Prediction of skirted foundation safety factors under combined loading in spatially variable soils using machine learning

Abstract

Skirted foundations are usually used in marine engineering. More researches revealed that the variations in soil undrained shear strength considerably influence the assessing performance of the bearing capacity of skirted foundations. This study proposes two machine learning-based methods to predict safety factors (F_{\mathrm{s}}) of skirted foundations under combined loadings. By comparing the prediction performance of models based on Convolutional Neural Networks (CNN) and Gaussian Process Regression, this study investigates the effect of input size of soil random field on prediction accuracy and identifies the optimal CNN model. The proposed CNN model efficiently predicts corresponding safety factors for different combined loadings under various soil random fields, achieving similar accuracy to the traditional time-consuming random finite element. Specifically, the coefficient of correlation exceeds 0.93 and the mean relative error is less than 2.8% for the variation of the horizontal scales of fluctuation under different combined loadings. The relative error of the predicted F_{\mathrm{s}} value is less than 3.00% given three failure probabilities considering the variation of the vertical scales of fluctuations. These results demonstrate satisfactory prediction performance of the proposed CNN model.

Graphical abstract

Keywords

spatial variability / skirted foundation / safety factor / convolutional neural network / gaussian process regression

References

[1] Roscoe K . The stability of short pier foundations in sand. British Welding Journal, 1956, 3(8): 343–354

[2] Bransby M F , Randolph M F . Combined loading of skirted foundations. Geotechnique, 1998, 48(5): 637–655

[3] Gourvenec S , Barnett S . Undrained failure envelope for skirted foundations under general loading. Geotechnique, 2011, 61(3): 263–270

[4] Luo W Z , Li J H . Effects of installation on combined bearing capacity of a spudcan foundation in spatially variable clay. Applied Ocean Research, 2022, 120: 103055

[5] Zou J X , Yang J Z , Hu F J . Bearing capacity of monopile-bucket composite foundation in sand-over-clay under V-H-M combined static loads. Applied Ocean Research, 2024, 150: 104092

[6] Randolph M F , Gaudin C , Gourvenec S M , White D J , Boylan N , Cassidy M J . Recent advances in offshore geotechnics for deep water oil and gas developments. Ocean Engineering, 2011, 38(7): 818–834

[7] Haddad A , Barari A , Amini R . The remedial performance of suction caisson foundations for offshore wind turbines under seismically induced liquefaction in the seabed: Shake table testing. Marine Structures, 2022, 83: 103171

[8] Cheng H J , Zhou M , Niu F J , Zhang X H , Tian Y H , Li J H . Numerical study of the bearing capacity of the hybrid skirted foundations in silty sand under combined loading. Applied Ocean Research, 2024, 150: 104129

[9] Yun G , Bransby M F . The horizontal-moment capacity of embedded foundations in undrained soil. Canadian Geotechnical Journal, 2007, 44(4): 409–424

[10] Bransby M F , Yun G J . The undrained capacity of skirted strip foundations under combined loading. Geotechnique, 2009, 59(2): 115–125

[11] Mehravar M , Harireche O , Faramarzi A . Evaluation of undrained failure envelopes of caisson foundations under combined loading. Applied Ocean Research, 2016, 59: 129–137

[12] Wang Y K , Zou X J , Zhou M , Zhang X H . Capacity and failure mechanism of monopile-wheel hybrid foundation in clay-overlaying-sand deposits under combined V-H-M loadings. Marine Structures, 2023, 90: 103443

[13] Cho S E . Probabilistic assessment of slope stability that considers the spatial variability of soil properties. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 136(7): 975–984

[14] Huang J , Griffiths D V , Fenton G A . Probabilistic analysis of coupled soil consolidation. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 136(3): 417–430

[15] Bari M W , Shahin M A . Probabilistic design of ground improvement by vertical drains for soil of spatially variable coefficient of consolidation. Geotextiles and Geomembranes, 2014, 42(1): 1–14

[16] Li K , Wang R , Ma H B , Zhang J M . Rising groundwater table due to restoration projects amplifies earthquake induced liquefaction risk in Beijing. Nature Communications, 2025, 16(1): 1466

