Evaluating long-term settlements under complex traffic loads via explicit cyclic model augmented by intelligent optimization

Shaofei Guo , Jiafeng Zhang , Zhenhao Shi , Yang Li , Jianjun Li , Jiangu Qian

AI in Civil Engineering ›› 2026, Vol. 5 ›› Issue (1) : 1

PDF
AI in Civil Engineering ›› 2026, Vol. 5 ›› Issue (1) :1 DOI: 10.1007/s43503-025-00083-5
Original Article
research-article

Evaluating long-term settlements under complex traffic loads via explicit cyclic model augmented by intelligent optimization

Author information +
History +
PDF

Abstract

Accurate prediction of long-term settlement under complex traffic loads remains a pivotal challenge for the safety and durability of transportation infrastructure. While explicit models for settlement calculation have been advanced to handle general three-dimensional stress states, a major practical hurdle lies in determining reliable model parameters. Parameter inversion offers a viable path to high-fidelity estimates, yet conventional inversion techniques often fall short in accuracy. Ensemble learning methods can improve data precision by synthesizing predictions from multiple intelligent models; however, commonly used soft voting strategies tend to overlook both systemic bias across base models and the distinct contribution of each predictor. To address this, this study proposes a Particle Swarm Optimization-Back Propagation Neural Network-Random Forest (PSO-BPNN-RF) inversion model that incorporates a refined soft voting method. Coupling this inversion model with a three-dimensional explicit settlement calculation framework for complex traffic loading enables high-precision parameter identification. The proposed approach is subsequently applied to parameter inversion for an explicit model of the Xiaoshan Airport taxiway, demonstrating strong generalization capability and superior accuracy.

Keywords

Explicit model / Ensemble learning / Soft voting method / Particle swarm optimization / Back propagation neural network / Random forest

Cite this article

Download citation ▾
Shaofei Guo, Jiafeng Zhang, Zhenhao Shi, Yang Li, Jianjun Li, Jiangu Qian. Evaluating long-term settlements under complex traffic loads via explicit cyclic model augmented by intelligent optimization. AI in Civil Engineering, 2026, 5(1): 1 DOI:10.1007/s43503-025-00083-5

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Abdelkrim M, Bonnet G, De Buhan P. A computational procedure for predicting the long term residual settlement of a platform induced by repeated traffic loading. Computers and Geotechnics, 2003, 30(6): 463-476

[2]

Asaoka A, Matsuo M. An inverse problem approach to the prediction of multi-dimensional consolidation behavior. Soils and Foundations, 1984, 24(1): 49-62

[3]

Bian X, Lu W, Jiang H, Chen Y. Experimental study of cumulative axial strain and residual dynamic modulus of silt soil. Rock and Soil Mechanics, 2013, 34(4): 974-980in Chinese.

[4]

Cai Y, Liu X, Guo L, Sun H, Cao Z. Long-term settlement of surcharge preloading foundation in soft clay area induced by aircraft loads. Journal of Zhejiang University(engineering Science), 2013, 47(7): 1157-1163in Chinese.

[5]

Chen C, Deng Y, Qian J, Ma H, Ma L, Wu J, Wu H. Deep learning-based inversion framework for fractured media characterization by assimilating hydraulic tomography and thermal tracer tomography data: Numerical and field study. Engineering Geology, 2025, 350 107998

[6]

Cui J, Wu S, Cheng H, Kui G, Zhang H, Hu M, He P. Composite interpretability optimization ensemble learning inversion surrounding rock mechanical parameters and support optimization in soft rock tunnels. Computers and Geotechnics, 2024, 165 105877

[7]

Dafalias, Y. F., & Herrmann, L. R. (1982). A generalized bounding surface constitutive model for clays. Application of plasticity and generalized stress-strain in geotechnical engineering

[8]

Dafalias YF, Herrmann LR. Bounding surface plasticity. II: Application to isotropic cohesive soils. Journal of Engineering Mechanics, 1986, 112(12): 1263-1291

[9]

Deng J, F LC, Ge X. Application of BP network and genetic algorithm to displacement back analysis of rock slopes. Chinese Journal of Rock Mechanics and Engineering, 2001, 20(1): 1-5in Chinese.

