PSI - Issue 84

Marialorenza Vescovi et al. / Procedia Structural Integrity 84 (2026) 1063–1070

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4. Results Figure 4a compares the stress distributions derived from the calibrated simplified approach and the non-linear FEM analysis. The FEM stress values were extracted at a depth of 15 cm from the intrados to ensure consistency with the measurements provided by the 30 cm width of the flat-jacks (corresponding to the mid-point of the measurement device). The numerical results align best with in-situ measurements when considering an intermediate deconfinement stage, specifically where only 10% of the potential rock load is transferred to the lining. This finding confirms that the rock mass effectively mobilizes a self-supporting arching effect, thereby validating the drastically reduced equivalent load height (h=2.05m) identified through the simplified back-analysis. The comparison demonstrates that the simplified method is conservative. While the non-linear FEM predicts a lower, more uniform stress distribution due to plastic redistribution capabilities, the Desimon approach yields higher peak stresses, thus providing a safe upper-bound estimate for structural verification. More in detail, the simplified approach exhibits higher stress at the keystone (approximately 0.6 MPa), decreasing towards the sidewall. This aspect was confirmed by the comparison of the eccentricity showed in Figure 4b. The FEM model displays extremely low eccentricity values (almost zero), except at the base of the sidewall. In contrast, the simplified method shows high variability in eccentricity along the lining, alternating toward intrados at the keystone and reaching limit values toward the extrados at the sidewall and invert. In Figure 4c variation of stress in intrados and extrados of the two models shows higher variability and stress in the simplified stress state approach compared to the NL FEM analysis, resulting in a more conservative stress condition.

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Figure 4 (a) Comparison of fitting in fitted stress models (b) eccentricity in fitted stress models (c) Intrados and extrados stress in fitted stress models.

Figure 5 presents a comparative analysis of the external loads acting on the lining as derived from the two methodologies. Figure 5a, illustrates the vertical stress distribution acting on the crown and sidewalls. It highlights that the NL FEM analysis yields consistently lower load values compared to the simplified analytical approach. This reduction is attributable not only to the soil arching effect but also to the frictional interaction modeled at the soil structure interface. Unlike the simplified approach, the FEM simulation incorporates a friction coefficient of  = 0.3, which significantly reduces the net normal pressure acting on the masonry lining. Similarly, at the invert level (Figure 5b), the FEM model predicts a lower reaction pressure compared to the simplified approach. Despite the difference in magnitude, both methods identify a significant stress concentration at the sidewall base, corresponding to the geometric transition zone. Finally, regarding the horizontal confinement, Figure 5c demonstrates that the FEM simulation results in lower horizontal stresses along the sidewall compared to the simplified procedure. This further confirms that the simplified Desimon method generally overestimates the acting loads, resulting in conservative pressures for safety verification.