Parametric deep learning model for predicting bearing capacity of strip foundation via neural operator

Abstract

Strip foundations, as a widely applied form of shallow foundation, involve foundation displacements and soil deformations under loading, which are critical issues in geotechnical engineering. Traditional limit analysis methods can only provide solutions for ultimate bearing capacity, while numerical methods require remeshing and remodeling for different scenarios. To address these challenges, this study proposes a deep learning approach based on the DeepONet neural operator for rapid and accurate predictions of load–displacement curves and vertical displacement fields of strip foundations under various conditions. A dataset with randomly distributed parameters was generated using finite element method, with the training set employed to train the neural network. Validation on the test set shows that the proposed method not only accurately predicts ultimate bearing capacity but also captures the nonlinear characteristics of high-dimensional data. As an offline model alternative to finite element methods, the proposed approach holds promise for efficient and real-time prediction of the mechanical behavior of shallow foundations under loading.

Keywords

Strip footing / Bearing capacity / DeepONet / Neurual operator / Machine learning / Engineering / Civil Engineering

References

[1] Ahmed, B., Qiu, Y., Abueidda, D. W., El-Sekelly, W., & Soto, B.G.d., Abdoun, T., & Mobasher, M.E. (2024). Physics-informed DeepONet with stiffness-based loss functions for structural response prediction. arXiv. https://doi.org/10.48550/arXiv.2409.00994

[2] AsgarkhaniN, KazemiF, JankowskiR. Machine learning-based prediction of residual drift and seismic risk assessment of steel moment-resisting frames considering soil-structure interaction. Computers & Structures, 2023, 289. 107181

[3] ChenW-FLimit Analysis and Soil Plasticity, 1975Elsevier

[4] ChenL, TianZ, ZhouS, GongQ, DiH. Attitude deviation prediction of shield tunneling machine using Time-Aware LSTM networks. Transportation Geotechnics, 2024, 45. 101195

[5] ChenB, WangC, LiW, FuH. A hybrid Decoder-DeepONet operator regression framework for unaligned observation data. Physics of Fluids, 2024, 362. 027132

[6] DehghanbanadakiA, MotamediS. Bearing capacity prediction of shallow foundation on sandy soils: a comparative study of analytical, FEM, and machine learning approaches. Multiscale and Multidisciplinary Modeling, Experiments and Design, 2024, 721293-1310.

[7] EbidAM, OnyeloweKC, SalahM. Estimation of bearing capacity of strip footing rested on bilayered soil profile using FEM-AI-coupled techniques. Advances in Civil Engineering, 2022, 202218047559.

[8] EbidAM, OnyeloweKC, SalahM. Load-settlement curve and subgrade reaction of strip footing on bi-layered soil using constitutive FEM-AI coupled techniques. Designs, 2022, 66104.

[9] FentonGA, GriffithsDV, ZhangX. Load and resistance factor design of shallow foundations against bearing failure. Canadian Geotechnical Journal, 2008, 45111556-1571.

[10] GoswamiS, KontolatiK, ShieldsMD, KarniadakisGE. Deep transfer operator learning for partial differential equations under conditional shift. Nature Machine Intelligence, 2022, 4121155-1164.

[11] GriffithsD. Computation of bearing capacity factors using finite elements. Geotechnique, 1982, 323195-202.

[12] HuangH-W, LiQ-T, ZhangD-m. Deep learning based image recognition for crack and leakage defects of metro shield tunnel. Tunnelling and Underground Space Technology, 2018, 77: 166-176.

[13] HuangL, LiJ, HaoH, LiX. Micro-seismic event detection and location in underground mines by using Convolutional Neural Networks (CNN) and deep learning. Tunnelling and Underground Space Technology, 2018, 81: 265-276.

[14] JinP, MengS, LuL. MIONet: Learning multiple-input operators via tensor product. SIAM Journal on Scientific Computing, 2022, 4463490-3514.

[15] KalosA. Numerical investigation of the bearing capacity of strip and rectangular shallow footings on cohesive frictional soils under eccentric loads. Geotechnical and Geological Engineering, 2022, 4041951-1972.

[16] KoltukS, Fernandez-SteegerT. Evaluation of seepage failure by heave in homogeneous cohesionless soils using finite element method. International Journal of Geotechnical Engineering, 2022, 16101201-1210.

