Hybrid Machine Learning Model for Predicting Shear Strength of Rock Joints
Source abstract
Abstract
The accurate prediction of joint shear strength is crucial for rock mass engineering design and geological hazard assessment. However, traditional machine learning (ML) models often suffer from local optima and limited generalization ability when dealing with complex nonlinear problems, thereby compromising prediction accuracy and stability. To address these challenges, this study proposes a hybrid ML model that integrates a multilayer perceptron (MLP) with the slime mold algorithm (SMA), termed the SMA-MLP model. While MLP exhibits strong nonlinear mapping capability, SMA enhances its training process through global optimization and parameter tuning, thereby improving predictive accuracy and robustness. A dataset with five input variables was constructed to evaluate the performance of the SMA-MLP model comprehensively. The proposed model was compared with other ML models. The results indicate that SMA-MLP outperforms these models in key metrics such as the root mean squared error (RMSE) and the correlation coefficient (R2), achieving an R2 of 0.97 and an RMSE as low as 0.10 MPa on the test set. Furthermore, feature importance analysis reveals that normal stress has the most significant influence on joint shear strength. This study demonstrates the superiority of SMA-MLP in predicting joint shear strength, highlighting its potential as an efficient and accurate tool for rock mass engineering analysis and providing reliable technical support for geological hazard assessment.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Rock Mechanics and Modeling · Tunneling and Rock Mechanics · Drilling and Well Engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Resources and Civil Engineering, GanNan University of Science and Technology, Ganzhou 341000, China
Key Laboratory of Intelligent and Green Development of Tungsten & Rare Earth Resources, Jiangxi Provincial Department of Education, Ganzhou 341000, China
School of Resources and Safety Engineering, Central South University, Changsha 410083, China
Funding
Jiangxi Provincial Department of Education Science and technology research Program · 2024 Annual Research Project on Humanities and Social Sciences in Universities of Jiangxi Province
References (80)
Show source-provided references
1. Evaluation of the ratio between uniaxial compressive strength and Schmidt hammer rebound number and its effectiveness in predicting rock strength10.1080/10589759.2014.977789 ↗
2. Shokri, B.J., Mirzaghorbanali, A., Nourizadeh, H., McDougall, K., Karunasena, W., Aziz, N., Entezam, S., and Entezam, A. (2024). Axial Load Transfer Mechanism in Fully Grouted Rock Bolting System: A Systematic Review. Appl. Sci., 14.10.3390/app14125232 ↗
3. A quantitative model considering crack closure effect of rock materials10.1016/j.ijsolstr.2022.111758 ↗
4. Improvements for the smooth joint contact model of the particle flow code and its applications10.1016/j.compgeo.2017.02.012 ↗
5. Laboratory study of the effects of grouted rebar bolts on shear failure of structural planes in deep hard rocks10.1016/j.ijrmms.2022.105308 ↗
6. A semiempirical constitutive relationship for rocks under uniaxial compression considering the initial damage recovery10.1111/ffe.13903 ↗
7. On the shear failure of incipient rock discontinuities under CNL and CNS boundary conditions: Insights from DEM modelling10.1016/j.enggeo.2018.01.012 ↗
8. Scale effect on the shear behaviour of rock joints based on a numerical study10.1016/j.enggeo.2014.07.018 ↗
9. Shear failure modes and AE characteristics of sandstone and marble fractures10.1515/geo-2019-0020 ↗
10. Stability investigation of road cut slope in basaltic rockmass, Mahabaleshwar, India10.1016/j.gsf.2014.03.002 ↗
11. Patton, F.D. (October, January 25). Multiple modes of shear failure in rock. Proceedings of the 1st Congress of International Society of Rock Mechanics, Lisbon, Portugal.
12. Study on strength behaviors of rock joints under different shearing deformation velocities
13. Ladanyi, B., and Archambault, G. (1969, January 16–19). Simulation of shear behavior of a jointed rock mass. In Proceedings of The 11th US Symposium on Rock Mechanics (USRMS), Berkeley, CA, USA.
