In this study, variable returns to scale (VRS) data envelopment analysis was integrated into the Taguchi approach to optimize ternary additives for expansive soil enhancement. The ternary additives selected were sawdust ash (SDA), quarry dust (QD) and ordinary Portland cement (OPC). The additives were set as the input variables while multiple responses obtained from the experiments performed with the Taguchi orthogonal array were set as the output variables. Each row in the orthogonal array were defined as a decision making unit (DMU) in the optimization process and output-oriented VRS model was used to obtain the efficiency score for each DMU. Next, benevolent formulation was utilized to obtain the multipliers for the inputs and outputs which were subsequently used to determine the cross efficiency scores for each DMU. The cross-efficiency scores were used to construct the cross-efficiency matrix. Thereafter, the mean cross-efficiency score (MCES) was determined for each DMU. Parameter level that maximizes the MCES was chosen as the optimal level for that parameter. Optimum combination of additives was found at A6 B2 C3. Lastly, confirmatory experiments performed by blending the soil with the optimum combination of additives showed the effectiveness of this method in the enhancement of expansive soil properties.

在这项研究中，可变规模收益 (VRS) 数据包络分析被整合到田口方法中，以优化膨胀土增强的三元添加剂。选择的三元添加剂是锯末灰 (SDA)、采石场粉尘 (QD) 和普通硅酸盐水泥 (OPC)。添加剂被设置为输入变量，而从田口正交阵列进行的实验中获得的多个响应被设置为输出变量。将正交阵列中的每一行定义为优化过程中的决策单元（DMU），并使用面向输出的 VRS 模型获得每个 DMU 的效率得分。接下来，利用仁慈公式获得输入和输出的乘数，随后将其用于确定每个 DMU 的交叉效率分数。交叉效率分数用于构建交叉效率矩阵。此后，确定每个 DMU 的平均交叉效率得分 (MCES)。最大化 MCES 的参数级别被选为该参数的最佳级别。在 A6 B2 C3 处发现了添加剂的最佳组合。最后，通过将土壤与最佳添加剂组合混合进行的验证性实验表明该方法在增强膨胀土特性方面的有效性。