Machine learning-based calibration of PBM meso-parameters and numerical simulation of unloading rockburst

doi:10.16265/j.cnki.issn1003-3033.2026.08.1168

Abstract

Abstract:

To accurately determine the mesoscopic parameters of the PBM, an integrated parameter calibration framework based on machine learning was developed. First, mesoscopic parameter samples were generated using orthogonal design, Latin hypercube sampling (LHS), and stratified sampling, and a macro-mesoscopic parameter mapping database was established through automated batch uniaxial compression simulations in PFC^2D. Subsequently, particle swarm optimization (PSO), sparrow search algorithm (SSA), and exponential triangle optimization (ETO) algorithms were employed to optimize the hyperparameters of random forest (RF), back propagation(BP) neural Network, support vector regression (SVR), and K-nearest neighbor (KNN) models, and a total of 16 machine learning models were constructed for performance comparison. Finally, the optimal model was applied to calibrate the meso-parameters of marble from the Jinping II Hydropower Station, followed by numerical simulations of unloading rockburst. The results indicate that the ETO-BP model achieves superior predictive performance compared with the other models. The calibration errors of the uniaxial compressive strength, elastic modulus, and Poisson's ratio for five rock specimens are all less than 5%. Under unloading conditions, the simulated rockburst process evolves through four stages, namely the quiet stage, small-particle ejection stage, slab spalling accompanied by particle ejection stage, and overall collapse stage, exhibiting typical failure characteristics including particle ejection, slab splitting, and block collapse.

Key words: parallel bond model (PBM), meso-parameters, machine learning, parameter calibration, unloading rockburst

CLC Number:

X936

Yu Hao, Wang Chao, He Ziwang, Liu Yu, Jin Zijun, Qi Shuai. Machine learning-based calibration of PBM meso-parameters and numerical simulation of unloading rockburst[J]. China Safety Science Journal, 2026, 36(8): 260-268.

Figures/Tables 11

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编号	模型细观参数				宏观参数
编号	${\stackrel{-}{\mathit{E}}}^{\mathrm{*}}$/GPa	${\stackrel{-}{\mathit{\kappa }}}^{\mathrm{*}}$	${\stackrel{-}{\mathit{\sigma }}}_{\mathit{c}}$/MPa	$\stackrel{-}{\mathit{\phi }}$/(°)	R_c/MPa	E/GPa	ν
1	10.00	1.50	10.00	0.00	11.32	11.81	0.179
2	56.67	1.50	40.00	20.00	42.10	47.37	0.143
3	103.03	1.50	70.00	40.00	68.10	69.40	0.123
︙	︙	︙	︙	︙	︙	︙	︙
114	37.68	6.37	11.67	42.03	12.91	24.44	0.331
115	24.75	3.99	53.93	31.82	52.96	19.62	0.326
116	121.19	2.18	89.75	16.85	90.62	71.07	0.161

模型	${\stackrel{-}{\mathit{E}}}^{\mathrm{*}}$		${\stackrel{-}{\mathit{\kappa }}}^{\mathrm{*}}$		${\stackrel{-}{\mathit{\sigma }}}_{\mathit{c}}$
模型	平均误差/%	R²	平均误差/%	R²	平均误差/%	R²
RF	15.48	0.926 9	13.90	0.803 0	7.26	0.973 1
PSO-RF	14.92	0.953 9	17.43	0.838 6	5.28	0.983 0
SSA-RF	14.68	0.951 7	17.43	0.834 2	5.46	0.980 6
ETO-RF	14.16	0.954 0	17.61	0.836 4	5.00	0.981 4
BP	12.89	0.945 5	9.57	0.920 4	5.96	0.976 6
PSO-BP	6.17	0.980 8	6.32	0.950 5	5.34	0.987 4
SSA-BP	8.25	0.973 3	7.62	0.964 9	5.92	0.984 2
ETO-BP	6.13	0.981 5	5.32	0.954 5	3.52	0.992 3
SVR	14.41	0.938 2	12.70	0.906 4	7.50	0.980 8
PSO-SVR	10.49	0.969 3	7.66	0.930 7	5.87	0.990 7
SSA-SVR	9.42	0.958 2	11.60	0.901 1	6.51	0.986 2
ETO-SVR	6.24	0.962 6	6.88	0.971 6	5.30	0.990 6
KNN	14.03	0.838 4	21.18	0.665 3	12.56	0.934 8
PSO-KNN	13.90	0.937 2	16.06	0.794 0	12.34	0.951 0
SSA-KNN	15.63	0.904 2	17.20	0.791 6	10.56	0.978 6
ETO-KNN	14.75	0.905 1	16.09	0.786 7	9.64	0.969 8

来源	岩石类型	R_c/MPa	E/GPa	ν
重庆彭水页岩气区块储层	页岩(1号)^[28]	65.2	26.0	0.237
重庆彭水页岩气区块储层	页岩(2号)^[28]	87.0	24.2	0.248
—	砂岩^[29]	47.31	16.71	0.270
Carrara矿区	大理岩(1号)^[30]	88.3	49.0	0.190
锦屏二级水电站引水隧洞	大理岩(2号)^[31]	199.2	24.13	0.282

岩样	R_c			E			v
岩样	实测值/MPa	模拟值/ MPa	误差/ %	实测值/GPa	模拟值/GPa	误差/ %	实测值	模拟值	误差/ %
1号页岩	65.2	67.89	4.13	26.0	26.30	1.15	0.237	0.232	2.11
2号页岩	87.0	88.23	1.41	24.2	24.88	2.81	0.248	0.241	2.82
砂岩	47.31	47.70	0.82	16.71	17.43	4.31	0.27	0.257	4.81
1号大理岩	88.3	86.58	1.95	49.0	51.07	4.22	0.19	0.189	0.53
2号大理岩	199.2	197.5	0.85	24.13	25.29	4.81	0.282	0.294	4.26