[10]

Dong X, Yu Z, Cao W, Shi Y, Ma Q. A survey on ensemble learning. Frontiers of Computer Science, 2020, 14: 241-258

[11]

Gao, J. (2017). A study on the long-term settlement of the metro tunnel in saturated soft soil. Zhejiang University. in Chinese.

[12]

Gao W. Back analysis algorithm in geotechnical engineering based on particle swarm optimization. Rock and Soil Mechanics, 2006, 27(5): 795-798in Chinese.

[13]

Guo Q, Zhang H, Cao H, Xiao W, Han F. Hybrid seismic inversion based on multi-order anisotropic Markov random field. IEEE Transactions on Geoscience and Remote Sensing, 2019, 58(1): 407-420

[14]

Huang, M., & Yao, Z. (2012). Analysis of traffic-load-induced permanent settlement of highway embankment on soft clay ground. 2nd International Conference on Transportation Geotechnics (ICTG) International Society of Soil Mechanics and Geotechnical Engineering (ISSMGE),

[15]

Huang H, Jun S. Generalized parameters back analysis method based on Bayesian theory. Chinese Journal of Rock Mechanics and Engineering, 1994, 13(3): 219-228in Chinese.

[16]

Huang M, Yao Z. Explicit model for cumulative strain of saturated clay subjected to cyclic loading. Chinese Journal of Geotechnical Engineering, 2011, 33(3): 325-331in Chinese.

[17]

Huang Q, Huang H, Ye B, Zhang D, Zhang F. Evaluation of train-induced settlement for metro tunnel in saturated clay based on an elastoplastic constitutive model. Underground Space, 2018, 3(2): 109-124

[18]

Ji H, Jin Y, Yin Z, Wu Z, Shen S. Enhancement of genetic algorithm and its application to the identification of soil parameters by inverse analysis. Chinese Journal of Computational Mechanics, 2018, 36(2): 224-229in Chinese.

[19]

Jia S, Wu G, Chen W. Application of finite element inverse model based on improved particle swarm optimization and mixed penalty function. Rock and Soil Mechanics, 2011, 32(S2): 598-603in Chinese.

[20]

Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. Proceedings of ICNN'95-international conference on neural networks,

[21]

Kiomarsi F, Shojaei AA, Soltani S. Choosing an optimal connecting place of a nuclear power plant to a power system using Monte Carlo and LHS methods. Nuclear Engineering and Technology, 2020, 52(7): 1587-1596

[22]

Lai, S. (2013). Research on dynamic properties of Hangzhou's saturated silty sands under metro vibration loading. Zhejiang University of Technology. in Chinese.

[23]

Li Y, Nie R, Yue Z, Leng W, Guo Y. Dynamic behaviors of fine-grained subgrade soil under single-stage and multi-stage intermittent cyclic loading: Permanent deformation and its prediction model. Soil Dynamics and Earthquake Engineering, 2021, 142 106548

[24]

Liu M, Huang M, Li J. Long-term settlement of saturated soft clay under subway loading. Chinese Journal of Underground Space and Engineering, 2006, 2(5): 813-817in Chinese.

[25]

Liu Y, Hu C, Liu H. An implicit integration algorithm in the bounding-surface plasticity model for cyclic behaviors of saturated clay. Rock and Soil Mechanics, 2013, 34(12): 3617-3624in Chinese.

[26]

Lu, W. (2012). Accumulative settlement of saturated silt subgrade under transportation cyclic loading. Zhejiang University. in Chinese.

[27]

Ma, X. (2014). Equivalent finite element method for long-term settlement of subgrade induced by traffic load. Tongji University. in Chinese.

