Metamodelos em engenharia geotécnica: aplicação à retroanálise de estruturas geotécnicas
DOI:
https://doi.org/10.14195/2184-8394_167_3Palavras-chave:
Escavações profundas, Método observacional, metamodelosResumo
Este artigo apresenta uma metodologia para efetuar a retroanálise de estruturas geotécnicas complexas recorrendo a metamodelos. A validação do método é efetuada através da análise da escavação multi-escorada executada para a estação de Tottenham Court Road, em Londres. Para o efeito, foi criada uma base de dados com 1943 análises de elementos finitos, nas quais se variaram 18 parâmetros do modelo, designadamente o coeficiente de impulso em repouso, e os parâmetros de rigidez dos solos e das escoras. Seis metamodelos foram treinados, um por fase de escavação, tendo-se obtido em todos coeficientes de determinação superiores a 0,977. Os parâmetros com maior influência nos deslocamentos da parede foram identificados através de um estudo de sensibilidade baseado em índices de Sobol. Por último, através do acoplamento dos metamodelos a um algoritmo genético, foi efetuada uma retroanálise com base na deformada da parede. Os parâmetros calibrados foram verificados recorrendo a um modelo numérico independente, confirmando a fiabilidade do processo proposto e a sua adequação à implementação do método observacional.
Downloads
Referências
Ansel, J.; Yang, E.; He, H.; Gimelshein, N.; Jain, A.; Voznesensky, M.; Bao, B.; Bell, P.; Berard, D.; Burovski, E.; Chauhan, G.; Chourdia, A.; Constable, W.; Desmaison, A.; DeVito, Z.; Ellison, E.; Feng, W.; Gong, J.; Gschwind, M.; Hirsh, B.; Huang, S.; Kalambarkar, K.; Kirsch, L.; Lazos, M.; Lezcano, M.; Liang, Y.; Liang, J.; Lu, Y.; Luk, C. K.; Maher, B.; Pan, Y.; Puhrsch, C.; Reso, M.; Saroufim, M.; Siraichi, M. Y.; Suk, H.; Zhang, S.; Suo, M.; Tillet, P.; Zhao, X.; Wang, E.; Zhou, K.; Zou, R.; Wang, X.; Mathews, A.; Wen, W.; Chanan, G.; Wu, P.; Chintala, S. (2024). PyTorch 2: Faster Machine Learning Through Dynamic Python Bytecode Transformation and Graph Compilation. Proceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS '24), Association for Computing Machinery, New York, NY, USA. https://doi.org/10.1145/3620665.3640366
Avgerinos, V.; Potts, D. M.; Standing, J. R. (2016) The use of kinematic hardening models for predicting tunnelling-induced ground movements in London Clay. Geotechnique. 66 (2), pp.106-120. https://doi.org/10.1680/jgeot.15.p.035
Bentley Systems (2025). PLAXIS2D 2024.3 - Reference Manual.
Cañavate-Grimal, A.; Falcó, A.; Calderón, P.; Payá-Zaforteza, I. (2015). On the use of stochastic spectral methods in deep excavation inverse problems. Computers & Structures. 159, pp. 41-60. https://doi.org/10.1016/j.compstruc.2015.06.009
Cerek, K.; Gupta, A.; Dao, D. A.; Hadjiloo, E.; Grabe, J. (2025). Predicting soil stress–strain behaviour with bidirectional long short-term memory networks. Machine Learning and Data Science in Geotechnics. 1 (1), pp. 60-77. http://doi.org/10.1108/mlag-08-2024-0007
Cerek, K.; Klos, D.; Hadjiloo, E.; Grabe, J. (2026). Hybrid surrogate models of quay walls. Proceedings of the Institution of Civil Engineers - Civil Engineering, pp. 1-13. https://doi.org/10.1680/jcien.25.00451
Chen, Y. (2018). Application of new observational method on deep excavation retaining wall design in London Clay. PhD Thesis. Department of Engineering, University of Cambridge.
Chen, Y.; Nicholson, D. P.; Ingram, P.; Hardy, S.; Liew, H. L.; Farooq, I.; Biscontin, G. (2015). Application of the observational method on Crossrail project. Proceedings of Crossrail: A Specialist Foundation Construction Lessons Learnt Conference, London, UK, ICE Publishing. pp. 63-72.
