Foundations serve as crucial substructures for transferring a structure’s loads to the underlying soil. Two critical parameters significantly influence a foundation’s reliability: bearing capacity and settlement. The ultimate bearing capacity denotes the maximum load per unit area that the soil beneath a foundation can sustain prior to experiencing failure or substantial deformation. This parameter is fundamental in geotechnical engineering and vital for designing safe and stable foundations for various structures.
Failures occurring beneath a foundation may arise from shear within the soil, excessive settlement, or a combination of both factors. These failures can be categorized into three types: general shear failure, which involves the formation of clear failure planes; local shear failure, characterized by the development of partial shear planes; and punching shear failure, which entails vertical shear failure without lateral displacement.
Numerous previous studies, including those utilizing conventional methodologies by researchers such as
Meyerhof and Hanna, Florkiewicz, and Lotfzadeh and Kamalian, have proposed formulas aimed at providing reliable approximations of the ultimate bearing capacity of foundations situated on layered soils. Additionally, various investigations employing advanced techniques, such as Artificial Neural Networks (ANN), High-Order Neural Network models (HON-PILE), and General Regression Neural
Networks (GRNN), have demonstrated substantial improvements in predictive accuracy, along with a diverse exploration of the features utilized in these studies.
A study conducted by Hossein Moayedi et al., at Ton Duc Thang University in Vietnam focused on predicting ultimate bearing capacity through advanced methodologies. The researchers employed several techniques, including optimized artificial neural networks (ANN), genetic algorithm-optimized ANN (GA-ANN), particle swarm optimization-optimized ANN (PSO-ANN), differential evolution algorithm (DEA), adaptive neuro-fuzzy inference system (ANFIS), general regression neural network (GRNN), and feedforward neural networks (FFNN). To evaluate the effectiveness of these approaches, the study utilized results derived from an extensive number of finite element method (FEM) simulations.
The dataset utilized for this study comprises 3515 samples generated from Finite Element Method (FEM)
simulations, which incorporate various soil properties and different thicknesses of soil layers. A total of 14 input parameters were employed, including friction angle, dilation angle, unit weight, elastic modulus,
Poisson’s ratio, upper layer thickness relative to foundation width, footing width, top soil layer characteristics, bottom soil layer characteristics, vertical settlement, applied stress on the footing, moisture content, and expected settlement. The dataset was systematically divided into 80% for training and 20% for testing purposes.
The study employed the Levenberg–Marquardt (LM) back-propagation training algorithm in the development of artificial neural networks (ANN). A total of eighty-four ANN-LM models were constructed by varying the number of neurons in the hidden layers from one to fourteen. The performance of each model was assessed using the root-mean-squared error (RMSE) metric, with a lower RMSE indicative of superior performance. Additionally, a color intensity rating system (CER) was established to visually represent the network performance based on the RMSE values. Model number 12, which included 12 hidden neurons, demonstrated the best performance compared to the other models. After thorough analysis, the selected ANN architecture for further research was determined to be 12 × 8 × 1,
even though the optimal architecture was identified as 12 × 12 × 1.
A new ranking system, known as the Color Intensity Rating (CER), has been developed to assess the performance of various predictive models, including GA-ANN, ANFIS, DEA, FFNN, GRNN, and PSO-ANN. The findings indicate that all models demonstrated acceptable predictive capabilities for estimating ultimate bearing capacity; however, the PSO-ANN model emerged as the most reliable option. Performance metrics, such as RMSE, R², and VAF, were consistently reported for the training datasets across all models. Notably, the FFNN model exhibited the highest performance throughout both the training and testing phases. In contrast, the DEA model received a lower ranking. Cumulatively, the results indicate that the PSO-ANN model, with an R² of 0.99, RMSE of 0.01, and VAF of 99.9, achieved the best overall performance, as evidenced by its total rank of 35, surpassing other models in the evaluation.
Reference
Moayedi, H., Moatamediyan, A., Nguyen, H., Bui, X. N., Bui, D. T., & Rashid, A. S. A. (2020). Prediction of ultimate bearing capacity through various novel evolutionary and neural network models. Engineering with Computers, 36(2), 671-687.
Meyerhof, G. G., & Hanna, A. M. (1978). Ultimate bearing capacity of foundations on layered soils under inclined load. Canadian Geotechnical Journal, 15(4), 565-572.
Florkiewicz, A. (1989). Upper bound to bearing capacity of layered soils. Canadian Geotechnical Journal, 26(4), 730-736.
Lotfizadeh, M. R., & Kamalian, M. (2016). Estimating bearing capacity of strip footings over two-layered sandy soils using the characteristic lines method. International Journal of Civil Engineering, 14, 107-116.