Curved Raypaths of Shear Waves and Measurement Accuracy of Bender Elements in Centrifuge Model Tests

In-flight measurement of shear-wave velocity ($V_s$) in centrifuge model test is important for real-time characterization and has multiple engineering applications. Accurate measurement of $V_s$ by bender elements (BE) in centrifuge models is still challenging, in part because of the curved raypath of shear-wave propagation. By focusing on the variable $g$-fields inside the models, this paper provides new equations with improved $V_s$-depth function to raypaths of shear waves for two typical centrifuge model setups. Parametric analyses including the centrifuge specifications, testing layout, and soil characteristics were carried out to study their effects on raypaths and $V_s$ accuracy. The results show that testing layout has significant effect on $V_s$ accuracy whereas soil characteristics have considerable effect. Variable $g$-fields will cause a further reduction of $V_s$ accuracy, which is dominated by centrifuge radius. To secure an accurate $V_s$ measurement in centrifuges, it is recommended that $D_i/L$ should be larger than 0.5 for cross hole measurement, and curved raypath inversion is necessary for tomography at shallow depth ($D_i/L<0.5$). Then two centrifuge model tests with BE testing corresponding to two cases of variable $g$-fields were performed to validate the proposed recommendations, where the apparent velocity is proved accurate enough to be used as the actual velocity when testing layouts meet the requirement.