We present a theoretical investigation of the titratable charge of clays with various structural charge (sigma(b)): pyrophyllite (sigma(b) = 0 e.nm(-2)), montmorillonite (sigma(b) = -0.7 e.nm(-2)) and illite (sigma(b) = -1.2 e.nm(-2)). The calculations were carried out using a Monte Carlo method in the Grand Canonical ensemble and in the framework of the primitive model. The clay particle was modeled as a perfect hexagonal platelet, with an "ideal" crystal structure. The only fitting parameters used are the intrinsic equilibrium constants (pK(0)) for the protonation/deprotonation reactions of the broken-bond sites on the lateral faces of the clay particles, silanol, =SiO- + H+ -> =SiOH, and aluminol, =AlO-1/2 + H+ -> =AlOH+1/2. Simulations are found to give a satisfactory description of the acid base titration of montmorillonite without any additional fitting parameter. In particular, combining the electrostatics from the crystal substitutions with ionization constants, the simulations satisfactorily catch the shift in the titration curve of montmorillonite according to the ionic strength. Change in the ionic strength modulates the screening of the electrostatic interactions which results in this shift. Accordingly, the PZNPC is found to shift toward alkaline pH upon increasing the permanent basal charge. Unlike previous mean field model results, a significant decrease in PZNPC values is predicted in response to stack Formation. Finally, the mean field approach is shown to be inappropriate to study the acid base properties of clays.