Correlation analysis of experimental results

The research goal is to investigate which parameters of a concrete-to-concrete interface influence the shear behavior. To examine the relationship between the experimental results and the

corresponding material parameters, statistical analysis is used. For each test specimen, the following variables are entered into the statistical analysis:

- Average shear stress at failure (N/mm²) - Average 𝜎𝑛 (N/mm²)

- 𝑓_{𝑐𝑘,𝑐𝑢𝑏𝑒} of the strongest concrete - 𝑓𝑐𝑘,𝑐𝑢𝑏𝑒 of the weakest concrete

- Ratio between 𝑓_{𝑐𝑘,𝑐𝑢𝑏𝑒} of the strongest concrete and the weakest concrete - Roughness parameters (^𝑅𝑎, 𝑅_{𝑧(𝐷𝐼𝑁)}, 𝑅_𝑝𝑚, 𝑅_𝑣𝑚 𝑎𝑛𝑑 𝑅_𝑞)

- Average horizontal displacement at failure - Average vertical displacement at failure

- Linear regression components of test results (𝜏0 and slope coefficient) - Eurocode 2 cohesion and friction components

- FIB Model Code 2010 adhesion and friction components - Shear resistance prediction of Eurocode 2

- Shear resistance prediction of FIB Model Code 2010 - Whether or not the precast floor plate is SCC

For every hypothesis, the Pearson correlation coefficient is computed to provide a measure of the linear correlation between the investigated variables. Statistical significance is studied by computing the p-value for the investigated variables, a two-tailed test is used because hypothesis direction is not always specified. This p-value is compared to an adopted 𝛼 of 0.05 as the threshold to reject the null hypothesis in the investigated relationship, additionally an 𝛼 of 0.01 is adopted to signify very significant relationships. The software suite SPSS Statistics is used to construct a correlation matrix for the entered variables. From this matrix, the correlations corresponding to the hypotheses can be extracted (fig 7.1). This correlation matrix describes whether or not the null-hypothesis could be rejected, the correlation, and the significance of this correlation. Both the full correlation matrix and the correlation matrix for the hypotheses can be found in appendix 5 – correlation matrices.

Figure 7.1: Correlation matrix of investigated variables

Average shear stress at failure

The averaged shear stress at failure has no direct one-on-one correlation with concrete strength, or roughness. This was expected, since the shear resistance is a linear function consisting of multiple components. Correlation with one of these components does not imply correlation with their sum.

These three components, 𝜏0, slope coefficient, and 𝜎𝑛 are also investigated.

The maximum shear resistance found in experimental testing, does have a significant, medium-size, positive correlation with the Eurocode 2 and FIB Model Code 2010 expression for shear resistance.

The FIB Model Code 2010 expression describes the found experimental results more accurately than the Eurocode 2 expression.

Compression perpendicular to the interface

The compression perpendicular to the interface has a very significant, large, positive correlation with the maximum shear resistance of an interface.

The compression perpendicular to the interface has no significant correlation with the interface displacements.

𝝉_𝟎 regression constant

The found shear strength in the absence of normal loading, 𝜏0 , has no significant correlation with any of the cube compressive strengths. However, the ratio between the two concrete strengths (presumably caused by difference in modulus of elasticity) does have a significant, medium-size, positive correlation with 𝜏0. Meaning that 𝜏0 increases when there is a large difference between the concrete strengths of the precast floor plate and the compression layer.

The found shear strength in the absence of normal loading, 𝜏₀ , has no significant correlation with any of the measured surface roughness parameters. This is contrary to the expressions found in codes.

The found shear strength in the absence of normal loading, 𝜏0 , has a very significant, large, negative correlation with the found regression slope coefficient. This suggests that specimens with a larger shear strength 𝜏₀ are less sensitive to compression perpendicular to the interface.

The found shear strength in the absence of normal loading, 𝜏0 , has no significant correlation with the cohesion described in both Eurocode 2 and FIB Model code 2010.

Regression slope coefficient

The regression slope coefficient has no significant correlation with the cube compressive strength of the strongest concrete. But does have a very significant, large, positive correlation with the concrete strength of the weakest concrete. This is contrary to the expressions found in codes, where the friction coefficient is not attributed to concrete strength.

The regression slope coefficient has a very significant, large, negative correlation with the ratio between the two concrete strengths. Meaning that when the two concretes have a more similar cube compressive strength, the found regression slope is steeper, and the shear resistance is more sensitive to compression perpendicular to the interface. This may be caused by differences in modulus of elasticity.

The regression slope coefficient has no significant correlation with any of the measured surface roughness parameters. This is contrary to the expressions found in codes.

The regression slope coefficient has a very significant, large, negative correlation with the slope coefficient described in Eurocode 2. This suggests that the coefficients of friction found in Eurocode 2 are inversely related to the found regression slope coefficients.

The regression slope coefficient has a significant, small, negative correlation with the slope

coefficient described in FIB Model Code 2010. This suggests that the coefficients of friction found in FIB Model Code 2010 are inversely related to the found regression slope coefficients.

Roughness parameters

The measured surface roughness parameters have no significant correlation with any of the other investigated variables. The roughness parameters have no correlation with either horizontal- or vertical displacements measured up until specimen failure.