Difference characteristics of stress similitude for geotechnical centrifuge modelling and design criteria

The advantage of geotechnical centrifuge modelling is founded on the exactly similar stress levels and distribution between models and prototypes. To recognize the differences and characterization parameters of stress similitude of model and prototype is of significant value to decreasing systematic errors and optimizing design parameters. Three new concepts of general distributed stress, additional lateral stress and coupling dynamic stress are proposed and defined, by using which the difference characteristics, characterization parameters and design principles of model stress compared to those of prototype are studied. The general distributed stress is represented by the stress error referring to the model height H and the maximum radius ${{R}_{\max }}$, and as $H/{{R}_{\max }}$≤0.3 and 0.15, the stress error limits of soil model are less than 10% and 5%. The magnitude of additional lateral stress increases from center section to two width boundaries, and is mainly governed by the model width b, effective radius ${{R}_{\text{ef}}}$ and effective centrifugal acceleration ${{a}_{\text{ef}}}$. Selecting 100 kPa as a criterion, the allowable model width limits with varying effective radius for different centrifugal accelerations are proposed. The influence of coupling dynamic stress is evaluated through the ratio of the target stress to the extra stress involving two key parameters of ${{R}_{\text{ef}}}$ and angular velocity $\omega$. With 10% and 20% as the criteria of the stress ratio, the critical curves of ${{a}_{\text{ef}}}$-${{R}_{\text{ef}}}$ are obtained and if ${{a}_{\text{ef}}}$≥10g and ${{R}_{\text{ef}}}$≥4 m, the influence of coupling dynamic stress can be ignored. The proposed new concepts, characterization parameters and design criteria provide the reference and basis for the parametric design of facilities and soil models and development of quantitative researches.