The rate of dewatering will be contingent on the stratigraphy (correctly stated above), the location of the water table before and after dewatering and the type of excavation bracing that is used. Equally important is the tendency for you to develop the "quick" condition owing to hydraulic exit gradients, which may steer the contractor toward well points or deep wells to provide a stable dewatered subgrade.
Consider the flow path for a sheet-pile bracing design - much longer than the flow path for soldier pile and lagging. This would factor into the rate of dewatering.
Once you have some idea on the stratigraphy and the likely dewatering methods, you would then evaluate the drawdown that would likely be realized beneath the adjacent structure(s). With drawdown, the effective stresses in the soils beneath the adjacent structure(s) will increase. You then need to consider how the change in effective stress will consolidate (or compress) the subgrade soils beneath the building(s). This can be done using one-dimensional consolidation characteristics or elastic modulus (again depending on the stratigraphy.
Good luck. These are fun problems and I'd love to be working on it!
fatt-dad, c.p.g., p.e.
Richmond, Virginia