基于里氏硬度法建立岩石单轴抗压强度测强曲线研究

江政贵

doi:10.20265/j.cnki.issn.1007-2993.2025-0011

基于里氏硬度法建立岩石单轴抗压强度测强曲线研究

doi: 10.20265/j.cnki.issn.1007-2993.2025-0011

江政贵

江苏地质矿产设计研究院（中国煤炭地质总局检测中心），江苏徐州　221006

详细信息

作者简介:
江政贵，男，1978年生，大学本科，高级工程师，主要从事岩土分析测试。E-mail：2833076727@qq.com

中图分类号: TU455
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- 文章访问数: 6
- HTML全文浏览量: 2
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- 被引次数: 0
出版历程
- 收稿日期: 2025-01-08
- 修回日期: 2025-06-06
- 录用日期: 2025-06-26
- 网络出版日期: 2026-04-09
- 刊出日期: 2026-04-09

Uniaxial compressive strength testing curve of rock based on the Leeb hardness method

JIANG Zhenggui

Jiangsu Institute of Geological and Mineral Design (China Coal Geology Administration Testing Center), Xuzhou 221006, Jiangsu, China

摘要

摘要: 里氏硬度计因冲击装置尺寸小、冲击能量小，具有便于携带和操作、对测试面要求低、对岩石尤其是软弱岩石的表面冲击破坏影响小的优势，能更好地应用于复杂地质环境下的岩石强度评估。本文通过使用里氏硬度计测试地质岩体中不同类型岩石里氏硬度值，再分别测试经冲击后各岩石对应的单轴抗压强度值，分析对比测试岩石的里氏硬度和对应的单轴抗压强度之间的关系，分别建立基于线性、乘幂以及二次多项式的测强曲线。在分析过程中引入强度曲线适用性评价指标，比较各类型测强曲线的相关系数、强度相对误差和强度相对标准差。结果表明，对于试验选取的花岗岩、砂岩、泥岩和石灰岩，单轴抗压强度范围7.63～161 MPa内，使用乘幂拟合所得的测强曲线相关评价参数最优。乘幂回归测强曲线公式为Y=(2×10^–5)X^2.2931，相关系数达到0.9616，对应的强度曲线平均相对误差为14.74%；相对标准差为17.41%，符合统一测强曲线强度适用性评价的要求。
- 岩石 /
- 单轴抗压强度 /
- 里氏硬度 /
- 测强曲线 /
- 相关系数 /
- 平均相对误差 /
- 相对标准差
Abstract: The Leeb hardness tester, due to its small impact device size and low impact energy, has the advantages of being easy to carry and operate, low requirements for the testing surface, and inducing minimal surface damage to rock specimens especially weak rocks. Therefore, it can be better applied in rock strength assessment in complex environments. This study tests the Leeb hardness of different types of rocks in geological bodies using a Leeb hardness tester, and then tests the uniaxial compressive strength of the rocks after impact. It analyzes and compares the relationship between the Leeb hardness and the corresponding uniaxial compressive strength of the tested rocks, and establishes the strength measurement curves based on linear, power, and quadratic polynomial functions. And the applicability evaluation indicators of the strength curve were introduced in the analysis. The correlation coefficients, relative errors of strength, and relative standard deviations different types of strength curves were compared. The results show that for the selected granites, sandstones, mudstones, and limestones, the uniaxial compressive range of 7.63 to 161 MPa, the fitting parameters obtained using the power function fitting are optimal. The power function regression formula the strength measurement curve is Y=(2×10^–5)X^2.2931, with a correlation coefficient of 0.9616, the average relative error of the corresponding strength curve is 14.74%. The relative standard deviation is 17.41%, which meets the applicability of the unified strength measurement curve.
- rock /
- uniaxial compressive strength /
- Leeb hardness /
- strength measurement curve /
- correlation coefficient /
- average relative error /
- relative standard

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图 1 花岗岩样品照片

Figure 1. Photograph of granite sample

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图 2 石灰岩样品照片

Figure 2. Photograph of limestone sample

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图 3 砂岩样品照片

Figure 3. Photograph of sandstone sample

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图 4 泥岩样品照片

Figure 4. Photograph of mudstone sample

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图 5 里氏硬度计照片

Figure 5. Photograph of Leeb hardness tester

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图 6 万能试验机照片

Figure 6. Photograph of universal testing machine

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图 7 花岗岩单轴抗压强度和里氏硬度拟合

Figure 7. Fitting relationship between uniaxial compressive strength and Leeb hardness for granite

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图 8 砂岩单轴抗压强度和里氏硬度拟合

Figure 8. Fitting relationship between uniaxial compressive strength and Leeb hardness for sandstone

