PSI - Issue 84

Daniela Boldini et al. / Procedia Structural Integrity 84 (2026) 175–182

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quasi-static phase; however, the simultaneous increase in axial compression prevents the section from reaching its interaction domain. These increments in axial force N at the crown are more pronounced for the lower value of K 0 . By contrast, sections outside the reduced-thickness zone (black symbols in Fig. 6) undergo either increases or significant reductions in axial force (see Figs. 4 and 5). In all analysed cases, the normal forces decrease to near-zero values at the left shoulder, where the tensile strength is reached in the circumferential direction. They are higher at the crown and the right sidewall, where the tensile strength is reached in different directions.

(a) full section – K 0 = 0.5

(b) full section – K 0 = 1.5

(c) 10 cm residual thickness – K 0 = 0.5

(d) 10 cm residual thickness – K 0 = 1.5

Fig. 5. Normal force ( N ), scaled to 0.005, and bending moment ( M ), scaled 0.05, acting in the tunnel lining after the quasi-static phase for different values of K 0 .

Fig. 6. N - M interaction diagrams for 10 cm residual thickness: (a) K 0 = 0.5; (b) K 0 = 1.5.

An additional comparison was then performed by considering two levels of imposed shear strain in the quasi-static phase: the Eurocode-based value (EC, γ EC = 0.00237%) and the average shear strain at tunnel depth derived from the local seismic response analyses (SR, γ SR =0.00420%). For the SR case, the analyses were further extended by introducing a degraded inner lining layer, representative of the pre-existing cracking observed during field inspections.