Shear modulus (G) and damping ratio (D) are both well known as principal soil dynamic parameters. In the present study, cyclic triaxial and simple shear tests are performed on Firuzkuh silica sand at various shear strain amplitudes using the developed testing devices and peripherals. It is well-understood that degrading curvature of G with shear strain appears in both triaxial and simple shear results. Nevertheless, mean confining stress has dissimilar effects in each of the two tests that does not provide comparable empirical correlations. It is noticed that the variations of G and D with suction stress in triaxial differs from those in simple shear. On the basis of cyclic simple shear results, the increase in suction pressure from zero to the end of transition zone in SWCC leads to increase in G values. In triaxial method, on the other hand, similar increase occurs only up to the inflection point in SWCC, starts reducing afterwards down to a limit value at residual water content. The damping ratio variations with shear strain are generally ascending despite local drops at the strain order of 0.1%, which has appeared in both triaxial and simple shear results.

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The thermal conductivity of materials is a crucial property with diverse applications, particularly in engineering. Understanding soil thermal conductivity is crucial for designing efficient geothermal systems, predicting soil temperatures, and assessing soil contamination. This paper aimed to predict quartz sand thermal conductivity by using four mathematical models: multiple linear regression (MLR), artificial neural network (ANN), classification and regression random forest (CRRF), and genetic programming (GP). A grey-box AI method, GP, was used for the first time in this topic. Seven inputs affecting thermal conductivity were evaluated in the study, including sand porosity, degree of saturation, coefficient of uniformity, coefficient of curvature, mean particle size, and minimum and maximum void ratios. In predicting thermal conductivity, the MLR model performed poorly, with a coefficient of determination R2 = 0.737 and a mean absolute error MAE = 0.300. Both ANN models using the Levenberg–Marquardt algorithm and the Bayesian Regularization (BR) algorithm outperformed the MLR model with an accuracy of R2 = 0.916 and an error of MAE = 0.151. In addition, the CRRF model had the best accuracy of R2 = 0.993 and MAE = 0.045. In addition, GP showed acceptable performance in predicting sand thermal conductivity. The R2 and MAE values of GP were 0.986 and 0.063, respectively. This paper presents the best GP equation for evaluating other databases. Additionally, the porosity and saturation of the sand were found to have the greatest impact on the model results, while coefficients of curvature and uniformity had the least influence. Overall, the results of this study demonstrate that grey-box artificial intelligence models can be used to accurately predict quartz sand thermal conductivity.