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Front Range mountains generally are steep. Recharge
<br />to the fractured crystalline -rock aquifer has been esti-
<br />mated to range from 0 to 21 percent of precipitation
<br />with an average of 3.2 percent (Hofstra and Hall,
<br />1975) to 10 percent (Mueller, 1979).
<br />In the Colorado Front Range, rock quarries typi-
<br />cally are mined dry (Langer, 2001). Although quarries
<br />may penetrate the water table, the discharge rate to
<br />quarries commonly is less than the rate of evaporation,
<br />and active dewatering measures are not needed. The
<br />quarry may drain freely. To produce aggregate, the
<br />rock is first drilled and blasted. Blasting commonly
<br />breaks the rock into pieces suitable for crushing, and
<br />the blasted material is extracted using conventional
<br />earth- moving equipment such as bulldozers, front
<br />loaders, and track hoes. Material is transported, either
<br />by truck or conveyor, from the mining face to the
<br />processing plant where it is crushed, washed, and
<br />sorted by size.
<br />GROUND -WATER HYDRAULICS
<br />AND MATHEMATICAL METHODS
<br />To evaluate the effects of aggregate mining on
<br />the surrounding water table, ground -water flow was
<br />simulated with analytical and numerical solutions to
<br />the ground -water flow equation. A general form of the
<br />equation describing transient (time - varying) three -
<br />dimensional ground -water flow can be written as
<br />(Konikow and Grove, 1977; McDonald and Harbaugh,
<br />1988):
<br />a(bxY ax ) a(WY ay A
<br />ax ay (1)
<br />a(bxz aZ � _ A + aZ - Sat + W(x, y, Z, 0
<br />where
<br />Kr is aquifer hydraulic conductivity in the
<br />x- direction (CI T),
<br />Kv is aquifer hydraulic conductivity in the
<br />y- direction (L2/T),
<br />K- is aquifer hydraulic conductivity in the
<br />z- direction (L2/T),
<br />b is aquifer saturated thickness (L),
<br />h is hydraulic head (L),
<br />S is storage coefficient (dimensionless),
<br />W is volumetric flux per unit area from a hydrologic
<br />source or sink as a function of location and
<br />time (LJT),
<br />x,y,z are Cartesian coordinates, and
<br />t is time (T).
<br />This equation assumes compressible fluid of
<br />constant density is flowing through a heterogeneous
<br />anisotropic aquifer according to Darcy's law (Fetter,
<br />1994). It also assumes the principal axes of the
<br />hydraulic conductivity tensor are aligned with the x, y,
<br />and z coordinate axes, respectively (McDonald and
<br />Harbaugh, 1988). Additional details of the ground-
<br />water flow equation and its derivation can be found in
<br />numerous texts and reports (Freeze and Cherry, 1979;
<br />Lohman, 1979; Huyakorn and Pinder, 1983;
<br />McDonald and Harbaugh, 1988; Domenico and
<br />Schwartz, 1990; Anderson and Woessner, 1992; Fetter,
<br />1994).
<br />The ground -water flow equation can be solved
<br />for the dependent variable head (h) by analytical or
<br />numerical methods. Analytical solutions use algebraic
<br />methods to derive closed -form solutions to the ground-
<br />water flow equation, whereas numerical solutions use
<br />finite- difference or finite - element numerical methods
<br />to solve the ground -water flow equation. Analytical
<br />solutions to the ground -water flow equation are most
<br />useful for evaluating simplified ground -water systems
<br />and often assume a homogeneous and isotropic
<br />hydraulic - conductivity distribution, horizontal flow,
<br />and infinite horizontal extent or limited boundary
<br />conditions. Analytical methods can be useful for esti-
<br />mating mine inflows and drawdowns during initial
<br />stages of mine planning when site - specific data may
<br />not yet be available (Marinelli and Niccoli, 2000). The
<br />applicability of an analytical solution depends on the
<br />extent to which the real problem under consideration is
<br />consistent with the simplifying assumptions of the
<br />analytical solution. Analytical solutions that assume
<br />infinite horizontal extent can be useful in predicting
<br />drawdown in real aquifers of finite extent when aquifer
<br />boundaries lie beyond the cone of depression in the
<br />water table (area of influence) caused by the pit. When
<br />boundaries he outside the area of influence, the aquifer
<br />within the area of influence responds as though it were
<br />6 Analytical and Numerical Simulation of the Steady -State Hydrologic Effects of Mining Aggregate in Hypothetical Sand- and - Gravel
<br />and Fractured Crystalline -Rock Aquifers
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