Direct and relaxation methods for soil-structure interaction due to tunneling

This paper deals with the problem of tunneling effects on existing buildings. The direct solution, using the condensation method, is presented. This method allows the structural and geotechnical engineers to treat the problem separately and then assemble a relatively small matrix that can be solved directly, even within a spreadsheet. There are certain concerns that the resultant matrix may be ill-conditioned when the structure is very stiff. This paper suggests an alternative method that essentially relaxes the system from an infinitely rigid structure solution. As such, it does not encounter the problems associated with stiff systems. The two methods are evaluated for an example problem of tunneling below a framed structure. It is found that while the direct method may fail to predict reasonable values when the structure is extremely rigid, the alternative method is stable. The relaxation method can therefore be used in cases where there are concerns about the reliability of a direct solution.