Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Prediction of Undrained Failure Envelopes of Shallow Foundations using Machine Learning Approaches:
A Comparative Study
Hongzhen Chen1, Zhichao Shen2, Yinghui Tian3, Le Wang1

School of Civil Engineering, Tianjin University,Tianjin, China
2
Department of Civil and Environmental Engineering, National University of SingaporeSingapore
3
Department of Infrastructure Engineering, University of Melbourne
Melbourne, Australia
1ABSTRACT2007; Vulpe et al., 2014; Vuple, 2015).

Fitting parameters in the failure envelope expression are influenced by
the complex boundary conditions. This paper carried out a comparative
study on the performance of five machine learning (ML) algorithms,
including decision tree (DT), support vector machine (SVM), random
forest (RF), multilayer perceptron neural networks (MLPNN) andgradient boosting machine (GBM), in the prediction of fitting
parameters. Results show that the GBM algorithm has the best
performance in predicting fitting parameters among all considered MLalgorithms. The relative importance of variables influencing fitting
parameters was also investigated.

Compared to simple linear interpolation of fitting parameters, themachine learning (ML) algorithm provides a potential solution tounderstand the complex interaction among several variables that
influence failure envelopes (Zhang et al., 2020). The application of ML
algorithms in engineering has recently proliferated such as offshore andgeotechnical engineering because of their high accuracy andcomputational efficiency (Chen et al., 2019; Zhang et al., 2019).
In this study, undrained load-carrying capacities of skirted circular
foundations with a wide range of embedment ratio d/D, soil strength
heterogeneity index κ , loading angle θ and level of vertical load
mobilisation v are derived by finite element limit analysis (FELA). The
performance of five ML algorithms, including decision tree (DT),support vector machine (SVM), random forest (RF), multilayer
perceptron neural networks (MLPNN) and gradient boosting machine(GBM), in predicting fitting parameters of failure envelope expression
are compared. Besides, variable importance that influences the shape offailure envelopes is discussed.

KEY WORDS: Shallow foundation; Failure envelopes; Bearing
capacity; Machine learning; Variable importance.

INTRODUCTION
It is usual to consider a shallow foundation as having an embedment
depth to foundation diameter ratio less than one. Shallow foundations
are widely used in offshore engineering due to their reliable capacity,
installation convenience and cost-effectiveness (Barari & Ibsen, 2012;
Kourkoulis et al., 2014). They are generally subjected to combined
vertical (V), horizontal (H) and moment (M) loading resulting from theharsh environmental conditions (Shen et al., 2017; Fu et al., 2017). The
failure envelope approach has been increasing popularly employed todefine the load-carrying capacity of shallow foundations under
combined V-H-M loading conditions, and its advantages are wellacknowledged (Gottardi & Butterfield, 1993; Gourvenec & Randolph,
2003; Gourvenec, 2011; Vuple et al., 2014), such as explicit
consideration of (H, M) interaction and concurrent consideration offoundation geometry, embedment and soil strength profile. An
algebraic expression is commonly introduced to describe the failureenvelope (Gourvenec & Barnett, 2011; Feng et al., 2014) with fitting
parameters for different boundary conditions (e.g., different
combinations of embedment ratio d/D and soil strength heterogeneityindex κ) provided in a table. Other boundary conditions that are notavailable in the table can be obtained through interpolation (Gourvenec,MACHINE LEARNING ALGORITHMS
The selected machine learning algorithms share certain characteristics
that make them interesting to the current analysis: (1) they are
increasingly used in offshore engineering; (2) they have goodpredictive performance in related works and are known to enable theanalysis of more complex nonlinear relationships; (3) they are maturealgorithms and standard procedures for the implementation of thesealgorithms are well established (Qi et al., 2018a; Zhou et al., 2016). A
brief introduction of each algorithm is provided, and readers refer to therelevant references for a more in-depth understanding.

Decision Tree (DT)DT algorithm is a non-parametric supervised learning method, and itaims to create a learner that predicts the value of a target variable bylearning simple decision rules inferred from the data features (Zhou et1505