# Force Analysis of Masonry Cave-Dwelling Structure Based on Elastic Center Method
## 1 Introduction  
Cave dwellings are widely distributed in the Loess Plateau of Northwest China. They are one of the most typical traditional dwellings in northern Shaanxi. In addition, they are favored by local residents for their advantages of adapting to the climate, using local materials, having a low cost, being warm in winter and cool in summer, and, particularly, the covering soil on the upper part of the cave dwelling being able to make use of its own temperature and heat insulation function. They are also known as energy-saving ecological residences. According to the different ways of construction, cave dwellings can be divided into three categories [1]: One is the excavation pattern cave dwelling, which includes the cliff-side-type loess cave dwelling excavated directly from the loess cliff face; the patio-type loess cave dwelling which was excavated along the four walls in the manually excavated square earth pit; and the earth-pit-type cave-dwelling which was excavated in a naturally formed earth pit, as shown in Figure 1a,b [1]. The second is the masonry pattern cave dwelling; that is, the free-standing cave dwelling or open hoop cave dwelling is an earth cave dwelling, brick cave dwelling, or stone cave dwelling directly hoop-built on the flat ground, and the upper part is covered with a certain thickness of soil, as shown in Figure 1c. The third is the half excavation and half masonry pattern cave dwelling, that is, the interface cave dwelling; a section of the masonry arch ring is connected to the mouth of the loesscave dwelling to prevent the cliff surface from collapsing, as shown in Figure 1d. With the improvement of people's living conditions and the convenience of production and living conditions, masonry cave dwellings have sprung up. However, the construction of masonry cave dwellings is based on experience without structural calculation and stress analysis, and the construction method lacks theoretical guidance, which causes the hidden dangers of the cave structures to occur from time to time. Cave-dwelling buildings are the concentrated carrier of the local residents' construction skills, survival wisdom, geographical environment, regional culture, and social economy, and they are a valuable architectural and cultural heritage. The in-depth studies on their stress have an important scientific significance and social value for the protection and inheritance of these traditional local-style dwellings. The cave dwellings are classified as earth-sheltered architectures that have been much studied by foreign scholars [2; 3; 4; 5; 6]. To preserve this valuable architectural heritage, Chinese scholars have carried out a great deal of research on it. In recent years, many scholars have focused on the structural principle [7; 8], stress characteristics [9; 10; 11], stability analysis under different influencing factors [12; 13; 14; 15; 16; 17; 18; 19], the effect of water on the stability of the cave dwelling [20; 21], and the reinforcement and protection measures using new materials and advanced methods for the loess cliff-side cave dwelling and earth-pit-type cave dwelling [22; 23; 24; 25; 26]. However, there is little research on the masonry cave dwelling. [PERSON] et al. [27] combined the actual earthquake damage with numerical simulation experiments; the vertical displacement of the arch vault and the ratio of the vault height to the calculated span were proposed as the damage indicators for the free-standing cave dwelling under an earthquake. [PERSON] et al. [28; 29] carried out a stress analysis and cross-sectional calculations on the arch ring of a stone masonry cave dwelling which adopted the three-hinged arch calculation model, but the arch axis was chosen as a reasonable arch axis (catenary), which did not match the curved arch axis in the actual cave dwelling. [PERSON] et al.