考虑各向异性形貌特征的岩体结构面刚度计算模型

包含; 胥勋辉; 兰恒星; 晏长根; 许江波; 刘长青

doi:10.19818/j.cnki.1671-1637.2022.02.012

考虑各向异性形貌特征的岩体结构面刚度计算模型

doi: 10.19818/j.cnki.1671-1637.2022.02.012

1.
长安大学公路学院，陕西西安 710064
2.
中国科学院地理科学与资源研究所，北京 100101
3.
长安大学地质工程与测绘学院，陕西西安 710054

基金项目:

国家自然科学基金项目 41807246

国家自然科学基金项目 41790443

国家自然科学基金项目 41927806

国家重点研发计划 2019YFC1520601

陕西省自然科学基础研究计划 2020JQ-349

中央高校基本科研业务费专项资金项目 300102212213

详细信息

作者简介:
包含(1988-)，男，河南商丘人，长安大学教授，工学博士，从事岩土力学研究

中图分类号: U451.2
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- 文章访问数: 535
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- PDF下载量: 44
- 被引次数: 0
出版历程
- 收稿日期: 2021-11-21
- 刊出日期: 2022-04-25

Calculation model of rock joint stiffness considering anisotropic morphology characteristics

1.
School of Highway, Chang'an University, Xi'an 710064, Shaanxi, China
2.
Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China
3.
School of Geological Engineering and Geomatics, Chang'an University, Xi'an 710054, Shaanxi, China

Funds:

National Natural Science Foundation of China 41807246

National Natural Science Foundation of China 41790443

National Natural Science Foundation of China 41927806

National Key Research and Development Program of China 2019YFC1520601

Basic Research Project of Natural Science of Shaanxi Province 2020JQ-349

Fundamental Research Funds for the Central Universities 300102212213

More Information

Author Bio:
BAO Han (1988-), male, professor, PhD, baohan@chd.edu.cn

摘要

摘要: 为了实现岩体结构面切向刚度和法向刚度的便捷化精准取值，准确分析结构面变形行为特征，以关山隧道闪长岩结构面为例，对结构面形貌信息进行数字化提取，应用3D打印技术制作结构面试样，开展单轴压缩与各向异性直剪试验，提出了各向异性新形貌参数，建立了结构面切向刚度与法向刚度计算新模型。研究结果表明：新形貌参数综合考虑了结构面起伏体上坡段的爬坡角与爬坡高度，有利于反映结构面形貌的各向异性特征，并且同一方向上结构面剖面线的形貌参数服从对数正态概率分布；在物理模型力学试验的基础上，结合结构面形貌参数、结构面壁面强度和法向应力构建的结构面切向刚度计算新模型，不仅降低了计算参数的获取难度，还可以更好地体现结构面切向变形能力的各向异性；改进的双曲函数法向刚度计算模型考虑了结构面初始法向刚度和最大法向闭合量与结构面壁面强度之间的量化关系，避免了复杂的力学测试，简化了法向刚度的获取过程；通过与经典计算模型和力学试验结果进行对比，发现采用新模型计算的刚度更为接近试验值，其中切向刚度与试验值的平均相对误差为2.09%~27.88%，法向刚度与试验值的平均相对误差为3.25%~17.25%，表明结构面切向刚度和法向刚度计算新模型可以更准确和便捷地获取结构面变形参数。
- 岩土工程 /
- 切向与法向刚度 /
- 模型试验 /
- 刚度计算模型 /
- 岩体结构面 /
- 形貌参数
Abstract: To accurately and conveniently achieve the shear and normal stiffnesses of rock joint and analyze the deformation behavior characteristics of rock joint, the diorite joint from the Guanshan Tunnel was scanned to obtain the digital information of morphology. According to the digitized joint surface, the replicate joint samples were made by the 3D printing technology. The uniaxial compression tests and anisotropic shear tests were performed for the joint replicas. The new shear and normal stiffness models were established based on the new anisotropic morphology parameter. Research results show that the proposed new morphology parameter takes into account the climbing angles and heights of positive asperities, which is helpful for expressing the anisotropic roughness of joint surface. The morphology parameter of joint profile in the same direction follows a lognormal probability distribution. On the basis of mechanical tests on the physical models, the new shear stiffness calculation model of rock joint established by considering the morphology parameter, joint compressive strength, and normal stress can lower the difficulty in obtaining the shear stiffness, and better reflect the anisotropy of tangent deformation as well. In consideration of the quantitative relationships of joint compressive strength with the initial normal stiffness and joint maximum closure, the improved hyperbolic-function normal stiffness model can simplify the calculation of normal stiffness by avoiding complex mechanical experiments. Compared with the classical calculation models and the mechanical test results, the stiffnesses calculated by the new models are closer to the test values. The average relative error between the calculated and experimental values of shear stiffness is 2.09%-27.88%, and the average relative error between the calculated and experimental values of normal stiffness is 3.25%-17.25%, which demonstrates that the new models can obtain the deformation parameters of the joint more precisely and conveniently. 5 tabs, 19 figs, 46 refs.
- geotechnical engineering /
- shear and normal stiffness /
- model test /
- stiffness calculation model /
- rock joint /
- morphology parameter

