Scaling the failure of concrete gravity dam subjected to underwater explosion — Part I: Suggestion of a dimensionless number

Abstract

The small-scale model test is the major feasible approach to experimentally investigate concrete gravity dams subjected to underwater explosions. However, speculating results of the dam prototype requires knowledge of scaling law. Our previous research finds that the dimensional analysis-based scaling law is violated since the strain-rate effects between small-scale dam models and prototypes are dissimilar, resulting in distinct tensile failures between them. The non-scalability of the strain-rate effect is one of the most troublesome issues in similarity analysis, plaguing the research community for years. This two-part paper attempts to address this challenge by proposing a correction method to the dimensional analysis-based scaling law for scaling the failure of concrete gravity dams subjected to underwater explosions. The strategy contains two steps. The first step is to derive dimensionless damage numbers through the dimensional analysis method. The second step is then to propose the correction method based on the verified dimensionless damage number. Part I of this work deals with the first step, while Part II addresses the second step.In Part I of this work, a dimensionless damage number is suggested to reflect the dynamic bending-induced tensile response mechanism of concrete gravity dams against underwater explosions. Three aspects can be reflected in this dimensionless damage number: the inertia force of the loading, the resistance ability of the material to deformation, and the resistance ability of the dam structure to deformation. For validation, a numerical scheme comprising 12 geometrically similar dam models with geometrical scaling factors β = 1, 1/2, 1/5, 1/10, 1/20, 1/30, 1/40, 1/50, 1/60, 1/70, 1/80, and 1/100 is devised based on small-scale centrifuge tests. Results have demonstrated that when strain-rate effects are close, such as for β = 1/40–1/100 dam models, the suggested dimensionless damage number can well predict the dam dynamic responses and failures, and shows an excellent linear relation with the dam dimensionless displacement. However, when strain-rate effects are dissimilar, such as for β = 1–1/30 dam models, the suggested dimensionless damage number fails, and correction methods are required that will be proposed in Part II of this work.