Twenty mixtures of self-compacting engineered cementitious composite (ECC) were prepared, cast, cured and tested at age of 28 days. The proportions of these mixtures are shown in Table 1. The main ingredients of ECC are: ordinary cement conforms to the requirements of ASTM C150, fly ash (FA), washed river sand having an average size of 450 µm, potable water, polyvinyl alcohol (PVA) fiber by volume fraction, and nano-silica (NS) in percentage of cementitious content (cement + fly ash). Two variables were considered in this study which are five levels of NS% (0%, 1%, 2%, 3% and 4%) and four levels of PVA fiber (0.5%, 1%, 1.5% and 2%). FA used in this study is class F conform to the requirements of ASTM C618 with the amount of SiO₂+Al₂O₃+Fe₂O₃ is about 82.12% and less than 6 loss on ignition. While the nano-silica (NS), used in this study, contains 99.8% of SiO₂ and has specific surface area of 100 ± 25 m²/g with average particle size of 10 – 25 nm. This NS is commercially available and has been produced using precipitation method. While the PVA has specific gravity of 1.3, tensile strength of 1600 MPa, modulus of elasticity of 41 GPa and 462 aspect ratio (length/diameter). All mixtures were prepared as self-compacting (SC) where the slump spread diameters ranging between 650 mm and 800 mm. Therefore, super-plasticizer was used to attain homogenous mix and to achieve the required flow.

The ingredients of NS-ECC mixture have been mixed and cast into 150 mm steel cube molds and left in laboratory for curing. After 24 hours, the cubes were de-molded and placed in curing tank for the duration of the testing periods which was at age of 28 days. On the day of testing, the cubes are taken out from the water, dried with the cloths and air blower if necessary to ensure a clean dry surface. After the cubes dried, they were marked at 5 testing points on each four faces (the loading faces not marked). The testing points are located about 20 mm from the edges of the cube as shown in Fig. (1a). Then each surface of the cube (four sides) is prepared for rebound hammer (RH) test according to ASTM C850 requirements. The cube was placed in compressive testing machine and a slight load was applied to hold the sample in order to prevent its movement during RH test as shown in Fig. (1b). Nine readings of RH were recorded at each of the five point on each surface and then average of readings were obtained. The concrete cubes were then prepared for the ultra pulse velocity (UPV) test according to ASTM C597 requirements as shown in Fig. (1c). Nine readings of UPV were recorded at each of the five points at the opposite faces of the cube and the average of these reading were recorded. Lastly, The NS-ECC cube was placed in the compressive strength testing machine and the compressive strength test was carried out in accordance to the requirement of BS 1881-116 as shown in Fig. (1d). The average readings of RH, UPV and compressive strength of three cubes are tabulated in Table 2.

Fig. (1). ECC cube is prepared for UPV and RH tests.

The polynomial equations (1) to (3), are in terms of actual factors and these can be used to make predictions about the responses compressive strength, rebound number and UPV values for given levels of each factor. Here, the levels should be specified in the original units i.e. PVA and Nano-silica are in percentage for each factor. This equations are not to be used to determine the relative impact of each factor because the coefficients are scaled to accommodate the units of each factor and the intercept is not at the center of the design space

(1)

(2)

(3)

Fig. (2). Compressive strength of NS-ECC mixtures.

Fig. (3). CCD design module: (a) Four corner points; (b) Four central points; (c) CCD design.

From the Fig. (4), it can be noted that the percentage of PVA is directly proportional in improving the compressive strength whereas the optimum of 2% nanosilica addition has shown the high compressive strength. In the contour diagram where the reddish color region shows that the compressive strength of 100 MPa and above can be achieved at the 2% nano-silica and 2% PVA. The greenish region indicates the 90MPa strength for PVA of 1 to 1.7% and nano-silica of 1 to 2%. In Figs. (5 and 6), it can be observed that the rebound number and UPV values were increased with the increase of PVA and up to 2% of nano-silica, beyond 2% of nano-silica rebound number and UPV values were decreased gradually. In the contour diagrams, the contour lines are oval shaped, this means that there is a good interaction between nano-silica and PVA on the responses and also from the contour diagrams it can be observed the ranges of variables NS and PVA for interval of response.

Fig. (4). Compressive strength: (a) 3D surface diagram; (b) 2D contour maps.

