Abstract Accurate prediction of the state-dependent shearing behaviors of sand in a rational way is a challenging task of the development of constitutive models. In the present study, a deformation type model is proposed based on a modified Duncan-Chang hyperbolic equation, which provides a simple and efficient way to characterize the stress–strain relationship. The hyperbolic equation is improved to tackle the limitations when predicting the strain-softening behavior of sand. By coupling with a flow rule, the volumetric response under a drained condition and excess pore pressure generation under an undrained condition can be modeled as well. An empirical state variable, known as the relative dilatancy index, is implemented in the modified hyperbolic equation and the flow rule to model the state-dependent shearing behaviors in a unified way. The flow rule evolves with the state of soil during shearing and provides realistic simulations of dilatancy-related response. The calibration process for dilatancy and hyperbolic equations is suggested. The model is validated by drained and undrained triaxial compression tests of two silica sand, showing a fairly good capability of unified modeling of the sand behaviors with a wide range of densities and stress levels.

中文翻译：

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基于修正双曲方程和状态相关剪胀的沙子统一单调模型

摘要 以合理的方式准确预测砂的状态相关剪切行为是本构模型发展的一项具有挑战性的任务。在本研究中，基于修正的 Duncan-Chang 双曲方程提出了一种变形类型模型，它提供了一种简单有效的方法来表征应力 - 应变关系。改进双曲线方程以解决预测砂的应变软化行为时的局限性。通过与流动规则耦合，还可以对排水条件下的体积响应和不排水条件下的超孔隙压力生成进行建模。一个经验状态变量，称为相对剪胀指数，在修正的双曲方程和流动规则中实现，以统一的方式模拟状态相关的剪切行为。流动规则随着剪切过程中土壤的状态而变化，并提供与剪胀相关的响应的真实模拟。建议了剪胀方程和双曲方程的校准过程。该模型通过两种硅砂的排水和不排水三轴压缩试验进行了验证，显示出较好的对各种密度和应力水平的砂岩行为进行统一建模的能力。