## 1 Introduction  
The quality of water conveyance tunnel linings plays a vital role in national economic stability and public welfare, serving as the key factor in maintaining the long-term safe operation of water conservancy projects [1, 2, 3, 4]. The construction of hydropower projects in high-altitude areas presents numerous challenges, including long tunnel routes, significant burial depths, complex regional tectonic conditions, and high levels of regional tectonic stress [5, 6, 7]. For instance, a water conveyance route for a hydropower station extends approximately 45 km in length, with the maximum burial depth of the tunnel groups reaching nearly 2000 m. Based on the results of existing in situ stress measurements, the maximum ground stress is estimated to range between 85 MPa and 102 MPa. The lining structures of deeply buried water conveyance tunnels are subjected to high ground stresses, high internal and external water pressures, and a significant risk of cracking [8, 9]. If cracks occur in the lining, the overall stiffness and load-bearing capacity of the tunnel are compromised. These cracks can also serve as channels for water seepage, which accelerates the erosion and degradation of concrete under high-speed water flow, leading to reinforcement corrosion. This significantly reduces the tunnel structure's reliability, stability, and durability. Recent advancements, including the use of smart controllers and shell-type dampers, have enhanced the performance of tunnel support structures [10, 11]. Studies have shown that smart sensors can effectively monitor tunnel conditions in real-time, while advanced friction dampers reduce dynamic loads on tunnel linings, thereby improving their resilience under varying conditions [12]. To ensure the long-term safety of the lining structures in deeply buried water conveyance tunnels, it is essential to identify the deformation characteristics of the surrounding rock and design appropriate support structures [13, 14, 15]. The core issue in the design of support structures lies in the interaction between the surrounding rock and the support [16, 17]. However, due to the insufficient understanding of the cooperative mechanism between the surrounding rock and the support, support structures are often designed too conservatively or result in substantial waste, posing significant risks to the construction of underground projects [18, 19]. Numerous studies have been conducted on the cooperative action of surrounding rock and support in shallow tunnels with homogeneous surrounding rock, with the majority focusing on theoretical analysis, numerical calculations, and experimental studies. Theoretical analysis is typically employed in the pre-design stage of support structures, which is suitable only for rough qualitative research. Experimental studies often fail to fully account for the actual service conditions of deeply buried tunnel lining structures, giving insufficient attention to the cooperative bearing action of surrounding rock and lining under the influence of multiple factors. The solution of numerical methods depends heavily on the model selection and the input of parameters [20]. Currently, the interaction between the surrounding rock and support structure is receiving increasing attention, with the core focus on predicting the time-varying behavior of surrounding rock for deeply buried tunnel groups and the mechanical properties of support structures. The convergence-confinement method (CCM), integrating the ground reaction curve (GRC) and support characteristic curve (SCC), is a core tool in tunnel support design [21, 22]. The GRC, a critical element of the CCM, characterizes the relationship between tunnel wall displacement and the internal support pressure, providing insight into the mechanical interaction between the surrounding rock and tunnel support systems. It has been refined to incorporate more complex rock mass behaviors and environmental factors.