Explicit-solvent molecular dynamics simulations were applied to four pairs of amorphous silica nanoparticles, two pairs having a diameter of 2.0 nm and two pairs with diameter 3.2 nm. The silica nanoparticles were immersed in a background electrolyte consisting of Ca(2+) and Cl(-) ions and water and mean forces acting between the pair of silica nanoparticles were extracted at four different background electrolyte concentrations. The pH was indirectly accounted for via the ratio of silicon to sodium used in the simulations. Dependence of the interparticle potential of mean force on the center-of-mass separation and the silicon to sodium ratio (5:1 and 20:1) is demonstrated. A Si:Na(+) ratio of 5:1 gave more repulsive interparticle potentials and lower numbers of internanoparticle or "bridging" hydrogen bonds. Conversely a Si:Na(+) ratio of 20:1 yielded more attractive potentials and higher numbers of bridging hydrogen bonds. The nature of the interaction of the counterions with charged silica surface sites (deprotonated silanols) was also investigated. The effect of the sodium double layer on water ordering was observed. The number of water molecules trapped inside the nanoparticles was investigated, and at the highest background ionic concentrations were found to consistently behave in accordance with there being an osmotic pressure. This study highlights the effect of divalent (Ca(2+)) background ions on the interparticle potentials compared with previous work using monovalent (Na(+)) background ions. Mechanisms of coagulation and the stability of silica nanocolloids found from this work appear to be in agreement with findings from experiments described in the literature.