PSI - Issue 84

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

177

condition was examined, with the tunnel crown located at a depth of 4 D , where D is the equivalent tunnel diameter, equal to 8.52 m. The lining material was assumed to be a C16/20 concrete, a common value obtained from tests carried out during inspections of existing tunnels. Its mechanical properties are listed in Tab.1 according to Eurocode 2 (EN1992-1-1:2023), with a unit weight of γ c = 24.5 kN/m 3 . The intact portion of the lining was represented as an elasto-plastic no-tension material, with shear behaviour governed by a Mohr-Coulomb strength criterion ( φ c ' = 58°, c c ' = 2.4 MPa), obtained as the tangent line to the Mohr circles in case of uniaxial compression and pure tension. The elastic modulus E cm was obtained assuming a coefficient k E of 9,900 for ordinary aggregates. To account for the pre existing cracking observed during field inspections, a 15-cm inner portion of the lining, measured from the intrados, was modelled as a degraded layer. For this cracked concrete, the Young’s modulus was reduced to half that of the intact material, while both tensile strength and friction angle were set equal to zero. Its shear resistance was described by a Tresca criterion, with cohesion equal to the Eurocode-based contribution provided by aggregate interlock only (683kPa). A medium-quality, undisturbed rock-mass was considered, defined by the parameters of the intact rock listed in Tab. 2, along with a Geological Strength Index (GSI) of 65, a disturbance factor D f = 0, unit weight  r =25.0kN/m 3 , and Poisson’s ratio of ν r =0.35. Using the empirical method of Hoek et al. (2002), the corresponding rock-mass strength properties were derived and are also reported in Tab.2. The Hoek-Brown strength parameters were subsequently converted into an equivalent Mohr-Coulomb model, giving shear strength values of φ ' =59° and c' =1.325MPa for both overburden cases. The static Young’s modulus of the rock-mass E s was estimated from the intact rock modulus E i according to Hoek & Diederichs (2006). Dry conditions were assumed.

Tab. 1. Characteristics of the concrete lining (C16/20) according to Eurocode 2 (EN1992-1-1:2023). Characteristic cylindrical compressive strength f ck 16 MPa Mean cylinder compressive strength f cm 24 MPa Mean tensile strength f ctm 1.9 MPa Young’s modulus E cm 28.6 GPa Poisson’s ratio ν c 0.2

Tab. 2. Intact rock and rock-mass parameters. Intact rock

Rock-mass

Uniaxial compressive strength σ ci

70MPa

Uniaxial compressive strength σ ca

9.94 MPa -0.50 MPa 17.06 GPa

Material constant m i Young’s modulus E i

10

Tensile strength σ ta Young’s modulus E s

27GPa

A severe seismic scenario was represented by assuming a peak ground acceleration PGA =0.35g at the rock outcropping. Seismic actions acting at tunnel depth were estimated using the method proposed in the second generation Eurocode 8, Part 5, Annex G (prEN 1998-5:2024). The maximum shear stress at the tunnel axis,  max , was derived from the equilibrium of horizontal forces acting on a soil column of unit width:

 

 

PGA

r

max  = 

(1)

 

v dt

g

In (1), g denotes gravity acceleration while σ v is the total vertical stress. The reduction of shear stress with depth was expressed through the depth-dependent factor r dt calculated as:

1.0

10m

z



  = −

t

(2)

1.2 0.02 10 z

35m

r

z  

  

dt

t

t

0.5

35m

z



t

with z t representing the depth of the tunnel axis.