.

Area sinks in the analytic element method for transient groundwater flow

In the analytic element method, regional groundwater flow is modeled by superposition of particular solutions to the governing differential equation. The domain of the solutions is the x, y plane with the possible exception of isolated points. The solutions are referred to as analytic elements and represent a feature of flow in the aquifer, such as a well or the leakage through an aquitard. The analytic element method was originally developed for regional steady groundwater flow. In this paper the method is extended to transient flow. Several transient analytic elements and a method of determining a transient solution are presented. The governing differential equation that is used is the heat equation in two spatial dimensions with a sink term. Solutions for a transient well and a transient line sink are available in the literature. Both have a discharge that is equal to zero before the starting time and has a constant value after the starting time. A solution for a transient area sink is presented that also has a constant strength after the starting time. The area sink is a polygon with an extraction inside that is constant in space. A validation of the approach presented here is obtained by comparison with an exact solution for a case of one-dimensional transient groundwater flow. The domain is semi-infinite with a prescribed head at one side. Initially, the water is at rest, and then the head is suddenly raised at the boundary. The use of the transient analytic element method is illustrated by an example model with analytic elements both for steady and for transient flow. The former elements represent the initial steady state. The transient elements simulate variations of the groundwater flow due to seasonal variations in recharge and pumping.

A mathematical model for dispersion with a moving front in groundwater

A new, non-Fickian, constitutive equation is presented for the mass flux due to macroscopic dispersion in porous media. This constitutive equation contains the classical term of the diffusive type as well as a new term that may be viewed as an inertia term. Combination of the constitutive equation with the mass balance equation for a conservative contaminant yields a set of four first-order partial differential equations in terms of the three components of the vector of dispersive mass flux and the concentration. For the case of longitudinal dispersion only, this system is reduced to a set of two first-order partial differential equations in terms of the convective and dispersive mass fluxes as the two unknown functions. The sets of differential equations are hyperbolic and can be used to simulate and predict the movement of the front of a contaminant plume at finite velocity. An expression of the velocity of the front is presented in terms of the Darcian velocity and the ratio of the two dispersion coefficients that enter into the model. The effect of the non-Fickian terms decreases for increasing times; the model reduces to the classical one as time increases. An exact solution is presented for the case of one-dimensional flow and compared with the results of simulated column experiments.

Some cases of interface flow towards drains

SummaryThe aim of the study, reported of in this paper, is to determine the shape and position of the interface which separates the fresh from the salt water in a coastal aquifer. In this aquifer, fresh water flows from land towards the sea because the head on the land is higher than on the seabottom. The upper boundary of the flow region, formed by the land surface and the seabottom has been approximated by a straight line.Firstly the problem is solved, by use of the method of conformal mapping and the hodograph, for the case that the head is constant along that part of the line which represents the land surface and also constant, but lower, on the part which represents the seabottom. Special attention is paid to the form and position of the interface when a drain is in operation in the fresh water region.The hodograph turns out to be multiple sheeted and contains internal branch points and poles. Therefore, a simple generalization of the Schwarz-Christoffel Integral is derived which maps such hodographs onto the upper half plane.Secondly it is shown that the solution can be generalized directly by superposition in the reference half plane. This permits the description of the flow case of an arbitrary number of drains. By superposition, also flow with drains and an arbitrary number of different levels in polders and dunes can be described.Thirdly the upconing of the interface under a drain is studied in more detail for a simple case.A test was run in a parallel plate model in order to verify some of the formulas for upcoming, derived in this paper. Test results and theory agree satisfactorily.