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图 9 石灰岩单轴抗压强度和里氏硬度拟合

Figure 9. Fitting relationship between uniaxial compressive strength and Leeb hardness for limestone

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图 10 泥岩单轴抗压强度和里氏硬度拟合

Figure 10. Fitting relationship between uniaxial compressive strength and Leeb hardness for mudstone

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图 11 岩石单轴抗压强度和里氏硬度拟合

Figure 11. Fitting relationship between uniaxial compressive strength and Leeb hardness for rock

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表 1 测试选取的岩石类型及状态

Table 1. Rock types and states selected for testing

序号	岩石名称	含水状态	结构	外观描述
1	花岗岩	自然含水	细晶、粗晶结构	无明显节理裂隙
2	石灰岩	自然含水	晶粒结构	无明显节理裂隙
3	砂岩	自然含水	粉粒、细粒、中粒、粗粒结构	无明显节理裂隙
4	泥岩	自然含水	泥粒、粉粒结构	无明显节理裂隙

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表 2 不同冲击方向岩石里氏硬度值

Table 2. Leeb hardness values of rocks under different impact directions

岩石类型	冲击方向	里氏硬度值
坚硬岩Ⅰ	垂直表面竖直向下	685
坚硬岩Ⅰ	垂直表面水平	698
坚硬岩Ⅱ	垂直表面竖直向下	692
坚硬岩Ⅱ	垂直表面水平	690
坚硬岩 Ⅲ	垂直表面竖直向下	717
坚硬岩 Ⅲ	垂直表面水平	709
较硬岩Ⅰ	垂直表面竖直向下	589
较硬岩Ⅰ	垂直表面水平	585
较硬岩Ⅱ	垂直表面竖直向下	552
较硬岩Ⅱ	垂直表面水平	543
较硬岩 Ⅲ	垂直表面竖直向下	475
较硬岩 Ⅲ	垂直表面水平	488
软岩Ⅰ	垂直表面竖直向下	385
软岩Ⅰ	垂直表面水平	398
软岩 Ⅱ	垂直表面竖直向下	390
软岩 Ⅱ	垂直表面水平	386
软岩 Ⅲ	垂直表面竖直向下	378
软岩 Ⅲ	垂直表面水平	383

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表 3 不同岩石里氏硬度值与对应单轴抗压强度值

Table 3. Leeb hardness values and corresponding uniaxial compressive strength values of different rocks

岩石名称	样品数 /组	单轴抗压强度/MPa	里氏硬度值
花岗岩	20	19.9～161	407～912
砂岩	20	19.7～81.3	395～675
石灰岩	20	13.2～129	314～881
泥岩	20	7.63～36.9	289～423

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表 4 不同岩石里氏硬度和单轴抗压强度回归公式及其对应的相关系数、强度相对误差、强度相对标准差

Table 4. Regression equations between Leeb hardness and uniaxial compressive strength of different rocks with correlation coefficients, relative strength errors, and relative standard deviations

岩石名称	回归公式	相关系数	强度相对误差/%	强度相对标准差/%
花岗岩	Y=0.2516X−93.204	0.9102	15.50	21.54
	Y=(5×10⁻⁶)X^2.5389	0.9463	15.37	21.05
	Y=0.0002X²+0.0121X−18.047	0.9190	17.58	24.15
砂岩	Y=0.2198X−75.25	0.8614	15.99	20.26
	Y=(2×10⁻⁶)X^2.6575	0.9005	13.81	16.00
	Y=0.0007X²−0.5839X+136.53	0.9225	31.98	34.18
石灰岩	Y=0.1913X−55.581	0.9251	14.54	20.97
	Y=(8×10⁻⁵)X^2.1002	0.9769	8.10	10.86
	Y=0.0002X²−0.0712X+16.475	0.9534	12.76	15.09
泥岩	Y=0.1756X−43.498	0.9073	11.93	13.90
	Y=(3×10⁻⁸)X^3.4125	0.9041	13.65	17.33
	Y=0.0005X²−0.2127X+25.31	0.9232	28.92	31.27

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表 5 各回归类型对应的岩石里氏硬度和单轴抗压强度回归公式及其对应的相关系数、强度相对误差、强度相对标准差

Table 5. Regression equations between Leeb hardness and uniaxial compressive strength for different rock types with corresponding correlation coefficients, relative strength errors, and relative standard deviations

曲线类型	回归公式	相关系数	强度相对误差/%	强度相对标准差/%
线性	Y=0.1965X−57.085	0.9174	26.45	35.30
乘幂	Y=(2×10^–5)X^2.2931	0.9616	14.74	17.41
二次多项式	Y=0.0002X²−0.0601X+9.3751	0.9498	16.56	19.49

