## 1 Introduction  
As an important part of modern transportation network construction, the structural safety and durability of tunnel engineering are directly related to the service life and operational safety of the project [1]. The lining structure, as the main load-bearing component of the tunnel, has an important influence on the overall stability of the tunnel in terms of its mechanical properties. In recent years, tunnels have developed in the direction of deeper and longer [2], and composite lining is widely used in China [3]. The scope of the application of single-layer lining is limited by materials and construction technology; however, in recent years, with the rapid progress of materials and construction technology, the advantages of its construction simplicity and economic efficiency have been given full attention, and single-layer lining has gradually become a hotspot for research. However, how thick the single-layer lining is greatly affects how well it can bend, and the way stress is spread and how it fails can vary a lot with different thicknesses. At present, the research on the effect of the thickness ratio of single-layer lining on its flexural performance is still insufficient, which limits its optimized design and safe application under complex engineering conditions. Concrete stacked beams, which are a common structural form, have been extensively studied by scholars both domestically and internationally regarding the factors that influence their flexural properties. The mechanical properties of concrete stacked beams are affected by their own material properties and structural configuration (fiber [4; 5; 6; 7; 8; 9; 10], aggregate [11; 12; 13], mineral admixture [14; 15; 16; 17; 18], splicing [19; 20]) multifaceted coupling and the mixing of a certain amount of fibers and silica fume, and selecting the appropriate aggregate and structural construction can help to improve the flexural properties and stiffness of concrete beams. [PERSON] [21; 22] analyzes the force characteristics of a multi-layer lining structure under interlayer action. There exists radial anti-slip action between layers of multi-layer shotcrete, which can form an integral bearing structure when composed of stacked lining. [PERSON] [23] quantitatively determined the integrity of the structure with strong interlayer adhesion but did not establish the mechanical relationship between the external loads and each stacked layer. [PERSON] et al. [24; 25; 26; 27] carried out a study on the effect of interlayer composite action on the synergistic performance of concrete composite beams in bending and fatigue performance, and the results show that the interface debonding will reduce the synergistic performance of concrete beams, and the interfacial factor should be introduced into the study of the bending performance of concrete beams. [PERSON] [28] found that the bonding properties of the materials between the two layers of concrete can increase the synergistic force of the structure, resulting in a class of composite load-bearing structures that improve the utilization of concrete. Some scholars have utilized the higher-order shear deformation theory [29] and Winkler theory [30; 31] to carry out the basic theoretical study on the bending performance of stacked beams and found that the interlayer modulus and the thickness ratio affect the bending performance of the concrete beams, but there is a lack of detailed experimental studies on the thickness ratio. On the basis of two-layer concrete laminated beams, different composite materials (wood-concrete laminated beams [32], UHPC-NC laminated beams [33], rubber-concrete laminated beams [34], ECC-concrete laminated beams [35; 36; 37; 38], reinforced bamboo-concrete laminated beams [39]) are used to study the bending performance, fatigue performance, flexural stiffness, and optimum distribution height of concrete beams.