## 1 Introduction  
With the development of underground spaces in cities and surrounding areas, the construction of shield tunnels is becoming more and more frequent. However, the development of a regional economy means that the length of the shield tunnel continues to extend. There is an urgent need to change the traditional construction technology to adapt to the rapid growth of tunnel demand. In terms of improving tunnel construction speed, this mainly depends on: (i) improving the shield tunneling speed; and (ii) simultaneous shield propulsion and segment assembly, i.e., synchronous propulsion and assembly technology. In the case of normal shield construction, the shield stops advancing. After the segments are assembled into rings, the hydraulic jack propels the newly assembled assembly ring to provide the support of the tunnel surface and the thrust of the shield. In the synchronous propulsion and assembly mode, the shield does not need to stop, and the jack acts directly on the unlooped segments to propel while assembling. The synchronous propulsion and assembly technology systematically reduces the suspension time during tunnel segment assembly [1]. As we all know, the shield propulsion force is borne by the lining ring during the construction of the traditional shield method, and the impact of shield propulsion on the lining ring does not need to be considered during the assembly process of the segment. The new construction method exposes the segments to propulsion loads before they are looped, which puts the segments at greater risk of damage [2; 3; 4; 5]. It is necessary to study the safety of this construction method to ensure the smooth progress of construction. In fact, the load and working state of shield tunnel segments in the construction stage are complex and uncertain [6]. Focusing on the engineering situation, many scholars have conducted in-depth research on segment damage caused by assembly error in the construction stage. The main research method involves using the integral design models, such as homogeneous ring, elastic hinge ring, and multi-hinge angle ring models. [PERSON] studied the concrete cracks detected at different locations [7]. Combined with finite element model analysis, it was shown that the shield machine and segment had an influence in terms of an inclined and uneven jacking load on the assembly quality of the segment. The Japanese Society of Civil Engineers statistically studied the damage frequency of segments in 50 tunnel sites during construction [8]. [PERSON] found that the damage types of segments focused on longitudinal cracks and corner spalling before or during shield propulsion. [PERSON] studied the causes of the above damage. The results show that when a jack is loaded, the longitudinal dislocation of the upper ring can easily cause a longitudinal crack in the next ring segment, and the collision and extrusion of the adjacent segments of the current ring are important causes of corner damage [9]. In addition to the direct relationship between assembly errors in segments and the damage of segments, the excessive vertical loadings caused by jacks during shield propulsion are also an important reason for segment cracking (prefabricated structures), spalling, and water leakage [10; 11; 12; 13]. In the construction process, due to the deformation and contraction of the segment or the low surface smoothness of the segment, the uneven support or load eccentricity in the construction process will further deepen the cracking of the segment [14]. [PERSON]'s research shows that segment torsion produces additional shear stress when the segment is supported unevenly, which causes oblique cracks. Under the action of axial thrust, the pipe section appears in the compression and tensile stress area, and longitudinal cracks may appear near the vault, inverted arch, and waist [15]. [PERSON] carried out a detailed study on the situation of segments subjected to radial force. Under symmetric radial force, a newly assembled tube deflects radially around the previously assembled tube [16].