Valorization of Iron Tailings and Pond ash for Sustainable Embankment Construction: Mechanical Performance and Sustainability Assessment

Orthogonal array determination The signal-to-noise (S/N) ratio forms the basis of the Taguchi method for evaluating process stability and determining the optimal parameter settings. Three performance characteristics are typically employed, namely nominal-is-better; larger-is-better; and smaller-is-better (Reyhani et al. 2013; Pourjafar et al. 2013). In the present study, the larger-is-better rule was used to calculate UCS, as shown in Eqs. S1 to S4, and the results were shown in Table S1. Eq. S1 Eq. S2 Eq. S3 Eq. S4 Here, refers to the S/N ratio, w is the total number of experimental replicates, yq represents the response measured for each replicate, denotes the average response, and is the corresponding sample variance. Parameter effects were evaluated from the difference between the mean response at each factor level and the overall mean, as given by Eq. S5. The optimized responses were then predicted using Eq. S6. As parameter interactions and experimental error were not included in the experimental design, the simplified form of the prediction equation was adopted. The normalized S/N ratio was also calculated using Eq. S7. Eq. S5 Eq. S6 Eq. S7 Where is the overall mean, Pe is the parameter effect, and N is the number of parameters. Smax and Smin indicate the maximum and minimum values of the S/N ratio. Table S1 S/N ratios for UCS (larger-is-better) Parameters L-1 L-2 L-3 L-4 Max-Min Rank PA 47.87 53.03 55.73 55.16 7.86 1 CP 48.56 52.14 54.25 55.85 7.29 2 Assessment of Taguchi design The obtained data were analyzed to evaluate the influence of process parameters on the UCS response. The S/N ratio was assessed with the “larger the better” criterion to optimize UCS, as shown in Table S2. Mean response and S/N ratio plots are shown in Fig. S1 (a-b). The findings show that optimum binder dosage and longer curing periods yield higher UCS. The enhancement in UCS is attributed to the development of cementitious hydration products through pozzolanic reactions during curing, whereas excess PA beyond the optimum dosage left unreacted particles that weakened particle bonding and reduced strength. It was observed that the optimum mixture achieved an S/N ratio of 59 dB and a normalized S/N ratio of 1.0, demonstrating superior performance and stability. The deviation sequence for each experimental combination was computed using the normalized S/N ratio values. Based on the obtained deviation sequences, grey relational coefficients were computed for each mix, and the grey relational grade was evaluated as the mean of these coefficients. The calculated grey relational grades were subsequently ranked, and the relative influence of each parameter at different levels was evaluated using the average rank of the corresponding experimental combinations, as shown in Table S3. The influence of PA at level 1 (0% PA) was evaluated by calculating the mean rank of the first four experimental combinations. An identical procedure was followed for all other parameter levels. The parameter level with the highest average rank was considered the optimal level. The analysis revealed that the optimum levels were 10% PA (L-3) and 28-days of curing (L-4), yielding the optimal parameter combination. The optimum experimental conditions, as determined from the S/N ratio analysis, consisted of a PA content of 10% and a curing period of 28-days. Following this, a one-way analysis of variance (ANOVA) was conducted to assess the relative importance of the process variables (PA and CP). Based on the ANOVA results, PA content was the most significant factor affecting UCS, followed by the curing period, as shown in Table S4. Table S2 Taguchi response analysis S. NO PA CP Mean of UCS (kPa) S/N ratio (dB) Normalized S/N ratio (dB) Predicted UCS (kPa) Error (%) 1 5 0 247 47.85 0.18 238.96 -3.25 2 5 7 412 52.29 0.51 426.83 3.60 3 5 14 567 55.07 0.71 567.37 0.06 4 5 28 698 56.87 0.84 706.44 1.21 5 10 0 365 51.24 0.43 401.66 09.04 6 10 7 577 55.22 0.72 589.53 2.17 7 10 14 746 57.45 0.88 730.072 -2.13 8 10 28 895 59.00 1.0 869.14 -2.88 9 15 0 310 49.82 0.33 284.36 -8.27 10 15 7 498 53.94 0.63 472.23 -5.17 11 15 14 602 55.59 0.75 612.77 1.78 12 15 28 731 57.27 0.87 751.84 2.85 Overall mean 554.0 54.30 MAPE (%) 3.53 Table S3 Grey relation analysis results ∆ Gray relational coefficient Grey relational grade Ranking 0.18 0.3543 0.3543 1 0.51 0.4787 0.4787 4 0.71 0.6081 0.6081 6 0.84 0.7377 0.7377 9 0.43 0.4412 0.4412 3 0.72 0.6164 0.6164 7 0.88 0.7895 0.7895 11 0.89 0.8036 0.8036 12 0.33 0.4018 0.4018 2 0.63 0.5488 0.5488 5 0.75 0.6429 0.6429 8 0.87 0.7759 0.7759 10 Table S4 ANOVA results for PA and CP Parameters Degree of freedom Sum of squares Mean squares % contribution PA 3 138.899 46.2997 52.65 CP 3 119.264 39.7547 45.22 Residual 9 5.577 0.6197 2.11 Total 15 263.740 99.98 Fig. S1(a-b) Influence parameter of a) Mean UCS; b) Mean S/N ratio of UCS Modelling The developed UCS model yielded an R2 of 0.96, indicating that a significant portion of the variability in UCS is explained by the selected independent variables. Residual analysis was used to test the assumptions of the regression model. A normal probability plot of the residuals in Fig. S2 reveals a roughly linear pattern of points close to the reference line, suggesting that the residuals are approximately normally distributed. This shows that the normality assumption holds, supporting the adequacy and reliability of the developed regression model. A confirmation test was performed to validate the optimization results using the optimum combination of 10% FeT and 28-days curing. The UCS obtained from the confirmation test was 870 kPa, which closely matched the maximum experimental UCS of 895 kPa. Furthermore, the low MAPE of 3.53% indicates excellent predictive accuracy, thereby confirming the reliability of the Taguchi optimization approach for FeT-PA stabilized soils. Fig. S2 Normal probability plot of residuals for the UCS model Table S5 ANOVA results for PA and CP Parameters Degree of freedom Sum of squares Mean squares % contribution PA 3 138.899 46.2997 52.65 CP 3 119.264 39.7547 45.22 Residual 9 5.577 0.6197 2.11 Total 15 263.740 99.98