## 1 Introduction  
The process of chamber excavation causes disturbance to the surrounding rock mass, which disturbs the stress state of the original rock and causes the stress in the surrounding rock to be redistributed. In this process, the maximum principal stress of the in situ stress component in the surrounding rock will exceed the stress intensity of the original rock. At this time, some surrounding rock will change from an elastic state to a plastic state. The damaged part of the surrounding rock is distributed around the chamber to form an annular broken belt area, which is called the loose zone in existing theory [1]. According to previous research and engineering experience, in the process of tunnel (chamber) construction, the loose zone exists in the surrounding rock. Many scholars have also conducted considerable research on the formation mechanism and determination of the ranges of loose zones. For the determination of the scope of a loose zone, the existing research methods include field measurements, the acoustic method [2; 3; 4], the multi-point displacement method [5], and the geological radar method [6] to test the loose zone on-site. Through numerical simulations [7; 8; 9; 10], the loose zone ranges under different working conditions have been simulated, and their influencing factors (surrounding rock damage coefficient, surrounding rock grade, blasting dynamic load, blasting cycle times)and variation characteristics have been discussed. The formation mechanism and scope of the loose zone are studied and discussed through indoor model tests [11; 12]. Most of the formulas for the loose zone are based on either the elastic-plastic theory or field-measured data. [PERSON] et al. [13; 14] proposed a support theory of surrounding rock loose zone and presented an empirical formula of the loose zone range, which was related to the original rock stress and surrounding rock strength in combination with practical engineering:  
\[L=af(P,R)+b \tag{1}\]  
or  
\[L=2.22B^{2.94}H^{4.30}R^{-1.05}10^{-11} \tag{2}\]  
where \(P\) is the initial in situ stress, \(R\) is the compressive strength of the rock, \(B\) is the tunnel span, \(H\) is the buried depth of the tunnel, and \(a\), \(b\) are correction factors. [PERSON] et al. [15] used grey system theory to classify the loose zone of surrounding rock and carried out grey prediction research on the loose zone under different rock strengths based on field measurements. [PERSON] et al. [16] established a mathematical model of the thickness of the surrounding rock loose zone, the uniaxial compressive strength of the rock mass, and the original rock pressure. They fitted a mathematical model with actual measured engineering data and obtained a prediction expression of the loose zone range:  
\[L_{p}=a_{1}\frac{h}{2}e^{\frac{P}{R}}+a_{2}R\left(\frac{l}{h}\right)+a_{3} \left(\frac{l}{h}\right)^{2} \tag{3}\]  
where \(l\) is the tunnel span, \(h\) is the tunnel height, and \(a_{1}\), \(a_{2}\), and \(a_{3}\) are correcting factors. [PERSON] [17] introduced the theory of dimensional analysis, selected the parameters related to the loose zone, and established a prediction model of the loose zone range. Combined with measured data, a quantitative function was derived. [PERSON] et al. [18], [PERSON] et al. [19], [PERSON] [20], and [PERSON] et al. [21] trained mathematical models by using an artificial neural network combined with field observation data, and they obtained the relationship between the loose zone range and its influencing factors, which could be used to predict the loose zone range. [PERSON] et al.