14. Jaeger, J.C., Cook, N.G., and Zimmerman, R. (2009). Fundamentals of Rock Mechanics, John Wiley & Sons.
15. The shear strength of rock joints in theory and practice10.1007/BF01261801 ↗
16. Rate-dependent mechanical behavior of rough rock joints10.1016/j.ijrmms.2015.10.013 ↗
17. Shear strength model of joints based on Gaussian smoothing method and macro-micro roughness10.1016/j.compgeo.2021.104605 ↗
18. Disturbed state concept as unified constitutive modeling approach10.1016/j.jrmge.2016.01.003 ↗
19. Study on a nonlinear shear damage constitutive of structural plane and application of discrete element10.1016/j.compgeo.2022.105190 ↗
20. A novel criterion for yield shear displacement of rock discontinuities based on renormalization group theory10.1016/j.enggeo.2023.107008 ↗
21. Review of a new shear-strength criterion for rock joints10.1016/0013-7952(73)90013-6 ↗
22. Displacement velocity effects on rock fracture shear strengths10.1016/j.jsg.2016.07.007 ↗
23. Joint surface matching and shear strength part B: JRC-JMC shear strength criterion10.1016/S0148-9062(96)00063-0 ↗
24. Constitutive law for the shear strength of rock joints based on three-dimensional surface parameters10.1016/S1365-1609(02)00101-6 ↗
25. Evaluation of existing criteria in estimating shear strength of natural rock discontinuities10.1016/j.enggeo.2017.11.023 ↗
26. Shear strength Criteria for rock, rock joints, rockfill and rock masses: Problems and some solutions10.1016/j.jrmge.2013.05.008 ↗
27. Hybrid machine learning models to predict the shear strength of discontinuities with different joint wall compressive strength10.1080/10589759.2024.2381083 ↗
28. Physics informed machine learning: Seismic wave equation10.1016/j.gsf.2020.07.007 ↗
29. Quantitative assessment of rock lithology from gamma-ray and mud logging data10.1016/j.geoen.2023.211664 ↗
30. Machine learning applications in sheet metal constitutive Modelling: A review10.1016/j.ijsolstr.2024.113024 ↗
31. Prediction of joint roughness coefficient via hybrid machine learning model combined with principal components analysis10.1016/j.jrmge.2024.05.059 ↗
32. Modelling the shear behaviour of clean rock discontinuities using artificial neural networks10.1007/s00603-017-1197-z ↗
33. Stacking ensemble machine learning-based shear strength model for rock discontinuity10.1007/s10706-022-02081-1 ↗
34. Constitutive modeling of rock fractures by improved support vector regression10.1007/s12665-018-7421-7 ↗
35. Predicting peak shear strength of rock fractures using tree-based models and convolutional neural network10.1016/j.compgeo.2023.105965 ↗
36. Multilayer perceptrons to approximate complex valued functions10.1142/S0129065795000299 ↗
37. Prediction of flyrock distance induced by mine blasting using a novel Harris Hawks optimization-based multi-layer perceptron neural network10.1016/j.jrmge.2021.08.005 ↗
38. A hybrid particle swarm optimization and multi-layer perceptron algorithm for bivariate fractal analysis of rock fractures roughness10.1016/j.ijrmms.2012.12.028 ↗
39. Prediction of roadheaders performance using artificial neural network approaches (MLP and KOSFM)10.1016/j.jrmge.2015.06.008 ↗
40. A new integrated intelligent computing paradigm for predicting joints shear strength10.1016/j.gsf.2024.101884 ↗
41. Adaptive multilayer perceptron networks for detection of cracks in anisotropic laminated plates10.1016/S0020-7683(00)00368-1 ↗
42. Identification of steel bars immersed in reinforced concrete based on experimental results of eddy current testing and artificial neural network analysis10.1080/10589759.2012.695783 ↗
43. Mfetoum, I.M., Ngoh, S.K., Molu, R.J.J., Nde Kenfack, B.F., Onguene, R., Naoussi, S.R.D., Tamba, J.G., Bajaj, M., and Berhanu, M. (2024). Author Correction: A multilayer perceptron neural network approach for optimizing solar irradiance forecasting in Central Africa with meteorological insights. Sci. Rep., 14.10.1038/s41598-024-55883-z ↗
44. Structural reliability analysis for implicit performance function using radial basis function network10.1016/j.ijsolstr.2005.05.055 ↗
45. Deep learning neural networks for spatially explicit prediction of flash flood probability10.1016/j.gsf.2020.09.007 ↗
46. Predicting the friction angle of clays using a multi-layer perceptron neural network enhanced by yeo-johnson transformation and coral reefs optimization10.1016/j.jrmge.2024.02.025 ↗
47. Effect of lithological variations on the performance of artificial intelligence techniques for estimating total organic carbon through well logs
48. Slime mould algorithm: A new method for stochastic optimization10.1016/j.future.2020.03.055 ↗
49. Slime mould algorithm: A comprehensive review of recent variants and applications10.1080/00207721.2022.2153635 ↗
