A new integrated intelligent computing paradigm for predicting joints shear strength

Abstract

Joints shear strength is a critical parameter during the design and construction of geotechnical engineering structures. The prevailing models mostly adopt the form of empirical functions, employing mathematical regression techniques to represent experimental data. As an alternative approach, this paper proposes a new integrated intelligent computing paradigm that aims to predict joints shear strength. Five metaheuristic optimization algorithms, including the chameleon swarm algorithm (CSA), slime mold algorithm, transient search optimization algorithm, equilibrium optimizer and social network search algorithm, were employed to enhance the performance of the multilayered perception (MLP) model. Efficiency comparisons were conducted between the proposed CSA-MLP model and twelve classical models, employing statistical indicators such as root mean square error (RMSE), correlation coefficient (R²), mean absolute error (MAE), and variance accounted for (VAF) to evaluate the performance of each model. The sensitivity analysis of parameters that impact joints shear strength was conducted. Finally, the feasibility and limitations of this study were discussed. The results revealed that, in comparison to other models, the CSA-MLP model exhibited the most appropriate performance in terms of R² (0.88), RMSE (0.19), MAE (0.15), and VAF (90.32%) values. The result of sensitivity analysis showed that the normal stress and the joint roughness coefficient were the most critical factors influencing joints shear strength. This paper presented an efficacious attempt toward swift prediction of joints shear strength, thus avoiding the need for costly in-site and laboratory tests.

Keywords

Rock discontinuities / Joints shear strength / Metaheuristic optimization algorithms / Machine learning

CRediT authorship contribution statement

Shijie Xie: Conceptualization, Methodology, Validation. Zheyuan Jiang: Resources, Supervision, Visualization, Writing – original draft, Conceptualization. Hang Lin: Funding acquisition, Supervision. Tianxing Ma: Methodology, Software, Writing – review & editing. Kang Peng: Funding acquisition, Software. Hongwei Liu: Formal analysis, Investigation. Baohua Liu: Writing – review & editing.

Declaration of competing interest

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 paper gets its funding from Projects (42277175) supported by National Natural Science Foundation of China, Project (2023JJ30657) supported by Hunan Provincial Natural Science Foundation of China and the National Key Research, Hunan Provincial Department of natural resources geological exploration project (BSDZSB43202403), The First National Natural Disaster Comprehensive Risk Survey in Hunan Province (2022-70) and the National Key Research and Development Program of China – 2023 Key Special Project (No. 2023YFC2907400).

References

A.L. Achu, C.D. Aju, M. Di Napoli, P. Prakash, G. Gopinath, E. Shaji, V. Chandra. Machine-learning based landslide susceptibility modelling with emphasis on uncertainty analysis. Geosci Front, 14 (2023), p. 101657,

H.A.H. Al-Najjar, B. Pradhan. Spatial landslide susceptibility assessment using machine learning techniques assisted by additional data created with generative adversarial networks. Geosci Front, 12 (2021), pp. 625-637,

N. Babanouri, H. Fattahi. Constitutive modeling of rock fractures by improved support vector regression. Environ. Earth Sci., 77 (2018),

N. Babanouri, H. Fattahi. An ANFIS–TLBO criterion for shear failure of rock joints. Soft Comput., 24 (2020), pp. 4759-4773,

M. Bahaaddini, P.C. Hagan, R. Mitra, M.H. Khosravi. Experimental and numerical study of asperity degradation in the direct shear test. Eng. Geol., 204 (2016), pp. 41-52,

N. Barton. Review of a new shear-strength criterion for rock joints. Eng. Geol., 7 (1973), pp. 287-332,

N. Barton, C. Wang, R. Yong. Advances in joint roughness coefficient (JRC) and its engineering applications. J. Rock Mech. Geotech, 15 (12) (2023), pp. 3352-3379,

S. Bastola, M. Cai, B. Damjanac. Slope stability assessment of an open pit using lattice-spring-based synthetic rock mass (LS-SRM) modeling approach. J. Rock Mech. Geotech., 12 (2020), pp. 927-942,

