Abstract
Based on machine-learning (ML) and analytical methods, a hybrid method is developed herein to predict the ground-displacement field (GDF) caused by tunneling. The extreme learning machine (ELM), as a single hidden layer feedforward neural network, is used as an ML model to predict maximum settlement smax of the ground surface. The particle swarm optimization (PSO) algorithm is applied to optimize the parameters for the ELM method, namely, weight and bias values from the input layer to the hidden layer. The mean square error of the k-fold cross validation sets is considered the fitness function of the PSO algorithm. For 38 data samples from published papers, 30 samples are used as the training set, and 8 samples are used as the test set. For the test samples, the error of five samples ranges between −5 and 5 mm. The error of only one sample is slightly greater than 10 mm. The proposed PSO-ELM method demonstrates good prediction performance of smax. A deformation parameter of the nonuniform displacement mode for the tunnel cross-section is calibrated based on predicted smax. When the determined nonuniform displacement mode is used as the boundary condition of the tunnel cross-section, the GDF of a shallow circular tunnel is analytically predicted based on the complex-variable method prior to tunnel excavation. For a specific engineering case, i.e., the Heathrow Express tunnel, the proposed PSO-ELM-analytical method can well predict the surface-settlement trough curve, horizontal displacements at different depths, and vertical displacements above the tunnel.
Similar content being viewed by others
References
Lu D C, Miao J B, Du X L, et al. A 3D elastic-plastic-viscous constitutive model for soils considering the stress path dependency. Sci China Tech Sci, 2020, 63: 791–808
Yu H, Yuan Y. Analytical solution for an infinite Euler-Bernoulli beam on a viscoelastic foundation subjected to arbitrary dynamic loads. J Eng Mech, 2014, 140: 542–551
Miao J B, Lu D C, Lin Q T, et al. Time-dependent surrounding soil pressure and mechanical response of tunnel lining induced by surrounding soil viscosity. Sci China Tech Sci, 2021, 64: 2453–2468
Bouayad D, Emeriault F. Modeling the relationship between ground surface settlements induced by shield tunneling and the operational and geological parameters based on the hybrid PCA/ANFIS method. Tunn Undergr Sp Tech, 2017, 68: 142–152
Zhang P, Chen R P, Wu H N. Real-time analysis and regulation of EPB shield steering using Random Forest. Automat Constr, 2019, 106: 102860
Zhang P, Wu H N, Chen R P, et al. Hybrid meta-heuristic and machine learning algorithms for tunneling-induced settlement prediction: A comparative study. Tunn Undergr Sp Tech, 2020, 99: 103383
Zhang W G, Li H R, Wu C Z, et al. Soft computing approach for prediction of surface settlement induced by earth pressure balance shield tunneling. Undergr Sp, 2021, 6: 353–363
Sun R, Cheng Q, Xie F, et al. Combining machine learning and dynamic time wrapping for vehicle driving event detection using smartphones. IEEE Trans Intell Transp Syst, 2021, 22: 194–207
Suwansawat S, Einstein H H. Artificial neural networks for predicting the maximum surface settlement caused by EPB shield tunneling. Tunn Undergr Sp Tech, 2006, 21: 133–150
Neaupane K M, Adhikari N R. Prediction of tunneling-induced ground movement with the multi-layer perceptron. Tunn Undergr Sp Tech, 2006, 21: 151–159
Hasanipanah M, Noorian-Bidgoli M, Jahed Armaghani D, et al. Feasibility of PSO-ANN model for predicting surface settlement caused by tunneling. Eng Comput, 2016, 32: 705–715
Darabi A, Ahangari K, Noorzad A, et al. Subsidence estimation utilizing various approaches — A case study: Tehran No. 3 subway line. Tunn Undergr Sp Tech, 2012, 31: 117–127
Pourtaghi A, Lotfollahi-Yaghin M A. Wavenet ability assessment in comparison to ANN for predicting the maximum surface settlement caused by tunneling. Tunn Undergr Sp Tech, 2012, 28: 257–271
Chen R P, Zhang P, Kang X, et al. Prediction of maximum surface settlement caused by earth pressure balance (EPB) shield tunneling with ANN methods. Soils Found, 2019, 59: 284–295
Wang F, Gou B, Qin Y. Modeling tunneling-induced ground surface settlement development using a wavelet smooth relevance vector machine. Comput Geotech, 2013, 54: 125–132
Ghiasi R, Ghasemi M R, Noori M. Comparative studies of metamodeling and AI-based techniques in damage detection of structures. Adv Eng Software, 2018, 125: 101–112
Matin S S, Farahzadi L, Makaremi S, et al. Variable selection and prediction of uniaxial compressive strength and modulus of elasticity by random forest. Appl Soft Comput, 2018, 70: 980–987
Zhou J, Shi X, Du K, et al. Feasibility of random-forest approach for prediction of ground settlements induced by the construction of a shield-driven tunnel. Int J Geomech, 2017, 17
Lu D, Lin Q, Tian Y, et al. Formula for predicting ground settlement induced by tunnelling based on Gaussian function. Tunn Undergr Sp Tech, 2020, 103: 103443
Zhang P, Yin Z Y, Jin Y F. Bayesian neural network-based uncertainty modelling: Application to soil compressibility and undrained shear strength prediction. Can Geotech J, 2022, 59: 546–557
Zhang P, Yin Z Y. A novel deep learning-based modelling strategy from image of particles to mechanical properties for granular materials with CNN and BiLSTM. Comput Method Appl Mech Eng, 2021, 382: 113858
