Deflection of foundation pit retaining wall in heterogeneous soil strata: Intelligent prediction methods based on physics-informed machine learning

Deflection of foundation pit retaining wall in heterogeneous soil strata: Intelligent prediction methods based on physics-informed machine learning

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Cong Zhou^a^,^b, Lei He^a^,^b^,^*, Junchen He^a, Yi Zhang^a, Huaiguang Xiao^a, Chee Kiong Soh^a

Journal of Rock Mechanics and Geotechnical Engineering | 2026, 18(5) : 4007 - 4022

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Journal of Rock Mechanics and Geotechnical Engineering | 2026, 18(5): 4007-4022

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Deflection of foundation pit retaining wall in heterogeneous soil strata: Intelligent prediction methods based on physics-informed machine learning

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Cong Zhou^a^,^b, Lei He^a^,^b^,^*, Junchen He^a, Yi Zhang^a, Huaiguang Xiao^a, Chee Kiong Soh^a

Affiliations

^aSchool of Civil Engineering, Southeast University, Nanjing, 211189, China

^bState Key Laboratory of Safety, Durability and Healthy Operation of Long Span Bridges, Southeast University, Nanjing, 211189, China

Lei He obtained his BEng degree in Naval Architecture and Marine Engineering from Tianjin University in 2004 and his PhD in Civil Engineering from Nanyang Technological University, Singapore, in 2011. In 2013, he was a visiting scholar at École Polytechnique Fédérale de Lausanne (EPFL), Switzerland. He is currently a Principal Young Professor at Southeast University. His research focuses on innovative planning, design, and construction methods for urban underground space, with a commitment to advancing the informatization and intelligent integration of underground infrastructure systems.

Published: 2026-05-25 doi: 10.1016/j.jrmge.2025.07.019

Outline

Abstract

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Excavation-induced retaining wall deflection (RWD) significantly influences the safety of surrounding built environment. To predict the three-dimensional RWD in heterogeneous strata, a new partial differential equation (PDE) is derived in this study, and two prediction models are proposed, i.e. the physics-informed neural network (PINN) model and the data-driven PINN model. As a physical constraint, the new PDE is crucial to the loss functions of these models. Then, the validity of the models is verified and analysed using a subway deep-foundation pit. The results show that the training times of both models are controlled within 900 s, which is a significant reduction compared to that of the conventional numerical model. In addition, the prediction accuracy of the data-driven PINN model is higher than that of the numerical model, while that of the PINN model is slightly lower than that of the numerical simulation. However, in contrast to the data-driven PINN model, the PINN model can identify irregular soil interfaces in heterogeneous strata to learn the deflection continuity conditions at irregular interfaces and realize RWD prediction in non-uniform distributed strata. In practical applications in foundation pit engineering, the selection of the PINN and data-driven PINN models can be conducted according to the in situ distribution conditions of the strata to enable the early prediction of potential RWD, thereby providing a reliable basis for the further optimisation of retaining structures design.

Key words

Heterogeneous soil strata / Braced excavation / Retaining wall deflection (RWD) / Soil-structure interaction / Physics-informed neural networks (PINNs)

Cite this Article

Cong Zhou, Lei He, Junchen He, Yi Zhang, Huaiguang Xiao, Chee Kiong Soh. Deflection of foundation pit retaining wall in heterogeneous soil strata: Intelligent prediction methods based on physics-informed machine learning[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2026 , 18 (5) : 4007 -4022 . DOI: 10.1016/j.jrmge.2025.07.019

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Funding

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Fundamental Research Funds for the Central Universities(2242023K5006)
Jiangsu Civil Defense Office Program(7605009117)

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Year 2026 volume 18 Issue 5

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Article Info

doi: 10.1016/j.jrmge.2025.07.019

Receive Date：2025-02-23
Online Date：2026-06-17
Published：2026-05-25

Article Data

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History

Received：2025-02-23
Revised：2025-06-23
Accepted：2025-07-01

Funding

Fundamental Research Funds for the Central Universities(2242023K5006)

Jiangsu Civil Defense Office Program(7605009117)

Affiliations

^aSchool of Civil Engineering, Southeast University, Nanjing, 211189, China

^bState Key Laboratory of Safety, Durability and Healthy Operation of Long Span Bridges, Southeast University, Nanjing, 211189, China

Corresponding:

^* Corresponding author. School of Civil Engineering, Southeast University, Nanjing, 211189, China. E-mail address: helei_civil@seu.edu.cn (L. He).

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表12种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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