PSI - Issue 13

Tuan Duc Le et al. / Procedia Structural Integrity 13 (2018) 1702–1707 T.D. Le, P. Lehner, P. Konečný / Structural Integrity Procedia 00 (2018) 000 – 000

1705

4

• = covariance matrix between the grid nodes and the center of the facet located at x . Since EOLE method is independent with the facet system and its geometry, every realization of the random field generated on a large grid can be used for different geometries of the beams and this help saving time of computation. In this research, random field generation and chloride ingress assessment were composed under the form of functions and procedures using Matlab environment. C xg

3. Numerical example

To evaluate the possibilities of the application of the above mentioned combination of Finite Element Analysis model (Lehner et al., 2014) and random field application from (Eliáš et al., 2015) , a test scenario is prepared. The chloride ingress into a cross-section of simply supported RC beam is studied. Dimensions of the cross section of the beam are 0.5 m wide and 0.25 m high, a 0.05 m concrete cover is assumed. For the sake of simplicity, the cross sectional will be divided into 50 triangular elements, only one random field will be created and one realization will be made for each basic point (center of mass of one element) in the simulations. Other input parameters for this analysis are summarized in Table 1. For the definition of spatial variation, the correlation length was considered accoriding to best fit (Kaděrová, 2018) for selected experimental data set (Grassl et al., 2012). Also the variation coefficient is defined.

Table 1. Input data for the analysis Parameter

Name

Value

Unit

C 0 C s D c

Surface chloride content

0.6

% weight of cement % weight of cement

Concentration of chloride in the cross section

0

Effective diffusion coefficient

5.5832

m²/s*10

-12

m

Aging factor Referent time

0.284

-

t ref

28

days

x

Depth of reinforcement Variation coefficient

0.05

m

cv

0.042

-

l c

Correlation length

0.1

m

The resulting chloride ingress 2D profile was computed for considered input parameters and it is given in Fig. 1 (a) for homogeneous as well as Fig.1 (b) for heterogeneous approach with the one random evaluation of random field.

0 Concentration at the cross section. (surface value C0 = 0.6 %. Year No.: 80

0 Concentration at the cross section. (surface value C0 = 0.6 %. Year No.: 80

0.55

0.55

-0.05

-0.05

0.5

0.5

0.45

0.45

-0.1

-0.1

0.4

0.4

-0.15

-0.15

0.35

0.35

0.3

0.3

-0.2

-0.2

0.25

0.25

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.25

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 -0.25

Fig. 1. Distribution of chloride concentration in homogeneous (a) and random field based (b) models at the age of 80 years.

The resulting time dependent chloride concentration at the most exposed place of steel reinforcement is shown in Fig. 2 (a) for homogeneous model (deterministic result) as well as Fig. 2 (b) for heterogeneous approach with the one random evaluation of random field. .