A finite element approach for seismic design of arch dam-abutment structures

We present a 3-D finite element (FE) approach to find the optimal distribution of seismic reinforcement force to secure high arch dam-abutment structures against certain earthquake actions. Nonlinear FE time history analysis is performed on the structure to find the seismic responses, using the associated elastic-perfectly plastic material description. The concept of plastic complementary energy is introduced to structural dynamics to quantify the structure's resistance against the seismic action throughout the time history and to indicate the critical moments when extreme extents of dynamic failure occur. Meanwhile the distributions of the unbalanced force at these critical moments reveal the dominant patterns of the dynamic failure. By the principle of minimum plastic complementary energy, the unbalanced force is just the counterforce of optimal reinforcement force to secure the self-unsupportable structure against the earthquake, which makes the seismic design more targeted and effective. Seismic design analysis is performed on Maji high arch dam-abutment structure. The results could to a large extent guide the seismic design, showing that several structural surfaces lying at the upper abutment are the most seismically vulnerable. This application indicates good applicability of this approach to large-scale projects.