节理几何参数对岩体力学特征的影响

王正堂; 张祺; 王晨龙; 赵婷婷; 王志勇

doi:10.11858/gywlxb.20210753

节理几何参数对岩体力学特征的影响

doi: 10.11858/gywlxb.20210753

太原理工大学机械与运载工程学院材料强度与结构冲击山西省重点实验室，山西太原　030024

基金项目: 国家自然科学基金（11502155）；山西省自然科学基金（201901D211112，201901D211066）

详细信息

作者简介:
王正堂（1993－），男，硕士研究生，主要从事离散元模拟研究. E-mail：2655726987@qq.com

通讯作者:
张　祺（1985－），男，博士，副教授，主要从事离散元模拟研究. E-mail：zq_2012@126.com

中图分类号: O346.5; TU458
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出版历程
- 收稿日期: 2021-03-26
- 修回日期: 2021-04-20

Influence of Joint Geometrical Parameters on Mechanical Properties of Rock Mass

Shanxi Key Laboratory of Material Strength & Structural Impact, School of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China

摘要

摘要: 岩体作为由完整岩块和节理组成的离散介质，其力学行为主要取决于节理的几何和力学特征，探明节理对岩体力学行为的影响具有重要的学术价值和工程意义。利用PFC2D软件，建立了人工合成岩体模型（SRM），研究了单轴压缩条件下节理几何参数对岩体力学强度指标和破坏模式等岩体力学特征的影响。通过正交实验分析，探讨了各节理几何参数对岩体强度指标的显著性影响。结果表明：当节理倾角为10°～50°时，节理长度、节理倾角、节理间距以及岩桥长度对岩体单轴压缩强度和弹性模量具有显著影响；当节理倾角为50°～90°时，岩桥长度对岩体单轴压缩强度和弹性模量的影响不明显；节理阶梯角在整个节理倾角范围内对岩体的单轴压缩强度和弹性模量没有显著影响。岩体破坏模式主要受节理倾角和节理阶梯角影响。研究结果可为岩体工程稳定性分析及支护方案设计提供借鉴。
- 岩体标定 /
- 节理几何参数 /
- 岩体强度指标 /
- 岩体破坏模式 /
- 正交实验设计
Abstract: Rock mass is a discontinuous medium composed of intact rock and joints, whose mechanical properties are mainly determined by the geometrical and mechanical characteristics of joint. It is significantly valuable to explore the influence of joint on the mechanical behaviors of rock mass. In this paper, a synthetic rock mass model (SRM) is established by PFC2D software at first. Then the influence of joint geometrical parameters on rock mass mechanical properties, such as the strength indices and failure modes under uniaxial compression are studied. Through the orthogonal experimental analysis, the influence of the joint geometrical parameter on the strength index of rock mass is discussed. The analysis results show that when the joint dip angle is between 10° and 50°, the joint length, dip angle, spacing and rock bridge length have significant effect on the uniaxial compressive strength and elastic modulus of rock mass. When the joint dip angle is between 50° and 90°, the influence of the rock bridge length on the uniaxial compressive strength and elastic modulus of rock mass is not significant. The joint step angle has no significant influence on the uniaxial compressive strength and elastic modulus of rock mass no matter how much the joint dip angle is. The failure mode of rock mass is mainly affected by the joint dip angle and step angle. The research results provide valuable reference for the stability analysis of rock mass and the support design.
- rock mass calibration /
- joint geometrical parameters /
- rock mass strength index /
- rock failure mode /
- orthogonal experimental design

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图 1 模型示意图

Figure 1. Model diagram

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图 2 岩体的节理几何参数示意图

Figure 2. Schematic of joint geometrical parameters

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图 3 光滑节理模型标定

Figure 3. Calibration of smooth-joint model

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图 4 节理倾角对岩体强度指标的影响

Figure 4. Influence of joint dip angle on strength indices of rock mass

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图 5 节理倾角对岩体破坏模式的影响（红色为受拉伸破坏裂纹，蓝色为受剪切破坏裂纹）

Figure 5. Influence of joint dip angle on failure mode of rock mass (The red denotes the tensile failure and the blue denotes the shear failure)

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图 6 节理阶梯角对岩体强度指标的影响

Figure 6. Influence of joint step angle on strength indices of rock mass

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图 7 节理阶梯角对岩体破坏模式的影响（$ \gamma $ = 90°）

Figure 7. Influence of joint step angle on failure mode of rock mass ($ \gamma $ = 90°)

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图 8 节理长度对岩体强度指标的影响

Figure 8. Influence of joint length on strength indices of rock mass

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图 9 节理长度对岩体破坏模式的影响（$ {L}_{\rm{j}}=20\;{\rm{mm}} $）

Figure 9. Influence of joint length on failure mode of rock mass ($ {L}_{\rm{j}}=20\;{\rm{mm}} $)

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图 10 岩桥长度对岩体强度指标的影响

Figure 10. Influence of rock bridge length on strength indices of rock mass

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图 11 岩桥长度对岩体破坏模式的影响（$ {L}_{\rm{r}}=40\;{\rm{mm}} $）

Figure 11. Influence of rock bridge length on failure mode of rock mass ($ {L}_{\rm{r}}=40\;{\rm{mm}} $)

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图 12 节理间距对岩体强度指标的影响

Figure 12. Influence of joint spacing on strength indices of rock mass

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图 13 节理间距对岩体破坏模式的影响（$ d=40\;{\rm{mm}} $）

Figure 13. Influence of joint spacing on failure mode of jointed rock mass ($ d=40\;{\rm{mm}} $)

