应力作用下粒状土颗粒破碎全过程的级配演化规律及其模型预测研究

Particle breakage under stresses has a great influence on the mechanical properties of granular soil and is mainly reflected by the amount of breakage. The growth of breakage leads directly to a change grading and describes the evolution of particle-size distribution which plays an important role on the analysis of mechanical response and breakage index. However, only a limited degree of particle breakage can be observed in existing tests due to a limitation of experimental techniques. The stresses or strains that are achievable in existing tests are insufficient to see whether the particle breakage has completely ceased or whether the granular soil will eventually reach a stable grading. This project is aimed towards exploring the evolution of particle-size distribution in the whole process of particle breakage, so identifying whether or not a stable grading can be reached. A series of confined and triaxial compression tests on two sands, one with a carbonate and one a quartz mineralogy, are conducted to investigate the development of particle breakage and the evolution of particle-size distribution and stress-strain relationship with compressive and shear stress. Based on the idea that any initial distribution of particles tends towards a self-similar distribution and particle-size distribution tends to be fractal, a series of fractal particle-size distribution models are established by means of the implied concept in statistical fractal and classic fractal graphics. These fractal models are optimized by fitting with the experimental data and used to simulate and predict the evolution of particle-size distribution from an initial to ultimate distributions that the particle breakage has completely ceased. A theoretical criterion that granular soil will reach a stable grading at which the particle contact stresses will not be sufficient to cause further breakage can be find out from the evolution of particle-size distribution predicted by the models. An ultimate particle-size distribution can be given by tracking the changes in the particle-size distribution during the particle breakage. The breakage index can be obtained by using the ultimate particle-size distribution. The stress-strain behaviors affected by particle breakage are studied by using the evolution of particle-size distribution and the breakage index. This study is to link between the particles breakage and the mechanical response of the granular soils through a fractal dimension that represents the evolution of particle-size distribution. Results of the project will enhance understanding of the evolution of particle-size distribution during the crushing of particles and further improve analysis of the breakage index, so as to promote the research and the development of theories and applications of particle breakage in granular soils.

应力作用下颗粒破碎对粒状土的力学性能有很大影响，并主要通过颗粒破碎量反映。由于颗粒破碎直接导致土的级配发生变化，研究颗粒破碎全过程的级配状况及演化规律，对颗粒破碎的力学行为和定量化研究起到重要的贡献。但受技术条件限制，现有实验仅能促成有限程度的颗粒破碎，不足以判断破碎是否终止。本项目以钙质砂和石英砂为研究对象，进行高压下的侧限和三轴压缩试验，研究颗粒破碎过程中的应力应变状态、颗粒级配及其演化规律；基于粒状土颗粒的连续破碎符合分形规律，构建表征粒径分布的分形模型，并通过与试验数据的拟合分析实现优化；利用模型模拟并预测颗粒破碎全过程的级配状况及演化规律，探索破碎终止状态的理论判据，揭示破碎终止时的极限粒径分布和影响因素，研究颗粒破碎对粒状土应力应变状态的影响机制。项目研究将从理论上帮助认识颗粒破碎全过程的粒径分布规律，并进一步完善破碎量化指标的应用，从而促进粒状土颗粒破碎相关理论的研究与发展。

荷载作用下粒状土的颗粒破碎改变了土的粒径分布，从而影响其力学特性。研究颗粒破碎全过程的粒径分布演化规律，对颗粒破碎的力学行为和定量化研究起到重要的贡献。但受技术条件限制，现有实验手段仅能促成有限程度的颗粒破碎。有实验证据显示，随着颗粒破碎的增加，任何初始分布的土粒都将趋向一种自相似的分形分布。为了揭示应力水平对土粒破碎的影响规律和粒径分布的分形演化机制，基于Menger分形海绵构造过程所隐含的分形概念，建立了以颗粒质量和数量为基础的粒径分布分形模型。利用一系列高压应力下的侧限压缩试验研究钙质砂和石英砂的压缩变形、应力～应变关系、粒径分布的演化和颗粒破碎特性，利用分形模型和粒径分布实测数据研究破碎过程中粒径分布的分形行为。在此基础上，建立了描述粒状土的应力水平与孔隙比、体应变、相对破碎率等相关关系的数学模型。模型研究表明，极限粒径分布的分形特性存在某种尺度效应，分维数D的取值范围为0<D<Du而非0<D<3，其中Du为极限分维数，是土粒最小与最大粒径之比的函数且1.5≤Du<3。试验结果显示，颗粒破碎增长导致粒状土趋向分形分布的过程与颗粒破碎量密切相关，可以通过增大的分形维数来描述。随着应力水平的增加，一旦颗粒破碎增长致使砂粒趋向分形分布，体应变与相对破碎率的比值将保持恒定，并且受初始分布的均匀性和颗粒大小的影响很小。恒定比值可用于分形分布的识别，并意味着试验中如果粒径分布是分形的，则无须为了粒径分析而终止试验，只需测量到体应变就可估计相对破碎率。研究还发现，如果颗粒分布发展至分形分布，其孔隙比、体应变、相对破碎率的增量随应力水平的变化规律，可用形式统一的数学模型表达。通过试验获得的模型参数，该模型可用于预测颗粒在分形分布阶段的相对破碎率。项目成果可从理论上认识颗粒破碎全过程的粒径分布规律，并进一步完善破碎量化指标的应用，从而促进粒状土颗粒破碎相关理论的研究与发展。