# Modeling of Tunneling Total Loads Based on Symbolic Regression Algorithm
## 1 Introduction  
In recent years, tunnel boring machines (TBMs) have been widely used in the construction of urban subways and tunnels through mountains [1; 2; 3; 4; 5]. TBMs are a kind of large-scale engineering equipment working under considerable loads, and often operate in complex and changeable construction environments [6; 7]. Safe and efficient tunneling is vital for the equipment and the stability of the ground environment [8]. The TBM construction process mainly involves the interaction between the machine and the local geology, in which the tunneling total load, mainly composed of the total thrust and the total torque, is one of the core control parameters [9; 10]. During the construction process, the equipment must overcome resistance to move forward under the action of the total thrust, and the cutter installed on the cutter head penetrates into the stratum and remains spinning under the action of the total torque. Therefore, modeling and predicting the tunneling total loads is of great significance. Modeling the tunneling load has long been a concern in this field. The classic approaches are [PERSON]'s empirical formula model for shield tunneling in soft soil [11] and the Colorado School of Mines (CSM) model for shield tunneling in hard rock [12; 13]. [PERSON]'s empirical formula reflects the basic mechanical equilibrium information through the power relationship between the load and the equipment diameter, with other influencing factors such as geology covered by empirical coefficients. This empirical formula provides a relatively broad range of predicted values, but the model is simple and easy to operate, and so it has been widely used. The CSM model is based on force calculations and statistical data fitting, mainly from indoor linear cutting experiments [14; 15]. To obtain load modelsthat are more suitable for actual complex construction environments, many scholars have carried out further related studies. Analytical methods can be divided into two categories: modeling based on theoretical derivation and modeling based on data analysis. Modeling based on theoretical derivation includes an improved version of [PERSON]'s empirical formula, in which the composition of the cutter head torque is analyzed for composite geology [10]. In Ref. [16], considering the structure of the cutter head, the cutting principle, and the interaction between the cutter head and soil, the composition of the cutter head torque is divided into eight parts that are calculated to obtain the final load model. In Ref. [17], the composition of the total thrust force is analyzed and divided into frontal resistance, frictional resistance, penetration resistance, segmental ring friction, and auxiliary facility resistance. The thrust model for a sandy geology is then obtained. In Refs. [18; 19], the coupling relationship between the cutter head and the local geology is analyzed and theoretical load models are established by considering the influence of three key factors on the load, namely the geological conditions, operating state, and equipment structure. However, the complexity of tunneling construction means that load models constructed based on theoretical analysis are often complicated and have limited consideration of the actual geological conditions; for example, the classic CSM model does not consider the influence of rock mass density and cohesion [2]. Therefore, many researchers have attempted to build load models through data analysis methods. There are two types of load modeling methods based on data analysis: traditional mathematical statistical methods and machine learning algorithms. The traditional mathematical statistical methods include a cutter head torque model established with multivariate statistical analysis based on orthogonal experiments [20]. In Ref. [21], an empirical estimation model of the cutter head load is established by linear regression based on data from improved traditional cutting experiments. In Ref.