A New Porosity Evaluation Method Based on a Statistical Methodology for Granular Material: A Case Study in Construction Sand

Sand porosity is an important compactness parameter that influences the mechanical properties of sand. In order to evaluate the temporal variation in sand porosity, a new method of sand porosity evaluation based on the statistics of target sand particles (which refers to particles within a specific particle size range) is presented. The relationship between sand porosity and the number of target sand particles at the soil surface considering observation depth is derived theoretically, and it is concluded that there is an inverse relationship between the two. Digital image processing and the k-means clustering method were used to distinguish particles in digital images where particles may mask each other, and a criterion for determining the number of particles was proposed, that is, the criterion of min(Dao). The execution process was implemented by self-written codes using Python (2021.3). An experiment on a simple case of Go pieces and sand samples of different porosities was conducted. The results show that the sum of the squared error (SSE) in the k-means method can converge with a small number of iterations. Furthermore, there is a minimum value between the parameter Dao and the set value of a single-particle pixel, and the pixel corresponding to this value is a reasonable value of a single-particle pixel, that is, the min(Dao) criterion is proposed. The k-means method combined with the min(Dao) criterion can analyze the number of particles in different particle size ranges with occlusion between particles. The test results of sand samples with different densities show that the method is reasonable.