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of infinite extent because no boundaries are contacted. <br />Numerical simulations are useful for evaluating more <br />complex flow systems such as heterogeneous or aniso- <br />tropic hydraulic- conductivity distributions, multiple <br />boundary conditions, and transient conditions. Numer- <br />ical methods may be required during advanced stages <br />of mine planning when more detailed geologic and <br />hydrologic data are available for a site (Marinelli and <br />Niccoli, 2000). Analytical and numerical methods can <br />be coded into computer programs to facilitate their <br />use. <br />Both analytical and numerical simulation <br />methods were used in this study to evaluate the steady - <br />state (time - invariant) effects of mining aggregate on <br />water -table conditions. A steady -state two- dimen- <br />sional analytical solution to the ground -water flow <br />equation by Marinelli and Niccoli (2000) and a steady - <br />state one - dimensional analytical solution derived <br />during this study were used to estimate the extent of <br />drawdown around a mine in a homogeneous, isotropic <br />aquifer of infinite extent. The U.S. Geological Survey <br />modular ground -water model, MODFLOW -2000 <br />(Harbaugh and others, 2000), was used to evaluate <br />steady -state effects of aggregate mining under more <br />complex hydrogeologic conditions. <br />The steady -state two - dimensional analytical <br />solution of Marinelli and Niccoli (2000) estimates <br />Center <br />Of Pit <br />Mine Pit hp +— Q <br />F <br />rp <br />radial ground -water flow toward a circular mine pit. <br />The analytical solution for head in the aquifer adjacent <br />to a circular pit of radius rp is given as: <br />z <br />h= h 2+ W r.21n r_ r- 2 rp (2) <br />P Kit p 2 <br />where <br />h is saturated thickness above the pit base at r (radial <br />distance from pit center) [L], <br />hp is saturated thickness above the pit base at rp (at <br />the mine wall) [L], <br />W is distributed recharge flux [LfF], <br />Kh is horizontal hydraulic conductivity of <br />surrounding geologic materials [UT], <br />r; is radius of influence (maximum extent of the <br />cone of depression) [L], <br />r is radial distance from pit center [L], <br />rp is effective pit radius [L] (fig. 3). <br />Given input values of hp, W, Kh, rp, and initial <br />(premining) saturated thickness above the pit base <br />(h = ha), the radius of influence (r;) can be determined <br />through iteration by setting r equal to rr . Once ri is <br />W <br />1 1_1 1 <br />ho—h <br />h Kh ho <br />No -Flow Boundary <br />Radial Distance from Center of Pit <br />rj <br />Figure 3. Conceptual diagram of the Marinelli and Niccoli analytical solution <br />(modified from Marinelli and Niccoli, 2000). <br />GROUND -WATER HYDRAULICS AND MATHEMATICAL METHODS 7 <br />