R.P. Bewick, P.K. Kaiser, E. Amann. Strength of massive to moderately jointed hard rock masses. J. Rock Mech. Geotech., 11 (2019), pp. 562-575,

J. Bidadi, J. Akbardoost, M.R.M. Aliha. Thickness effect on the mode III fracture resistance and fracture path of rock using ENDB specimens. Fatigue Fract. Eng. m., 43 (2020), pp. 277-291,

M.S. Braik. Chameleon Swarm Algorithm: A bio-inspired optimizer for solving engineering design problems. Expert Syst. Appl., 174 (2021),

E.T. Brown. Reducing risks in the investigation, design and construction of large concrete dams. J. Rock Mech. Geotech., 9 (2017), pp. 197-209,

J. Chen, Z. Zhao, J. Zhang. Predicting peak shear strength of rock fractures using tree-based models and convolutional neural network. Comput. Geotech., 166 (2024), Article 105965,

K. Fang, H. Tang, C. Li, X. Su, P. An, S. Sun. Centrifuge modelling of landslides and landslide hazard mitigation: A review. Geosci. Front., 14 (2023), Article 101493,

A. Faramarzi, M. Heidarinejad, B. Stephens, S. Mirjalili. Equilibrium optimizer: A novel optimization algorithm. Knowl. Based Syst., 191 (2020), Article 105190,

H. Fathipour-Azar. New interpretable shear strength criterion for rock joints. Acta Geotech., 17 (2022), pp. 1327-1341,

W. Feng, S. Niu, C. Qiao, D. Zou. Nonlinear constitutive models of rock structural plane and their applications. J. Rock Mech. Geotech., 16 (3) (2024), pp. 790-806,

X.-T. Feng, H. Xu, S.-L. Qiu, S.-J. Li, C.-X. Yang, H.-S. Guo, Y. Cheng, Y.-H. Gao. In situ observation of rock spalling in the deep tunnels of the China jinping underground laboratory (2400 m Depth). Rock Mech. Rock Eng., 51 (2018), pp. 1193-1213,

T. Frühwirt, D. Pötschke, H. Konietzky. Simulation of direct shear tests using a forces on fracture surfaces (FFS) approach. Environ. Earth Sci., 80 (2021), p. 312,

R.-G. Gao, H. Wang, R.-H. Cao, X. Xiong, H. Lin, C. Xu. Damage deterioration mechanism and damage constitutive modelling of marble after cyclic impact loading. J. Mater Res. Technol., 29 (2024), pp. 1293-1304,

H. Gong, G. Wang, Y. Luo, T. Liu, X. Li, X. Liu. Shear failure and mechanical behaviors of granite with discontinuous joints under dynamic disturbance: laboratory tests and numerical simulation. Arch. Civ. Mech. Eng., 23 (2023), p. 171,

G. Grasselli. Manuel Rocha Medal recipient - Shear strength of rock joints based on quantified surface description. Rock Mech. Rock Eng., 39 (2006), pp. 295-314,

J.-Y. Gui, M.A. González-Fernández, X. Estévez-Ventosa, F. Song, L.R. Alejano. Toppling susceptibility of a single rock block resting on a regularly rough base. Eng. Geol., 313 (2023), Article 106982,

Y. Gui, C.H. Xia, W.Q. Ding, X. Qian, S.G. Du. Modelling shear behaviour of joint based on joint surface degradation during shearing. Rock Mech Rock Eng, 52 (2019), pp. 107-131,

G. Han, C. Zhang, H. Zhou, C. Zhang, Y. Gao, H.K. Singh. A new predictive method for the shear strength of interlayer shear weakness zone at field scales. Eng. Geol., 295 (2021), Article 106449,

F. Homand, T. Belem, M. Souley. Friction and degradation of rock joint surfaces under shear loads. Int. J. Numer. Anal. Met., 25 (2001), pp. 973-999,

F. Johansson, H. Stille. A conceptual model for the peak shear strength of fresh and unweathered rock joints. Int. J. Rock Mech. Min. Sci., 69 (2014), pp. 31-38,

