evaluation line, whereas any two‑shaft arrangement produced noticeably higher stresses. The most intense stress concentrations occurred at the tightest spacing (S1). As the distance between shafts increased, these stresses diminished steadily, trending toward the levels observed in the single‑shaft scenario. At the widest spacing (S3), the stress field became very similar to the 1‑shaft baseline. For instance, when averaged between depths of –50 m and –350 m, the stresses in S1 were roughly 1.5 times greater (1.4–1.6 range) than those in the single‑shaft case for both scenarios. In contrast, the ratios at S3 were much smaller, approximately 1.04–1.12 in Case One and 1.02–1.05 in Case Two. A notable pattern is the sharp decline in stress immediately after S1. Once spacing increases beyond S1, the two‑shaft configurations begin to behave far more like the single‑shaft system. The strain response (Figure 4) followed the same general pattern. Maximum strains occurred at S1, then dropped substantially as spacing increased. By S3, strain values nearly matched those of the single‑shaft configuration. However, the magnitude of the two‑shaft to one‑shaft strain ratio differed between the two cases: in Case One, the average volumetric strain in S1 was about 1.5 times the single‑shaft value, whereas in Case Two the ratio was lower, around 1.27. (a) Case One (b) Case Two -450 -400 -350 -300 -250 -200 -150 -100 -50 0 -3.0E-04 -2.5E-04 -2.0E-04 -1.5E-04 -1.0E-04 -5.0E-05 0.0E+00 Depth (m) Strain (1) Volumetric 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) Volumetric Strain S1-F S2-F S3-F 1Sh-F -450 -400 -350 -300 -250 -200 -150 -100 -50 0 -2.5E-04 -2.0E-04 -1.5E-04 -1.0E-04 -5.0E-05 0.0E+00 Depth (m) Strain (1) First 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) First Principal Strain S1-F S2-F S3-F 1Sh-F
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