A model of karstification in the vicinity of hydraulic structures
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Hydrogeological Processes in Karst Terranes
To model the development of karst channels from primary fissures in limestone a computer simulation of solutional widening of a fracture by calcite aggressive water is suggested. The parameters defining the problem are the initial width a0 of the fracture, its length 1 and the hydraulic gradient i driving water through it. The dissolution rates of limestone determine how fast enlargement of the fractures proceeds. At a calcite concentration c far from equilibrium they follow a first order rate law F(1) = ap(ceq ~ c); close to the equilibrium concentration c a slow fourth order rate law pw = /3(c — c)4 is valid. The results show that at the time of initiation the water flow through theTcarst 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 , 1 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 after less than 100 years, if (i/1) > 1.1 • 10"7 a0"263 PCo2"0'55, 1 is in m and a0 in cm; (i/1) is given in m . PCo2 [atm] is the C02 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. Finally, we discuss critical values of the parameters i, 1, a0, which give the conditions of failure in various types of hydraulic structures.
Dreybrodt, W., "A model of karstification in the vicinity of hydraulic structures" (1990). KIP Articles. 6554.