Chen, Y.; Pillai, A. K.; Nicholson, D. P.; Biscontin, G. (2018). Back analysis Crossrail deep excavations using three-dimensional finite element modelling. Proceedings of the 9th European Conference on Numerical Methods in Geotechnical Engineering, Porto, Portugal.
Ferrero, J. A.; Ruiz López, A.; Taborda, D. M. G.; Brasile, S. (2023). Applying the observational method to a deep braced excavation using an artificial neural network. Proceedings of the 10th European Conference on Numerical Methods in Geotechnical Engineering, London, UK. https://doi.org/10.53243/NUMGE2023-303
Finno, R. J.; Calvello, M. (2005). Supported Excavations: Observational Method and Inverse Modeling. Journal of Geotechnical and Geoenvironmental Engineering. 131 (7), pp. 826-836. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:7(826)
Forrester, A. I. J.; Sobester, A.; Keane, A. J. (2008). Engineering design via surrogate modelling: a practical guide. Chichester, John Wiley & Sons, Ltd.
Gawecka, K. A.; Taborda, D. M. G.; Potts, D. M.; Cui, W. J.; Zdravkovic, L.; Kasri, M. S. H. (2017). Numerical modelling of thermo-active piles in London Clay. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering. 170 (3), pp. 201-219. http://doi.org/10.1680/jgeen.16.00096
Ghaboussi, J.; Garrett, J. H.; Wu, X. (1991). Knowledge-Based Modeling of Material Behavior with Neural Networks. Journal of Engineering Mechanics. 117 (1), pp. 132-153. http://doi.org/10.1061/(ASCE)0733-9399(1991)117:1(132)
Ghalandari, T.; Taborda, D. M. G.; Kia, A.; Vuye, C. (2024) Hybrid framework for surrogate modelling of massive solar collectors in road pavements. Geomechanics for Energy and the Environment. 40, 100617. https://doi.org/10.1016/j.gete.2024.100617
Hashash, Y. M. A.; Jung, S.; Ghaboussi, J. (2004) Numerical implementation of a neural network based material model in finite element analysis. International Journal for Numerical Methods in Engineering. 59 (7), pp. 989-1005. http://doi.org/10.1002/nme.905
Hight, D. W.; Gasparre, A.; Nishimura, S.; Minh, N. A.; Jardine, R. J.; Coop, M. R. (2007). Characteristics of the London Clay from the Terminal 5 site at Heathrow Airport. Geotechnique. 57 (1), pp. 3-18. https://doi.org/10.1680/geot.2007.57.1.3
Homma, T.; Saltelli, A. (1996). Importance measures in global sensitivity analysis of nonlinear models. Reliability Engineering & System Safety. 52 (1), 1-17. https://doi.org/10.1016/0951-8320(96)00002-6
Joseph, V. R.; Gul, E.; Ba, S. (2020). Designing computer experiments with multiple types of factors: The MaxPro approach. Journal of quality technology. 52 (4), pp. 343-354. https://doi.org/10.1080/00224065.2019.1611351
Kingma, D. P.; Ba, J. L. (2015). Adam: A Method for Stochastic Optimization. Proceedings of the 3rd International Conference on Learning Representations (ICLR), San Diego, CA, USA. https://arxiv.org/abs/1412.6980
Kudela, J.; Matousek, R. (2022) Recent advances and applications of surrogate models for finite element method computations: a review. Soft Computing. 26 (24), pp. 13709-13733. http://doi.org/10.1007/s00500-022-07362-8
Kung, G. T.; Hsein Juang, C.; Hsiao, E. C.; Hashash, Y. M. A. (2007). Simplified Model for Wall Deflection and Ground-Surface Settlement Caused by Braced Excavation in Clays. Journal of Geotechnical and Geoenvironmental Engineering. 133 (6), pp. 731-747. http://doi.org/10.1061/(ASCE)1090-0241(2007)133:6(731)
Kwang, C. W.; Chen, Y. (2025). A method of isolating different components of prop axial force through FFT&BWF signal filters. Proceedings of the Institution of Civil Engineers - Geotechnical Engineering. 178 (5), pp. 574-587. https://doi.org/10.1680/jgeen.24.00241
Ledesma, A.; Gens, A.; Alonso, E. E. (1996). Estimation of parameters in geotechnical backanalysis — I. Maximum likelihood approach. Computers and Geotechnics. 18 (1), pp. 1-27. https://doi.org/10.1016/0266-352X(95)00021-2
Masi, F.; Stefanou, I.; Vannucci, P.; Maffi-Berthier, V. (2021). Thermodynamics-based Artificial Neural Networks for constitutive modeling. Journal of the Mechanics and Physics of Solids. 147, 104277. https://doi.org/10.1016/j.jmps.2020.104277
McKay, M. D.; Beckman, R. J.; Conover, W. J. (1979) Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code. Technometrics. 21 (2), 239-245. https://doi.org/10.1080/00401706.1979.10489755
New, B. M.; Bowers, K. H. (1994). Ground movement model validation at the Heathrow Express trial tunnel. Tunnelling ’94: Papers presented at the seventh international symposium, ‘Tunnelling’94’. Boston, MA, Springer US, pp. 301-329.
