PSI - Issue 22

Elise Zgheib et al. / Procedia Structural Integrity 22 (2019) 25–32 Elise Zgheib – Wassim Raphael / Structural Integrity Procedia 00 (2019) 000 – 000

28 4

  n j 1

ij ObsX ij CalX

n 1

M i



(2)

N i 1

Mi

  

M CEB

(3)

N

where, Obs X ij refers to the experimental measurements while Cal X ij refers to the Eurocode 2 creep predictions. n refers to the number of measurements for each test and N to the total number of tests. The M CEB indicates if a model overestimates or underestimates systematically the experimental values, (ACI 209.2R-08 (2008)). When M CEB coefficient is near 1, then the model predicts accurately experimental measurements. If M CEB exceeds 1, this means that the model overestimates the experimental measurements. Contrary, the model underestimates experimental measurements, if the M CEB coefficient is less than 1. The CEB mean square error F CEB The CEB mean square error F CEB method calculates the mean square error of the predicted values using the difference between the calculated and observed values relative to the observed value. It may be calculated according to the following formulas: 2.3.2.

ij ) (ObsX ij ) ij ObsX (CalX 

f j

100





(4)

n j 1

n 1 1

2 f j

Fi



(5)

  

  N i 1

N 1

2 Fi

(6)

FCEB



Small values of F CEB show that the predicted compliance is close to experimental measurements.

2.3.3. Results of Eurocode 2 creep model evaluation’s In this paper, the CEB mean deviation and the CEB mean square error described above are applied to study the accuracy of Eurocode 2 model in predicting the compliance function when admixtures, specifically silica fume (SF) is added to the concrete mix composition (Table 1).

Table 1. The CEB statistical methods results of Eurocode 2 creep predictions for concrete with silica fume. Eurocode 2 M CEB (expected value 1) F CEB (expected value 0) J (t, t 0 ) 1.9 108

When using the silica fume as additive in the mix composition of concrete, the evaluation of the Eurocode 2 compliance function shows an overestimation of creep at long term. In fact, the M CEB result is bigger than the target value 1 and the F CEB has large value.