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参考文献(19)

[1]	中华人民共和国住房和城乡建设部. 工程岩体试验方法标准: GB/T 50266—2013[S]. 北京: 中国计划出版社, 2013. (Ministry of Housing and Urban Rural Development of the People’s Republic of China. Standard for test methods of engineering rock mass: GB/T 50266—2013[S]. Beijing: China Planning Press, 2013. (in Chinese) Ministry of Housing and Urban Rural Development of the People’s Republic of China. Standard for test methods of engineering rock mass: GB/T 50266—2013[S]. Beijing: China Planning Press, 2013. (in Chinese)
[2]	AOKI H, MATSUKURA Y. A new technique for non-destructive field measurement of rock-surface strength: an application of the Equotip hardness tester to weathering studies[J]. Earth Surface Processes and Landforms, 2007, 32(12): 1759-1769. doi: 10.1002/esp.1492
[3]	ALDEEKY H, AL HATTAMLEH O, RABABAH S. Assessing the uniaxial compressive strength and tangent Young's modulus of basalt rock using the Leeb rebound hardness test[J]. Materiales de Construcción, 2020, 70(340): e230. doi: 10.3989/mc.2020.15119
[4]	侯志鑫, 者瑞, 张中俭, 等. 基于里氏硬度计无损测量方法评价石质文物的风化程度[J]. 工程地质学报, 2018, 26(S1): 384-387. (HOU Z X, ZHE R, ZHANG Z J, et al. Estimating the weathering degree of rock surface of cultural relic from Leeb hardness for non-destructive measurement[J]. Journal of Engineering Geology, 2018, 26(S1): 384-387. (in Chinese) HOU Z X, ZHE R, ZHANG Z J, et al. Estimating the weathering degree of rock surface of cultural relic from Leeb hardness for non-destructive measurement[J]. Journal of Engineering Geology, 2018, 26（S1）: 384-387. (in Chinese)
[5]	王彬, 李苍松, 蔡建华, 等. 岩石里氏硬度值与单轴饱和抗压强度相关性分析初步探讨[J]. 隧道建设(中英文), 2020, 40(S2): 174-179. (WANG B, LI C S, CAI J H, et al. Study of correlation between rock Leeb hardness and uniaxial saturated compressive strength[J]. Tunnel Construction, 2020, 40(S2): 174-179. (in Chinese) WANG B, LI C S, CAI J H, et al. Study of correlation between rock Leeb hardness and uniaxial saturated compressive strength[J]. Tunnel Construction, 2020, 40（S2）: 174-179. (in Chinese)
[6]	管圣功, 钟杨, 曹润青, 等. 基于里氏硬度的岩石拉、压强度预测模型研究[J]. 金属矿山, 2023(6): 24-32. (GUAN S G, ZHONG Y, CAO R Q, et al. Research on prediction model of uniaxial compressive and tensile strength of rock based on equotip hardness[J]. Metal Mine, 2023(6): 24-32. (in Chinese) GUAN S G, ZHONG Y, CAO R Q, et al. Research on prediction model of uniaxial compressive and tensile strength of rock based on equotip hardness[J]. Metal Mine, 2023（6）: 24-32. (in Chinese)
[7]	TURK N, DEARMAN W R. Improvements in the determination of point load strength[J]. Bulletin of Engineering Geology and the Environment, 1985, 31(1): 137-142.
[8]	朱江江, 罗强, 唐学启, 等. 非规则软质千枚岩点荷载强度评价的等效面积法[J]. 岩石力学与工程学, 2018, 37(12): 2762-2771. (ZHU J J, LUO Q, TANG X Q, et al. An equivalent area method for evaluating the point load strength of irregular soft phyllite[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(12): 2762-2771. (in Chinese) ZHU J J, LUO Q, TANG X Q, et al. An equivalent area method for evaluating the point load strength of irregular soft phyllite[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37（12）: 2762-2771. (in Chinese)
[9]	代领, 姚华彦, 张飞阳, 等. 不同形状红砂岩的点荷载强度试验研究[J]. 科学技术与工程, 2019, 19(7): 209-214. (DAI L, YAO H Y, ZHANG F Y, et al. Study on point load strength of red sandstone under shape effect[J]. Science Technology and Engineering, 2019, 19(7): 209-214. (in Chinese) doi: 10.3969/j.issn.1671-1815.2019.07.035 DAI L, YAO H Y, ZHANG F Y, et al. Study on point load strength of red sandstone under shape effect[J]. Science Technology and Engineering, 2019, 19（7）: 209-214. (in Chinese) doi: 10.3969/j.issn.1671-1815.2019.07.035
