PSI - Issue 84

Gerardo Sorrentino et al. / Procedia Structural Integrity 84 (2026) 1071–1078

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V p generated by a loading body which increases linearly with depth—with a slope related to the soil unit weight—up to the value V g ⋅ γ at the base of the sidewall. Additionally, the passive resistance of the soil may be included by applying an amplification factor (1+f) related to the soil properties since f is the internal friction coefficient of the material.

(a) (b) Figure 2 (a) SRE method supposed equivalent loading body (b) SRE method lining external loads scheme.

The horizontal forces transmitted to the crown ( H 1R ) or the invert ( H 2R ) are then obtained from the arch geometry, following the approach proposed by Falchi Delitala (1971). The total thrust acting at the sidewall foundation ( P p )or the invert ( h ∙α ) is determined as a component of the total vertical thrust transmitted above the sidewall base, by computing rotational equilibrium about the invert center O . The computation proceeds by dividing the arch into voussoirs and evaluating all forces acting on each. A force-polygon construction is used to combine vertical and horizontal loads, giving the thrust line and the normal force in each voussoir. With the normal force and its eccentricity known, stress distribution across the voussoir section can be derived. 2.3. Stress limits at the sidewall base Desimon considers different arch configurations. He establishes that the stresses at the base of the sidewall should not exceed a limit stress, which are calculated as the in-situ maximum vertical pressure p above the tunnel plus a constant increment, which is 6kg/cm 2 for linings without invert and 8kg/cm 2 for linings with invert. When it is not possible to directly measure the in-situ pressure p , Desimon suggests that pressure p is equal to: = ℎ ∙ (3) where γ soil is the unit weight of soil and h is the soil height for 15-20m above the tunnel. For deeper tunnels, h is the equivalent loading body height plus the height of the tunnel from the base of the sidewall to the keystone. According to Falchi Delitala (1971), the structural interaction between the invert arch and the sidewall foundation improves load distribution to the ground. Consequently, the effective bearing area at the sidewall base AB ( Figure 3 b) is assumed to extend by an additional width equal to half the sidewall thickness (t/2).