D. Katsuki, M. Gutierrez, A. Almrabat. Stress-dependent shear wave splitting and permeability in fractured porous rock. J. Rock Mech. Geotech., 11 (2019), pp. 1-11,

D.V. Kennedy, B.B. Guzina, J.F. Labuz. A machine learning framework for in situ sensing of pile length from seismic cone penetrometer data. Comput. Geotech., 159 (2023), Article 105505,

M. Koopialipoor, A. Noorbakhsh, E.N. Ghaleini, D.J. Armaghani, S. Yagiz. A new approach for estimation of rock brittleness based on non-destructive tests. Nondestruct Test Eva, 34 (2019), pp. 354-375,

R.L. Kranz. Microcracks in rocks: A review. Tectonophysics, 100 (1983), pp. 449-480,

P.H.S.W. Kulatilake, G. Shou, T.H. Huang, R.M. Morgan. New peak shear strength criteria for anisotropic rock joints. Int. J. Rock Mech. Min. Sci., 32 (1995), pp. 673-697,

J. Larsson, F. Johansson, D.M. Ivars, E. Johnson, M. Flansbjer, N.W. Portal. A novel method for geometric quality assurance of rock joint replicas in direct shear testing – Part 1: Derivation of quality assurance parameters and geometric reproducibility. J. Rock Mech. Geotech. (2023),

D.J. Lary, A.H. Alavi, A.H. Gandomi, A.L. Walker. Machine learning in geosciences and remote sensing. Geosci Front, 7 (2016), pp. 3-10,

A.I. Lawal, S. Kwon. Application of artificial intelligence to rock mechanics: An overview. J. Rock Mech. Geotech., 13 (2021), pp. 248-266,

S. Li, H. Chen, M. Wang, A.A. Heidari, S. Mirjalili. Slime mould algorithm: A new method for stochastic optimization. Future Gener. Comput. Syst., 111 (2020), pp. 300-323,

H. Lin, J.J. Feng, R.H. Cao, S.J. Xie. Comparative analysis of rock damage models based on different distribution functions. Geotech. Geol. Eng., 40 (2022), pp. 301-310,

J. Liu, Y. Jiang, W. Han, O. Sakaguchi. Optimized ANN model for predicting rock mass quality ahead of tunnel face using measure-while-drilling data. Bull. Eng. Geol. Environ., 80 (2021), pp. 2283-2305,

B.R. Murlidhar, H. Nguyen, J. Rostami, X. Bui, D.J. Armaghani, P. Ragam, E.T. Mohamad. Prediction of flyrock distance induced by mine blasting using a novel Harris Hawks optimization-based multi-layer perceptron neural network. J, Rock Mech, Geotech, 13 (2021), pp. 1413-1427,

X.K. Pan, F. Berto, X.P. Zhou. Creep mechanical characteristics and nonlinear viscoelastic-plastic creep model of sandstone after high temperature heat treatment. Fatigue Fract, Eng, M, 46 (2023), pp. 2982-3000,

Patton, F.D., 1966. Multiple modes of shear failure in rock. Proceeding of the1st Congress of International Society of Rock Mechanics.

K. Peng, M. Nait Amar, H. Ouaer, M.R. Motahari, M. Hasanipanah. Automated design of a new integrated intelligent computing paradigm for constructing a constitutive model applicable to predicting rock fractures. Eng. Comput., 38 (2022), pp. 667-678,

P. Pereira Dias, L. Bhagya Jayasinghe, D. Waldmann. Machine learning in mix design of Miscanthus lightweight concrete. Constr. Build Mater., 302 (2021), Article 124191,

B. Pradhan, A. Dikshit, S. Lee, H. Kim. An explainable AI (XAI) model for landslide susceptibility modeling. Appl. Soft Comput., 142 (2023), Article 110324,

L.J. Pyrak-Nolte, D.D. Nolte. Approaching a universal scaling relationship between fracture stiffness and fluid flow. Nat. Commun., 7 (2016), p. 10663,

