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Numerical simulations of the water dissolution of a random ternary solid are presented. The three elements represent silica, soluble oxides (alkalis and boron) and quasi-insoluble oxides (Al2O3, ZrO2, Fe2O3, …). The soluble species are dissolved immediately when they are in contact with the solution. Their proportion is kept below the percolation threshold. For the other species, one introduces a model of dissolution-recondensation. It is shown that the dissolution rate constants should be dependent on the bonding environment in order to include surface tension. The condensation fluxes are proportional to the concentration of each species in solution. In the dynamic regime (no recondensation), one observes the congruent dissolution of silica and soluble species, after a short initial phase of selective extraction of the soluble species. The common rate of dissolution decreases with the proportion of insoluble species and increases sharply with that of soluble species. This is mainly due to the formation of a porous hydrated layer whose active surface area increases markedly with the proportion of soluble species. In the static regime (finite solution volume), the equilibrium solubility of silica decreases with the proportion of insoluble species and is practically independent of the proportion of soluble species. The porous hydrated layer is rearranged and almost free of soluble species. The ripening of the surface layer makes it protective and inhibits further extraction of the soluble species. These results are in general agreement with the experimental observations on the dissolution of durable glasses.