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determined, h can be calculated for any radial distance vated into a steep hillside such as in the mountainous <br /> from the pit, and drawdown can be calculated as part of the Front Range area. The derivation of the <br /> ho—h.In addition, the inflow rate, Q [Lj/T], through one-dimensional solution is similar to the Marinelli <br /> the pit wall can be calculated as: and Niccoli (2000) solution, but the mine is repre- <br /> sented as a straight line along a hillside rather than a <br /> Z circular pit. The mine in this situation intercepts only <br /> Q = Wn(r; —r; ) (3) the upgradient ground water within the hillside. <br /> Ground-water flow toward the mine at distance x <br /> upgradient from the mine wall can be expressed as: <br /> The analytical solution of Marinelli and Niccoli <br /> (2000) is valid for ground-water flow systems that dh <br /> meet the following assumptions: Q =K,,h— (4) <br /> • The geologic materials are homogeneous and <br /> dx <br /> isotropic; <br /> where <br /> • Ground-water flow is steady state,unconfined, hori- <br /> zontal, radial, and axially symmetric; <br /> Q is flow per unit length of the mine [L2/T], <br /> • Recharge is uniformly distributed at the water table Kh is horizontal hydraulic conductivity of <br /> and all recharge within the radius of influence is surrounding geologic materials [L/T], <br /> captured by the pit; h is saturated thickness above the mine base at <br /> distance x from the mine wall [L], and <br /> • Pit walls are approximated as a right circular x is distance upgradient from mine wall [L]. <br /> cylinder; If all ground-water flow to the mine is assumed <br /> • The static premining water table is approximately to originate from uniform distributed recharge (W <br /> horizontal; and within the drawdown distance of influence (xi) of the <br /> mine,then flow toward the mine also can be expressed <br /> • The base of the pit is coincident with the base of the as: <br /> aquifer, and there is no flow through the pit <br /> bottom. Q= W(x; —x) (5) <br /> Marinelli and Niccoli (2000) also present an <br /> analytical solution for upward ground-water flow Substituting equation 5 into equation 4 and inte- <br /> through the bottom of a pit that partially penetrates an grating from the mine wall to distance x gives: <br /> aquifer. <br /> However, inflow to the bottom of a pit is not W X h (6) <br /> considered in this report because (1) analytical solu- K f(xi —x)dx = f hdh <br /> tions are used only to calculate hydraulic head at the n o n„, <br /> water table, which is independent of ground-water <br /> flow through the mine bottom in the solution, (2)the where <br /> bottom of aggregate mines in sand-and-gravel aquifers <br /> in the Front Range area generally are near the base of <br /> the aquifer, and(3)hydraulic conductivity of fractured is saturated thickness above the mine base at the <br /> mine <br /> crystalline-rock aquifers generally becomes exceed- <br /> ingly small with depth,which limits inflow to the mine Carrying out the integration leads to an analyt- <br /> bottom. For pits that do not meet these conditions, ical solution for head in the aquifer adjacent to a linear <br /> consideration of flow to the mine bottom may be mine that is given as: <br /> important. <br /> A steady-state, one-dimensional analytical solu- h = h ` + [2x;x—x2 (7) <br /> tion is derived for ground-water flow to a nine exca- 1i <br /> 8 Analytical and Numerical Simulation of the Steady-State Hydrologic Effects of Mining Aggregate in Hypothetical Sand-and-Gravel <br /> snnl Cr�M...w.i/`.,.M.Il:ww_Gww4 Aw..:iwrr. <br />