深部礦山非規則礦巖點載荷強度指標分布特性

李地元; 蔡榮廳; 余一松; 王勇兵; 李華華

doi:10.13374/j.issn2095-9389.2021.11.12.004

深部礦山非規則礦巖點載荷強度指標分布特性

doi: 10.13374/j.issn2095-9389.2021.11.12.004

李地元^1, ,,
蔡榮廳¹,
余一松^{1, 2},
王勇兵³,
李華華²

1.
中南大學資源與安全工程學院，長沙 410083
2.
長沙有色冶金設計研究院有限公司，長沙 410019
3.
云南馳宏鋅鍺股份有限公司會澤礦業分公司，會澤 654200

基金項目: 國家自然科學基金資助項目（52074349）；湖南省自然科學基金杰出青年基金資助項目（2019JJ20028）

詳細信息

通訊作者:
E-mail: diyuan.li@csu.edu.cn

中圖分類號: TD853
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出版歷程
- 收稿日期: 2021-11-12
- 網絡出版日期: 2022-02-10
- 刊出日期: 2023-03-01

Distribution characteristics of the point load strength index of irregular ore rock samples in deep mines

1.
School of Resources and Safety Engineering, Central South of University, Changsha 410083, China
2.
CINF Engineering Co., Ltd., Changsha 410019, China
3.
Huize Mining Company, Yunnan Chihong Zinc and Germanium Co., Ltd., Huize 654200, China

More Information

Corresponding author: E-mail: diyuan.li@csu.edu.cn

摘要

摘要: 針對深部礦巖在高地應力下鉆孔巖芯餅化現象頻發、現場取完整芯樣困難等問題，選取采場爆破后的巖石與礦塊進行現場點載荷試驗，通過測試獲得不規則尺寸試樣的點載荷強度指標。采用指數型和線性型兩種修正系數($ {f_1} $,$ {f_2} $)對點載荷強度指標進行修正，得到修正后的點載荷強度指標為$I_{{\rm{s}}50\text{-}1}$和$I_{{\rm{s}}50\text{-}2}$，獲得修正前后的點載荷強度指標的分布特性及規律：修正前后的點載荷強度指標的分布頻率基本滿足正態分布，修正前的點載荷強度指標呈偏態型分布，修正后的點載荷強度指標基本呈標準正態分布。采用線性型修正后點載荷強度指標的正態分布更加明顯，其點載荷強度值整體上大于指數型修正后的點載荷強度值，且在等效直徑為50 mm左右時點載荷強度基本相等。指數型修正方式所得結果受尺寸效應影響較大，強度值偏差較大；而線性型修正方式所得結果更具準確性。在95%的置信度下，巖樣標準點載荷強度指標的置信區間為1.09～1.57 MPa，均值為1.33 MPa；礦樣的置信區間為0.37～0.45 MPa，均值為0.39 MPa。由于試樣受爆破損傷的影響，巖樣與礦樣基于單軸抗壓強度的點載荷強度指標計算值約為本試驗結果的1.62和3.67倍。
- 深部礦山 /
- 點荷載強度指標 /
- 非規則巖樣 /
- 修正系數 /
- 分布特征
Abstract: The frequent occurrence of core disking in boreholes under high in-situ stress in deep rock engineering leads to the difficulty in intact core sampling on sites. In this study, rock and ore blocks with irregular sizes after blasting in stopes were selected to perform a point load strength index test, and the equivalent diameter and failure load of the samples with irregular sizes were obtained through the test. Then, the point load strength index of the sample was obtained. However, the results are affected by the size effect of the samples. Two correction coefficients ($ {f_1} $ and $ {f_2} $), including an exponential type related to the failure load as well as equivalent diameter and a linear type related to the equivalent diameter, were used to modify the point load strength index. The modified point load strength indexes are $I_{{\rm{s}}50\text{-}1}$ and $I_{{\rm{s}}50\text{-}2}$. The distribution characteristics of the point load strength index before and after modification were obtained. The distribution frequency of the point load strength index before and after modification basically meets the normal distribution requirements. Before modification, it presented a normal skewness distribution, and after modification, it basically presented a standard normal distribution. The normal distribution of the point load strength index after the linear-type modification is obvious, and its strength value is larger than that after the exponential-type modification on the whole. The point load strength is basically equal for the two modification methods when the equivalent diameter is approximately 50 mm. The results obtained by the exponential correction method are greatly affected by the size effect, and the deviation of the strength value is large. By contrast, the results obtained by the linear correction method are more accurate than that of the exponential correction menthod. With a 95% confidence interval, the confidence interval of the standard point load strength index of the rock sample is 1.09–1.57 MPa, and the mean value is 1.33 MPa. The confidence interval of the ore sample is 0.37–0.45 MPa, and the mean value is 0.39 MPa. Due to the small size of the regular samples and the influence of the blasting damage, the calculated values of the point load strength index based on the uniaxial compressive strength of the rock and ore samples are approximately 1.62 and 3.67 times of the test results, respectively. Therefore, to reduce the influence of the sample size effect and excavation blasting disturbance on the test results of the mechanical properties of surrounding rocks, rock blocks with less blasting disturbance and size of approximately 50 mm in three directions should be selected to perform the point load test in the deep engineering site, where it is difficult to obtain intact rock cores.
- deep mine /
- point load strength index /
- irregular rock samples /
- correction factor /
- distribution characteristics

