## 4 Analysis of LDP Characteristics Under Different Stratigraphic Parameters
### Characteristic Analysis of Surrounding Rock Longitudinal Deformation Profile  
The computed LDP curves for all cases and comparative z-direction displacement contour maps at the z = \(-\)50 m cross-section (Cases 3, 6, 9) are presented in Figure 4. Analysis of Figure 4a reveals that Case 1 exhibits significantly smaller longitudinal deformation magnitudes compared to Cases 2 and 3. The longitudinal deformation curves of Cases 2 and 3 predominantly overlap in the pre-interface zone, whereas distinct divergence emerges post-interface. Case 2 demonstrates deformation attenuation, while Case 3 undergoes rapid deformation escalation. As illustrated in Figure 4b, Cases 4-6 exhibit marked numerical discrepancies. Case 6 achieves maximum deformation magnitude of \(-\)3.47 mm at 0.5 m ahead of the tunnel face, followed by an abrupt post-interface reduction in deformation. Figure 4c identifies Case 9 to have peak deformation (\(-\)4.49 mm) localized at 0.75 m ahead of the face. Cases 7 and 8 demonstrate negligible divergence prior to the interface; however, post-interface deformation magnitudes diverge significantly, with Case 8 exceeding Case 7. The characteristic features of LDP curves across all cases are systematically summarized in Table 5.  
In summary, homogeneous strata cases generally exhibit deformation patterns characterized by an initial increase followed by gradual attenuation. Conversely, cases involving stratigraphic interfaces exhibit biphasic behavior, where deformation follows an increase-decrease trend prior to the interface, while post-interface deformation magnitudes are governed by lithological parameters of the subsequent stratum.  
Figure 3: (**a**) Tunnel cross-section model; (**b**) schematic diagram of tunnel and tunnel face positions; (**c**) mesh model; and (**d**) schematic diagram of measuring point positions.  
Figure 4: (**a**) Comparison results of LDP curves for Scheme 1, Scheme 2 and Scheme 3 and displacement cloud charts in the z-direction for the section where z = \(-\)50 m of Scheme 3. (**b**) Comparison results of LDP curves for Scheme 4, Scheme 5 and Scheme 6 and displacement cloud charts in the z-direction for the section where z = \(-\)50 m of Scheme 6. (**c**) Comparison results of LDP curves for Scheme 7, Scheme 8 and Scheme 9 and displacement cloud charts in the z-direction for the section where z = \(-\)50 m of Scheme 9.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Scheme** & **Parameters of the** & **Characterization of the LDP Curve** \\
**Number** & **Surrounding Rock** & \\ \hline
1 & A-A & The deformation amount increases slightly and then decreases slowly, and the overall deformation amount is very small \\
2 & A-B & The deformation amount increases slightly and the decreases slowly. After passing through the stratum interface, the deformation amount decreases rapidly, and the overall deformation amount is relatively small. \\
3 & A-C & The deformation amount increases slightly and then decreases slowly. After passing through the stratum interface, it \\
4 & B-A & Before reaching the stratum interface, the deformation amount first increases and then decreases. After passing through the \\
5 & B-B & The deformation amount first increases and then decreases slowly, and the overall deformation amount is relatively small \\
6 & B-C & Before reaching the stratum interface, the deformation amount first increases and then decreases. After passing through the \\
7 & C-A & Before reaching the stratum interface, the deformation amount first increases and then decreases, and the overall deformation amount is relatively small \\
8 & C-B & Before reaching the stratum interface, the deformation amount first increases and then decreases, and the overall deformation amount is relatively large \\
9 & C-C & The deformation amount first increases and then decreases, and the overall deformation amount is relatively large \\ \hline \hline \end{tabular}
\end{table}
Table 5: A summary of the characteristics of LDP curves for different stratum combination schemes.