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Objectives: Complex construction organization strategies such as parallel same direction and reverse boring for long railroad tunnel projects lead to sparse spatiotemporal distribution and large spatiotemporal overlap in the digital twin three-dimensional model. The existing spatiotemporal indexes for the continuous uniform spatiotemporal distribution characteristics can not satisfy the needs of efficient retrieval of time, mileage, and semantics in multi-dimensions, and they also restrict the efficiency of the digital twin application in real-time virtual and real mutual feeds. Methods: This paper proposes a multi-dimensional efficient spatiotemporal indexing method applicable to the digital twin model of railroad tunnels. First, a 3D tile data structure of railroad tunnels associated with time, mileage, and semantic multi-dimensions is designed. Second, an oriented bounding box corrective mechanism constrained by the global optimal solution is established, and then a multi-granular spatiotemporal index of railroad tunnel lines-tiles-components is realized. Finally, the effectiveness of the method is verified using typical long railroad tunnel twin model data. Results: The results show that the average value of the proposed method in the mixed retrieval time of time, mileage and semantic multi-dimensions is 135.44 ms, which improves the retrieval efficiency of the 3D spatial single dimension and the time-mileage mixed dimension comparing with the existing typical spatial and temporal index. Conclusions: The proposed method can effectively support the efficient spatial and temporal retrieval of the digital twin 3D model of railroad tunnels, and the application of high-performance visualization and analysis. [ABSTRACT FROM AUTHOR]

Laterite is a special type of soil in tropical and subtropical humid areas. It is evolved from carbonate rocks to physical, chemical, and biological weathering, as well as laterization with the color of brown-red, maroon and yellowish-brown. Furthermore, laterite is very likely to crack in a dry environment, due to its sensitivity to ambient humidity. The resulting dry shrinkage cracks have posed a great threat to the strength and stability of the soil. Therefore, there is a commonly-hidden danger of collapse from the shrinkage cracking of laterite in slope projects. Most cracking of cohesive soil comes from the evaporation of water in the soil. Boundary constraints and uneven shrinkage can result in the formation and development of a stress-strain field in the soil. Once the tensile exceeds the maximum tensile strength of the soil, the cracks gradually occur and continue to develop during evolution. In this study, a quantitative analysis was performed on the dry shrinkage cracking of red clay in high liquid-limit laterite in Shaoyang area of Hunan Province in China. A drying test was also conducted to explore the evolution and formation mechanism of cracks in the laterite using slurry samples under natural hot-humid conditions. A three-dimensional strain measurement system was adopted to collect the moisture, displacement, strain, and crack of the soil. Then, a quantitative description was made on the evolution characteristics of crack morphology and strain field during dehumidification, thereby investigating the influence of water content on fracture morphology and strain field. The results show that: 1) Six stages were found in the evolution of dry shrinkage cracks on the surface of the soil sample. The cracks were formed in the later stages with the cracking surroundings from the previous stages. Specifically, the intersection angle of fractures was close to 90º in different stages. 2) Most soil was in the tensile state with a nearly 0.5% strain at the crack tip during the initial stage of crack development. The soil around the cracks gradually evolved into a compressive state, as the crack developed. Once all the cracks developed, the soil around the crack was totally in a compressive state. 3) The evolution of cracks was closely related to the limited water content. Specifically, the cracks on the soil surface began to rapidly develop, widen and extend, when the soil water content approached the liquid limit of 67.7%. The developing rate of crack began to slow down when the soil water content reached the plastic limit of 28.3%. Once the soil water content was less than the plastic limit of 18.8%, there was no obvious change of fracture, indicating that the fracture development was nearly completed. 4) The cracking time and width of early fracture exceeded those of later fracture in the process of fracture evolution. The displacement and strain varied at the different parts of the soil surface. The vertical shrinkage at the center of the soil block was greater than that at the edge, but the displacement and strain at the center of the soil block were much less than that at the edge. The finding can offer a great engineering reference to prevent geological diseases or environmental disasters in laterite areas. [ABSTRACT FROM AUTHOR]