## 1 Introduction  
With the rapid expansion of urban transportation renovation and transportation networks in China, a growing number of large-span, large cross-section tunnels are being constructed beneath sensitive environments, including airport runways, critical infrastructure, and high-speed railways. These projects often demand stringent settlement control within millimeter-level tolerances, underscoring the need to advance theoretical approaches and key techniques for micro-settlement control. Numerous researchers around the world have investigated settlement control for tunnels beneath sensitive environments through theoretical analysis, numerical simulations, and physical model tests. These studies evaluate the effectiveness of various surface settlement control measures, including enhancing support stiffness, optimizing pipe-roof construction, and managing groundwater levels. [PERSON] [1] performed finite element numerical simulations to analyze the impact of support timing and primary support strength on surrounding rock deformation and surface settlement during shallow tunnel excavation. [PERSON] et al. [2] optimized the original support scheme of \"single-layer steel arch primary support + double-layer secondary lining\" through numerical simulations and field monitoring. This optimization effectively controlled the surrounding rock deformation and reduced the stress on the secondary lining. [PERSON] et al. [3] conducted a safety performance optimization analysis of support design parameters for a three-lane, large cross-section highway tunnel under construction in Guangdong Province. This analysis took into account factors such as surrounding rock conditions, burial depth, tunnel shape, and cross-section dimensions. [PERSON] [4] modified the Peck formula [5] to account for construction-induced stress and ground loss, enabling more accurate predictions of surface settlement during pipe-jacking operations. [PERSON] et al. [6] applied random medium theory to evaluate surface settlement resulting from curved pipe jacking construction in ultra-shallow drainage layers. [PERSON] et al. [7] utilized numerical simulations to analyze the patterns of soil displacement around the pipe-roof structures and surface settlement during pipe-roof construction in soft soils. [PERSON] et al. [8] conducted three-dimensional numerical simulations to examine the interactions and effects of closely spaced multi-pipe-jacking operations on soil deformation and surface settlement. They concluded that multi-pipe-jacking construction produced a cumulative effect on the settlement trough. [PERSON] et al. [9] investigated the impact of densely arranged, large-diameter steel pipe installations on the surface settlement in the pipe-roof pre-construction method. They further analyzed the impact of completed steel pipes at different intervals on the surface settlement during subsequent pipe-roof operations. [PERSON] et al. [10] proposed a water level variation curve and a flow-around zone division formula through model experiments. Furthermore, they developed a simplified calculation method for surface settlement outside the foundation pit, which was further modified using the seepage principles within the flow-around zone. [PERSON] [11] partitioned the soil layers in the dewatering area into distinct zones and calculated the settlement of each zone using the layerwise summation method, thereby determining the total surface settlement. [PERSON] [12] investigated the stress variations in the surrounding rock of a karst tunnel under seepage conditions and proposed a method for calculating surface settlement in the soil-surrounding rock section under these circumstances. [PERSON] et al. [13] studied the consolidation compression of soil units in dewatering areas based on the effective stress principle and one-dimensional consolidation compression theory. They also predicted the surface settlement around the foundation pit using the stochastic medium theory method. [PERSON] et al.