Pore features and seepage characteristics of natural gap-graded sand with two size distributions

Pore features and seepage characteristics of mixed granular materials are of great significance in many subjects, including engineering, for instance geotechnical engineering, petroleum extraction, hydrogeology, environmental science and hydraulic engineering. In this paper, two types of mathematical models are proposed that consider different packing methods for porosity and permeability - namely, the filling model (FM) and the replacement model (RM). On this basis, incomplete coverage (overlap between large and small grains during the replacement process) is considered as the 'replacement model considering incomplete coverage' (RMCIC) and the 'replacement model considering incomplete coverage and roundness' (RMCICR). Roundness is considered in the 'filling model considering roundness' (FMCR), the 'replacement model considering roundness' (RMCR) and the RMCICR. Four kinds of natural sand are chosen as the source material, with median grain sizes of 1733, 1050, 449 and 190 mu m. All models can be divided into two components - one in which the porosity decreases with large grain ratios and the other in which the porosity increases. When roundness is considered, the RMCICR model has the largest porosity, and the FMCR model has the lowest porosity. In addition, the porosity increases when roundness is considered for all models in this study. The porosity in the RMCICR model better coincides with the test results, which can be explained by the consideration of both incomplete coverage and roundness. The order of porosity values is as follows: RMCICR, RMCR, RMCIC, RM, FMCR and FM. Permeability presents a tendency similar to porosity - that is, permeability decreases first and then increases. Moreover, the slope in the declining stage is relatively small, and the slope in the ascending stage is relatively large. The ratio of large grains to minimum porosity and permeability has significant differences. The results suggest the effectiveness of previous mathematical models.