Dynamics Of Karstification: A Model Applied To Hydraulic Structures In Karst Terranes

Abstract

To model the development of karst channels from primary fissures in limestone, a computer simulation of solutional widening of a fracture by calcite agressive water is proposed. The parameters defining the problem are the initial width a0 of the fracture, its length l, and the hydraulic gradient i driving water through it. The dissolution rates limestone determine how fast enlargement of the fractures proceeds. At a calcite concentration, c, far from equilibrium, the dissolution follows a first-order rate law, F(1)=α0(ceq-c); close to the equilibrium concentration, ceq, a slow fourth-order rate law F(4)=β0(ceq-c)4 is valid. The results show that, at the time of initiation, the water flow through the karst channels increases slowly in time until an abrupt increase occurs. After this moment of breakthrough, the channel enlarges rapidly and evenly over its entire length by first-order kinetics. Breakthrough times have been calculated for karstification under natural conditions for low hydraulic gradients as functions of a0, l, and i. Special attention is given to karstification in the vicinity of hydraulic structures where hydraulic gradients are high (>0.5) and channel lengths are below 200 m. We find that the breakthrough event will occur in less than 100 years, if: (i/l) > (5.3·10−8a0 −2.63PCO2 −0.77) where l is in m and a0 is in cm, (i/l) is given in m-1, and PCO2[atm] is the CO2 pressure of the water entering the fracture. After this event, the channels will widen to a width of about 1 cm within only 10 years, which can cause considerable leakage near or through hydraulic structures. Finally, critical values of the parameters i, l, a0, which give the conditions of failure in various types of hydraulic structures are discussed.