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圖 1 巖石點載荷試驗設備及試樣尺寸. (a)點載荷試驗儀;(b)標準試樣與不規則試樣尺寸示意圖

Figure 1. Point load test equipment and sample size: (a) point load test instrument; (b) standard sample size and irregular sample size

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圖 2 不規則尺寸試樣.(a) 巖石試樣;(b) 礦石試樣

Figure 2. Irregular-sized sample: (a) rock sample; (b) ore sample

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圖 3 試樣$ \lg D_{\text{e}}^{\text{2}} - \lg P $的趨勢線關系.(a) 巖塊試樣；(b) 礦塊試樣

Figure 3. Fitting relationship between $ \lg D_{\text{e}}^{\text{2}} - \lg P $: (a) rock samples； (b) ore samples

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圖 4 未修正的點載荷強度與等效直徑的關系

Figure 4. Relationship between the uncorrected point load strength and equivalent diameter

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圖 5 修正后的試樣點載荷強度指標與等效直徑的關系.(a) 巖塊試樣；(b) 礦塊試樣

Figure 5. Relationship between the corrected point load strength index and equivalent diameter of the samples: (a) rock samples; (b) ore samples

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圖 6 未修正點載荷強度直方圖與正態分布曲線.(a) 巖塊試樣;(b) 礦塊試樣

Figure 6. Uncorrected point load strength histogram and normal distribution curve: (a) rock sample; (b) ore sample

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圖 7 修正后試樣點載荷強度指標直方圖與正態分布曲線.(a) $ f_{j} $修正后巖塊試樣的點載荷強度;(b) $ f_{2} $修正后巖塊試樣的點載荷強度;(c) $ f_{j} $修正后礦塊試樣的點載荷強度;(d) $ f_{2} $修正后礦塊試樣的點載荷強度

Figure 7. Modified point load strength index histogram of the samples and normal distribution curve: (a) $ f_{j} $ modified point load strength of the rock sample; (b) $ f_{2} $ modified point load strength of the rock sample; (c) $ f_{j} $ modified point load strength of the ore sample; (d) $ f_{2} $ modified point load strength of the ore sample

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表 1 不同尺寸和形狀巖塊試樣點載荷試驗數據結果

Table 1. Results of the point load test for rock samples of different sizes and shapes