Peck, R. B. (1969). Advantages and Limitations of the Observational Method in Applied Soil Mechanics. Geotechnique. 19 (2), pp. 171-187. http://doi.org/10.1680/geot.1969.19.2.171
Pedro, A. M. G. (2007) Mato Forte tunnel – Back analysis of its Behaviour. MSc Thesis. University of Coimbra, Coimbra, Portugal (in Portuguese).
Pedro, A. M. G.; Taborda, D. M. G.; Repsold, L. M.; Almeida e Sousa, J. (2025). The influence of the construction methodology on the modelled response of shafts. Soils and Rocks. 48 (4). https://doi.org/10.28927/SR.2025.004025
Pirrone, A. I.; Taborda, D. M. G. (2023). An application of machine learning to the back analysis of monopile response. 9th International Society for Underwater Technology Offshore Site Investigation and Geotechnics Conference, London, UK. https://doi.org/10.3723/XENI6047
Rechea, C.; Levasseur, S.; Finno, R. (2008). Inverse analysis techniques for parameter identification in simulation of excavation support systems. Computers and Geotechnics. 35 (3), pp. 331-345. https://doi.org/10.1016/j.compgeo.2007.08.008
Ruiz López, A. (2024). IC MAGE GenAlgo - Genetic Algorithms for Geotechnics (Version 1.0). Zenodo. https://doi.org/10.5281/zenodo.13998194
Ruiz López, A.; Taborda, D. M. G.; Tsiampousi, A.; Go, J.; Dingle, H. (2025). A data-driven macroelement model for suction buckets in sand. Proceedings of the 5th International Symposium on Frontiers in Offshore Geotechnics, Nantes, France. https://doi.org/10.53243/ISFOG2025-347
Ruiz López, A.; Taborda, D. M. G.; Tsiampousi, A.; Pedro, A. M. G.; Hardy, S. (2024). Applying machine learning to the development of surrogate models for shafts in clay. Proceedings of the XVIII ECSMGE 2024, Lisbon, Portugal, CRC Press. https://doi.org/10.1201/9781003431749-133
Sacks, J.; Welch, W. J.; Mitchell, T. J.; Wynn, H. P. (1989). Design and Analysis of Computer Experiments. Statistical science. 4 (4), pp. 409-423. http://doi.org/10.1214/ss/1177012413
Sailer, E.; Taborda, D. M. G.; Zdravkovic, L.; Potts, D. M. (2019). Fundamentals of the coupled thermo-hydro-mechanical behaviour of thermo-active retaining walls. Computers and Geotechnics. 109, pp. 189-203. https://doi.org/10.1016/j.compgeo.2019.01.017
Saltelli, A.; Annoni, P.; Azzini, I.; Campolongo, F.; Ratto, M.; Tarantola, S. (2010). Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications. 181 (2), pp. 259-270. https://doi.org/10.1016/j.cpc.2009.09.018
Sanchez Fernandez, J.; Provost, A.; Ruiz López, A.; Taborda, D. M. G. (2025). A data-driven approach to predicting the long-term thermal performance of thermo-active piles. Proceedings of the 3rd International Conference on Energy Geotechnics, Paris. https://hal.science/hal-05343917v1
Sheil, B.; Anagnostopoulos, C.; Buckley, R.; Ciantia, M. O.; Febrianto, E.; Fu, J.; Gao, Z.; Geng, X.; Gong, B.; Hanley, K.; He, P.; Kolomvatsos, K.; Lopes, B. de C. F. L.; Ninic, J.; Previtali, M.; Rezania, M.; Ruiz Lopez, A.; Sun, J.; Suryasentana, S.; Taborda, D. M. G.; Utili, S.; Whyte, S.; Zhang, P. (2026). Artificial intelligence transformations in geotechnics: progress, challenges and future enablers. Computers and Geotechnics. 189, 107604. https://doi.org/10.1016/j.compgeo.2025.107604
