Abstract
Dynamic dam-foundation interaction is great important in the design and safety assessment of the dam structures. Two classic boundary conditions, i.e., the viscous-spring boundary and the viscous boundary, are employed to consider the radiation damping of the unbounded rock foundation. The input models of seismic excitation of the viscous-spring boundary and the viscous boundary are derived. The accuracy of the two boundary conditions in the dynamic analysis of the dam foundation is verified through the foundation analysis using an impulsive load. The influences of two boundary conditions and their earthquake input models on the seismic analysis of the Pine Flat and Jin’anqiao gravity dam-foundation-reservoir systems are then investigated. The results of displacements, hydrodynamic pressure, and principal stresses show that the agreement between the results of the viscous-spring boundary and viscous boundary is good. The relative errors of the two models in the Pine Flat and Jin’anqiao gravity dams are both less than 5%. They are both acceptable from an engineering point of view.
Highlights
Dynamic dam-foundation interaction is of importance in the design and safety assessment of the dam structures. e main challenge in this topic is the accurate modelling of the unbounded domain, i.e., the radiation damping at infinity
A rational and commonly used approach for modelling the whole system is to divide it into two parts. e first part is the near-field bounded domain, which contains the dam structure and a part of the adjacent foundation rock and can be efficiently modelled by the finite element method (FEM). e second part is the far-field unbounded domain, which includes the rest of the infinite foundation. e wellestablished finite element method cannot be used straightforwardly, since the outgoing waves are reflected at the artificial boundaries of the finite element mesh
It could be seen that the agreement between the results of the viscous-spring boundary and viscous boundary is good in this case. e absolute values of relative errors vary between 0.23% and 4.42%. e relative errors are less than 5% and are acceptable from an engineering point of view
Summary
Dynamic dam-foundation interaction is of importance in the design and safety assessment of the dam structures. e main challenge in this topic is the accurate modelling of the unbounded domain, i.e., the radiation damping at infinity. Mohammadnezhad et al [34] and Sotoudeh et al [35] developed a finite element model for earthquake analysis of a concrete gravity dam-foundation-reservoir system, where the viscous boundary condition is applied at the truncated foundation boundary to simulate the radiation damping of the semi-unbounded foundation rock. Mandal and Maity [43] adopted a cone-type local nonreflecting boundary condition (spring-dashpot artificial boundary) to model the semiinfinite soil domain and conducted the seismic analysis of the dam-foundation coupled system considering a direct coupling approach. Guo et al [45] established a dynamic analysis model of a dam-foundationreservoir system in consideration of the interactions between the gravity dam and foundation and the radiation damping effect of the far-field boundary based on the contact model together with the viscous-spring boundary conditions. (3b) where the superscripts s and f denote the scattered and free fields, respectively. e scattered field is represented by a suitable boundary condition imposed on the truncated boundary
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