Document Type : Original Article

Authors

• Fatemeh Razani ¹
• Ali Reza Bagherieh ²

¹ Master's student Department of Civil Engineering, School of Civil Engineering and Architecture, Malayer University, Malayer, Iran.

² Assistant Professor, Department of Civil Engineering, Faculty of Civil Engineering and Architecture, Malayer University, Malayer, Iran.

Abstract

Objective

The soil–water retention curve (SWRC), also referred to as the soil–water characteristic curve (SWCC), is a fundamental property of unsaturated soils describing the relationship between water content and matric suction. Its laboratory determination is time-consuming, costly and requires specialised equipment. In many practical situations, particularly in preliminary design or where many soil layers must be characterised, it is not feasible to perform full SWRC testing for every soil. This motivates the development of reliable data-driven models that approximate the SWRC from basic index properties while remaining consistent with the physics of unsaturated soil behaviour. The present study has four objectives: (i) to develop a deep-learning model based on a multilayer perceptron (MLP) for predicting the SWRC of low-plasticity soils using only porosity, Atterberg limits and particle-size distribution; (ii) to incorporate matric suction explicitly as an independent input variable so that the model represents the SWRC as a continuous function of water content with respect to suction rather than at a few discrete suction values; (iii) to train and test the model on a large database of 1,727 laboratory-measured soil samples from the USDA geospatial database to assess its generalisation capability; and (iv) to examine, through parametric analyses, the sensitivity of the predicted SWRC to key input variables and to verify that the model reproduces physically meaningful trends.

Method

The study employed a feed-forward MLP neural network to predict the SWRC using the dataset of Mostafa et al., which comprises 1,727 soil samples representing coarse-grained, fine-grained and organic soils. Only the main drying branch of the SWRC was considered. Eight variables were used as inputs: matric suction, porosity, liquid limit (LL), plasticity index (PI) and the percentages passing the No. 4, 10, 40 and 200 sieves. The targets were gravimetric water contents at suction levels of 0.1, 0.33 and 15 bar. All variables were normalised to the range [0, 1] using min–max normalisation, and the dataset was randomly split into training (70 %), validation (15 %) and testing (15 %) subsets. Several network configurations were explored, starting from a single hidden layer and progressively increasing the number of layers and neurons to balance predictive power and generalisation. The final architecture is a deep MLP with four hidden layers and a 10–5–5–10 neuron structure. Training was carried out in MATLAB using the Levenberg–Marquardt (trainlm) algorithm. Model performance was quantified by the coefficient of determination (R²), mean squared error (MSE) and mean absolute error (MAE), and parametric analyses were performed by varying selected inputs while holding others constant.

Results

The developed deep MLP model reproduced the soil–water retention behaviour of low-plasticity soils with high accuracy. The selected four-hidden-layer architecture (10–5–5–10) achieved high R² values and low MSE and MAE for the training, validation and testing subsets, indicating a close agreement between predicted and measured water contents. Scatter plots of predicted versus measured values showed that data points clustered tightly around the 1:1 line, confirming good generalisation. The ability of the model to generate continuous SWRCs was assessed by fixing the physical soil properties and varying matric suction over a wide range. For representative soils, the predicted curves were smooth and monotonically decreasing, and the measured data points lay on or very close to the predicted curves, demonstrating that the network can interpolate effectively between training suction levels.

Parametric analyses confirmed that the model captures the expected qualitative trends of unsaturated soil behaviour. Increasing porosity led to a systematic upward shift of the SWRC, reflecting greater water-holding capacity at a given suction, whereas decreasing porosity shifted the curve downward. Making the soil finer, by increasing the percentage passing the finer sieves, also resulted in higher predicted water contents at the same suction. Likewise, increases in LL and PI produced higher SWRCs, consistent with the greater affinity of more plastic soils for water. In all cases, the predicted curves remained physically plausible and free from oscillations or non-monotonic segments.

Conclusions

The proposed deep-learning framework provides an accurate, stable and physically meaningful representation of the SWRC for a wide range of low-plasticity soils using only basic physical and geotechnical properties. By treating matric suction as an explicit input, the model represents the SWRC as a continuous function of water content with respect to suction, avoiding the need to train separate networks for individual suction levels or soil types. Within its intended domain, it offers a practical and cost-effective alternative to laboratory SWRC determination for applications such as slope stability assessment, embankment design and analysis of compacted fills. The main limitations are the focus on low-plasticity soils and the consideration of only the main drying branch of the SWRC; extension to highly plastic or strongly structured soils and to problems where hysteresis is significant is left for future work.

Keywords

• Soil&ndash
• Water Retention Curve (SWRC)
• Artificial Neural Network (ANN)
• Unsaturated Soil
• Artificial Intelligence (AI)
• Deep Learning

Main Subjects

• Geotechnics