A digital twin-based multiscale framework for predicting full-scale TBM rock cutting performance from miniature point load tests

Abstract

Tunnel Boring Machine (TBM) cutter head performance prediction relies heavily on costly and labor-intensive full-scale rock cutting tests, whereas existing numerical models struggle with limitations in scale resolution, dimensionality, and fracture dynamics. This study introduces a digital twin framework that integrates automated rock parameter calibration—based on small-scale physical tests—with advanced numerical simulations to enhance large-scale TBM cutting predictions. Using point load tests on miniature rock specimens, an inverse analysis algorithm iteratively optimizes material properties, including elastic modulus, tensile strength, and cohesion, by calibrating them against experimental load-displacement curves. These optimized parameters drive a digital twin-based coupled Four-Dimensional Lattice Spring Model (4D-LSM) and Discontinuous Deformation Analysis (DDA) framework to predict full-scale TBM rock cutting forces. Validation against linear cutting machine (LCM) experiments confirms the model’s ability to replicate cutting forces (i.e., normal and rolling) and fracture propagation in jointed rock masses across varying penetration depths. Further application to conical cutter head tests demonstrates the framework’s predictive accuracy, with rolling forces falling within the range of experimental data. By bridging laboratory-scale testing with field-scale TBM operations, this methodology offers a cost-effective digital twin approach for optimizing cutter head design and rock fragmentation strategies, advancing geotechnical engineering through data-driven, high-fidelity simulations.

Keywords

Rock cutting / Digital twin / Point load test / 4D-LSM

CRediT authorship contribution statement

Gaofeng Zhao: Writing -review & editing, Supervision, Software, Methodology, Funding acquisition, Conceptualization. Zhuang Li: Writing -review & editing, Writing -original draft, Data curation. Yifeng Chen: Writing -original draft, Validation, Data curation. Qiuming Gong: Supervision, Data curation. Shijin Li: Writing -review & editing, Supervision. Xindong Wei: Writing -review & editing, Writing -original draft, Supervision, Funding acquisition.

Declaration of competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This study was supported by the National Natural Science Foundation of China (Grant Nos. 12472405 and 12402485).

References

[1] Q. Gong, Q. Liu, Q. Zhang, Tunnel boring machines (TBMs) in difficult grounds, Tunn. Undergr. Space Technol. 57 (2016) 1-3, doi: 10.1016/j.tust.2016.05.010.

[2] Q. Gong, X. Zhou, Y. Liu, B. Han, L. Yin, Development of a real-time muck analysis system for assistant intelligence TBM tunnelling, Tunn. Undergr. Space Technol. 107 (2021) 103655, doi: 10.1016/j.tust.2020.103655.

[3] W. Xie, X. Zhang, X. Liu, C. Xu, X. Li, D. Song, Q. Ma, N. Hu, Real-time perception of rock-machine interaction information in TBM tunnelling us-ing muck image analysis, Tunn. Undergr. Space Technol. 136 (2023) 105096, doi: 10.1016/j.tust.2023.105096.

[4] X. Shang, J. Zhou, X. Liao, F. Liu, J. Shen, Peridynamics simulation of TBM cutting process in soft and hard composite strata with a simplified loading scheme, Comput. Geotech. 171 (2024) 106387, doi: 10.1016/j.compgeo.2024.106387.

[5] Z. Wu, P. Zhang, L. Fan, Q. Liu, Numerical study of the effect of confining pressure on the rock breakage efficiency and fragment size distribution of a TBM cutter using a coupled FEM-DEM method, Tunn. Undergr. Space Technol. 88 (2019) 260-275, doi: 10.1016/j.tust.2019.03.012.

[6] Q. Gong, Y. Jiao, J. Zhao, Numerical modelling of the effects of joint spacing on rock fragmentation by TBM cutters, Tunn. Undergr. Space Technol. 21 (2005) 46-55, doi: 10.1016/j.tust.2005.06.004.

[7] J. Choo, Y. Sun, F. Fan, Size effects on the strength and cracking behavior of flawed rocks under uniaxial compression: from laboratory scale to field scale, Acta Geotech. 18 (2023) 3451-3468, doi: 10.1007/s11440-023-01806-7.

[8] Y. Pan, Q. Liu, X. Peng, Q. Liu, J. Liu, X. Huang, X. Cui, T. Cai, Full-scale linear cutting tests to propose some empirical formulas for TBM disc cutter performance prediction, Rock Mech. Rock Eng. 52 (2019) 4763-4783, doi: 10.1007/s00603-019-01865-x.

