PSI - Issue 44

Carlo Vienni et al. / Procedia Structural Integrity 44 (2023) 2270–2277 Vienni et al. / Structural Integrity Procedia 00 (2022) 000–000

2272

3

a c Fig. 1. (a) Sketch of a CRM coupon in clamping grid test; (b) Specimen C_X_03 during the test; (c) coupons constitutive law. b

Table 1. Results of the clamping-grid test. Specimen F cr [kN]

F u [kN]

σ u = F u /A f [MPa]

E 1 [GPa]

E 2 [GPa]

3,67 3,02 3,06 2,49 2,62 3,43 2,67

C_X_01 C_X_02 C_X_03 C_X_04 C_Y_01 C_Y_02 C_Y_03

8,03

406 414 581 612 454 535 467

1613 1430 1070

43 45 55 48 39 33 40

8,2

11,5 12,12 10,81 12,74 11,11

978

Average (CoV)

3,06 (13%)

9,96 (18%)

503 (18%)

1273 (20%)

48 (10%)

1683 1702

-

Average (CoV)

2,91 (14%)

11,55 (7%)

485 (7%)

1693 (1%)

37 (9%)

CRM was bonded to the specimens for a length of 300 mm. All specimens were cured at laboratory conditions for at least 28 days before testing. Masonry specimens were restrained against vertical movements with a steel plate connected to the testing machine with four steel bars. The upper ends of the fibers were clamped to the testing machine using steel tabs reinforced with epoxy resin to avoid damage to the load application area. Tests were carried out under displacement-controlled loading at a constant rate of 0.0033 mm/s. Axial displacements of the fabric at the loaded ends of the matrix were measured with two LVDTs. The bond test setup is shown in Fig. 2a. Experimental results of bond tests are shown in Table 2 in terms of peak load F u_B , peak stress in the fibers σ u_B = F u_B /A f , and ultimate tensile stress at the interface τ u_B = F u_B /A b , where A b is the total surface of the bonded area. Failure always occurred due to a brittle detachment at the matrix-to-support interface. The detachment of CRM from masonry was always preceded by mortar cracking (Fig. 2b-c). 3. Finite element parametrical analysis The in-plane seismic behavior of reinforced and unreinforced masonry was studied by three-dimensional homogenized finite element models. A smeared crack constitutive law was used, namely the total strain-rotating-crack model. Linear softening in tension and parabolic hardening/softening in compression were used to simulate masonry. The parameters of the constitutive model are the Young modulus E , Poisson ratio v , compressive strength f c , tensile strength f t , compressive fracture energy G c, and tensile fracture energy G t . The calibration of the input parameters of the model was carried out using the results of several experimental tests under shear-compression loading contained in the database collected by Vanin et al. (2017). The mechanical characteristics of masonry considered in the numerical simulations are shown in Table 3. Numerical models for CRM reinforced walls were created using 3D elements for both the masonry and the reinforcement system, externally applied to the wall. Plaster was modeled with a smeared crack constitutive model: compressive strength f c was set equal to 14.4 MPa, mean value from compressive tests on mortar samples, tensile strength f t was set equal to 0.75 MPa, the value obtained as the ratio between the average force at first crack F cr derived from clamping grid test (Table 1) and the area of CRM coupons (120x30 mm 2 ). Compressive and tensile fracture energy were calculated using the formulation proposed by Model Code 90 (CEB-FIP, 1990).