Research on the ratio of similar materials in water-absorbent mudstone based on fuzzy mathematics

To determine the suitability and credibility of similar water-absorbent mudstone materials in model experiments, the prototype mudstone parameter similarity index was determined based on the similarity theory. Similar materials use cement and Plaster as binders and quartz sand as aggregate. The sensitivity of similar indicators of similar materials to control factors was analyzed through range statistics. Multiple regression analysis was used to establish the quantitative relationship between each control factor and similar indicators. Finally, the optimal matching scheme was refined through the combination of fuzzy mathematics and analytic hierarchy process. The results show that the physical and mechanical property indicators of similar materials with different proportions have a wide distribution range, and under certain similar conditions, they can meet the requirements of rock model tests with different properties. The aggregate-binder ratio is a direct indicator of material density, elastic modulus, and compressive strength. The main controlling factors, material density, elastic modulus, and compressive strength all increase with the decrease in aggregate-binder ratio. The cement-plaster ratio is the main control factor of material water absorption, and the water absorption gradually decreases with the increase of the cement-plaster ratio. The formula obtained through linear analysis can better represent the changing trend and distribution characteristics of various parameters of similar materials with the aggregate-binder ratio and cement-plaster ratio, and initially optimize the proportioning scheme of similar materials. Use fuzzy mathematics to evaluate the membership degree of each parameter index of similar materials, and the optimal ratio scheme was further determined to improve the credibility of later model experiments.