This study investigates the response of shallow strip foundations of width (B = 1 m) placed above a circular tunnel of diameter ‘D’ in rock mass under three loading scenarios: (a) uniformly distributed load, (b) eccentric vertical load with offset ‘e’ and (c) eccentrically inclined load with inclination angle ‘β’ at the same offset. Numerical analyses were carried out using finite element limit analysis (FELA). Evaluate the foundation–tunnel interaction, a semicircle domain of radius ‘DP’ from the centre of footing is defined beneath the foundation. Both DP and ‘e’ are normalized with respect to the footing width B, expressed as DP/B and e/B, respectively. For clarity, the normalized semicircle radius (DP/B) is further denoted as the semicircular region factor (R). Tunnel positions are systematically defined using coordinates obtained from the polar coordinate system along the semicircular domain. In the case of uniformly distributed loading, symmetry allows consideration of tunnels only on one side of the footing axis at representative coordinates, (− √3/4)R, − R/4; − R/4, (− √3/4)R; and 0, − R/2. For eccentric and eccentrically inclined loadings (asymmetric cases), tunnel locations are extended to both sides of the footing’s vertical axis at the five positions: (− √3/4)R, − R/4; − R/4, (− √3/4)R; 0, − R/2; R/4, (− √3/4)R; and (√3/4)R, − R/4 enabling comprehensive evaluation under varied conditions. To evaluate the influence of key input variables including geometrical parameters (R, tunnel location), loading conditions (e/B, and β), and rock mass strength properties defined by the Generalized Hoek–Brown criterion (geological strength index, GSI, disturbance factor, DF, and material constant, mi), two dimensionless parameters are considered: stability number (Ns) and reduction coefficient (Rc). The findings reveal that for uniformly loaded foundations, tunnel influence becomes negligible (Rc ≈ 1.0) when R ≥ 10 for DF = 0, 0.5, and R ≥ 8 for DF = 1.0. For eccentric loading, foundation stability reduces from Ns ≈ 2.0 (e/B = 0, R = 10) to Ns ≈ 1.0 at e/B = 0.25 (R = 8), while Rc ≈ 1.0, indicating minimal tunnel influence. At e/B = 0.40, despite Rc ≈ 1.0 across all R, Ns drops to ≈ 0.02–0.08, confirming failure due to rotational instability rather than tunnel interaction. Under inclined loading (e/B = 0, β = 60°, R = 4), critical tunnel influence is observed (Ns ≈ 0.28, Rc ≈ 0.62). For e/B = 0.25 and β = 45°– 60°, significant interaction occurs at R = 4 – 6, whereas at β = 30° and e/B ≥ 0.25, tunnel influence remains negligible across all positions.

Foundation Stability Over Subsurface Tunnels in Rock Masses Under Complex Loading

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发表日期：

2025年10月31日

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Piyush Kumar,
Ravi Prakash Tripathi,
Rajyavardhan Rathour

摘要

This study investigates the response of shallow strip foundations of width (B = 1 m) placed above a circular tunnel of diameter ‘D’ in rock mass under three loading scenarios: (a) uniformly distributed load, (b) eccentric vertical load with offset ‘e’ and (c) eccentrically inclined load with inclination angle ‘β’ at the same offset. Numerical analyses were carried out using finite element limit analysis (FELA). Evaluate the foundation–tunnel interaction, a semicircle domain of radius ‘D_P’ from the centre of footing is defined beneath the foundation. Both D_P and ‘e’ are normalized with respect to the footing width B, expressed as D_P/B and e/B, respectively. For clarity, the normalized semicircle radius (D_P/B) is further denoted as the semicircular region factor (R). Tunnel positions are systematically defined using coordinates obtained from the polar coordinate system along the semicircular domain. In the case of uniformly distributed loading, symmetry allows consideration of tunnels only on one side of the footing axis at representative coordinates, (− √3/4)R, − R/4; − R/4, (− √3/4)R; and 0, − R/2. For eccentric and eccentrically inclined loadings (asymmetric cases), tunnel locations are extended to both sides of the footing’s vertical axis at the five positions: (− √3/4)R, − R/4; − R/4, (− √3/4)R; 0, − R/2; R/4, (− √3/4)R; and (√3/4)R, − R/4 enabling comprehensive evaluation under varied conditions. To evaluate the influence of key input variables including geometrical parameters (R, tunnel location), loading conditions (e/B, and β), and rock mass strength properties defined by the Generalized Hoek–Brown criterion (geological strength index, GSI, disturbance factor, DF, and material constant, m_i), two dimensionless parameters are considered: stability number (N_s) and reduction coefficient (R_c). The findings reveal that for uniformly loaded foundations, tunnel influence becomes negligible (R_c ≈ 1.0) when R ≥ 10 for DF = 0, 0.5, and R ≥ 8 for DF = 1.0. For eccentric loading, foundation stability reduces from N_s ≈ 2.0 (e/B = 0, R = 10) to N_s ≈ 1.0 at e/B = 0.25 (R = 8), while R_c ≈ 1.0, indicating minimal tunnel influence. At e/B = 0.40, despite R_c ≈ 1.0 across all R, N_s drops to ≈ 0.02–0.08, confirming failure due to rotational instability rather than tunnel interaction. Under inclined loading (e/B = 0, β = 60°, R = 4), critical tunnel influence is observed (N_s ≈ 0.28, R_c ≈ 0.62). For e/B = 0.25 and β = 45°– 60°, significant interaction occurs at R = 4 – 6, whereas at β = 30° and e/B ≥ 0.25, tunnel influence remains negligible across all positions.