PSI - Issue 13

Oldřích Sucharda et al. / Procedia Structural Integrity 13 (2018) 1533 – 1538 Sucharda O., Lehner P., Kone č ný P., Ponikiewski T./ Structural Integrity Procedia 00 (2018) 000–000

1536

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kg). The water/cement ratio (W/C) was 0.41. Two selected cases of SCC concrete were chosen, the first without fibres and the second with 1% of steel fibres. The type of these fibres is KE20/1.7 (see Fig. 2 a). The results from three-point bending test corresponding to a fracture test are presented. Testing is based on the normative procedure of RILEM TC 162-TDF (162-TDF, 2002) and EN 14651 (UNE 14651:2005+A1, 2008). The beam of the dimensions 150 x 150 x 550 mm in the laboratory compression machine is shown in Fig. 2b. For the purposes of evaluation of the subsequent inverse analysis, the results of the basic mechanical tests in Table 1 are also given.

Table 1. Results of basic mechanical properties tests. Properties Units Specimen

SCC 0% Fibres

SCC 1% Fibres

Compressive strength Compressive strength Tensile splitting strength Modulus of elasticity

MPa MPa MPa GPa

Cylinder

47.85 56.11

50.61 62.26

Cube

Cylinder Cylinder

3.92

4.06

35.26

39.73

3. Inverse analysis of fracture properties The evaluation of basic material properties by inverse analysis follows. The actual use of inverse analysis involves the use of different methods. In particular, stochastic modelling is combined with multi-criteria analysis for the decision-making process for identifying material characteristics (Karvetski et al., 2010; Sucharda et al., 2017). However, the use of these methods is always optimally optimized for choosing specific tasks. This depends on the amount of input information, the effectiveness and the extent of the information requested. To generate data for the identification of material properties, the method Latin Hypercube Sampling was used. The method is implementend into the software FREET (Novák et al., 2014). The processing and evaluation of the information obtained by means of a multi-criteria analysis is performed by a computational algorithm in the Matlab software (Information of the Program Matlab n.d.). Non-linear analysis uses the SBETA material model and the ATENA software (Cervenka and Cervenka, 2002). As part of the analysis the several variants of stochastic modelling with different variables are illustrated. First, a larger number of variables is considered and the number of simulations is then reduced, due to demonstrate the sensitivity and complexity of the task. Initial properties of the material are based on basic laboratory tests. In Table 2 the variants prepared are shown.

Table 2. Random input parameters for three variants of stochastic analysis. Variant Properties Units

Mean

COV

Tensile splitting strength Modulus of elasticity Specific fracture energy

MPa GPa N/m

4.06

0.1

39.73

0.05

642

0.1 0.1

A: 100 simulation

Coefficient c1 Coefficient c2 Coefficient c1 Coefficient c2

- - - -

0.6

0.25

0.15

0.6

0.1 0.1 0.1

B: 40 simulation

0.35 642

C: 10 simulation

Specific fracture energy

N/m

In variant A, most parameters are selected as variable. The results of LD diagram and experiments are shown in Fig. 3a. There are large differences in all parts of the graph. Different values of maximum load, slope and final residual strength. In B, the second variant the modelling aimed at the influence of softening coefficients. The result is shown in Fig. 3b. The biggest differences are in the maximum load and in the middle of the graph. The last variant C includes stochastic modelling only by effect of the specific fracture energy. The significant effect on the overall course of the load-displacement diagram can be seen in Fig. 4a. For all parameters, a normal distribution was selected.