Piles are slender structural components designed to transfer the load of a support structure deep into the
ground, reaching more stable soil layers or rock layers. The primary purpose is to provide adequate support in situations where surface soils are weak or unstable and cannot adequately bear the imposed loads from structures such as buildings, bridges, or other infrastructure. The accurate determination of the
ultimate bearing capacity of driven piles is a vital task in the field of geotechnical engineering, as it directly impacts the safety and stability of the structures they support.
A study conducted by Pijush Samui, Centre for Disaster Mitigation and Management, VIT University, Vellore, India, and published in the journal Geotechnical and Geological Engineering in July 2012, specifically focused on predicting the ultimate bearing capacity of driven piles embedded in cohesionless soils. To achieve this, the author utilized a machine learning technique known as the Relevance Vector Machine (RVM), which offers advantages in terms of probabilistic predictions compared to traditional methods.
Additionally, the study also involved the development of an Artificial Neural Network (ANN) model to serve as a comparative benchmark. While ANN has been employed in various past studies concerning bearing capacity predictions, it has demonstrated several limitations. These include a lack of insight into the relative importance of different input features, poorer generalization performance, slower convergence
rates, a tendency to overfit data, and non-probabilistic prediction outcomes. To address these shortcomings, the author explored the effectiveness and influence of RVM on predicting the ultimate bearing capacity of piles, aiming to provide a more reliable and informative methodology for geotechnical engineers faced with challenging soil conditions.
The Relevance Vector Machine (RVM) is an advanced version of the Support Vector Machine (SVM) that employs Gaussian processes within a Bayesian framework. This methodology provides valuable insights into the relevance of data points and exhibits a reduced tendency to overfit, attributable to its Bayesian nature and automatic relevance determination. Consequently, RVM is particularly suitable for applications that demand probabilistic outputs and sparse solutions. Various kernels, including polynomial, Gaussian, and spline functions, are evaluated within the context of RVM. A significant advantage of RVM is its ability to automatically estimate parameters, thereby facilitating the use of arbitrary basis functions that do not necessarily comply with Mercer’s conditions, which are required for SVM kernel functions.
The study utilizes 59 samples, incorporating input parameters such as the length of the pile, the cross-sectional area of the pile, the angle of shear resistance of the soil surrounding the shaft, the angle of shear resistance of the soil at the tip of the pile, and the effective overburden pressure at the pile tip. The primary output from the model is the ultimate capacity (Q) of the pile. The dataset was divided into training and testing sets in a 70:30 ratio, respectively.
The models included in this study were rigorously assessed using the coefficient of correlations (R) for each type of kernel employed in the Relevance Vector Machine (RVM) framework. The evaluation yielded impressive results, demonstrating that the R value for the Gaussian kernel was 0.981, for the polynomial kernel it was 0.956, and for the spline kernel it stood at 0.976. These findings suggest that RVMs utilizing the Gaussian kernel significantly outperformed the other models in terms of predictive accuracy.
In more detail, the RVM model used a substantial portion of the training data to identify relevance vectors, which are critical for its effectiveness. Specifically, the Gaussian kernel accounted for approximately 24.39% of the training data as relevance vectors, while the polynomial kernel utilized 56.09%, and the spline kernel incorporated 70.73%. The presence of these relevance vectors indicates the prototypical examples that the RVM model relies on for making predictions.
This study underscores RVMs’ potential as a robust alternative to traditional physically based models, particularly in predicting the ultimate capacity of driven piles in cohesionless soils. By leveraging RVMs’ strengths and relevance vector components, researchers and engineers may achieve more accurate and reliable predictions in civil engineering applications.
Reference
Samui, P. (2012). Application of relevance vector machine for prediction of ultimate capacity of driven piles in cohesionless soils. Geotechnical and Geological Engineering, 30, 1261-1270.