Dynamic Mechanical Properties and Damage Constitutive Model of Copper-bearing Garnet-biotite Schist

doi:10.12382/bgxb.2023.0690

Abstract

Abstract:

The dynamic mechanical properties and damage law of deep ore rock under different loading conditions are explored by taking the copper-bearing garnet biotite schist in deep mining as an object of study. A combined dynamic and static impact test is performed under the conditions of six kinds of axial pressure σ_ap(0MPa, 6MPa, 12MPa, 18MPa, 24MPa, 30MPa), six kinds of confining pressure σ_p (0MPa, 4MPa, 8MPa, 12MPa, 16MPa, 20MPa) and six kinds of impact velocity v (18.68m/s, 20.93m/s, 23.54m/s, 26.63m/s, 29.26m/s, 31.95m/s), and the factors of impact velocity, axial pressure, confining pressure and strain rate are considered. Based on the statistical damage theory and Drucker-Prager failure criterion, a dynamic damage constitutive model of copper-bearing garnet-biotite schist under combined static and dynamic loading is established. The results show that there is almost no compaction stage in the stress-strain curve of ore rock specimen. When the stress increases to 65%-80% of peak stress, the stress-strain curve of this stage shows a step phenomenon. The dynamic failure mode of deep surrounding rock is significantly affected by the stress state and impact velocity of ore rock at different buried depths.When σ_p=12MPa and v=31.95m/s, the dynamic compressive strength increases first and then decreases with the increase of axial compression σ_ap, while the peak strain decreases linearly. When σ_p=12MPa and σ_ap=24MPa, the dynamic compressive strength increases linearly with the increase of strain rate, while the peak strain increases as quadratic polynomial with the increase of strain rate. The theoretical curve of the model is in good agreement with the experimental curve, which verifies the reliability of the dynamic constitutive model, and can provide some reference for the research and engineering application of the dynamic constitutive model of deep buried rock mass.

Key words: copper-bearing garnet-biotite schist, static-dynamic coupling loading, failure mode, Drucker-Prager failure criterion, dynamic damage constitutive model

CLC Number:

DT235

ZHAO Zehu, LI Xianglong, HU Qiwen, WANG Jianguo. Dynamic Mechanical Properties and Damage Constitutive Model of Copper-bearing Garnet-biotite Schist[J]. Acta Armamentarii, 2023, 44(12): 3805-3814.

Figures/Tables 9

Table 1 Static parameters of copper-bearing garnet schist

抗压强度/MPa	抗拉强度/MPa	弹性模量/GPa	内聚力/ MPa	内摩擦角/(°)	泊松比	容重/ (kN·m^-3)
59.82	7.54	31.0	3.76	58.34	0.31	33.8

Fig.1 Partially processed specimen

Fig.2 Three-dimensional dynamic and static combined loading SHPB test equipment

Fig.3 Propagation law of stress wave under different schemes

Fig.4 Stress-strain curves under different combined loading

Fig.5 The relationship between dynamic compressive strength and peak strain under different stress conditions

Fig.6 Micro-element model diagram

Table 2 Calculated results of constitutive model parameters

σ_ap/ MPa	σ_p/ MPa	v/ (m·s^-1)	E/ GPa	S_E/ %	m	S_m/ %	F₀/ MPa	$S F 0$ / %
0	12	31.95	57.82	49.56	2.28	25.75	428.72	16.53
6	12	31.95	59.5	75.32	3.56	120.10	323.89	60.70
12	12	31.95	77.05	2.30	3.04	161.60	466.85	178.90
18	12	31.95	81.20	56.10	2.42	75.28	490.15	237.70
24	12	31.95	80.53	476.00	2.35	34.01	467.44	60.13
30	12	31.95	105.10	73.52	2.05	43.33	198.95	99.52
24	0	31.95	59.13	36.76	1.67	78.32	453.53	14.79
24	4	31.95	62.90	43.92	1.98	92.98	443.33	16.60
24	8	31.95	60.39	166.40	2.80	20.04	397.49	58.74
24	12	31.95	80.53	111.60	2.35	143.90	467.44	106.90
24	16	31.95	74.20	8.10	3.55	97.75	416.11	4.88
24	20	31.95	97.52	69.20	4.12	100.20	355.88	31.46
24	12	18.68	121.30	51.36	2.24	48.83	238.33	60.73
24	12	20.93	93.51	11.18	3.26	33.87	226.39	104.00
24	12	23.54	94.04	24.65	2.87	19.99	337.76	2.79
24	12	26.63	95.52	13.54	2.75	59.11	342.22	8.82
24	12	29.26	96.90	2.30	4.18	136.40	421.38	78.84
24	12	31.95	80.53	33.15	2.35	39.36	467.44	74.16

Table 2 Calculated results of constitutive model parameters

σ_ap/ MPa	σ_p/ MPa	v/ (m·s^-1)	E/ GPa	S_E/ %	m	S_m/ %	F₀/ MPa	$S F 0$ / %
0	12	31.95	57.82	49.56	2.28	25.75	428.72	16.53
6	12	31.95	59.5	75.32	3.56	120.10	323.89	60.70
12	12	31.95	77.05	2.30	3.04	161.60	466.85	178.90
18	12	31.95	81.20	56.10	2.42	75.28	490.15	237.70
24	12	31.95	80.53	476.00	2.35	34.01	467.44	60.13
30	12	31.95	105.10	73.52	2.05	43.33	198.95	99.52
24	0	31.95	59.13	36.76	1.67	78.32	453.53	14.79
24	4	31.95	62.90	43.92	1.98	92.98	443.33	16.60
24	8	31.95	60.39	166.40	2.80	20.04	397.49	58.74
24	12	31.95	80.53	111.60	2.35	143.90	467.44	106.90
24	16	31.95	74.20	8.10	3.55	97.75	416.11	4.88
24	20	31.95	97.52	69.20	4.12	100.20	355.88	31.46
24	12	18.68	121.30	51.36	2.24	48.83	238.33	60.73
24	12	20.93	93.51	11.18	3.26	33.87	226.39	104.00
24	12	23.54	94.04	24.65	2.87	19.99	337.76	2.79
24	12	26.63	95.52	13.54	2.75	59.11	342.22	8.82
24	12	29.26	96.90	2.30	4.18	136.40	421.38	78.84
24	12	31.95	80.53	33.15	2.35	39.36	467.44	74.16

Fig.7 Comparison of theoretical curves and experimental results under different combined loading conditions

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