PSI - Issue 78

Eugênio Moreira et al. / Procedia Structural Integrity 78 (2026) 1967–1974

1971

Table 1. Linear elastic material properties adopted in the numerical model Property Stone leaf

Inner mortar

Soil

Density (kg / m³)

2,700

1,650

2,050

Young’s modulus (GPa)

77

1

0.2

Poisson’s ratio

0.25

0.20

0.30 1e-5 1.00 920

Thermal exp. coe ff . (1 / °C) 1.6e-5

2.4e-5

Conductivity (W / m·°C) Specific heat (J / kg·°C)

2.16 910

0.75 840

pl t ) , σ c = E 0 ( ε c − ε pl c )

σ t = E 0 ( ε t − ε

(1)

Viscoplastic regularization was utilized to improve numerical convergence in softening regimes, with viscosity parameter µ = 0 . 001 applied following Pereira et al., 2015, 2014. CDP parameters and associated uniaxial behaviors, adapted from Venanzi et al., 2019, 2020, are provided in Tables 2 and 3. Table 2. CDP plasticity parameters Parameter φ (°) K c f b 0 / f c 0 ϵ µ Value 21 0.667 1.16 0.10 0.002

Table 3. Uniaxial material behaviour in CDP

Stone leaf

Inner mortar

State

Stress (Pa)

Plastic strain

Stress (Pa) 3,500,000

Plastic strain

Compression 6,000,000

0 0

0 0

160,000 120,000 84,000 16,000

148,000 120,000 84,000 16,000

0.000175 0.000377 0.000759

0.000175 0.000377 0.000759

Tension

4.4. Model Validation and Seismic Analysis Framework

The model reproduces daily inclination cycles from non-uniform thermal expansion. Validation uses two stages: (1) gravitational loading for initial stress state, (2) thermal loading for May 10–19, 2021 using PVGIS data to assess equilibrium under realistic environmental conditions. Seismic input is from the May 15, 2021 local event (ML = 3.9, depth 9.9 km), recorded at Monte Urbino (MURB). Four scenarios use amplification factors of 1 × , 10 × , 20 × , and30 × (PGAs: 0.139, 1.39, 2.78, 4.17 m / s 2 ). The analysis sequence is: (1) gravitational load, (2) pre-seismic thermal load (May 10–15), (3) seismic loading, (4) post-seismic thermal load. The accelerograms were truncated to 15 s to capture peak motion while optimizing computation (Fig. 3).

5. Results

The baseline scenario (pure thermal loading, May 10–19, 2021) shows pronounced daily inclination cycles from − 20 mdeg (day) to + 29 mdeg (night), with close agreement between monitoring data and numerical predictions (Fig. 4). Daily averages remain between 1 mdeg and 16 mdeg , establishing thermal equilibrium as a reference for seismic scenario changes. The model identifies principal strain accommodation in upper wall regions, consistent with di ff erential expansion between limestone faces and mortar core.