Issue 50

S. Gavela et alii, Frattura ed Integrità Strutturale, 50 (2019) 383-394; DOI: 10.3221/IGF-ESIS.50.32 388 The left part in the above Eq.(1), as described in Eq.(2). ௥௘௙ ൌ ଴ ൅ ଵ ∙ ሺ / ሻ (2) provides the value of compressive strength estimated for a reference curing age. In the case of Eq.(1) where the multi- factorial model function incorporates the variation of CS(W/C,t) for the entire range of curing age span, CS ref represents the tested specimens’ compressive strength at infinite curing age, which could be called the final compressive strength CS inf . In the case of experiment I, Eq.(2) was used for testing specimens at a nominal curing age of about 28 days. The exponential part of Eq.(1) provides an estimation of the proportion of the final compressive strength reached at curing age t: ሺ ሻ ൌ ቂି൫ ఛ ௧ൗ ൯ ೙ ቃ (3) Sensitivity analysis and application of the law of propagation of uncertainty is easily performed according to the ISO GUM procedure when such a multifactorial function is used. Specifically, the sensitivity coefficients C W/C and C t can be estimated as the corresponding derivatives of the function in Eq.(1). These coefficients provide an assessment for the uncertainty of the result of concrete specimen compressive strength measurement which is attributed to the uncertainty in estimating the values for water-to-cement ratio and curing age, respectively. These two sensitivity coefficients are provided by the following equations: ௐ/஼ ൌ ଵ ∙ ቂି൫ ఛ ௧ൗ ൯ ೙ ቃ ൌ ଵ ∙ ሺ ሻ (4) ௧ ൌ ஼ௌሺ௧ሻ∙௡∙ఛ ೙ ௧ ೙శభ (5) A laboratory performing testing in well-known concrete syntheses could use Eq.(1) as a baseline in the frame of quality control. That is, for concrete specimens that are similar in synthesis as those used for establishing Eq.(1), the result of any future compressive strength testing should not deviated significantly from the reference value provided by Eq.(1). For significantly different syntheses a laboratory should repeat the herein presented experimental procedure in order to fit Eq.(1) to the results of the corresponding compressive strength tests. R ESULTS AND DISCUSSION ccording to experiment I results, the values c 0 = 124 ± 11 MPa and c 1 = -150 ± 22 MPa were obtained for the least squares regression line of Fig.2a, with a satisfying fitting quality ( R 2 = 0.68). By interpreting the value obtained for parameter c 1 , each percentage change in the water to cement ratio (i.e., a change in W/C by 0.01), causes a change for the mean value of the compressive strength of the specimens by approximately 1.5 MPa. At the same time, no statisti- cally significant correlation of CS and CC was detected based on experiment I results (Fig.2b). Fig.2a depicts the con- fidence bands of the regression line at the level of 95%. But these limits are not expected to provide a generic conclusion as they correspond only to an experiment based on a similar set of specimens. In contrast, the prediction bands of the regression line can yield the 95% probability limits within which any single iteration of the test is expected to occur. The regression procedure for experiment II compressive strength tests provided a statistically significant multifactorial function [see Fig.3a for the relation of the multifactorial model as a function of W/C and Fig.3b for the relation of the model as a function of curing age t ] with parameter values: c 0 = 143 ± 24 MPa, c 1 = -136 ± 38 MPa, τ = 0.45 ± 0.18 days and n = 1.0 ± 0.2, at a confidence level of 95%. The fitting quality is very satisfying ( R 2 = 0.92). One of the laboratory test results was omitted as an outlier, so 64 results were used in the regression procedure, instead of 65. It should be noted that values for c 0 , c 1 obtained from experiment II provide a linear function of CS(t) with W/C , which provides an estimation of CS inf , i.e. Cs(t) for infinite curing age, when values for parameters c 0 , c 1 obtained from experiment I provide a corresponding estimate, strictly dedicated to the nominal value of 28 days for curing age t . If a comparison between these two results is aimed at, then the right part of Eq.(1), the P(t) , should be taken into account. The correlation of the compressive strength with the curing age parameter was strongly confirmed by the results of ex- periment II (Fig.3b). For this reason, Eq.(1) was applied to the results of experiment I tests, keeping the left part of the equation unchanged and, so limiting the regression process for optimizing the values for the sigmoidal shape parameters A