The transport of pollutants in the subsurface can be affected by random geologic events. Prediction of such transport therefore requires solution of a partial differential equation whose coefficients are random processes. A method of finding the expected (mean) values of solutions of such equations is derived. This method is used to assess the impact of fault movement and formation of breccia pipes on risk from radioactive waste disposal. Preliminary results indicate that these events, considered probabilistically, do not make a large contribution to risk.