Sample No.	D/mm	L/mm	W/mm	P/kN	D_e/mm	$ \mathrm{lg}P $	$ \mathrm{lg}{D}_{\mathrm{e}}^{2} $	$ {f}_{1} $	$ {f}_{2} $	I_S/MPa	I_S50-1/MPa	I_S50-2/MPa	Discarded data
1	52.60	34.94	69.14	1.47	68.06	3.17	3.67	1.54	1.15	0.32	0.49	0.36	①
2	46.94	25.56	48.95	3.85	54.10	3.27	3.47	0.97	1.07	1.32	1.50	1.40	②
3	41.35	23.34	63.97	0.93	58.05	2.97	3.53	1.12	1.09	0.28	0.31	0.30	①③
4	39.91	26.56	48.93	3.19	49.88	3.34	3.40	0.82	1.00	1.28	1.28	1.28
5	33.80	18.88	34.81	1.97	38.71	3.29	3.18	0.50	0.84	1.31	0.65	1.10
6	32.20	27.20	42.31	5.06	41.66	3.70	3.24	0.58	0.88	2.92	1.68	2.56	②
7	31.89	29.67	36.81	4.35	38.67	3.64	3.17	0.50	0.84	2.91	1.44	2.43
8	31.52	28.76	46.42	3.00	43.17	3.48	3.27	0.62	0.90	1.61	0.99	1.45
9	29.68	20.81	37.26	1.64	37.53	3.21	3.15	0.47	0.82	1.16	0.54	0.95
10	29.61	23.22	42.95	2.23	40.25	3.35	3.21	0.54	0.86	1.38	0.74	1.18
11	29.57	18.95	40.97	2.36	39.28	3.13	3.19	0.51	0.84	1.53	1.03	1.29
12	29.17	20.53	33.15	1.89	35.10	2.95	3.09	0.41	0.78	1.53	0.85	1.20
13	28.48	27.11	52.45	2.38	43.62	3.14	3.28	0.63	0.91	1.25	1.00	1.33
14	28.40	27.78	51.32	2.58	43.09	3.41	3.27	0.62	0.90	1.39	0.86	1.25
15	26.34	21.08	44.66	2.22	38.71	3.35	3.18	0.50	0.84	1.48	0.74	1.24
16	26.26	20.15	32.97	2.27	33.21	3.36	3.04	0.37	0.76	2.06	0.75	1.56
17	26.06	24.87	39.37	2.59	36.15	3.41	3.12	0.43	0.80	1.98	0.86	1.58
18	26.03	15.12	34.20	2.41	33.68	3.38	3.05	0.38	0.76	2.13	0.80	1.62
19	25.87	25.06	42.36	3.73	37.36	3.57	3.14	0.46	0.82	2.67	1.24	2.18
20	24.92	22.69	45.18	1.17	37.87	3.07	3.16	0.48	0.82	0.82	0.39	0.67
21	24.74	15.27	33.68	4.02	32.58	3.60	3.03	0.35	0.75	3.79	1.33	2.83	①③
22	24.31	23.26	34.33	1.98	32.61	3.30	3.03	0.35	0.75	1.86	0.66	1.39
23	24.28	11.82	23.11	2.71	26.74	3.43	2.85	0.24	0.66	3.79	0.90	2.51
24	23.62	18.94	39.34	2.69	34.41	3.43	3.07	0.39	0.77	2.27	0.89	1.76
25	22.32	14.12	25.36	1.77	26.85	3.25	2.86	0.24	0.66	2.45	0.59	1.63
26	21.38	15.98	32.00	1.18	29.52	3.07	2.94	0.29	0.70	1.35	0.39	0.95
27	21.23	19.10	30.48	3.57	28.71	3.55	2.92	0.27	0.69	4.33	1.18	2.99	①③
28	21.12	16.24	28.43	0.38	27.66	2.58	2.88	0.25	0.67	0.50	0.13	0.34	②③
29	17.21	12.93	27.24	1.57	24.44	3.20	2.78	0.20	0.63	2.63	0.52	1.65
30	15.42	16.90	30.64	0.49	24.53	2.69	2.78	0.20	0.63	0.81	0.16	0.51	②
Note：①②③ represents discarded test data for the three different calculation methods.

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表 2 不同尺寸和形狀礦塊試樣點載荷試驗數據結果

Table 2. Results of the point load test for ore block samples of different sizes and shapes

