Discrete crack analysis of concrete gravity dams based on the known inertia force field of linear response analysis

• We present a two-step approach for discrete crack analysis of concrete gravity dams.
• The time-varying inertia forces are obtained first by linear response analysis.
• Discrete crack analysis is then performed under the known force condition.
• The method is valid because of the small effect of cracks on dams’ acceleration.
• We also present a mathematical generalisation of the two-step approach.

This paper presents a two-step approach for discrete crack analysis of concrete gravity dams under earthquake force. In this approach, the time-varying inertia forces in a dam are first obtained by linear response analysis. Then, for each time-step increment a discrete crack analysis of the dam is performed under the known force condition. This two-step approach transforms the seismic crack analysis of dams from dynamic analysis to static analysis, based on the intuitive conjecture that the effect of cracks on structural acceleration in gravity dams is small, thus allowing the actual inertia force (the product of mass and acceleration) to be approximately obtained by linear response analysis. This conjecture was proved, and numerical studies showed the strength of the method in tracing discrete cracking behaviours of a dam during large earthquakes. A mathematical generalisation of the solution strategy is also presented to enable the method to be applied to other nonlinear response problems that do not have exact solutions due to various mathematical difficulties in their solution processes.