SOIL-STRUCTURE INTERACTION

Abstract

Many analytical and numerical models of stream aquifer interaction have been developed in the past. Analytical expressions for obtaining aquifer responses to a damped sinusoidal flood wave passing in a fully penetrating stream was proposed by Cooper and Rorabaugh (1963). In order to use these solutions, a flood wave is required to be expressed in the form proposed by them. However, a flood wave may not conform to a sinusoidal wave. Though in most of the stream-aquifer interaction studies the stream has been assumed to completely penetrate the entire depth of an aquifer, in nature, a stream generally penetrates an aquifer partially. An extra resistance over the usual aquifer resistance to the flow is imparted by the curved flow lines near the partially penetrating stream. The bed of a partially penetrating stream may be comprised of fine sediments deposited by the stream. In such a case, the bed of the partially penetrating stream has a lower hydraulic conductivity than that of the aquifer material and this also offers an additional resistance to the flow. For these reasons, the theories developed for fully penetrating streams can not be applied to a partially penetrating stream with or without clogged bed. Treating the groundwater system as a linear system, Maddock (1972) and Morel Seytoux (1975) have proposed the use of algebraic technological coefficients or discrete kernel coefficients to solve many groundwater flow problems. Hantush (1965) has considered the resistance of a partially penetrating stream to analyze stream aquifer interaction due to a step rise in the stream stage. The concept of retardation coefficient/resistance or substitute-length as proposed by Hantush (1965) to model a semi-pervious stream has not been used so far in a discrete kernel frame-work for obtaining aquifer responses (piezometric head, rate of flow and cumulative volume of flow) to time varying stream stages. (i) In a sedimentary groundwater basin, it is often found that several aquifers separated by aquicludes or aquitards constitute the basin. There are only a few studies (Hemker 1984 and Mass 1986) which address the problem of a stream in a multi-aquifer system for steady flow. The transient behaviour of the interaction of a partially penetrating stream and multi-aquifer system has not been subjected to a detailed analysis so far. The potential of discrete kernel approach has not been fully exploited to the various situations of stream-aquifer interaction in a single or inulti aquifer system. The objective of the present thesis is to analyze interaction of a partially . penetrating stream with a single or multiple aquifer system during passage of a flood wave. Discrete kernels for finding evolution of piezometric surface, exchange of flow between the partially penetrating stream and the aquifer, and rate and volume of flow at any section in the aquifer have been generated. The stream stage perturbation can be discretized in two ways, viz., by a train of pulses or by a series of incremental steps. When the stream stage perturbation is approximated by train of pulses having uniform time-step duration, At, the relevant discrete kernel, <x(.), is defined as a(x,n,At) = U(x,nAt) - U(x,(n-l)At) and when the perturbation is approximated by a series of ramps having uniform time step duration, At, the relevant discrete kernel, 5(.), is defined as At 5(x,n,At) = fU(x,nAt-T)dx 0 where, U(.) is the unit response function for a selected aquifer response. These two types of discrete kernel coefficients have been generated. The discrete pulse kernel, a(x,n,At), is convoluted with the stream stage perturbations and the discrete ramp kernel, <5(x,n,At) is convoluted with the derivatives of the perturbations in order to get the aquifer responses to a time varying stream stage. The expressions for (ii) both types of kernels for different aquifer responses have been derived in case of fully penetrating as well as semi-pervious stream. The aquifer responses obtained using the two types of kernels have been found to compare well to those obtained using analytical solution given by Cooper and Rorabaugh (1963) for a symmetric flood wave in a fully penetrating stream. With respect to simulation of aquifer responses, the ramp kernels are found to have distinct advantages over the step kernels in terms of the accuracy and computational efficiency. The expressions for both type of discrete kernels for partially penetrating stream convert to those of fully penetrating stream as a particular case when the stream resistance is taken as zero. A salient feature of the developed discrete kernels are that they render the respective equations for various aquifer responses dimensionally homogeneous. For a fixed value of stream resistance, R, the cumulative volume of exchange of flow at the stream aquifer interface increases up to a certain time when a maximum is reached, then it decreases with increasing time till a minimum is attained after sufficiently long time. This minimum denotes the water volume permanently transferred to the aquifer storage. Both the maxima and minima for different values of R decrease as R increases. For a typical asymmetric flood wave