Experimental and Statistical Studies of the Microstructure Characteristics of Nano-Silica-Modified Silty Clay in the Qinghai–Tibet Plateau

Nanomaterials have been widely used for improving the physicochemical properties of geomaterials. However, quantitative interpretation of the microscopic mechanisms is still not well understood. In this study, a statistical principle was applied to study the microscopic characteristics of nano-silica (NS) modified silty clay. We use mercury intrusion porosimetry (MIP) to measure the micro-pore parameters (median pore diameter and cumulative volume of pore diameters smaller than 0.1 µm) based on various NS-modified silty clays (NS mass contents 0, 0.25%, 1%, and 3%). The test results indicate two micro-pore parameters have significant randomness and uncertainty, and soil pores become smaller and more compacted. Furthermore, four potential probability distributions were selected to compare with measured data. All distributions agree excellently with the experimental data, and three distributions satisfy the hypothesis testing, except the Weibull distribution. Finally, according to the information spread estimation method and chi-square test effect evaluation indexes, the normal distribution was proposed because it has the optimal described effect for the statistical characteristics of NS-modified silty clay. These results have important implications for understanding the randomness and evolution of microstructures of NS geomaterials, which are helpful to guide the evaluation of freezing process and water transport in modified soils.