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

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 multi-scale 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.