Surface/ground waters could be polluted when rain-water and/or snow-melt water infiltrate through waste rock piles at mine sites and dissolve secondary minerals (salts) from rock surfaces. It is important to reduce solute loading by the optimal configuration of waste rock piles. This requires the proper definition and determination of the characteristic properties of waste rock piles in terms of metal leaching and, in particular, rate control mechanisms and scaling laws, and their dependence upon configuration variables. For revealing these characteristic properties this paper proposes a pile-scale C-Q relation: C = Cs(1 − e-P/Q), (P ≡ kλβψ), where C and Cs are respectively solute concentration and particle's saturation concentration, Q is the flow rate of the water through a waste rock pile, k represents the effective or average dissolution coefficient of a mineral specie from rock surfaces, β represents rock pile depth, λ represents the ratio of the sum of the surface areas of rocks to the volume that the rocks occupy, and ψ is the sum of the cross-sections of water-flow channels in a waste rock pile. The two characteristic properties revealed by the C-Q relation are: (1) P, the product of k, λ, β, and ψ (P ≡ kλβψ), which is the characteristic property of a waste rock pile in terms of metal leaching, named here the solute production potential; and (2) the ratio of P to Q, P/Q, a non-dimensional number, designated as α (α ≡ P/Q), named here the rate control quotient, which is the scaling law and the rate control mechanism indicator. The value of α quantitatively indicates what controls the rate of mineral dissolution, and it also relates smaller-scale metal-leaching testing results to their corresponding full scales. When α becomes small, say α < 0.5, the rate of solute production potential P becomes in control, and the solute loading is nearly independent of Q; when α becomes larger, say α > 2.5, solute concentration would become close to its saturation concentration Cs, and Q determines solute loading (that is, the solute loading is proportional to Q). When 0.5 < α < 2.5, both Q and P are in control, a mixed control mechanism. The 20 years of measurements of mine drainage chemistry from the main waste rock piles at the Equity Silver mine, BC, Canada, are used to illustrate how to determine the two characteristic properties P and α, and how well they are able to describe the waste rock piles in terms of metal leaching.