适用于堆石料的分数阶下加载面模型  

A fractional sub-loading surface model for rockfill

作　　者：李海潮[1] 马博 张升[1,2] LI Hai-chao;MA Bo;ZHANG Sheng(School of Civil Engineering,Central South University,Changsha,Hunan 410075,China;National Engineering Laboratory for High Speed Railway Construction,Changsha,Hunan 410075,China)

机构地区：[1]中南大学土木工程学院,湖南长沙410075 [2]中南大学高速铁路建造技术国家工程实验室,湖南长沙410075

出　　处：《岩土力学》2021年第1期68-76,共9页Rock and Soil Mechanics

基　　金：国家自然科学基金优秀青年科学基金项目(No.51722812);湖湘高层次人才聚集工程(No.2018RS3016);中南大学研究生科研创新项目(No.1053320170586);湖南省研究生科研创新项目资助(No.CX20200126)。

摘　　要：堆石料的应力-应变曲线具有应变硬化和软化的特性,并且体积变形会伴随着剪缩和剪胀现象的发生;此外,应力水平、应力路径和密度等因素均会对堆石料的力学特性产生显著的影响。基于临界状态土力学的理论框架,建立了适用于堆石料的分数阶下加载面模型,该模型为典型的双屈服模型。在平均主应力p-剪应力q平面,剪切过程中堆石料当前应力状态点和参考应力点分别位于下加载面和参考屈服面上,两者之间的相对位置与孔隙比之差ρ相关。相比于状态参量Ψ,ρ能够额外考虑应力路径对堆石料剪胀特性的影响。新模型的另一个显著特点在于能够考虑堆石料塑性流动方向与加载方向之间的差异性。在不引入塑性势函数的情况下,新模型对屈服函数进行Caputo微分并得到分数阶塑性流动法则,进而统一描述相关联和非相关联的塑性流动法则。新模型具有形式简单且参数较少等优点,所包含的7个材料参数均具有明确的物理意义,并且可以采用常规的室内试验结果进行标定。通过将模型计算结果与Tacheng堆石料在不同初始孔隙比和围压条件下的三轴压缩排水试验结果进行对比分析,结果表明新模型能够准确地描述堆石料的应力-应变曲线和体积变形特点;同时,新模型也能够合理地描述初始孔隙比对堆石料在e-lnp平面(e为孔隙比)临界状态线的影响。The mechanical behaviors of rockfills exhibit strain-softening and dilative features, which is also influenced by the pressure, loading paths and density. In this paper, a new fractional sub-loading surface model for rockfills is proposed based on the critical state mechanism, which is a typical double yield surfaces model. In the p-q plane, the current and reference stress points are located on the sub-loading surface and the reference yield surface, respectively. The relative position between the sub-loading surface and reference yield surface is controlled by the void ratio difference ρ. Compared with the state parameter Ψ,ρ is able to account for the effect of loading paths additionally. The proposed model is able to account for the extent between the plastic flow direction and the loading direction without introducing a plastic potential function. A fractional plastic flow rule is developed by applying the Caputo fractional stress operator on the yield function, which provides a unified description for the associated and non-associated plastic flow rules. The formula of the proposed model is quite simple and the included seven model parameters can be determined through laboratory tests conveniently. The model predictions were compared with the drained triaxial test results of Tacheng rockfill under the conditions of various initial void ratios and confining pressures. A good agreement between the model predictions and experimental results is obtained, which indicates that the proposed model is capable of describing the stress-strain curves and deformation features of Tacheng rockfill. In addition, the effect of initial void ratios on the critical state line in the e-lnp plane is also captured by the proposed model.

关 键 词：堆石料 分数阶流动法则 强度 状态参量 连续方程 

分 类 号：TU411[建筑科学—岩土工程]