## 1 Introduction  
Tunnel boring machines (TBMs) are now widely used in tunnels for water conservation and hydropower projects, highways, urban subways, and other fields around the world due to their technical characteristics of fast excavation speed, high quality, low disturbance to surrounding rocks, high equipment safety, and good environmental protection [1]. Among the various TBM excavation grounds, mixed-face ground is one of the most difficult conditions. Within the excavation section and in the direction of the excavation extension, the mixed-face ground includes two or more separate geological strata with extremely varied geotechnical property, engineering geology, and hydrogeological properties. Modified earth pressure balance (EPB) TBMs are commonly employed in the development of composite strata to deal with complicated and changing geological conditions as well as the difficulties of excavation. The modified EPB TBM features two types of cutters installed on the front of the cutterhead (disc cutter and drag cutter), which work together to remove the rock and soil from the surface as the machine goes ahead. Many aspects influence TBM performance, including device characteristics, rock and soil properties, each cutter's parameters, the composition of the excavation face, and the operators' operation [2]. Accidents like severe cutter wear, cutterhead blockage, and jamming are common during the construction of mixed-face ground, for example, in the Shanggongshan diversion tunnel in Kunming, the Pinglin highway tunnel in Taiwan, or the Dul Hasti hydroelectric project diversion tunnel in India [3]. As a result, predicting TBM performance is critical for improving construction quality and minimizing construction costs. Modeling the distribution of disc cutters and drag cutters on the cutterhead in different excavation faces can reflect the cutting process of cutters more intuitively when the cutterhead is rotating, but such models are very scarce. [PERSON] et al. [4] fixed the positions of each tool and stratum in the coordinate system, identified the types of rocks under each cutter using a ray intersection algorithm, and then utilized the Colorado School of Mines (CSM) model to determine the cutter cutting forces. However, the model was only applied to the layer-banded rock (LBR) and the random-distributed rock (RDR) conditions. [PERSON] et al. [5] developed a dynamic torsional model for the TBM cutting system in mixed-face conditions by considering a sketch of the multiple pinion concentric drive of the TBM cutterhead. [PERSON] et al. [2] developed a model that fixed the location of the cutter in the coordinate system, meanwhile changing the position of OXY. When the cutterhead is spinning in the rock-soil interface (RSI) of mixed ground, the parameters for the force calculation of the cutter are different. During the design phase, estimating the thrust and torque of a TBM can offer the thrust and torque capability for commissioning the machine. Power is another critical component that can directly reflect TBM performance. Many studies have been conducted to forecast the thrust and torque of TBM under various situations. [PERSON] et al. [6] developed a model for estimating the force of a hard rock TBM, which can also determine the thrust and torque needs of the TBM. [PERSON] et al. [7] proposed the torque composition of an EPB TBM and calculated each torque component by considering the cutterhead structure, cutting principles, and cutter-soil interaction. [PERSON] et al. [8] calculated the thrust and torque of several types of TBMs operating in soft strata. [PERSON] et al. [9] proposed a calculation method to estimate the thrust and torque of TBM when tunneling in soil and soft rock composite strata, but the model did not explain each component of the thrust and torque in detail. It is not too difficult to notice that there is little research about TBM power. [PERSON] et al.