## 5 Conclusions  
In this study, a novel rock sample with a prefabricated inverted arch was designed and subjected to biaxial step loads. Based on 3D-DIC, the deformation mechanism of rock samples with prefabricated inverted arches was analyzed. The main conclusions are listed as follows:  
1. Under the combined compression effect of vertical stress and horizontal stress in the biaxial step-loading test, the tensile stress of the interlayer weak plane exceeded the tensile strength. Then, the sample was cut into a layered platy structure. Due to stress concentration and the influence of the weak planes between layers, the outermost rock blocks near the surface of the inverted arch peeled off under continuous loads parallel to the bedding planes. After that, the stress was transferred to the deep part of the rock toward the negative direction of the \(X\)-coordinate. Subsequently, the separated plate-shaped sample buckled under the effect of force and fractured in the middle position. Eventually, the bottom of the inverted arch uplifted, and an \"S\"-shaped crack on the surface was formed near the center of the inverted arch;
2. The layered structure is an important factor causing uplift deformation at the bottom of the rock sample. The failure of schist is mainly due to weak cementation between layers. The orientation and propagation of cracks depend on the position of weak joint surfaces. The main failure mode of schist is splitting tensile failure, while that of homogeneous sandstone is compression shear failure. As the lateral stress increases, the time required to reach the maximum axial load increases;
3. Floor heave initially occurs near the bottom of the inverted arch, rapidly and continuously moving away from the arch surface. The displacement of the uplift gradually decreases from the position near the bottom of the inverted arch to the direction away from the arch surface. The displacement of the bottom surrounding rock increases significantly within the \(Y\)-coordinate range of 0-20 mm compared to the adjacent area. The curve of displacement in the \(X\)-direction along the \(Y\)-coordinate exhibited a protruding shape, with the maximum displacement at Y = 11.7 mm;
4. During the experiment, the phenomena of rock plate separation, fracture, and surface uplift displacement were observed, which is consistent with floor heave damage in actual engineering tunnels.  
The careful investigation and analysis of the deformation mechanism and pattern of layered rock masses for tunnel floor heave is a key issue for tunnel-support design and subsequent remediation. The main objectives of upcoming research will be to investigate the rheological deformation mechanism of the weak surrounding rock as well as suitable support approaches.  
Conceptualization, D.L. and Z.P.; methodology, D.L. and Z.P.; software, H.G.; validation, Q.Z. and J.M.; formal analysis, Q.Z.; investigation, D.L. and Z.P.; writing--original draft preparation, Z.P.; writing--review and editing, Q.Z. and J.M.; supervision, D.L.; funding acquisition, D.L. All authors have read and agreed to the published version of the manuscript.  
The work presented in this paper was financially supported by the National Natural Science Foundation of China (No. U1934211).  
Not applicable.  
The data presented in this study are available in the article.  
The authors declare no conflict of interest.