Thermal properties of sand are of importance in numerous engineering and scientific applications ranging from energy storage and transportation infrastructures to underground construction. All these applications require knowledge of the effective thermal parameters for proper operation. The traditional approaches for determination of the effective thermal property, such as the thermal conductivity are based on very costly, tedious and time-consuming experiments. The recent developments in computer science have allowed the use of soft and hard computational methods to compute the effective thermal conductivity (ETC). Here, two computation methods are presented based on soft and hard computing approaches, namely, the deep neural network (DNN) and the thermal lattice element method (TLEM), respectively, to compute the ETC of sands with varying porosity and moisture content values. The developed models are verified and validated with a small data set reported in the literature. The computation results are compared with the experiments, and the numerical results are found to be within reasonable error bounds. The deep learning method offers fast and robust implementation and computation, even with a small data set due to its superior backpropagation algorithm. However, the TLEM based on micro and meso physical laws outperforms it at accuracy.

Soil thermal conductivity plays a critical role in the design of geo-structures and energy transportation systems. Effective thermal conductivity (ETC) of soil depends primarily on the degree of saturation, porosity and mineralogical composition. These controlling parameters have nonlinear dependencies, thus making prediction a nontrivial task. In this study, an artificial neural network (ANN) model is developed based on the deep learning (DL) algorithm to predict the effective thermal conductivity of unsaturated soil. A large dataset is constructed including porosity, degree of saturation and quartz content from literature to train and validate the developed model. The model is constructed with a different number of hidden layers and neurons in each hidden layer. The standard errors for training and testing are calculated for each variation of hidden layers and neurons. The network with the least error is adopted for prediction. Two sand types independent of training and validation data reported in the literature are considered for prediction of the ETC. Five simulation runs are performed for each sand, and the computed results are plotted against the reported experimental results. The results conclude that the developed ANN model provides an efficient, easy and straightforward way to predict soil thermal conductivity with reasonable accuracy.

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The effective thermal conductivity (ETC) of soil is an essential parameter for the design and unhindered operation of underground energy transportation and storage systems. Various experimental, empirical, semi-empirical, mathematical, and numerical methods have been tried in the past, but lack either accuracy or are computationally cumbersome. The recent developments in computer science provided a new computational approach, the neural networks, which are easy to implement, faster, versatile, and reasonably accurate. In this study, we present three classes of neural networks based on different network constructions, learning and computational strategies to predict the ETC of the soil. A total of 384 data points are collected from literature, and the three networks, Artificial neural network (ANN), group method of data handling (GMDH) and gene expression programming (GEP), are constructed and trained. The best accuracy of each network is measured with the coefficient of determination (R2) and found to be 91.6, 83.2 and 80.5 for ANN, GMDH and GEP, respectively. Furthermore, two sands with 80% and 99% quartz content are measured, and the best performing network from each class of ANN, GMDH and GEP is independently validated. The GEP model provided the best estimate for 99% quartz sand and GMDH with 80%.