[17] Li J H , Tian Y H , Cassidy M J . Failure mechanism and bearing capacity of footings buried at various depths in spatially random soil. Journal of Geotechnical and Geoenvironmental Engineering, 2015, 141(2): 04014099

[18] Jiang S H , Li D Q , Cao Z J , Zhou C B , Phoon K K . Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation. Journal of Geotechnical and Geoenvironmental Engineering, 2015, 141(2): 04014096

[19] Li X Y , Liu X , Liu Y D , Yang Z Y , Zhang L M . Probabilistic slope stability analysis considering the non-stationary and spatially variable permeability under rainfall infiltration-redistribution. Bulletin of Engineering Geology and the Environment, 2023, 82(9): 350

[20] Jiang S H , Hu H P , Wang Z Z . Improved Bayesian model updating of geomaterial parameters for slope reliability assessment considering spatial variability. Structural Safety, 2025, 112: 102536

[21] Ali A , Lyamin A V , Huang J S , Sloan S W , Cassidy M J . Undrained stability of a single circular tunnel in spatially variable soil subjected to surcharge loading. Computers and Geotechnics, 2017, 84: 16–27

[22] Chen R P , Zhang P , Wu H , Wang Z , Zhong Z . Prediction of shield tunneling-induced ground settlement using machine learning techniques. Frontiers of Structural and Civil Engineering, 2019, 13(6): 1363–1378

[23] Zhang W G , Han L , Gu X , Wang L , Chen F Y , Liu H L . Tunneling and deep excavations in spatially variable soil and rock masses: A short review. Underground Space, 2022, 7(3): 380–407

[24] Fan S T , Zhang Y R , Li S , Han M L . Probabilistic failure envelopes of tripod bucket-supported offshore wind turbines in spatially variable clay based on a novel continuous method. Computers and Geotechnics, 2024, 170: 106305

[25] Ismail A , Jeng D S , Zhang L L . An optimised product-unit neural network with a novel PSO-BP hybrid training algorithm: Applications to load-deformation analysis of axially loaded piles. Engineering Applications of Artificial Intelligence, 2013, 26(10): 2305–2314

[26] Zhou C , Xu H C , Ding L Y , Wei L C , Zhou Y . Dynamic prediction for attitude and position in shield tunneling: A deep learning method. Automation in Construction, 2019, 105: 102840

[27] Nguyen-Le D H , Tao Q B , Nguyen V H , Abdel-Wahab M , Nguyen-Xuan H . A data-driven approach based on long short-term memory and hidden Markov model for crack propagation prediction. Engineering Fracture Mechanics, 2020, 235: 107085

[28] Deb P , Pal S K . Interaction behavior and load sharing pattern of piled raft using nonlinear regression and LM algorithm-based artificial neural network. Frontiers of Structural and Civil Engineering, 2021, 15(5): 1181–1198

[29] Fu Y P , Lin M S , Zhang Y , Chen G F , Liu Y J . Slope stability analysis based on big data and convolutional neural network. Frontiers of Structural and Civil Engineering, 2022, 16(7): 882–895

[30] Fernández A , Sanchidrian J A , Segarra P , Gomez S , Li E M , Navarro R . Rock mass structural recognition from drill monitoring technology in underground mining using discontinuity index and machine learning techniques. International Journal of Mining Science and Technology, 2023, 33(5): 555–571

[31] Abdollahi A , Li D L , Deng J , Amini A . An explainable artificial-intelligence-aided safety factor prediction of road embankments. Engineering Applications of Artificial Intelligence, 2024, 136: 108854

[32] Kong X R , Wu Y C , Zhu P , Zhi P , Yang Q F . Novel artificial neural network aided structural topology optimization. Applied Sciences, 2024, 14(23): 11416

[33] Chen H Z , Shen Z C , Wang L , Qi C C , Tian Y H . Prediction of undrained failure envelopes of skirted circular foundations using gradient boosting machine algorithm. Ocean Engineering, 2022, 258: 111767

