In the presence of dispersant molecules currently used in cement industry and based on polyethylene oxide (PEO) we found a strong discontinuous shear thickening (DST) at high volume fraction in suspensions of calcium carbonate particles. The transition was reversible and the critical shear rate and shear stress for which this instability appears are reported versus the volume fraction of particles. A model of repulsive forces between polymers, taking into account the thickness of the polymer layer and the density of adsorption on the surface of the particles, can explain the differences of critical stresses observed between these three dispersant molecules. In particular it explains why a small polymer densely adsorbed can be more efficient to repel the transition at higher stress than a larger molecule less densely adsorbed. Above the transition, we find that the suspension presents a special kind of stick-slip instability with even the presence of a negative shear rate under constant applied stress. A model is proposed which well predicts this regime by taking into account both the inertia of the apparatus and the viscoelasticity of the suspension.