## 1 Introduction  
Geological disasters such as ground subsidence caused by coal mining have become increasingly prominent in China. According to a statistic in 2015, the area of abandoned coal mines in Shanxi province exceeded 20,000 km\({}^{2}\), which is equivalent to one-seventh of the total land of the major coal-producing province. Of this, 6000 km\({}^{2}\) of land suffered geological disasters caused by the subsidence of mined-out areas [1]. With the rapid construction of highways and urban highway networks in China, there has been an increasing amount of highway construction running through coal mining subsidence areas; for example, part of the expressways in Guangdong province [2], and the construction of the Outer Ring Expressway of Xuzhou, Jiangsu province [2, 3], encountered geotechnical engineering problems due to passing through the goat of coal mines. Meanwhile, research on the impact of the underlying goal on the stability of expressways has been widely conducted in recent years [4, 5, 6, 7, 8, 9, 10]. [PERSON] et al. [11] revealed the evolution law of the surrounding rock rupture during the construction of the tunnel under the point-column goaf by using a similar model test. [PERSON] [12] conducted research on the surrounding rock stress of a tunnel by on-site monitoring and the numerical simulation method, presenting that the secondary lining receives the contact pressure created by rheological rock. The rheological stress release rate is less than 7% in rock arches and more than 55% in spandrels and hances. Mining subsidence is a complicated geological and mechanical change process, and the surface movement and deformation as well as engineering geological stability of the overburden above the goaf area are affected by various conditions, including geological conditions and mining situations [13]. The probability integral method proposed based on the random medium theory has been widely used in the mining industry in China [14; 15]. FLAC analysis shows that the railway can subside due to the mined caves located 50 m to the west, although the deformation modes can vary, and the subsidence can be protected by filling the caves in Korea [16]. Considering that the stability of the goaf is a systemic problem that involves many factors, such as geology and mining, and by using similar simulation experiments and numerical simulations, recent research on the overburdened rock and surface deformation in goaf areas has obtained satisfying results [17; 18; 19; 20; 21; 22; 23; 24]. [PERSON] et al., [PERSON], and [PERSON] [25; 26; 27] described the analysis method for the numerical calculation of the stability of the goaf and discussed the method of construction and subsidence in the goaf and the examples applied in the engineering. [PERSON] et al. [28] used the significance between the influence of the depth of building loads and the developing height of the crack zone to judge the stability of the foundation in the goaf area. Some scholars [29; 30; 31; 32] carried out prediction and analysis with a focus on the effect of the remaining deformation of the goaf area on the expressway and conducted systematic research using an analysis theory on the interaction between the highway and the underlying goaf and the relevant treatment technology for the goaf. For the deformation monitoring of a goaf, total-station instruments and optical leveling instruments, or conventional geodetic methods are generally used for monitoring localized and smaller-scale deformations of buildings or structures. The Tianzimiao Highway Tunnel is a double-line parallel tunnel of the 307 national highway double-line reconstruction projects in Yangquan city, Shanxi province, and it is divided into the left and the right lines. The total length of the tunnel is 1707.15 m. It is located within the boundary of the mined-out areas of the Yangquan Coal Mining Group and the Hanhegou coal mines. A total of four seams (seam no. 3, 8, 12, and 15) with a maximum cumulative thickness of up to 11 m were mined below the tunnel.