[34] Beygi M , Fallahi M , Vali R , Mousavi E , Saberian M , Li J , Barari A . FELA-DNN framework to predict the seismic bearing capacity of skirted strip footing built on a non-cohesive slope. Soil Dynamics and Earthquake Engineering, 2023, 171: 107932

[35] Wang Y , Cao Z J . Probabilistic characterization of Young’s modulus of soil using equivalent samples. Engineering Geology, 2013, 159: 106–118

[36] Cao Z J , Wang Y , Li D Q . Quantification of prior knowledge in geotechnical site characterization. Engineering Geology, 2016, 203: 107–116

[37] Vanmarcke E H . Probabilistic modeling of soil profiles. Journal of the Geotechnical Engineering Division-ASCE, 1977, 103(11): 1227–1246

[38] Lacasse S , Nadim F . Uncertainties in characteriscing soil properties. In: Uncertainty in the Geologic Environment: From Theory to Practice, 1996, 1(58): 49–75

[39] Phoon K K , Kulhawy F H . Characterization of geotechnical variability. Canadian Geotechnical Journal, 1999, 36(4): 612–624

[40] Butterfield R , Houlsby G T , Gottardi G . Standardized sign conventions and notation for generally loaded foundations. Geotechnique, 1997, 47(5): 1051–1054

[41] Ye Z T , Gao Y F , Shu S , Wu Y X . Probabilistic undrained bearing capacity of skirted foundations under HM combined loading in spatially variable soils. Ocean Engineering, 2021, 219: 108297

[42] Hung L C , Kim S R . Evaluation of combined horizontal-moment bearing capacities of tripod bucket foundations in undrained clay. Ocean Engineering, 2014, 85: 100–109

[43] Selmi M , Kormi T , Hentati A , Bel Hadj A N . Capacity assessment of offshore skirted foundations under HM combined loading using RFEM. Computers and Geotechnics, 2019, 114: 103148

[44] Bransby M F , Randolph M F . The effect of embedment depth on the undrained response of skirted foundations to combined loading. Soil and Foundation, 1999, 39(4): 19–33

[45] Wu Y X , Zhang H L , Shu S . Probabilistic bearing capacity of spudcan foundations under combined loading in spatially variable soils. Ocean Engineering, 2022, 248: 110738

[46] Huang H W , Xiao L , Zhang D M , Zhang J . Influence of spatial variability of soil Young’s modulus on tunnel convergence in soft soils. Engineering Geology, 2017, 228: 357–370

[47] Cha Y J , Choi W , Büyüköztürk O . Deep learning-based crack damage detection using convolutional neural networks. Computer-Aided Civil and Infrastructure Engineering, 2017, 32(5): 361–378

[48] Yin X L , Wang H , Pisanò F , Gavin K , Askarinejad A , Zhou H P . Deep learning-based design model for suction caissons on clay. Ocean Engineering, 2023, 286: 115542

[49] Mahmoodzadeh A , Mohammadi M , Salim S G , Ali H F H , Ibrahim H H , Abdulhamid S N , Nejati H R , Rashidi S . Machine learning techniques to predict rock strength parameters. Rock Mechanics and Rock Engineering, 2022, 55(3): 1721–1741

[50] Tamhidi A , Kuehn N M , Bozorgnia Y . Uncertainty quantification of ground motion time series generated at uninstrumented sites. Earthquake Spectra, 2023, 39(1): 551–576

[51] Ching J , Yoshida I , Phoon K K . Comparison of trend models for geotechnical spatial variability: Sparse bayesian learning vs. gaussian process regression. Gondwana Research, 2023, 123: 174–183

[52] Zhang H L , Wu Y X , Yang S C . Probabilistic analysis of tunnel convergence in spatially variable soil based on Gaussian process regression. Engineering Applications of Artificial Intelligence, 2024, 131: 107840

[53] Li R Z , Sudjianto A . Analysis of computer experiments using penalized likelihood in Gaussian kriging models. Technometrics, 2005, 47(2): 111–120

RIGHTS & PERMISSIONS

Higher Education Press