M.H. Qais, H.M. Hasanien, S. Alghuwainem. Transient search optimization: a new meta-heuristic optimization algorithm. Appl. Intell., 50 (2020), pp. 3926-3941,

J. Shang, Z. Zhao, S. Ma. On the shear failure of incipient rock discontinuities under CNL and CNS boundary conditions: Insights from DEM modelling. Eng. Geol., 234 (2018), pp. 153-166,

Z.M. Shi, J.T. Li, J. Wang. Effect of creep load on fatigue behavior and acoustic emission characteristics of sandstone containing pre-existing crack during. Theor. Appl. Fract. Mec., 119 (2022),

Z. Shi, J. Li, J. Wang, J. Chen, H. Lin, P. Cao. Experimental and numerical study on fracture characteristics and constitutive model of sandstone under freeze-thaw-fatigue. Int. J. Fatigue, 166 (2023), Article 107236,

B.P. Simser. Rockburst management in Canadian hard rock mines. J. Rock Mech. Geotech., 11 (2019), pp. 1036-1043,

H.K. Singh, A. Basu. Evaluation of existing criteria in estimating shear strength of natural rock discontinuities. Eng. Geol., 232 (2018), pp. 171-181,

S. Talatahari, H. Bayzidi, M. Saraee. Social network search for global optimization. IEEE Access, 9 (2021), pp. 92815-92863,

Z.C. Tang, Q.S. Liu, J.H. Huang. New criterion for rock joints based on three-dimensional roughness parameters. J. Cent. South Univ., 21 (2014), pp. 4653-4659,

K.E. Taylor. Summarizi.g multiple aspects of model performance in a single diagram. J. Geophys. Res. Atmos., 106 (2001), pp. 7183-7192,

R. Ulusay. The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007–2014. Springer (2014)

R. Viswanathan, P. Samui. Determination of rock depth using artificial intelligence techniques. Geosci. Front., 7 (2016), pp. 61-66,

G. Walton, S. Sinha. Challenges associated with numerical back analysis in rock mechanics. J. Rock Mech. Geotech., 14 (2022), pp. 2058-2071,

J. Wang, J.T. Li, Z.M. Shi. Crack evolution law and failure mode of red sandstone under fatigue-creep interaction. Fatigue Fract. Eng. Mater. Struct., 45 (2022), pp. 270-284,

Q. Wu, Y. Xu, H. Tang, K. Fang, Y. Jiang, C. Liu, X. Wang. Peak shear strength prediction for discontinuities between two different rock types using a neural network approach. Bull. Eng. Geol. Environ., 78 (2019), pp. 2315-2329,

S. Xie, H. Lin, Y. Chen, H. Duan, H. Liu, B. Liu. Prediction of shear strength of rock fractures using support vector regression and grid search optimization. Mater Today Commun, 36 (2023), p. 106780,

S.J. Xie, H. Lin, Y.F. Chen, T.X. Ma. Modified Mohr-Coulomb criterion for nonlinear strength characteristics of rocks. Fatigue Fract Eng M, 47 (2024), pp. 2228-2242,

S.J. Xie, H. Lin, Y.F. Chen, Y.X. Wang, R.H. Cao, J.T. Li. Statistical damage shear constitutive model of rock joints under seepage pressure. Front. Earth Sci., 8 (2020), p. 16,

F. Yamashita, E. Fukuyama, K. Mizoguchi, S. Takizawa, S. Xu, H. Kawakata. Scale dependence of rock friction at high work rate. Nature, 528 (2015), pp. 254-257,

Q. Zhang, J. Song, X. Nie. Application of neural network models to rock mechanics and rock engineering. Int. J. Rock Mech. Min. Sci., 28 (1991), pp. 535-540,

Zhang et al., 2021b W. Zhang, C. Wu, H. Zhong, Y. Li, L. Wang. Prediction of undrained shear strength using extreme gradient boosting and random forest based on Bayesian optimization. Geosci. Front., 12 (2021), pp. 469-477,