Simpson, T. W.; Poplinski, J. D.; Koch, P. N.; Allen, J. K. (2001). Metamodels for Computer-based Engineering Design: Survey and recommendations. Engineering with computers. 17 (2), pp. 129-150. http://doi.org/10.1007/PL00007198
Sloan, S. W. (1987). Substepping schemes for the numerical integration of elastoplastic stress-strain relations. International Journal for Numerical Methods in Engineering. 24 (5), pp. 893-911. https://doi.org/10.1002/nme.1620240505
Sloan, S. W.; Abbo, A. J.; Sheng, D. (2001). Refined explicit integration of elastoplastic models with automatic error control. Engineering Computations. 18 (1/2), pp. 121-194. https://doi.org/10.1108/02644400110365842
Sobol′, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation. 55 (1), pp. 271-280. https://doi.org/10.1016/S0378-4754(00)00270-6
Taborda, D. M. G.; Kontoe, S.; Tsiampousi, A. (2023). IC MAGE Flow Model 01 – Nonlinearly varying anisotropic permeability (Version 1.0). Zenodo. https://doi.org/10.5281/zenodo.7796383
Taborda, D. M. G.; Kontoe, S.; Tsiampousi, A. (2024a). IC MAGE Model 01 – Strain-hardening/softening Mohr-Coulomb failure criterion with isotropic small strain stiffness (Version 2.2). Zenodo. https://doi.org/10.5281/zenodo.13891265
Taborda, D. M. G.; Kontoe, S.; Tsiampousi, A. (2024b) IC MAGE UMIP - Universal model interface for PLAXIS (Version 3.6). Zenodo. https://doi.org/10.5281/zenodo.13890543.
Taborda, D. M. G.; Pedro, A. M. G.; Xia, H.; Hardy, S. (2025). A methodology for improved predictions of surface ground movements around shafts. Proceedings of the Institution of Civil Engineers - Geotechnical Engineering. 178 (4), pp. 479-493. https://doi.org/10.1680/jgeen.24.00258
Taborda, D. M. G.; Potts, D. M.; Zdravkovic, L. (2016). On the assessment of energy dissipated through hysteresis in finite element analysis. Computers and Geotechnics. 71, pp. 180-194. https://doi.org/10.1016/j.compgeo.2015.09.001
Yang, Y.; Ruiz López, A.; Tsiampousi, A.; Taborda, D. M. G. (2026). A novel adaptive sampling approach with batch selection for the automatic generation of surrogate models in geotechnical engineering. Data-Centric Engineering. 7, e2. https://doi.org/10.1017/dce.2025.10036
Yeow, H.-C.; Nicholson, D.; Man, C.-L.; Ringer, A.; Glass, P.; Black, M. (2014). Application of observational method at Crossrail Tottenham Court Road station, UK. Proceedings of the Institution of Civil Engineers - Geotechnical Engineering. 167 (2), pp. 182-193. https://doi.org/10.1680/geng.13.00035
Yin, X.; Wang, H.; Pisanò, F.; Gavin, K.; Askarinejad, A.; Zhou, H. (2023). Deep learning-based design model for suction caissons on clay. Ocean Engineering. 286, 115542. https://doi.org/10.1016/j.oceaneng.2023.115542
Zhang, P.; Yin, Z.-Y.; Zheng, Y.; Gao, F.-P. (2020). A LSTM surrogate modelling approach for caisson foundations. Ocean Engineering. 204, 107263. https://doi.org/10.1016/j.oceaneng.2020.107263
Downloads
Publicado
Edição
Secção
Licença
Direitos de Autor (c) 2026 David M. G. Taborda, António M. G. Pedro, Manuel Matos Fernandes, Jorge Almeida e Sousa
Este trabalho encontra-se publicado com a Licença Internacional Creative Commons Atribuição 4.0.
