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 引用本文: 万征, 孟达. 复杂加载条件下的砂土本构模型[J]. 力学学报, 2018, 50(4): 929-948.
Wan Zheng, Meng Da. A CONSTITUTIVE MODEL FOR SAND UNDER COMPLEX LOADING CONDITIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 929-948.
 Citation: Wan Zheng, Meng Da. A CONSTITUTIVE MODEL FOR SAND UNDER COMPLEX LOADING CONDITIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 929-948.

## 复杂加载条件下的砂土本构模型

• 摘要: 试验表明,饱和砂土的应力应变关系具有显著的密度以及压力依存性,上述两点构成了描述砂土静力加载下变形特性无法忽视的因素. 此外,在循环加载等复杂加载作用下,砂土还会表现出明显的应力诱导各向异性以及相变转换特性. 基于在$e$--$p$空间中存在唯一的临界状态线这一基本假定,通过在$e$--$p$空间中引入当前状态点与临界状态线的距离$R$来作为反映密度与压力依存特性的状态参量, 将变相应力比以及峰值应力比表达为状态参量的指数函数,将上述应力比参量引入到统一硬化参量中可准确地反映初始状态下围压、密度 对于单调加载下应力应变关系的影响规律,能描述砂土剪缩、剪胀,应变软化、硬化等特性. 采用非相关联流动法则,$p$--$q$空间中采用水滴型屈服面,塑性势面为椭圆面,松砂在单调加载下的静态液化现象也可描述. 为反映循环加载下塑性体积应变的累积特性以及塑形偏应变的滞回特性,在循环加载下将状态参量$R$表达为应力比参量,并在硬化参数中引入描述应力诱导各向异性特性的旋转硬化部分,所提模型可有效地描述循环加载下剪切模量的衰减特性、刚度衰化性质、强度减小特性,在不排水约束作用下,则会产生往返活动性现象. 通过一系列的模型模拟与试验结果对比,验证了本构模型的有效性及适用性.

Abstract: Abstract The test shows that stress-strain relationship of saturated sand has significant dependence on density and confining pressure. The above two factors can not be ignored to describe the deformation behavior of sand under static load conditions. In addition, saturated sand also exhibits obvious stress-induced anisotropy and phase transformation behaviors under complex loading, such as cyclic loading conditions. The distance $R$ between the current stress state and its corresponding point in critical state line (CSL) can be treated as a state parameter is introduced into the proposed model to reflect the density and confining pressure dependent behaviors based on the assumption that there is a unique CSL in $e$--$p$ space. The influence principle to stress-strain relationship under monotonic loading condition due to density and confining pressure is accurately described by using unified hardening parameter introduced by phase changing stress ratio and peak stress ratio expressed by exponential functions of state parameter. The shear volume compression, dilatancy, strain softening and hardening are all described for sand. By using non-associated flow rule, a water drop shape yield surface and an ellipse shape plastic potential surface are adopted in $p$--$q$ space. The liquefaction phenomenon under monotonic loading condition are also be described. To reflect the accumulation of plastic volume strain and hysteresis loops of deviatoric plastic strain under cyclic loading condition, the state parameter $R$ can be expressed as stress ratio parameter and the rotational hardening part can be adopted to describe the stress-induced anisotropy are introduced into the hardening parameter. The attenuation of shear modulus, stiffness weaken and strength decreasing behaviors are described effectively by using the proposed model. The cyclic mobility phenomenon is predicted under undrained cyclic loading conditions. The effectiveness and applicability of the proposed constitutive model is verified by the comparison of a series of simulation and test results.

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