Fig. (5). Rebound number: (a) 3D surface diagram; (b) 2D contour maps.

Fig. (6). UPV: (a) 3D surface diagram; (b) 2D contour maps.

The model validation has been performed using the ANOVA (analysis of variance) in order get the relationship by the interaction of the two process variables PVA and nano-silica. Thus the validation for the responses (compressive strength, rebound number and UPV) can be obtained. The ANOVA validation results are tabulated in (Table 3). From the Table 3, it can be witnessed that the model is significant by observing the F-value. There is only a 0.95% chance that an F-value this large could occur due to noise. Values of “Prob > F” less than 0.0500 indicate model terms are significant

The adequacy of the ANOVA model can be determined by the values of the factors prescribed in the Table 4. For all the three responses compressive strength, rebound number, and UPV, it can be observed that the “Predicted R-Squared” is in sensible agreement with the “Adjustable R-Squared”; i.e. the variance is less than 0.2. “Adeq Precision” measures the signal to noise ratio and this ratio greater than 4 is desirable. This model can be used to navigate the design space. The co-efficient of variable (CV) for all the three responses within the 5%, this indicates the residual errors are lower than the predicted values. Also, the predicted residual error sum of squares (PRESS) indicates that the model has the high predicting capacity.

The diagnostic plots are also important in validating the predicted models. The normal probability plot in the Fig. (7), from which we can observe that the residual points lying approximately on straight line and also follow the “S” shaped curve, therefore it can be said that the residuals are distributed normally and the response transformation provides the better analysis.

Fig. (7). Normal probability plot: (a) Compressive strength; (b) Rebound number; (c) UPV.

In the Fig. (8), of studentized residuals. More significantly in this instance, all points lie within the parameters (calculated at the 95 percent confidence level). In other words, Mark’s high game does not exhibit anything more than common-cause variability, so it should not be disqualified.

Fig. (8). Studentized residual: (a) Compressive strength; (b) Rebound number; (c) UPV.

Fig. (9) shows the predicted versus actual values plot for all the three responses, and these were ranged adjacent to the straight line, thus it can be said that the predicted and actual results were in good agreement and can be fit with each in mutually. Therefore, the established RSM models are relevant and applicable in predicting compressive strength of ECC.

The compressive strength based on RN and UPV can be obtained by using the equations (4) and (5). These equations are developed by using the RSM analysis model. Table 5 shows the P-values for model is less than 0.05 and thus the obtained model is significant and from the Table 6 it can be observed that the difference between adj R squared and pred R squared is less than 2, with the high efficiency of 97%, this indicates the high correlation degree between the predicted and observed values.

(4)

(5)

A multi-objective optimization technique has been performed by using the RSM. For the given range of variables the predicted responses can be obtained by using the optimization technique. In RSM technique all the responses have the optimal values which are localized in various regions; therefore it will be more tedious to find the circumstances which suit all the responses. The difficulty level for optimization increases as the optimal regions do not intersect and moves away from each other. In most of the cases it was observed that all the response surfaces are found to be absent in its optimum under the similar set of experimental situations. Thus, modification in the level of a factor can improve and have negative cause on another factor. Therefore, the use of multi-objective methodology is one of the approaches in solving the problem of optimization for numerous responses. In this study the multi-response optimization method has been used to optimize the UPV and RN for compressive strength of ECC. The possibility of solutions by the RSM optimization is measured by the desirability scale, which is a dimensionless function. The desirability function is the most significant criteria in obtaining the desired responses. The individual desirability scale are obtained in the range of zero to 1, where zero indicates a completely undesirable and 1 indicates fully desirable response [23, 24].

Here in this case for the compressive strength of 100MPa is optimized for the best proportions of PVA and nano-silica with the desirability factor 1, thus the other responses rebound number and UPV are found with respect to the targeted strength. The ramp diagram for optimized response has been shown in the Fig. (10). Here in this case for the compressive strength of 100MPa is optimized for the best proportions of PVA and nano-silica with the desirability factor 1, thus the other responses rebound number and UPV are found with respect to the targeted strength. The ramp diagram for optimized response has been shown in the Fig. (10).

Fig. (10). Ramp diagram for optimization.

The experimental validation for the above optimized mixture had been performed in the laboratory and it was found less than 5% of variation from the obtained results. The results for validation are tabulated in the Table 7.