## 3 Physical Model Test
### Physical Model Test Instrument and Process  
To achieve horizontal non-uniform loading, the experimental setup shown in Figure 5, includes the following components from the inside out: the model shaft lining, surrounding rock, and loading steel plates capable of applying differential loads in the X and Y directions. Each steel plate surface uses a 100 T hydraulic jack for pressure control, enabling combined horizontal and vertical non-uniform loading on the inclined shaft lining. Strain monitoring combines distributed optical fibers (detailed in Section 2.1) with BQ120-10 AA strain gauges from Zhonghang Electric Measurement. Temperature compensation was achieved using embedded copper-constant thermocouples, with data collected through a DT85G data logger from Australia.  
The test procedure was conducted as follows: (1) Fiber Pre-installation. Optical fibers were attached to planned positions in the mold using low-viscosity double-sided tape. Hotspot identification ensured accurate alignment of each test segment. (2) Shaft Lining Casting. The concrete shaft lining model was cast using molds. Three 100 \(\times\) 100 \(\times\) 100 mm concrete cubes and three 100 \(\times\) 100 \(\times\) 300 mm concrete prisms were also cast. (3) Demolding and Curing. After 24 h, the shaft lining model was demolded-inner molds first, then outer molds. The model and specimens were cured under natural conditions for 7 days. (4) Strain Gauge and Thermocouple Installation: Strain gauges and thermocouples were installed at planned locations along the inner edge of the shaft lining. (5) Surrounding Rock Casting: Cement mortar porous surrounding rock was cast around the shaft lining. Each layer was compacted equally to ensure uniformity. (6) Surrounding Rock Curing and Demolding: The surrounding rock was cured for 5 days under natural conditions, then demolded. (7) Preloading Test: Apply synchronous graded loading in the X and Y directions, the X-direction confining pressure was 0.2 MPa, and the Y-direction confining pressure was 0.22 MPa; (8) Elastoplastic loading Test: Apply synchronous graded loading in the X and Y directions until shaft wall failure, with a loading gradient of 0.24 MPa in the X direction and 0.4 MPa in the Y direction. (9) Data Collecting: The shaft lining model was placed in the loading apparatus. Sensors were connected to the data acquisition system, and data collection began. (10) Test Recording: Crack development in the shaft lining was observed, and data were saved. (11) Elastic Modulus and Poisson's Ratio Testing: Specimens cast with the shaft lining were tested under compression to measure  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Elastic Modulus** & **Poisson’s Ratio** & **Elastic Modulus of** & **Poisson’s Ratio of** & **Allowable Tensile** & **Friction** \\
**of Shaft Lining** & **Surrounding Rock** & **Surrounding Rock** & **Stress** & **/MPa** & **Coefficient** \\ \hline
30 & 0.3 & 18 & 0.2 & 0.5 & 0.4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Shaft lining model parameters.  
Figure 5: Schematic diagram of physical simulation experiment loading model.  
elastic modulus and Poisson's ratio. Surrounding rock specimens were tested using the same method.