[9] A. Pandey, S. Kumar, A multi-level adaptive mesh refinement strategy for uni-fied phase field fracture modeling using unstructured conformal simplices, Comput. Methods Appl. Mech. Eng. 433 (2025) 117514, doi: 10.1016/j.cma.2024.117514.

[10] A. Gupta, U.M. Krishnan, T.K. Mandal, R. Chowdhury, V.P. Nguyen, An adaptive mesh refinement algorithm for phase-field fracture models: Application to brittle, cohesive, and dynamic fracture, Comput. Methods Appl. Mech. Eng. 399 (2022) 115347, doi: 10.1016/j.cma.2022.115347.

[11] T. Guo, K. Liu, R. Song, Crack propagation characteristics and fracture toughness analysis of rock-based layered material with pre-existing crack un-der semi-circular bending, Theor. Appl. Fract. Mech. 119 (2022) 103295, doi: 10.1016/j.tafmec.2022.103295.

[12] X. Zhou, Y. Wang, Numerical simulation of crack propagation and coalescence in pre-cracked rock-like Brazilian disks using the non-ordinary state-based peridy-namics, Int. J. Rock Mech. Min. Sci. 89 (2016) 235-249, doi: 10.1016/j.ijrmms. 2016.09.010.

[13] S. Boschert, R. Rosen, Digital twin-the simulation aspect, in: P. Hehenberger, D. Bradley (Eds.), Challenges and Solutions for Mecha-tronic Systems and their Designers, Springer International Publishing, Cham, 2016, pp. 59-74.

[14] M. Shafto, M. Conroy, R. Doyle, E. Glaessgen, C. Kemp, J. LeMoigne, L. Wang, Tech-nology Area, NASA, 2010.

[15] M. Schluse, J. Rossmann, From simulation to experimentable digital twins: simulation-based development and operation of complex technical systems, in: Pro-ceedings of the 2016 International Symposium on Systems Engineering (ISSE), Ed-inburgh, IEEE, 2016, doi: 10.1109/SysEng.2016.7753162.

[16] M. Grieves, J. Vickers, Digital twin: Mitigating unpredictable, undesirable emergent behavior in complex systems, in: J. Kahlen, S. Flumerfelt, A. Alves (Eds.), new Findings and Approaches, Springer International Publishing, Cham, 2016, pp. 85-113.

[17] K. Bruynseels, F.S. de Sio, J. van den Hoven, Digital twins in health care: ethi-cal implications of an emerging engineering paradigm, Front. Genet. 9 (2018) 31, doi: 10.3389/fgene.2018.00031.

[18] J. Leng, H. Zhang, D. Yan, Q. Liu, X. Chen, D. Zhang, Digital twin-driven manufac-turing cyber-physical system for parallel controlling of smart workshop, J. Ambient Intell. Hum. Comput. 10 (2019) 1155-1166, doi: 10.1007/s12652-018-0881-5.

[19] P. Wang, M. Yang, Y. Peng, J. Zhu, R. Ju, Q. Yin, Sensor control in anti-submarine warfare-a digital twin and random finite sets based approach, Entropy. 21 (2019) 767, 10.3390/e21080767.

[20] M. Liu, S. Fang, H. Dong, C. Xu, Review of digital twin about concepts, technologies, and industrial applications, J. Manuf. Syst. 58 (2021) 346-361, doi: 10.1016/j.jmsy.2020.06.017.

[21] W. Long, Z. Bao, K. Chen, S.T. Ng, I.Y. Wuni, Developing an integrative framework for digital twin applications in the building construction industry: A systematic liter-ature review, Adv. Eng. Inform. 59 (2024) 102346, doi: 10.1016/j.aei.2023.102346.

[22] P. Aivaliotis, K. Georgoulias, Z. Arkouli, S. Makris, Methodology for enabling digital twin using advanced physics-based modelling in predictive maintenance, Proc. CIRP (2019) 417-422, doi: 10.1016/j.procir.2019.03.072.

[23] R. Magargle, L. Johnson, P. Mandloi, P. Davoudabadi, O. Kesarkar, S. Krishnaswamy, J. Batteh, A. Pitchaikani, A simulation-based digital twin for model-driven health monitoring and predictive maintenance of an automotive braking system, in: Pro-ceedings of the 12th International Modelica Conference, Prague, Linköping Univer-sity Electronic Press, 2017, pp. 35-46.

