The stress–dilatancy relation is of critical importance for constitutive modelling of geomaterial. A novel fractional-order stress–dilatancy equation had been developed for granular soil, where a nonlinear stress–dilatancy response was always predicted. However, it was experimentally observed that after a certain extent of shearing, an almost linear response between the stress ratio and the dilatancy ratio, rather than the nonlinear response, usually existed. To capture such stress–dilatancy behaviour, a new fractional stress–dilatancy model is developed in this study, where an apparent linear response of the stress–dilatancy behaviour of soil after sufficient shearing is obtained via analytical solution. As the fractional order varies, the derived stress–dilatancy curve and the associated phase transformation state stress ratio keep changing. But, unlike existing researches, no other specific parameters, except the parameter related to fractional order, concerning such shift are required. Then, the developed stress–dilatancy model is applied to constitutive modelling of granular soil and soil–structure interface, for further validation. A series of test results of different granular soils and soil–structure interfaces under different loading conditions are simulated and compared, where a good model performance is observed.

应力-剪胀关系对于土工材料的本构模型至关重要。已经为粒状土壤开发了一个新的分数阶应力-剪胀方程，该方程总是预测非线性应力-剪胀响应。然而，实验观察到，在一定程度的剪切之后，通常存在应力比和膨胀率比之间几乎线性的响应，而不是非线性响应。为了捕获这种应力-剪胀行为，本研究开发了一种新的分数应力-剪胀模型，其中通过分析解决方案获得了充分剪切后土壤的应力-剪胀行为的表观线性响应。随着分数阶的变化，导出的应力-剪胀曲线和相关的相变状态应力比不断变化。但，与现有研究不同，除了与分数阶有关的参数外，不需要其他特定参数。然后，将已开发的应力-剪胀模型应用于颗粒状土和土-结构界面的本构模型，以进行进一步的验证。模拟并比较了在不同载荷条件下不同颗粒状土壤和土壤-结构界面的一系列测试结果，并观察到了良好的模型性能。