Study on Mechanical Calculation Model of Arch Ring in Freestanding Stone Cave-Dwelling

The freestanding stone cave-dwelling is a kind of arched and sheltered house built with stones in the Loess Plateau region of northwest China. Amazingly, before construction, this kind of cave-dwelling was not formally calculated and designed in theory, but only built on the experience passed down by predecessors. The arch ring is the main load-bearing component of the freestanding stone cave-dwelling, through which the upper loads are transmitted to the legs on the left and right sides of the cave-dwelling and then to the foundations. Therefore, it is a prerequisite to ensure the safety of cave dwellings by adopting a reasonable and accurate mechanical calculation model for the arch ring of a stone cave-dwelling to reveal the distribution of internal forces in the arch ring and scientifically design the arch ring accordingly. Three mechanical calculation models (structural calculation diagrams) are adopted for the arch ring of stone cave-dwelling, namely, hingeless arch, two-hinged arch, and three-hinged arch. Based on the force equilibrium and the force method from the structure mechanics, the formulae for calculating the internal force of the stone arch ring under these three different mechanical calculation models are derived respectively. The mechanical calculation results of three calculation models are compared and analyzed to clarify the difference and rationality of the stress results of the arch ring under the three mechanical calculation models and the degree of influence on the force of the lower cave-dwelling leg members. Lastly, in accordance with the internal force calculation results, the calculation formulae for the design of the arch ring thickness are proposed. The study shows that the hingeless arch and two-hinged arch models are more consistent with the actual failure characteristics, two-hinged arch calculation model is safer, more accu-rate, and more reliable than the hingeless arch calculation model when it is used in the mechanical analysis of circular arc arch ring. The findings are intended to serve as theoretical references for the design and construction, protection and reinforcement, and sustainable development and inheritance of cave dwellings in the future.