[24] M. Vathoopan, M. Johny, A. Zoitl, A. Knoll, Modular fault ascription and correc-tive maintenance using a digital twin, IFAC-PapersOnLine 51 (2018) 1041-1046, doi: 10.1016/j.ifacol.2018.08.470.

[25] A.K. Ghosh, A.S. Ullah, A. Kubo, Hidden markov model-based digital twin construc-tion for futuristic manufacturing systems, Artif. Intell. Eng. Des.,Anal. Manuf. 33 (2019) 317-331, doi: 10.1017/S089006041900012X.

[26] X. Sun, J. Bao, J. Li, Y. Zhang, S. Liu, B. Zhou, A digital twin-driven approach for the assembly-commissioning of high precision products, Robot. Comput. Integr. Manuf. 61 (2020) 101839, doi: 10.1016/j.rcim.2019.101839.

[27] E.J. Tuegel, A.R. Ingraffea, T.G. Eason, S.M. Spottswood, Reengineering aircraft structural life prediction using a digital twin, Int. J. Aerosp. Eng. 2011 (2011).

[28] R. Lu, I. Brilakis, Digital twinning of existing reinforced concrete bridges from labelled point clusters, Autom. Constr. 105 (2019) 102837, doi: 10.1016/j.autcon.2019.102837.

[29] B.R. Seshadri, T. Krishnamurthy, Structural health management of damaged aircraft structures using the digital twin concept, 25th AIAA/AHS Adaptive Structures Con-ference, AIAA, 2017, doi: 10.2514/6.2017-1675.

[30] E.Y. Song, M. Burns, A. Pandey, T. Roth, IEEE 1451 smart sensor digital twin fed-eration for iot/cps research, in: Proceedings of the 2019 IEEE Sensors Applications Symposium (SAS), Sophia Antipolis, IEEE, 2019, doi: 10.1109/SAS.2019.8706111.

[31] R. Tomar, J. Piesk, H. Sprengel, E. Isleyen, S. Duzgun. J.I. Rostami, Digital twin of tunnel construction for safety and efficiency, in: D. Peila, G. Viggiani, T. Celestino (Eds.), Tunnels and Underground Cities: engineering and Innovation Meet Archae-ology, Architecture and Art, CRC Press, Boca Raton, 2020, pp. 3224-3234.

[32] Y. Li, G. Zhao, A numerical integrated approach for the estimation of the uniaxial compression strength of rock from point load tests, Int. J. Rock Mech. Min. Sci. 148 (2021) 104939, doi: 10.1016/j.ijrmms.2021.104939.

[33] S. Li, J. Wang, J. Rong, W. Wei, A digital twin framework for product to-be-designed analysis based on operation data, Proc. CIRP. 109 (2022) 179-184, doi: 10.1016/j.procir.2022.05.233.

[34] B. Jiang, G. Zhao, Q. Gong, X. Zhao, Three-dimensional coupled numerical modelling of lab-level full-scale TBM disc cutting tests, Tunn. Undergr. Space Technol. 114 (2021) 103997, doi: 10.1016/j.tust.2021.103997.

[35] G. Zhao, Y. Li, B. Jiang, Coupling DDA and 4D-LSM through contact the-ory for rock cutting, IOP Conf. Ser.: Earth Environ. Sci. 570 (2020) 022054, doi: 10.1088/1755-1315/570/2/022054.

[36] G. Zhao, Developing a four-dimensional lattice spring model for mechanical re-sponses of solids, Comput. Methods Appl. Mech. Eng. 315 (2017) 881-895, doi: 10.1016/j.cma.2016.11.034.

[37] G. Zhao, J.J Lian, A.R. Russell, J. Zhao, Three-dimensional DDA and DLSM cou-pled approach for rock cutting and rock penetration, Int. J. Geomech. 17 (2017) E4016015, doi: 10.1061/(ASCE)GM.1943-5622.0000754.

[38] G. Shi, Discontinuous deformation analysis: A new numerical model for the static and dynamics of block systems, Ph.D. Thesis, University of California, 1989, doi: 10.1108/eb023855.

[39] L. Yin, C. Miao, G. He, F. Dai, Q. Gong, Study on the influence of joint spacing on rock fragmentation under TBM cutter by linear cutting test, Tunn. Undergr. Space Technol. (2016) 137-144, doi: 10.1016/j.tust.2016.02.018.

[40] Q. Gong, X. Du, Z. Li, Q. Wang, Development of a mechanical rock break-age experimental platform, Tunn. Undergr. Space Technol. 57 (2016) 129-136, doi: 10.1016/j.tust.2016.02.019.