Issue 31

A. Abrishambaf et alii, Frattura ed Integrità Strutturale, 31 (2015) 38-53; DOI: 10.3221/IGF-ESIS.31.04 48 0 0 u u w w iEXP iNUM iEXP i i err F F F       (12) where F iEXP and F iNUM were the experimental and the numerical load value at i th crack width value, respectively. The final σ – w relationship was defined by the parameters set that lead to the lowest normalised error between the experimental and numerical compressive force versus crack width curves. Numerical results Fig. 12 illustrates the numerical response obtained from the inverse analysis of the splitting test results (NUM SPLT ), as well as the average and envelope (experimental force – crack width curves, EXP SPLT Avg and EXP SPLT Envelope, respectively. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0 10 20 30 40 50 60 70 80 EXP SPLT Envelope EXP SPLT Avg NUM SPLT Force [kN] w [mm] 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0 10 20 30 40 50 60 70 80 EXP SPLT Envelope EXP SPLT Avg NUM SPLT Force [kN] w [mm] (a) (b) Figure 12 : Experimental and numerical force – crack width relationship, F-w , for: (a) θ= 0 ° and (b) θ = 90 ° . As shown in Fig. 12, a good accuracy between the experimental and numerical simulation was achieved, even though a slight difference was observed, but the estimated error ( err ) was lower than 5%. Fig. 13 depicts the σ – w relationship obtained from the inverse analysis that leads to the smallest error. The numerical tensile strengths for the θ = 0 ° and θ = 90 ° series were 3.6 and 3.2 MPa, respectively. By comparing the response for both series, similar to the uniaxial tensile test, the post-cracking residual stresses in θ = 0 ° series were also significantly higher due to the fibre tendency to be reoriented perpendicular to concrete flow direction as previously discussed. Therefore, in θ = 0 ° specimens there are more effective fibres to bridge the crack plane than in θ = 9 0 ° series. 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Stress [MPa] w [mm] 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Stress [MPa] w [mm] (a) (b) Figure 13 : Numerical uniaxial stress – crack width relationship, σ – w , obtained from inverse analysis for: (a) θ= 0 ° and (b) θ = 90 ° . Comparison of results Figs 14(a) and (b) shows for each series the uniaxial σ – w relationships obtained from the inverse analysis procedure of the splitting tensile test ( NUM SPL T ), the envelope and average curves from uniaxial tensile test (EXP UTT Envelope, EXP UTT Avg.) executed according to the RILEM TDF-162 recommendations [13]. Moreover, the σ – w response for the splitting test was determined from Eq. 13 as recommended by ASTM C-496 standard (EXP SPLT ) [12] and is also represented in Fig. 14.