HTML全文

图 1 起伏体i几何形态与参数

Figure 1. Geometrical shape and parameters of undulating body i

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图 2 关山隧道基本信息与结构面样品的获取

Figure 2. Basic information of Guanshan Tunnel and acquisition of joint sample

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图 3 结构面研究窗口的形貌信息处理

Figure 3. Disposal of morphology information of studied window on joint

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图 4 形貌参数在8个方向上的分布

Figure 4. Distributions of morphology parameter in eight directions

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图 5 结构面制作流程与直剪试验

Figure 5. Joint replicas preparation process and shear test

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图 6 结构面剪应力与剪切位移曲线

Figure 6. Shear stress-displacement curves of joints

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图 7 不同结构面壁面强度与法向应力下的各向异性切向刚度

Figure 7. Anisotropic shear stiffnesses of joints with different compressive strengths under different normal stresses

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图 8 结构面切向刚度与形貌参数的关系

Figure 8. Relations between shear stiffnesses and morphology parameters of joints

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图 9 切向刚度与结构面壁面强度的关系

Figure 9. Relations between shear stiffnesses and compressive strengths of joints

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图 10 结构面k_s与λ的关系

Figure 10. Relations between k_s and λ of joints

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图 11 p与σ_JCS的拟合关系

Figure 11. Fitting relation between p and σ_JCS

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图 12 两种切向刚度计算方法的比较

Figure 12. Comparison of two calculation methods of shear stiffness

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图 13 试样各组成部分法向应力-法向位移关系

Figure 13. Relations between normal stress and normal displacement of each component of samples

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图 14 结构面试样初始刚度和最大闭合量与结构面壁面强度的关系

Figure 14. Relations between k_ni, V_m and σ_JCS of joint sample

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图 15 法向刚度计算值与实测值的对比

Figure 15. Comparison between calculated and experimental normal stiffnesses

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图 16 含单条结构面岩体受力状态

Figure 16. Mechanical status of rock mass with a single joint

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图 17 圆柱试样的制作与单轴压缩试验

Figure 17. Preparation of cylindrical samples and unixial compression test

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图 18 三组圆柱试样的单轴压缩试验结果

Figure 18. Uniaxial compression test results of three groups of cylindrical samples

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图 19 三组结构面试样的模量试验值与计算值对比

Figure 19. Comparison between experimental and calculated moduli of three-group joint samples

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表 1 结构面重构样品材料的质量配合比

Table 1. Mass proportions of materials of reconstructed joint samples

材料	水	砂	水泥	减水剂	硅粉
a	10	20	20
b	10	30	20	1	1
c	10	30	20	2	2

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表 2 结构面剪切力学参数

Table 2. Shear mechanical parameters of joints

组别	a			b			c
α/(°)	c/MPa	φ/(°)	φ_r/(°)	c/MPa	φ/(°)	φ_r/(°)	c/MPa	φ/(°)	φ_r/(°)
0	0.06	27.46	21.07	0.08	35.27	30.50	0.09	35.49	30.21
45	0.10	29.61	22.54	0.11	36.46	31.78	0.11	37.31	31.52
90	0.14	37.09	28.53	0.17	40.59	31.07	0.17	40.87	35.06
135	0.08	28.31	24.54	0.10	35.39	32.66	0.11	35.94	31.37
180	0.16	31.06	29.09	0.14	38.36	34.50	0.14	39.56	32.54
225	0.08	28.12	20.14	0.08	36.56	29.88	0.09	37.03	32.47
270	0.09	27.29	24.73	0.13	35.56	28.86	0.14	36.73	30.33
315	0.16	38.14	33.11	0.15	39.44	32.29	0.17	40.49	31.58

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表 3 三种试样在三种法向应力下的法向刚度实测值

Table 3. Experimental normal stiffnesses of three groups of joint samples under three normal stresses MPa·mm^-1

σ_n/MPa	0.2	0.5	1.0
a	11.33	20.98	32.86
b	40.50	47.06	59.06
c	205.03	211.61	229.74

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表 4 法向刚度计算值

Table 4. Calculated normal stiffnesses

σ_JCS/MPa	k_ni/(MPa·mm^-1)	V_m/mm	k_{n, Bandis}/(MPa·mm^-1)
σ_JCS/MPa	k_ni/(MPa·mm^-1)	V_m/mm	σ_n=0.2 MPa	σ_n=0.5 MPa	σ_n=1.0 MPa
10.50	8.29	0.100	12.77	21.30	40.35
33.88	35.90	0.077	41.28	50.06	66.57
54.40	201.03	0.049	209.55	222.23	244.19

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表 5 用于刚度计算模型检验的相关参数

Table 5. Related parameters used to examine calculated stiffness model

组别	E/GPa	σ_JCS/MPa	β/(°)	G	σ_n/MPa	k_s/(MPa·mm^-1)	k_n/(MPa·mm^-1)
a	4.02	10.48	15	2.77	9.88	3.98	1 323.46
			30	2.96	2.75	1.47	148.99
			45	3.10	2.00	1.20	93.38
			60	3.36	0.97	0.74	38.08
b	6.82	33.76	15	2.77	31.31	21.85	4 847.74
			30	2.96	18.09	14.31	1 853.42
			45	3.10	9.34	8.79	648.34
			60	3.36	4.09	5.04	222.28
c	15.03	54.37	15	2.77	51.56	47.44	7 707.74
			30	2.96	34.02	34.57	3 933.79
			45	3.10	18.16	21.61	1 603.82
			60	3.36	8.07	12.43	656.58

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