In this paper, Desirability Optimization Methodology (DOM) is employed to achieve optimum sand bentonite mixture (SBM) based on multiple antagonist macro-geotechnical responses of the compacted SBM prepared using poorly graded sand with the mean grain size around 0.2 mm and bentonite with plasticity index around 157% for the stable engineered barriers (EBs). For this purpose, varying mix designs of SBM compacted at compaction energy of 2,700 kN-m/m³ are initially tested to determine their mechanical properties, volumetric-change behavior, and hydraulic conductivity. The unconfined compressive strength, cohesion, angle of internal fiction, swell pressure, compression index, and hydraulic conductivity are taken as the geotechnical design parameters for the SBM. Mathematical models are developed and statistically validated for these design parameters using sand content (SC) and bentonite content (BC) as the predictors. In addition, models are also developed to predict compression curves for compacted SBMs. Moreover, microstructural evaluation is conducted through scanning electron microscope (SEM) analysis to determine the SBM having a desirable microstructure for stable EB. It is observed that a major shift in the microstructure from medium pores to micro-pores occurs for the BC between 20% and 30%. Afterward, optimization of SBM is carried out by integrating developed models for the geotechnical design parameters in a desirability function (D) algorithm, which is subsequently simulated by setting maximization of strength and minimization of swell pressure, compressibility and hydraulic conductivity of compacted SBM as the goals. A reasonably high D-value is achieved for the SBMs having SC:BC in a range of 74:26 to 78:22 with the highest at 75.63:24.37 against the set goals. This study manifests an effective and pragmatic strategy for designing the SBM for a stable EB considering its antagonist hydraulic, volumetric change, and mechanical responses.

An attempt has been made to correlate relative density and relative compaction based on laboratory and field test data. In this investigation, 185 sandy soil samples were tested in the laboratory. The experimental investigations include classification tests, maximum and minimum density tests, and standard and modified Proctor and in-situ density tests. The values of the dry unit weight of these samples obtained by performing different tests fall between 14.7 kN/m3 and 20.8 kN/m3. Based on these results, linear and multivariate regression analyses were carried out to (a) relate relative compaction and relative density, (b) relate maximum (emax) and minimum void ratios (emin), and (c) express emax and emin in terms of median grain size (D50) and uniformity coefficient (Cu). Experimental and predicted values varied ± 5%, with a 95% confidence interval for the relation between relative compaction and relative density, and for other relations the variation was ± 10%. The proposed equations were validated using a new data set which had not been used for the development of the correlations. Proposed equations were also compared with equations presented by various other researchers. Validation of the proposed equations suggests that these equations may be used for future prediction of the respective variables.