PSI - Issue 44

P. Morandi et al. / Procedia Structural Integrity 44 (2023) 1060–1067 Author name / Structural Integrity Procedia 00 (2022) 000–000

1064

5

softening rule for both cohesive and frictional equivalent parameters is introduced as function of the plastic deformation experienced by the internal tetrahedral elements.

Fig. 3. Distinct element modelling of masonry: unit-joint interface model, joint and block constitutive models.

Before modelling the response of the tested full-scale piers, the proposed modelling strategy was validated against the available characterization tests performed on small-scale specimens. Specifically, shear-compression and uniaxial compression tests were reproduced numerically to calibrate the required properties. Table 2 summarizes all the experimental and inferred properties assigned in the models to blocks and interface springs.

Table 2. Experimental and inferred material employed in the DEM models.

fc m (MPa) E m (MPa) G m (MPa)

ρ m (kg/m

3 ) -

- -

- - - -

Masonry

7.03

4265

1706

1300

-

fc b (MPa)

E b (MPa)

G b (MPa)

c b,eq (MPa) ϕ b,eq (°)

ft b,eq (MPa)

FD Blocks

19.22

7207

2883

1.59 ϕ (°)

35

1.06

k n (Pa/m) 7.92e10

k s (Pa/m) 3.17e10

c (MPa)

ft mo (MPa) G f,s (N/m)

G f,t (N/m)

Joints

0.15

31.38

0.05

50

10

The joint normal stiffness was computed as k n = E mo /t mo where E mo is the Young modulus of the mortar, and t mo is the mortar joint thickness of 10 mm. A value of E mo equal to 1259 MPa was estimated employing the homogenization equations employed by Malomo et al. (2019). Blocks elastic modulus was computed as E b = 375 ∙ fc b , using an empirical relation proposed for clay bricks by Kaushik et al. (2007) as function of brick compressive strength, fc b . The related joint shear stiffness, k s , and the block shear modulus, G b , were derived assuming material isotropy with a Poisson ratio of 0.25. Regarding the equivalent shear parameters assigned to the blocks, ϕ b,eq was assumed equal to 35° while c b,eq was iteratively calibrated to match the actual strength exhibited by the masonry prisms in uniaxial compression tests (Malomo et al. 2019). The softening rule of the MPM shear parameters was defined to attain the peak strength at a vertical deformation ε p of 0.65%. After reaching the peak value f cm the shear parameters linearly decrease to a small value (10% f cm ) at a vertical deformation ε u of around 1.0%.