Scaling the failure of concrete gravity dam subjected to underwater explosion — Part II: Correction method to consider the strain-rate effect

Part I of this work indicates that the dimensional analysis-based scaling law fails to scale the dynamic tensile responses and failures of concrete gravity dams subjected to underwater explosions owning to the dissimilar strain-rate effects between small-scale dam models and prototypes. In Part II of this work, a correction method is proposed to address this challenge based on a dimensionless damage number Dni suggested in Part I of this work. The core idea is to keep Dni equal for small-scale dam models and prototypes by adjusting the other terms of Dni according to the differences in the strain-rate effects between small-scale dam models and prototypes. Detailed scaling procedure with the correction method using a small-scale dam model as a reference is given, where both the explosive weight and the static tensile strength of the concrete gravity dam of the prototype need to be corrected. For validation purposes, the fully-coupled numerical model established based on centrifuge tests in Part I of this work is still employed. 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 are used. Results demonstrate that the proposed correction method can well address the non-scalability of the strain-rate effect between small-scale dam models and prototypes. With the correction method, the failures of geometrically similar dam models with β = 1–1/100 are almost identical, and Dni exhibits a uniformly linear relation with the dimensionless displacement δ/H of geometrically similar dam models with β = 1–1/100. Besides, the proposed correction method makes it possible to apply the well-known concept of “modeling of models” to verify the scaling relations of concrete gravity dams subjected to underwater explosions in a centrifuge.