Zhang W, Wu C, Li Y, et al. Assessment of pile drivability using random forest regression and multivariate adaptive regression splines. Georisk, 2021, 15: 27–40
Zhang R, Wu C, Goh A T C, et al. Estimation of diaphragm wall deflections for deep braced excavation in anisotropic clays using Ensemble Learning. Geosci Front, 2021, 12: 365–373
Huang G B, Zhu Q Y, Siew C K. Extreme learning machine: A new learning scheme of feedforward neural networks. In: 2004 IEEE International Joint Conference on Neural Networks. Budapest, 2004. 985–990
Huang G B, Zhu Q Y, Siew C K. Extreme learning machine: Theory and applications. Neurocomputing, 2006, 70: 489–501
Yaseen Z M, Deo R C, Hilal A, et al. Predicting compressive strength of lightweight foamed concrete using extreme learning machine model. Adv Eng Software, 2018, 115: 112–125
Xue Y, Bai C, Qiu D, et al. Predicting rockburst with database using particle swarm optimization and extreme learning machine. Tunn Undergr Sp Tech, 2020, 98: 103287
Zhang P, Li H, Ha Q P, et al. Reinforcement learning based optimizer for improvement of predicting tunneling-induced ground responses. Adv Eng Inf, 2020, 45: 101097
Verruijt A. A complex variable solution for a deforming circular tunnel in an elastic half-plane. Int J Numer Anal Meth Geomech, 1997, 21: 77–89
Verruijt A. Deformations of an elastic half plane with a circular cavity. Int J Solids Struct, 1998, 35: 2795–2804
Wang L Z, Li L L, Lv X J. Complex variable solutions for tunneling-induced ground movement. Int J Geomech, 2009, 9: 63–72
Fang Q, Song H, Zhang D. Complex variable analysis for stress distribution of an underwater tunnel in an elastic half plane. Int J Numer Anal Meth Geomech, 2015, 39: 1821–1835
Bobet A. Analytical solutions for shallow tunnels in saturated ground. J Eng Mech, 2001, 127: 1258–1266
Fu J, Yang J, Yan L, et al. An analytical solution for deforming twin-parallel tunnels in an elastic half plane. Int J Numer Anal Meth Geomech, 2015, 39: 524–538
Pinto F, Whittle A J. Ground movements due to shallow tunnels in soft ground. I: Analytical solutions. J Geotech Geoenviron Eng, 2014, 140
Fu J, Yang J, Klapperich H, et al. Analytical prediction of ground movements due to a nonuniform deforming tunnel. Int J Geomech, 2016, 16
Zhang Z, Huang M, Xi X, et al. Complex variable solutions for soil and liner deformation due to tunneling in clays. Int J Geomech, 2018, 18
Zhang Z, Pan Y, Zhang M, et al. Complex variable analytical prediction for ground deformation and lining responses due to shield tunneling considering groundwater level variation in clays. Comput Geotech, 2020, 120: 103443
Park K H. Elastic solution for tunneling-induced ground movements in clays. Int J Geomech, 2004, 4: 310–318
Kong F, Lu D, Du X, et al. Displacement analytical prediction of shallow tunnel based on unified displacement function under slope boundary. Int J Numer Anal Meth Geomech, 2019, 43: 183–211
Kong F, Lu D, Du X, et al. Elastic analytical solution of shallow tunnel owing to twin tunnelling based on a unified displacement function. Appl Math Model, 2019, 68: 422–442
Avci E. A new method for expert target recognition system: Genetic wavelet extreme learning machine (GAWELM). Expert Syst Appl, 2013, 40: 3984–3993
Zhang P, Yin Z Y, Jin Y F, et al. A novel hybrid surrogate intelligent model for creep index prediction based on particle swarm optimization and random forest. Eng Geol, 2020, 265: 105328
Zhang P, Yin Z Y, Jin Y F, et al. Intelligent modelling of clay compressibility using hybrid meta-heuristic and machine learning algorithms. Geosci Front, 2021, 12: 441–452
Yin Z Y, Jin Y F, Shen J S, et al. Optimization techniques for identifying soil parameters in geotechnical engineering: Comparative study and enhancement. Int J Numer Anal Meth Geomech, 2018, 42: 70–94
Das M T, Dulger L C. Signature verification (SV) toolbox: Application of PSO-NN. Eng Appl Artif Intel, 2009, 22: 688–694
Lu D, Kong F, Du X, et al. Fractional viscoelastic analytical solution for the ground displacement of a shallow tunnel based on a time-dependent unified displacement function. Comput Geotech, 2020, 117: 103284
Kong F, Lu D, Du X, et al. Analytical solution of stress and displacement for a circular underwater shallow tunnel based on a unified stress function. Ocean Eng, 2021, 219: 108352
Shi J, Ortigao J A R, Bai J. Modular neural networks for predicting settlements during tunneling. J Geotech Geoenviron Eng, 1998, 124: 389–395
Kim C Y, Bae G J, Hong S W, et al. Neural network based prediction of ground surface settlements due to tunnelling. Comput Geotech, 2001, 28: 517–547
Ahangari K, Moeinossadat S R, Behnia D. Estimation of tunnelling-induced settlement by modern intelligent methods. Soils Found, 2015, 55: 737–748
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the National Natural Science Foundation of China (Grant No. 52025084).
Rights and permissions
About this article
Cite this article
Kong, F., Lu, D., Ma, Y. et al. Novel hybrid method to predict the ground-displacement field caused by shallow tunnel excavation. Sci. China Technol. Sci. 66, 101–114 (2023). https://doi.org/10.1007/s11431-022-2079-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-022-2079-8