[17] KoricS, AbueiddaDW. Data-driven and physics-informed deep learning operators for solution of heat conduction equation with parametric heat source. International Journal of Heat and Mass Transfer, 2023, 203. 123809

[18] Krishnapriyan, A. S., Gholami, A., Zhe, S., Kirby, R. M., & Mahoney, M. W.: Characterizing possible failure modes in physics-informed neural networks. (2021). https://doi.org/10.48550/arXiv.2109.01050

[19] LawalAI, KwonS. Development of mathematically motivated hybrid soft computing models for improved predictions of ultimate bearing capacity of shallow foundations. Journal of Rock Mechanics and Geotechnical Engineering, 2023, 153747-759.

[20] LiJ, YanG, ChenH. Predict the properties of self-compacting concrete using the optimized support vector regression models. Multiscale and Multidisciplinary Modeling, Experiments and Design, 2023, 63431-450.

[21] LiuJ, WuL, YinK, SongC, BianX, LiS. Methods for solving finite element mesh-dependency problems in geotechnical engineering-a review. Sustainability, 2022, 1452982.

[22] LuL, JinP, PangG, ZhangZ, KarniadakisGE. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nature Machine Intelligence, 2021, 33218-229.

[23] LuL, MengX, MaoZ, KarniadakisGE. DeepXDE: A deep learning library for solving differential equations. SIAM Review, 2021, 631208-228.

[24] LuL, PestourieR, JohnsonSG, RomanoG. Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport. Physical Review Research, 2022.

[25] MaoZ, LuL, MarxenO, ZakiTA, KarniadakisGE. DeepM &Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators. Journal of Computational Physics, 2021, 447. 110698

[26] MeyerhofGG. The Ultimate Bearing Capacity of Foudations. Géotechnique, 1951, 24301-332.

[27] MeyerhofGG. Some recent research on the bearing capacity of foundations. Canadian Geotechnical Journal, 1963, 1116-26.

[28] PrandtlL. Über die härte plastischer körper. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1920, 1920: 74-85

[29] RaissiM, PerdikarisP, KarniadakisGE. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 2019, 378: 686-707.

[30] RayR, KumarD, SamuiP, RoyLB, GohATC, ZhangW. Application of soft computing techniques for shallow foundation reliability in geotechnical engineering. Geoscience Frontiers, 2021, 121375-383.

[31] Reissner, H. (1924). Zum erddruckproblem. In Proceedings of the 1st International Congress for Applied Mechanics. Paper presented at the conference.

[32] ShieldR. Plastic potential theory and prandtl bearing capacity. Transactions of the ASME. Journal of Applied Mechanics, 1954, 21: 193-194.

[33] ShieldR. Stress and velocity fields in soil mechanics. Journal of Mathematics and Physics, 1954, 331–4144-156.

[34] TaccariML, WangH, GoswamiS, NuttallJ, ChenX, JimackPK. Developing a cost-effective emulator for groundwater flow modeling using deep neural operators. Journal of Hydrology, 2023.

[35] TerzaghiKTheoretical Soil Mechanics, 19431Wiley.

[36] WangS, WangH, PerdikarisP. Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. Science Advances, 2021, 7408605.

[37] XiaoL, MeiG, XuN. Knowledge-integrated deep learning for predicting stochastic thermal regime of embankment in permafrost region. Journal of Rock Mechanics and Geotechnical Engineering, 2024.

[38] XuC, CaoBT, YuanY, MeschkeG. A multi-fidelity deep operator network (DeepONet) for fusing simulation and monitoring data: Application to real-time settlement prediction during tunnel construction. Engineering Applications of Artificial Intelligence, 2024, 133. 108156

[39] YangG, MahboubKC, RenfroRL, GravesC, WangKCP. A machine learning tool for pavement design and analysis. KSCE Journal of Civil Engineering, 2023, 271207-217.

[40] YuanW, ZhuJ, WangN, ZhangW, DaiB, JiangY, WangY. A dynamic large-deformation particle finite element method for geotechnical applications based on abaqus. Journal of Rock Mechanics and Geotechnical Engineering, 2022.

[41] ZhangZ. MODNO: Multi-operator learning with distributed neural operators. Computer Methods in Applied Mechanics and Engineering, 2024, 431. 117229

[42] ZienkiewiczOC, HumphesonC, LewisRW. Associated and non-associated visco-plasticity and plasticity in soil mechanics. Geotechnique, 1975, 254671-689.

Funding

Natural Science Foundation of Shanghai(23ZR1468500)

RIGHTS & PERMISSIONS

The Author(s)