## 1 Introduction  
In recent years, numerous tunnels have been constructed for highways, railways, water conservancy, and for hydropower infrastructure in China. As the construction environment is becoming increasingly complex, such as shallow tunnels, long tunnels, and soft-rock tunnels, attention is drawn to the challenges posed by shallow-buried soft-rock tunnels. These tunnels exhibit weak surrounding rock, poor stability, and significant excavation-induced deformation, leading to potential disasters such as surface settlement, vault collapse, and damage to supporting structures during tunnel excavation. Such instability can impact the safety of construction procedures and personnel [1; 2; 3].  
To address these issues, experts and scholars have dedicated substantial efforts to stabilize shallow-buried soft-rock tunnels, yielding valuable insights. [PERSON] et al. [4] investigated how different constitutive models influence surface settlement predictions. [PERSON] et al. [5] developed an expression for tunnel surface settlement in composite strata tunnels based on random medium theory. [PERSON] et al. [6] proposed a formula to estimate ultimate deformation and strain in soft-surrounding-rock tunnels. [PERSON] et al. [7] analyzed deformation characteristics and acceleration in the rock surrounding tunnels, deriving a comprehensive deformation model for both deep and shallow-buried tunnels. [PERSON] et al. [8] explored the relationship between tunnel section size, construction method, surrounding rock grade, and excavated surface stability using orthogonal experiments and range analysis. [PERSON] et al. [9] investigated the effects of joints, fissures, and cross-section shape in shallow-buried tunnels. [PERSON] et al. [10] put forth a support scheme for soft-rock tunnels, combining weakening anchors with enhanced rigidity and initial support strength. Additionally, [PERSON] et al. [11] conducted long-term stability studies on soft-rock tunnels through experiments and field tests. [PERSON] et al. [12] conducted some laboratory tests and examined the mechanical characteristics of mudstone based on the Badong Tunnel, and the large deformation collapse process of the tunnel face was simulated. [PERSON] et al. [13] studied the reinforcement effect of high-pressure rotary jet method on surface in shallow-buried sections of tunnels. [PERSON] et al. [14] studied the stress characteristics of the supporting structure of expansive soft-rock tunnels and built a swelling force release method of tunnel support with expansive soft rock.  
In practice, tunneling plans, optimal construction times for tunnel support, and the stability of tunnel construction are closely linked to the mechanisms and processes of surrounding rock deformation. On-site monitoring and numerical simulation serve as crucial methods [15; 16]. However, there is a relative scarcity of studies focusing on the time-varying characteristics and laws governing surface settlement, deformation of the surrounding rock, and stress within supporting structures in shallow-buried tunnels. In this study, the Heimaguan Tunnel serves as the subject of investigation. Researchers analyze the time-dependent settlement characteristics of the tunnel surface, vault subsidence, and horizontal convergence through on-site monitoring and regression analysis. This analysis informs the determination of the optimal secondary lining construction time. Based on these findings, a numerical simulation model is developed to assess the deformation of the surrounding rock and stress characteristics relevant to supporting structures. The study's conclusions provide a theoretical foundation and serve as a reference for the design, maintenance, and research of shallow-buried soft-rock tunnels.