[10]	DEERE D U, MILER R P. Engineering classfication and index properties for intact rock[D]. Urbana: University of Illinois, 1966.
[11]	崔立军, 王刚. 利用回弹仪测定岩石强度[J]. 中南工学院科技通讯, 1995, 11(1): 10-13, 16. (CUI L J, WANG G. Use the rebound instrument to measure the strength of the rock[J]. Science and Technology Communication of Zhongnan University of Technology, 1995, 11(1): 10-13, 16. (in Chinese) CUI L J, WANG G. Use the rebound instrument to measure the strength of the rock[J]. Science and Technology Communication of Zhongnan University of Technology, 1995, 11(1): 10-13, 16. (in Chinese)
[12]	杨泽君. 岩石强度回弹法测定的研究[D]. 湘潭: 湖南科技大学, 2015. (YANG Z J. The study of Schmidt hammer for estimating the compressive strength of rock[D]. Xiangtan: Hunan University of Science and Technology, 2015. (in Chinese) YANG Z J. The study of Schmidt hammer for estimating the compressive strength of rock[D]. Xiangtan: Hunan University of Science and Technology, 2015. (in Chinese)
[13]	曹贵, 雷磊. 基于回弹法测试岩石表面强度影响因素分析[J]. 中国建材科技, 2014, 23(3): 16-18. (CAO G, LEI L. Analysis the strength influence factors of rock surface based on Rebound test[J]. China Building Materials Science & Technology, 2014, 23(3): 16-18. (in Chinese) doi: 10.3969/j.issn.1003-8965.2014.03.007 CAO G, LEI L. Analysis the strength influence factors of rock surface based on Rebound test[J]. China Building Materials Science & Technology, 2014, 23（3）: 16-18. (in Chinese) doi: 10.3969/j.issn.1003-8965.2014.03.007
[14]	徐先锋, 邢鹏飞, 汪泳, 等. 基于L型回弹仪的岩石力学特性试验研究[J]. 黄金科学技术, 2022, 30(4): 550-558. (XU X F, XING P F, WANG Y, et al. Experimental study on rock mechanical properties based on L-type rebound instrument[J]. Gold Science and Technology, 2022, 30(4): 550-558. (in Chinese) XU X F, XING P F, WANG Y, et al. Experimental study on rock mechanical properties based on L-type rebound instrument[J]. Gold Science and Technology, 2022, 30（4）: 550-558. (in Chinese)
[15]	MOL L. Investigations into the relationship between changes in internal moisture regimes and rock surface deterioration in cavernous sandstone features[J]. Earth Surface Processes and Landforms, 2014, 39(7): 914-927. doi: 10.1002/esp.3497
[16]	钟杨. 基于里氏硬度和点荷载试验的岩石拉压强度间接测量研究[D]. 绍兴: 绍兴文理学院, 2023. (ZHONG Y. Study on indirect measurement of rock tensile and compressive strength based on Leeb hardness and point load tests[D]. Shaoxing: Shaoxing University, 2023. (in Chinese) ZHONG Y. Study on indirect measurement of rock tensile and compressive strength based on Leeb hardness and point load tests[D]. Shaoxing: Shaoxing University, 2023. (in Chinese)
[17]	江苏省市场监督管理局. 装配整体式混凝土结构检测技术规程: DB32/T 3754—2020[S]. (Jiangsu Provincial Administration for Market Regulation. Technical standard for inspection of monolithic precast concrete structure: DB32/T 3754—2020[S]. (in Chinese) Jiangsu Provincial Administration for Market Regulation. Technical standard for inspection of monolithic precast concrete structure: DB32/T 3754—2020[S]. (in Chinese)
[18]	李卓, 于洪洋, 史京松, 等. 影响里氏硬度试验结果的因素分析[J]. 农机质量与监督, 2024(5): 18-19. (LI Z, YU H Y, SHI J S, et al. Analysis of factors affecting the results of Leeb hardness[J]. Agricultural Machinery Quality & Supervision, 2024(5): 18-19. (in Chinese) LI Z, YU H Y, SHI J S, et al. Analysis of factors affecting the results of Leeb hardness[J]. Agricultural Machinery Quality & Supervision, 2024(5): 18-19. (in Chinese)
[19]	DESARNAUD J, KIRIYAMA K, BICER SIMSIR B, et al. A laboratory study of Equotip surface hardness measurements on a range of sandstones: what influences the values and what do they mean?[J]. Earth Surface Processes and Landforms, 2019, 44(7): 1419-1429. doi: 10.1002/esp.4584