50. Albedran, H., Alsamia, S., and Koch, E. (2025). Flower fertilization optimization algorithm with application to adaptive controllers. Sci. Rep., 15.10.1038/s41598-025-89840-1 ↗
51. Ghiasi, R., Noori, M., Kuok, S.C., Silik, A., Wang, T.Y., Pozo, F., and Altabey, W.A. (2022). Structural Assessment under Uncertain Parameters via the Interval Optimization Method Using the Slime Mold Algorithm. Appl. Sci., 12.10.3390/app12041876 ↗
52. A damage constitutive model for shear behavior of joints based on determination of the yield point10.1016/j.ijrmms.2020.104269 ↗
53. Tunnel behaviour and support associated with the weak rock masses of flysch10.1016/j.jrmge.2014.04.003 ↗
54. Numerical study on cracking behavior and fracture failure mechanism of fractured rocks under shear loading10.1007/s40571-023-00660-4 ↗
55. An ANFIS–TLBO criterion for shear failure of rock joints10.1007/s00500-019-04230-w ↗
56. Simulation of carbonate reservoirs acidizing using machine and meta-learning methods and its optimization by the genetic algorithm10.1016/j.geoen.2023.211509 ↗
57. Machine learning-based evaluation of eccentricity and acoustic impedance in oil well using VDL data10.1016/j.geoen.2023.212288 ↗
58. Application of several optimization techniques for estimating TBM advance rate in granitic rocks10.1016/j.jrmge.2019.01.002 ↗
59. Machine-learning based landslide susceptibility modelling with emphasis on uncertainty analysis10.1016/j.gsf.2023.101657 ↗
60. Liu, H.Y., Ma, T.X., Lin, Y., Peng, K., and Hu, X.Q. (2024). Deep Learning in Rockburst Intensity Level Prediction: Performance Evaluation and Comparison of the NGO-CNN-BiGRU-Attention Model. Appl. Sci., 14.10.3390/app14135719 ↗
61. A novel triaxial strength criterion for rocks based on the ultimate strength and its application10.1016/j.geoen.2024.213590 ↗
62. Modified Mohr–Coulomb criterion for nonlinear strength characteristics of rocks10.1111/ffe.14278 ↗
63. Prediction of compaction parameters for fine-grained soil: Critical comparison of the deep learning and standalone models10.1016/j.jrmge.2022.12.034 ↗
64. Examination of the correlation between SPT and undrained shear strength: Case study of clay till in Alberta, Canada10.1016/j.enggeo.2024.107510 ↗
65. Splitting tensile strength of basalt fiber reinforced coral aggregate concrete: Optimized XGBoost models and experimental validation10.1016/j.conbuildmat.2024.135133 ↗
66. Spatiotemporal pore-water pressure prediction using multi-input long short-term memory10.1016/j.enggeo.2023.107194 ↗
67. Elastic modulus prediction for high-temperature treated rock using multi-step hybrid ensemble model combined with coronavirus herd immunity optimizer10.1016/j.measurement.2024.115596 ↗
68. Prediction of undrained shear strength using extreme gradient boosting and random forest based on Bayesian optimization10.1016/j.gsf.2020.03.007 ↗
69. Investigation of electrical resistivity for fiber-reinforced coral aggregate concrete10.1016/j.conbuildmat.2024.135011 ↗
70. Sun, Z., Wang, X., Han, T., Huang, H., Huang, X., Wang, L., and Wu, Z. (2025). Pipeline deformation monitoring based on long-gauge FBG sensing system: Missing data recovery and deformation calculation. J. Civ. Struct. Health Monit., 1–25.10.1007/s13349-025-00943-9 ↗
71. Development and application of feature engineered geological layers for ranking magmatic, volcanogenic, and orogenic system components in Archean greenstone belts10.1016/j.gsf.2023.101759 ↗
72. A machine learning approach to tungsten prospectivity modelling using knowledge-driven feature extraction and model confidence10.1016/j.gsf.2020.05.016 ↗
73. Pipeline deformation prediction based on multi-source monitoring information and novel data-driven model10.1016/j.engstruct.2025.120461 ↗
74. An explainable artificial-intelligence-aided safety factor prediction of road embankments10.1016/j.engappai.2024.108854 ↗
75. Prediction of fracture characteristics of high strength and ultra high strength concrete beams based on relevance vector machine10.1177/1056789514520796 ↗
76. Machine learning approaches for prediction of fine-grained soils liquefaction10.1016/j.compgeo.2022.105014 ↗
77. Performance evaluation of hybrid fiber-reinforced concrete based on electrical resistivity: Experimental and data-driven method10.1016/j.conbuildmat.2024.137992 ↗
78. A novel multi-dimensional viscoelastic mitigation device: Shake table tests and numerical assessment of precast concrete sandwich wall panel structure10.1016/j.engstruct.2025.120388 ↗
79. Machine learning approaches to predict compressive strength of fly ash-based geopolymer concrete: A comprehensive review10.1016/j.conbuildmat.2024.135519 ↗
80. The rheological intelligent constitutive model of debris flow: A new paradigm for integrating mechanics mechanisms with data-driven approaches by combining data mapping and deep learning10.1016/j.eswa.2025.126405 ↗