of 100 hr duration with time to peak as 20 hr and the peak stage as 2.0 m passing in a semi-pervious stream, the maximum and the minimum volume of flow transferred to the aquifers are 69.1 m and 13.5 m respectively per unit length of the stream when the stream resistance is zero (a fully penetrating case). The reduction in the peak values are 65.3%, 47.9%, 37.9% and 18.7% and the minimum values are 97.8%, 94.1%, 88.9%, and 64.4% respectively for R equal to 250 m, 500 m, 750 m, and 2000 m respectively. "^Application of the models of stream-aquifer interaction requires the model parameters be known a priori. These parameters are (i) aquifer diffusivity in case of a fully penetrating stream, and (ii) aquifer diffusivity and stream resistance in case of a partially penetrating or a semi-pervious stream. It is possible to estimate these parameters, by analyzing the response of the aquifer to the (iii) fluctuation in the stream stage. This approach uses the natural excitation of the aquifer and has the advantage over the conventional pump-test as no energy is required to excite the aquifer in order to estimate the parameters. Aquifer diffusivity has been identified by many investigators using water level fluctuation at an observation well on account of the variation in the stream stage. Most of these studies assume linear or sinusoidal stream-stage variations. Stream stages that occur in nature may not always be approximated by such idealized variations. The problem of parameter identification has not been solved for a semi-pervious or partially penetrating stream so far. ^ In this thesis Marquardt (1963) algorithm has been used for the identification of the aquifer parameters and stream resistance. It has been observed that the algorithm is efficient and robust in the sense that it has fast convergence to the true minimum even with a poor initial guess for the parameter values. Methodologies have been developed to identify (1) aquifer diffusivity using stage variation in a fully penetrating stream and corresponding piezometric head variation, and (2) aquifer diffusivity and stream resistance in case of a partially penetrating stream using stream stage variation and corresponding piezometric head variation. In both the cases, the piezometric head variations on account of the variations in the stream stage have been obtained using respective discrete ramp kernels. y It has been observed that the present method predicts aquifer responses with better accuracy than that of Reynolds (1987). Reynolds has adopted the piezometric head variation in a well close to the stream (near well) as the stream stage and estimated the aquifer diffusivity using piezometric head at a distant well. The present study does not have such restriction and the aquifer diffusivity along with stream resistance was estimated using true stream stage variation and corresponding piezometric head variations at both the near and the distant well. The stream resistance has been observed to consist of two parts. The first part is contributed by the low conductivity material deposited at the bottom and (iv) banks of the stream and the second part is due to the curvature of the stream lines originating from the partially penetrating stream. In case of a partially penetrating and semi-pervious stream, the resistance assumed to be placed by the side of the hypothetical fully penetrating stream, should be computed as the sum of both parts of the stream resistance. Values of stream resistance estimated using the available data in the literature are found to increase with increasing distance away from the streamaquifer interface. This is in conformity with the available results in the literature (Chin 1991, and Genereux and Guardiario 1998). A mathematical model has been developed for the study of stream aquifer interaction in a multiple aquifer system in which reach transmissivity concept has been used with discrete kernel. Complete mathematical formulation in case of a system of three aquifers separated by two aquitards, is given. The formulation provides the basis for developing the model for any number of aquifers and aquitards combinations. With appropriate substitutions, the model reduces to two-aquifer and single aquifer system. Salient features of the model are (1) vertical transfer of flow through the aquitards can be accounted, storage in the aquitards has been considered negligible, (2) the stream has been assumed semi-pervious and recharging to the top aquifer. On account of this recharge, the other aquifers are recharged due to the flow occurring through the aquitards, (3) the model is applicable for any variation in the stream stage. The outputs of the model are: (i) temporal variation of the exchange of flow between the stream and the first aquifer, (ii) temporal and spatial variation of exchange of flow between the aquifers through the intervening aquitards, and (iii) the spatial and temporal variation of piezometric head in the aquifers. The model outputs have been validated using the three dimensional groundwater flow model, MODFLOW. MODFLOW source code was modified to get the cumulative exchange of flow. Good agreement between the model outputs and MODFLOW results have been obtained.