Abstract In this study, a large amount of stress-dilatancy data of Karlsruhe fine sand were examined at first, where it was found that the stress-dilatancy behaviour of Karlsruhe fine sand depended on its void ratio and pressure. To capture such state-dependent stress-dilatancy behaviour, the fractional-order dilatancy equation and Li and Dafalias [1]'s dilatancy equation, were adopted and compared. In addition, a kinematic loading surface characterising the loading/unloading directions was proposed, where the current loading surface moved kinematically within the maximum loading surface. Three hardening moduli were defined for virgin loading, unloading and reloading, respectively. Further validation against a series of monotonic and cyclic test results of Karlsruhe fine sand revealed that: models based on these two dilatancy equations can simulate the drained and undrained behaviour of Karlsruhe fine sand under monotonic and cyclic loads. The unloading-induced contractive response and reloading-induced dilative response during drained loading, as well as the butterfly-shaped liquefaction response under undrained loading can be reasonably reproduced. Li and Dafalias [1]'s dilatancy equation had a relatively better match of the stress-dilatancy data.

中文翻译：

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卡尔斯鲁厄细砂在单调和循环载荷下：建模和验证

摘要 本研究首先对卡尔斯鲁厄细砂的大量应力-剪胀数据进行了研究，发现卡尔斯鲁厄细砂的应力-剪胀行为取决于其孔隙比和压力。为了捕捉这种状态相关的应力剪胀行为，采用并比较了分数阶剪胀方程和 Li 和 Dafalias [1] 的剪胀方程。此外，还提出了表征加载/卸载方向的运动加载表面，其中当前加载表面在最大加载表面内运动。分别为原始加载、卸载和重新加载定义了三个硬化模量。针对卡尔斯鲁厄细砂的一系列单调循环试验结果的进一步验证表明：基于这两个剪胀方程的模型可以模拟卡尔斯鲁厄细砂在单调和循环载荷下的排水和不排水行为。可以合理再现排水加载过程中卸载引起的收缩响应和重新加载引起的膨胀响应，以及不排水加载下的蝴蝶形液化响应。Li 和 Dafalias [1] 的剪胀方程与应力剪胀数据具有较好的匹配性。