###### Abstract  
In recent years, TBM has been widely applied in deep coal mining to lift the TBM tunneling efficiency and avoid accidents, and more flexible support schemes are expected and required. This research aims to evaluate the performance of the two different support schemes and to study the law of the support effect. A three-dimensional continuum model was established based on the available geological information, and the support effect at the three-dimensional level was studied by changing the support spacing and was assessed in term of the stress, displacement, failure zone, bolt force distributions, and axial deformation behavior of the tunnel. The results show that no matter what the geological condition was, the support of the non-radial support was a little lower than that of the radial support, and with a worse geological condition, the non-radial support had a better performance in the stabilizing tunnel. Additionally, the law of the support effect was found. The interlapping of the support influence domain was the essence of the increase in the support effect. Finally, according to the support law, the appropriate support spacing is found, which is smaller than 50% of the support influence domain length. TBM; equivalent continuum; radial support; non-radial support; support effect +
Footnote †: journal: Applied Sciences  
14 August 2022  
Accepted: 18 September 2022  
Published: 21 September 2022  
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**1. Introduction**  
In China, about 95% of coal mining work takes place underground [1]. With the depletion of coal resources within shallow ground, coal mining has been entering greater depths in recent years [2]. In deep coal mines, the behavior of the surrounding rock mass is quite different from that of shallow mines. This difference results in challenges for underground excavation projects, where the traditional drill and blast method cannot satisfy the demands for tunneling and support. Meanwhile, the development of rapid excavation is extremely desired in the mining industry. Therefore, deep mining demands a new alternative construction method [3]. The tunnel boring machine (TBM, as shown in Figure 1) is typified as full-face excavation equipment that combines the functions of rock breaking, support installation, mucking, and conveying into one machine [4]. It has been applied in tunnelling, hydropower, traffic, and municipal engineering for over 50 years. In recent years, because of its significant advantages, such as a high construction efficiency, low project cost, being conductive to environmental protection, and favorable stability control for surrounding rock, compared with the traditional drill and blast method, TBM has been applied to the coal mining industry [5]. In 1970, TBM was first successfully used in a drift excavation project in [PERSON], Germany [6]. In addition, in Germany, in 1980, the application of TBMwas done through an 8000 m conveyor drift excavation project in the Franz Haniel Coal Mine [7]. In China, the Methane Gas Extraction Roadway of the Zhangji Coal Mine was constructed using TBM in 2014. This was the first TBM boring line for a full-face hard rock roadway in a vertical shaft mine [8]. In the Xinjie Coal Mine Inclined Shaft Tunnel Project, the single-shield TBM with an earth pressure balance function was first used to construct a long inclined shaft tunnel coal mine with a steep slope [9]. In the process of tunneling using TBM, the mucking speed of the rock and soil in front of the face largely determines the advance rate of the machine because the accumulation of the rock and soil could cause a drop in the tunneling speed or even the capture of TBM.