新拌水泥浆体中邻近胶凝材料粒子表面最近间距分布的解析解

Analytical solution of the nearest surface spacing between neighboring binder grains in fresh cement paste

依据Torquato的最邻近表面函数公式,推导了新拌水泥浆体邻近水泥粒子表面最近间距分布的解析解,并采用计算机模拟生成了1个水泥浆体结构模型,选取邻近粒子表面最近间距概率密度分布曲线、区间概率曲线和累计概率分布曲线这3个函数检验模拟结果与理论结果之间的差别。结果表明,该解析解与计算机模拟实验结果吻合良好。利用该解析解,以Rosin-Rammler分布为例,研究了胶凝材料细度以及水胶比对邻近水泥粒子表面最近间距分布及其平均值的影响。结果显示,水泥细度对邻近粒子表面最近间距平均值的影响高于水胶比的影响。邻近粒子表面最近间距解析解的获得,不但为基于不同粒径分布以及尺度范围粉体之间搭配的高粉体初始堆积密度的实现提供了依据,而且对多尺度模拟方法中选取各级模型的尺度、量化粉煤灰浆体中粉煤灰颗粒的微集料效应、了解邻近集料间的交互作用程度以及界面重叠程度等问题具有参考价值。

Based on the nearest surface function formula given by Torquato, an analytical solution of the nearest surface spacing between neighboring binder particles was derived. Computer simulation technology was employed to generate one model paste. By comparison of probability density curve, subinterval probability curve and cumulative probability curves of the nearest surface spacing between neighboring aggregate grains, it was found that the theoretical results are consistent with the simulation very well. Furthermore, for model binder which follows Rosin- Rammler function, these analytical formula were used to study the influence of fineness of cement and water to binder ratio （w/b ratio） on the distribution of the nearest surface spacing between neighboring binder particles. The simulation data show that the fineness of cement exerts more significant influence on the mean value of the nearest surface spacing between neighboring particles than w/b ratio. These analytical solutions provide the criterion to set the proper ratio between powder materials with different particle size distribution and diameter range so as to reach higher packing density. They also provide the criterion to set the size of the model at different scale levels in multiscale modeling approaches. In addition, these analytical formulas are valuable to quantify the action of micro-aggregate effect of fly ash, and to learn about the interacting degree between neighboring aggregate grains as well as the interference between neighboring interfacial transition zones.