Application of Fractal to Evaluate the Drying Shrinkage Behavior of Soil Composites from Recycled Waste Clay Brick

Soil drying cracking is the most common natural phenomenon affecting soil stability. Due to the complexity of the geometric shapes of soil cracks during the cracking process, it has become a major problem in engineering science. The extremely irregular and complex crack networks formed in civil engineering materials can be quantitatively investigated using fractal theory. In this paper, fractal dimension is proposed to characterize the drying cracking characteristics of composite soil by adding recycled waste brick micro-powder. At the same time, the concept of the probability entropy of cracking is introduced to quantify the ordered state of crack development. Correspondingly, the endpoint value of probability entropy was solved mathematically, and the meaning of the probability entropy of cracking was clarified. In this study, the fracture fractal characteristics of composite soil mixed with different materials were first investigated. Then, five groups of composite soil-saturated muds with added recycled waste brick micro-powder of different contents were prepared in the laboratory. Using the evaporation test under constant temperature and humidity, the change rules of the fractal dimensions, probability entropy, crack ratios, and water contents of cracks during the cracking process of the soil samples were obtained. The results show that: (1) on the whole, the fractal dimensions of the soil samples added with recycled waste brick micro-powder of different contents increased over time, and the fractal dimensions of the soil samples without recycled waste brick micro-powder were obviously larger than those of the soil samples with recycled waste brick micro-powder. With the increase in the content of recycled waste brick micro-powder, the maximum fractal dimension decreased in turn. The maximum fractal dimensions of the five groups of soil samples were 1.74, 1.68, 1.62, 1.57, and 1.45. (2) The change trends of the probability entropy and fractal dimensions were similar; both of them showed an upward trend over time, and the probability entropy of the soil samples without recycled waste brick micro-powder was greater than that of the soil samples with recycled waste brick micro-powder. With the increase in the contents of recycled waste brick micro-powder, the probability entropy decreased in turn. The maximum values of the crack probability entropy of the five groups of soil samples were 0.99, 0.92, 0.87, 0.83, and 0.80. (3) Under the action of continuous evaporation, the moisture contents of the soil samples gradually decreased over time, while the crack ratios increased over time. To sum up, both from the perspective of the development process of the cracks of the soil samples and from the perspective of the final stable crack networks of the soil samples, the geometric shapes of the cracks of the soil samples without recycled waste brick micro-powder were the most complex. With the increase in the content of recycled waste brick micro-powder, the fractal characteristics of the cracks gradually changed from complex to simple.