[28]

McKay MD, Beckman RJ, Conover WJ. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 2000, 42(1): 55-61

[29]

Ni J, Indraratna B, Geng X-Y, Carter JP, Chen Y-L. Model of soft soils under cyclic loading. International Journal of Geomechanics, 2015, 15(4): 04014067

[30]

Nie R, Mei H, Leng W, Ruan B, Li Y, Chen X. Characterization of permanent deformation of fine-grained subgrade soil under intermittent loading. Soil Dynamics and Earthquake Engineering, 2020, 139 106395

[31]

Pearce, K. J., Ipsen, I. C., Haider, M. A., Saibaba, A. K., & Smith, R. C. (2022). Robust Parameter Identifiability Analysis via Column Subset Selection. arXiv preprint arXiv:2205.04203. https://doi.org/10.48550/arXiv.2205.04203

[32]

Pichler B, Lackner R, Mang HA. Back analysis of model parameters in geotechnical engineering by means of soft computing. International Journal for Numerical Methods in Engineering, 2003, 57(141943-1978

[33]

Qian J, Du Z, Lu X, Gu X, Huang M. Effects of principal stress rotation on stress–strain behaviors of saturated clay under traffic–load–induced stress path. Soils and Foundations, 2019, 59(1): 41-55

[34]

Qian J, Lin Z, Ma X. Equivalent finite element method considering coupling pore pressure accumulation and dissipation. Rock and Soil Mechanics, 2015, 36(S1): 125-130in Chinese.

[35]

Qian J, Xu W, Mu L, Wu A. Calibration of soil parameters based on intelligent algorithm using efficient sampling method. Underground Space, 2021, 6(3): 329-341

[36]

Rammay MH, Alyaev S, Elsheikh AH. Probabilistic model-error assessment of deep learning proxies: An application to real-time inversion of borehole electromagnetic measurements. Geophysical Journal International, 2022, 230(3): 1800-1817

[37]

Ringel LM, Jalali M, Bayer P. Stochastic inversion of three‐dimensional discrete fracture network structure with hydraulic tomography. Water Resources Research, 2021, 57(12 e2021WR030401

[38]

Song J, Ntibahanana M, Luemba M, Tondozi K, Imani G. Ensemble deep learning-based porosity inversion from seismic attributes. IEEE Access, 2023, 11: 8761-8772

[39]

Sun, C. (2023). Study on long-term settlement of operational airport taxiways and underlying subway tunnels. Tongji University. in Chinese.

[40]

Wei X, Wang G, Wu R. Prediction of traffic loading–induced settlement of low-embankment road on soft subsoil. International Journal of Geomechanics, 2017, 17(2): 06016016

[41]

Wesseling J, Kroes J, Oliveira TC, Damiano F. The impact of sensitivity and uncertainty of soil physical parameters on the terms of the water balance: Some case studies with default R packages. Part I: Theory, methods and case descriptions. Computers and Electronics in Agriculture, 2020, 170 105054

[42]

Yang J, Yin Z-Y, Liu X-F, Gao F-P. Numerical analysis for the role of soil properties to the load transfer in clay foundation due to the traffic load of the metro tunnel. Transportation Geotechnics, 2020, 23 100336

[43]

Yang Z, Liu Z. Preliminary application of displacement back-analysis method in underground engineering design. Underground Engineering, 1981, 2(9024in Chinese.

[44]

Yao Z, Zhang M, Chen J. Cyclic accumulative pore pressure explicit model of saturated soft clay and long-term settlement calculation of subway tunnel roadbed. Journal of the China Railway Society, 2012, 34(987-92in Chinese.

[45]

Yuan Y, Sun J. Objective function in optimal back analysis for rock engineering. Chinese Journal of Geotechnical Engineering, 1994, 16(2): 29-37in Chinese.

[46]

Zhang, J. (2016). Experimental study and long-term settlement analysis of saturated soft clay under aircraft moving loads. Tongji University. in Chinese.

[47]

Zhang D, Li Y. Long-term settlement of shield tunnel in soft clay due to vehicle vibration. Journal of Disaster Prevention and Mitigation Engineering, 2015, 35(5): 563-567

[48]

Zheng D, Cheng L, Bao T, Lv B. Integrated parameter inversion analysis method of a CFRD based on multi-output support vector machines and the clonal selection algorithm. Computers and Geotechnics, 2013, 47: 68-77

Funding

National Natural Science Foundation of China(51578413)

Fundamental Research Funds for Central Universities of the Central South University(20232ZD08)

RIGHTS & PERMISSIONS

The Author(s)

PDF

32

Accesses

0

Citation

Detail

Sections
Recommended

/