Figure 4 – The strain analysis results along the cut line analysis for (a) Case One and (b) Case Two. The results from both Case One and Case Two clearly demonstrate the strong influence of shaft spacing on the mechanical response of the surrounding rock mass. Introducing a second shaft consistently increased the stress and strain experienced by the first shaft, confirming the expected interaction effects between closely spaced underground openings. The single‑shaft configuration therefore served as a stable baseline, with all two‑shaft arrangements producing elevated stress levels to varying degrees depending on spacing. The most critical condition occurred at the smallest spacing, S1, where the proximity of the two excavations caused significant stress amplification. The von Mises and principal stresses at S1 were approximately 1.5 times those of the single‑shaft case, indicating substantial overlap of stress influence zones. This behavior aligns with classical rock mechanics principles, where closely spaced openings lead to superposition of stress fields and heightened deformation. A key observation is the rapid reduction in stress once spacing increases beyond S1. The transition from S1 to S2 (and ultimately S3) reflects a diminishing interaction effect, with the stress field progressively decoupling between the two shafts. By the time the spacing reaches S3, the stress distribution closely resembles that of the single‑shaft configuration, with stress ratios only slightly above unity. This suggests that beyond a certain threshold distance, the shafts behave almost independently, and the mechanical disturbance caused by the second excavation becomes minimal. -450 -400 -350 -300 -250 -200 -150 -100 -50 0 -2.0E-04 -1.6E-04 -1.2E-04 -8.0E-05 -4.0E-05 0.0E+00 Depth (m) Strain (1) Second Principal Strain S1-U S2-U S3-U 1Sh-U -450 -400 -350 -300 -250 -200 -150 -100 -50 0 -2.0E-04 -1.5E-04 -1.0E-04 -5.0E-05 0.0E+00 Depth (m) Strain (1) Second Principal Strain S1-F S2-F S3-F 1Sh-F -450 -400 -350 -300 -250 -200 -150 -100 -50 0 0.E+00 2.E-05 4.E-05 6.E-05 8.E-05 1.E-04 Depth (m) Strain (1) Third Principal Strain S1-U S2-U S3-U 1Sh-U -450 -400 -350 -300 -250 -200 -150 -100 -50 0 4.6E-06 5.0E-06 5.4E-06 5.8E-06 6.2E-06 Depth (m) Strain (1) Third Principal Strain S1-F S2-F S3-F 1Sh-F
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