Before the Richards equation can be used to simulate the flow of moisture through a soil it is necessary to estimate the water capacity and hydraulic conductivity functions which appear as coefficients. We present four parameter identification methods and one direct method for estimating these hydraulic properties. For the sample problem considered, the parameter identification method which used cumulative discharge data to estimate water capacity and hydraulic conductivity performed the best in predicting water content as a function of depth and time during drainage.
Abstract.A slender, inextensible elastic rod is acted upon by a twisting couple and an axial load. The position of the rod's centerline is determined by two fourth-order, coupled, nonlinear boundary value problems, each of which contains two eigenparameters. These equilibrium equations admit the trivial solution for all values of the eigenparameters, i.e., for any axial load and any twisting couple. The linearized equilibrium equations have a countable number of eigencurves. Through using the implicit function theorem for Banach spaces it is shown that from each of the eigencurves of the linear problem there bifurcates a two-parameter sheet of nontrivial solutions of the nonlinear equilibrium equations.
An exact mathematical solution is obtained for two‐dimensional steady infiltration from a line source into an inclined porous medium with an impermeable lower boundary. Unsaturated hydraulic conductivity is assumed to be an exponential function of pressure head. Equations for a stream function and the pressure head are developed and stream lines and contours of constant pressure head are plotted for a sandy soil and a clay soil using inclinations of 5° and 20° from horizontal.
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