Sample No.	D/mm	L/mm	W/mm	P/kN	D_e/mm	$ \mathrm{lg}P $	$ \mathrm{lg}{D}_{e}^{2} $	$ {f}_{1} $	$ {f}_{2} $	I_S/MPa	I_S50-1/MPa	I_S50-2/MPa	Discarded data
1	60.87	36.76	69.34	3.49	73.33	3.54	3.73	1.70	1.18	0.65	1.34	0.77	②
2	46.36	34.35	67.54	2.28	63.16	3.36	3.60	1.38	1.12	0.57	0.99	0.64	②
3	41.10	33.47	68.69	1.41	59.97	3.15	3.56	1.29	1.10	0.39	0.89	0.43
4	47.37	29.62	58.47	1.36	59.40	2.75	3.55	1.27	1.10	0.39	0.49	0.42
5	50.97	32.14	48.42	3.54	56.07	3.55	3.50	1.17	1.08	1.13	0.78	1.22	①③
6	36.75	26.86	57.09	0.49	51.70	2.69	3.43	1.05	1.02	0.18	0.66	0.19
7	39.80	29.70	48.50	0.85	49.59	2.93	3.39	0.99	0.99	0.35	0.61	0.34
8	40.20	29.09	46.46	0.94	48.78	2.73	3.38	0.97	0.98	0.40	0.38	0.39
9	37.09	21.47	49.22	0.76	48.22	2.88	3.37	0.95	0.97	0.33	0.58	0.32
10	40.49	27.50	43.24	0.93	47.23	2.97	3.35	0.92	0.96	0.42	0.55	0.40
11	38.17	27.06	45.79	0.85	47.19	2.74	3.35	0.92	0.96	0.38	0.35	0.37
12	36.93	20.48	46.60	0.74	46.82	2.64	3.34	0.91	0.95	0.34	0.31	0.32
13	41.60	21.87	39.13	3.20	45.54	3.51	3.32	0.88	0.94	1.54	0.52	1.44	①③
14	33.53	26.57	47.97	0.94	45.27	2.97	3.31	0.87	0.93	0.46	0.51	0.43
15	33.33	27.88	43.22	0.59	42.84	2.77	3.26	0.81	0.90	0.32	0.46	0.29
16	30.72	25.54	40.34	1.09	39.73	3.04	3.20	0.73	0.85	0.69	0.39	0.59
17	30.52	20.72	37.25	0.69	38.06	2.84	3.16	0.69	0.83	0.48	0.36	0.39
18	23.23	24.60	48.29	0.68	37.80	2.45	3.16	0.68	0.82	0.48	0.32	0.39
19	31.66	18.58	34.95	0.13	37.54	2.11	3.15	0.67	0.82	0.09	0.35	0.08	①③
20	28.02	20.64	36.01	0.57	35.85	2.76	3.11	0.63	0.79	0.44	0.32	0.35
21	26.76	19.41	37.49	0.58	35.75	2.76	3.11	0.63	0.79	0.45	0.32	0.36
22	27.02	19.32	36.20	0.39	35.30	2.59	3.10	0.62	0.79	0.31	0.31	0.25
23	25.39	20.52	38.00	1.00	35.06	3.00	3.09	0.61	0.78	0.81	0.31	0.64
24	25.30	16.51	33.72	0.36	32.97	2.56	3.04	0.56	0.75	0.33	0.27	0.25
25	28.66	17.20	29.40	0.31	32.76	2.49	3.03	0.56	0.75	0.29	0.27	0.22
26	22.88	19.36	34.38	0.06	31.66	1.78	3.00	0.53	0.73	0.06	0.25	0.04	①③
27	23.53	15.16	30.40	0.76	30.19	2.88	2.96	0.50	0.71	0.83	0.23	0.59
28	25.67	12.27	27.55	0.29	30.02	2.46	2.95	0.49	0.71	0.32	0.22	0.23
29	16.22	16.79	37.69	0.36	27.91	2.56	2.89	0.45	0.68	0.46	0.19	0.31	②
30	25.79	11.19	20.78	0.23	26.13	2.36	2.83	0.41	0.65	0.34	0.17	0.22	②

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表 3 試樣點載荷強度的統計結果

Table 3. Statistical results of the point load strength of the sample

Sample	Parameter	Average/MPa	Standard deviation/MPa	Coefficient of variation	Confidence interval/MPa	Confidence/%
Rock sample	$I_{\rm{s}}$	1.70	0.82	0.48	1.34–2.06	95
	$I_{{\rm{s}}50\text{-}1}$	0.72	0.27	0.38	0.60–0.83
	$I_{{\rm{s}}50\text{-}2}$	1.33	0.55	0.42	1.09–1.57
Ore sample	$I_{\rm{s}}$	0.38	0.19	0.49	0.30–0.47
	$I_{{\rm{s}}50\text{-}1}$	0.46	0.19	0.43	0.38–0.55
	$I_{{\rm{s}}50\text{-}2}$	0.39	0.14	0.41	0.37–0.45

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