• Analysis of Borehole Infiltration Tests Above the Water Table

      Stephens, Daniel Bruce; Neuman, Shlomo P. (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1980-03)
      Constant head borehole infiltration tests are widely used for the in situ evaluation of saturated hydraulic conductivities of unsaturated soils above the water table. The formulae employed in analyzing the results of such tests disregard the fact that some of the infiltrating water may flow under unsaturated conditions. Instead, these formulae are based on various approximations of the classical free surface theory which treats the flow region as if it were fully saturated and enclosed within a distinct envelope, the so- called "free surface." A finite element model capable of solving free surface problems is used to examine the mathematical accuracy of the borehole infiltration formulae. The results show that in the hypothetical case where unsaturated flow does not exist, the approximate formulae are reasonably accurate within a practical range of borehole conditions. To see what happens under conditions closer to those actually encountered in the field, the effect of unsaturated flow on borehole infiltration is investigated by means of two different numerical models: A mixed explicit - implicit finite element model, and a mixed explicit -implicit integrated finite difference model. Both of these models give nearly identical results; however, the integrated finite difference model is considerably faster than the finite element model. The relatively low computational efficiency of the finite element scheme is attributed to the large humber of operations required in order to reevaluate the conductivity (stiffness) matrix at each iteration in this highly nonlinear saturated -unsaturated flow problem. The saturated -unsaturated analysis demonstrates that the classical free surface approach provides a distorted picture of the flow pattern in the soil. Contrary to what one would expect on the basis of this theory, only a finite region of the soil in the immediate vicinity of the borehole is saturated, whereas a significant percentage of the flow takes place under unsaturated conditions. As a consequence of disregarding unsaturated flow, the available formulae may underestimate the saturated hydraulic conductivity of fine grained soils by a factor of two, three, or more. Our saturated -unsaturated analysis leads to an improved design of borehole infiltration tests and a more accurate method for interpreting the results of such tests. The analysis also shows how one can predict the steady state rate of infiltration as well as the saturated hydraulic conductivity from data collected during the early transient period of the test.
    • Investigations of stream-aquifer interactions using a coupled surface-water and ground-water flow model

      Vionnet, Leticia Beatriz; Maddock, Thomas, III; Goodrich, David C.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1997-01)
      A finite element numerical model is developed for the modeling of coupled surface-water flow and ground-water flow. The mathematical treatment of subsurface flows follows the confined aquifer theory or the classical Dupuit approximation for unconfined aquifers whereas surface-water flows are treated with the kinematic wave approximation for open channel flow. A detailed discussion of the standard approaches to represent the coupling term is provided. In this work, a mathematical expression similar to Ohm's law is used to simulate the interacting term between the two major hydrological components. Contrary to the standard approach, the coupling term is incorporated through a boundary flux integral that arises naturally in the weak form of the governing equations rather than through a source term. It is found that in some cases, a branch cut needs to be introduced along the internal boundary representing the stream in order to define a simply connected domain, which is an essential requirement in the derivation of the weak form of the ground-water flow equation. The fast time scale characteristic of surface-water flows and the slow time scale characteristic of ground-water flows are clearly established, leading to the definition of three dimensionless parameters, namely, a Peclet number that inherits the disparity between both time scales, a flow number that relates the pumping rate and the streamflow, and a Biot number that relates the conductance at the river-aquifer interface to the aquifer conductance. The model, implemented in the Bill Williams River Basin, reproduces the observed streamflow patterns and the ground-water flow patterns. Fairly good results are obtained using multiple time steps in the simulation process.
    • Modeling of Ground-Water Flow and Surface/Ground-Water Interaction for the San Pedro River Basin Part I Mexican Border to Fairbank, Arizona

      Vionnet, Leticia Beatriz; Maddock, Thomas, III; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1992)
      Many hydrologic basins in the southwest have seen their perennial streamflows turn to ephemeral, their riparian communities disappear or be jeopardized, and their aquifers suffer from severe overdrafts. Under -management of ground -water exploitation and of conjunctive use of surface and ground waters are the main reasons for these events.