The main aim of this study is to develop a suitable method for the calibration and validation of mathematical models of large and complex aquifer systems. Since the calibration procedure depends on the nature of the model to be calibrated and since many kinds of models are used for groundwater, the question of model choice is broached first. Various aquifer models are critically reviewed and a table to compare them as to their capabilities and limitations is set up. The need for a general calibration method for models in which the flow is represented by partial differential equations is identified from this table. The calibration problem is formulated in the general mathematical framework as the inverse problem. Five types of inverse problems that exist in modeling aquifers by partial differential equations are identified. These are, to determine (1) parameters, (2) initial conditions, (3) boundary conditions, (4) inputs, and (5) a mixture of the above. Various methods to solve these inverse problems are reviewed, including those from fields other than hydrology. A new direct method to solve the inverse problem (DIMSIP) is then developed. Basically, this method consists of transforming the partial differential equations of flow to algebraic equations by substituting in them the values of the various derivatives of the dependent variable (which may be hydraulic pressure, chemical concentration or temperature). The parameters are then obtained by formulating the problem in a nonlinear optimization framework. The method of sequential unconstrained minimization is used. Spline functions are used to evaluate the derivatives of the dependent variable. Splines are functions defined by piecewise polynomial arcs in such a way that derivatives up to and including the order one less than the degree of polynomials used are continuous everywhere. The natural cubic splines used in this study have the additional property of minimum curvature which is analogous to minimum energy surface. These and the derivative preserving properties of splines make them an excellent tool for approximating the dependent variable surfaces in groundwater flow problems. Applications of the method to both a test situation as well as to real-world data are given. It is shown that the method evaluates the parameters, boundary conditions and inputs; that is, solves inverse problem type V. General conditions of heterogeneity and anisotropy can be evaluated. However, the method is not applicable to steady flows and has the limitation that flow models in which the parameters are functions of the dependent variable cannot be calibrated. In addition, at least one of the parameters has to be preassigned a value. A discussion of uncertainties in calibration procedures is given. The related problems of model validation and sampling of aquifers are also discussed.

Multiple aquifer systems similar to those that exist at coal gasification sites are complicated groundwater situations. In these types of systems, the aquifers are separated by aquitards through which interaction between aquifers can occur. The movement of the products of combustion into the coal seam and adjacent aquifers is a serious problem of interest. This dissertation presents two-dimensional finite element models for water flow and water quality in multiple aquifer systems. These models can be applied for general problems as well as the problems associated with the burned cavities in coal gasification sites. The Galerkin weightedresidual method is used in both models. Eight-noded isoparametric elements are used. Spatial numerical integration is performed using Gaussian quadrature. A weighted finite difference scheme is used, in both of them, for time integration. The two models are written in FORTRAN V for the CDC CYBER 175. They are applicable to one- or two-dimensional problems involving steady-state or transient flow. Each aquifer can have different initial conditions and boundary conditions. Boundary conditions, pumping rates, and the recharge can be specified as a function of time. The output of the flow program-nodal heads and velocity components is used as an input to the quality program. The numerical models were validated for simple problems that have available analytical solutions.

The water level in an open well tapping a confined formation is influenced by natural forces including the solid Earth tide (SET) and atmospheric pressure variation (APV). The spectral method is used to derive an analytical solution for well response to both the random and the periodic components of the combined SET and APV (CSA) forcings. Previously posed models for the individual SET and APV forcings are subsets of this more general model. An inverse theory and an algorithm are developed in order to provide improved results when using such models to estimate the hydraulic parameters associated with a given formation. A complex vector estimation criterion is used in developing a nonlinear, Gauss-Marquardt estimation algorithm. When compared to previous methods of fitting modulus and phase, the complex vector estimation methodology has less bias and variance, and is more robust. An examination of the response surface of the estimation criterion reveals that storativity (S) is relatively non-unique, and thus is not considered in the context of the parameter estimation problem. However, since there is little correlation between transmissivity (T) and S estimators, a good estimate for T is still possible independent of having knowledge of S. An estimate of T is possible only if the data contain sufficient information so that the analysis occurs within an identifiability window, which is defined with respect to the dimensionless transmissivity of the system. The CSA estimation methodology is compared to individual SET and APV schemes. The CSA scheme gives the greatest probability that sufficient information is contained in a data record so that T is identifiable. The results of applications to synthetic data indicate that the OEA scheme gives a T estimate with the most precision, and also that it requires collecting fewer observations.

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The most popular method in dynamic soil-structure interaction analysis is the finite element method. The versatility in problems involving different materials and complex geometries is its main advantage, yet FEM can not simulate unbounded domains completely. A hybrid method is proposed in this research, which models the near field (structure and surrounding soil) by finite elements and the far field by a continuum approach. The system is excited by monochromatic body waves (P and SV) propagating with oblique incidence and harmonic time dependence. The far field problem is solved using Thomson-Haskell formulation associated with the delta matrix technique. The soil profile does not contain any soft layer and the layers are assumed to be linearly elastic, isotropic, homogeneous and perfectly bonded at the interfaces. Two-dimensional (in-plane) formulation is considered and the analysis is performed on both k- and o-planes through time and spatial Fourier transforms of the field equations and boundary conditions. (Abstract shortened with permission of author.)

This study utilizes a Monte Carlo simulation to examine the performance of multivariate geometric moving average control chart schemes for controlling the mean of a multivariate normal process. The study compares the performance of the proposed method with a multivariate Shewhart chart, a multiple univariate cumulative sum (CUSUM) control chart, a multivariate CUSUM control chart and a multiple univariate geometric moving average control chart.

CSLIP2 (De Natale, 1987) is the only slope stability program that utilizes a "direction set" optimization routine in its search for the minimum safety factor. However, CSLIP2 which employs Powell's Conjugate Direction Method permits only the horizontal and vertical directions (x and y) to be used as the initial direction set. The efficiency of the existing search routine is improved by replacing the x-y coordinate directions with initial directions that are parallel to and perpendicular to the principal axis of the safety factor contours.

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