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图 14 不同尺寸节理岩体的破坏模式

Figure 14. Failure modes of jointed rock masses in different sizes

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图 15 不同尺寸完整岩体和节理岩体的力学强度指标

Figure 15. Mechanical strength indices of intact and jointed rock mass in different sizes

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表 1 颗粒和平直节理模型的细观参数

Table 1. Meso parameters of particle and flat-joint model

$\,\rho /$ (g·${\rm{cm} }{^{-3}}$)	${R}{_{\rm{min} } }/{\rm{mm} }$	${R}{_{\rm{max} }}/{R}{_{\rm{min} }}$	${\overline {E} }{_{\rm{c} }}/$GPa	${\sigma }{_{\rm{c} }}/$MPa	$ c/ $MPa	${\overline {k} }{^{\rm{n} }}/{\overline {k} }{^{\rm{s} } }$	$ \overline {\mu } $	$ \overline {\varphi } $/(°)
2.1	1.5	1.5	2.31	1.52 ± 0.38	1.52 ± 0.38	2.5	0.38	20

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表 2 数值模型和实际物理模型的宏观参数对比

Table 2. Comparison of macro parameters between numerical and physical model

Method	${\sigma }{_{\rm{u} }}$/MPa	E/GPa	$ \nu $
Numerical	3.88	2.42	0.15
Experimental^[17]	3.84	2.40
Relative error/%	1.04	0.83

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表 3 光滑节理模型的宏观参数标定值和物理实验值对比

Table 3. Comparison between the calibrated and the tested macro parameters for smooth-joint model

Method	${\overline {\mu } }{_{\rm{j} }}$	${k}{_{ {\rm{n} }{\rm{j} } }}$/(GPa·m⁻¹)	${k}{_{ {\rm{s} }{\rm{j} } }}$/(GPa·m⁻¹)
Numerical	0.65	1.64	22.04
Experimental^[17]	0.65	1.60	22.00
Relative error/%	0	2.50	0.18

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表 4 因数水平表

Table 4. Factor level table

Joint geometrical parameters	Factor levels
Joint geometrical parameters	1	2	3	4	5
$\,\beta /$(°)	10（50）	20（60）	30（70）	40（80）	50（90）
${L}{_{\rm{j} }}/{\rm{mm} }$	10	20	30	40	50
${L}{_{\rm{r} }}/{\rm{mm} }$	10	20	30	40	50
$ d/{\rm{mm}} $	10	20	30	40	50
$ \gamma / $(°)	60	75	90	105	120

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表 5 实验设计及结果（$ \,\beta $为10°～50°）

Table 5. Experimental design and results ($ \,\beta $: 10°–50°)

No.	$\,\beta /\left(^{\circ }\right)$	${L}{_{\rm{j} }}/{\rm{mm} }$	${L}{_{\rm{r} }}/{\rm{mm} }$	$ d/{\rm{mm}} $	$\gamma /\left(^{\circ }\right)$	m	${\sigma }{_{\rm{u} }}$/MPa	E/GPa	$ \nu $
1	10	10	10	10	60	1	2.91	2.07	0.200
2	10	20	30	40	120	2	3.72	2.29	0.158
3	10	30	50	20	105	3	3.28	2.20	0.163
4	10	40	20	50	90	4	2.71	2.22	0.163
5	10	50	40	30	75	5	2.64	2.17	0.175
6	20	10	50	40	90	5	3.76	2.32	0.153
7	20	20	20	20	75	1	2.28	2.11	0.175
8	20	30	40	50	60	2	2.79	2.16	0.164
9	20	40	10	30	120	3	1.06	1.64	0.222
10	20	50	30	10	105	4	0.88	1.14	0.080
11	30	10	40	20	120	4	3.65	2.24	0.153
12	30	20	10	50	105	5	1.99	2.00	0.175
13	30	30	30	30	90	1	1.96	1.91	0.164
14	30	40	50	10	75	2	0.76	1.12	0.222
15	30	50	20	40	60	3	0.95	1.56	0.080
16	40	10	30	50	75	3	3.49	2.27	0.153
17	40	20	50	30	60	4	2.14	1.99	0.164
18	40	30	20	10	120	5	0.69	0.75	0.151
19	40	40	40	40	105	1	1.92	1.03	0.131
20	40	50	10	20	90	2	0.54	0.67	0.224
21	50	10	20	30	105	2	2.93	2.09	0.153
22	50	20	40	10	90	3	1.00	1.36	0.172
23	50	30	10	40	75	4	1.53	1.42	0.065
24	50	40	30	20	60	5	1.06	1.20	0.168
25	50	50	50	50	120	1	1.10	1.53	0.231

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表 6 实验设计及结果（$ \,\beta $为50°～90°）

Table 6. Experimental design and results ($ \,\beta $: 50°–90°)

No.	$\,\beta /\left(^{\circ }\right)$	${L}{_{\rm{j} } }/{\rm{mm} }$	${L}{_{\rm{r} }}/{\rm{mm} }$	$ d/{\rm{mm}} $	$ \gamma /\left(^{\circ }\right) $	m	${\sigma }{_{\rm{u} }}$/MPa	E/GPa	$ \nu $
1	50	10	10	10	60	1	1.66	1.53	0.165
2	50	20	30	40	120	2	2.42	1.97	0.155
3	50	30	50	20	105	3	1.01	1.55	0.124
4	50	40	20	50	90	4	1.87	1.59	0.164
5	50	50	40	30	75	5	1.03	1.14	0.148
6	60	10	50	40	90	5	3.36	2.24	0.150
7	60	20	20	20	75	1	2.03	1.54	0.116
8	60	30	40	50	60	2	1.54	1.82	0.220
9	60	40	10	30	120	3	0.79	1.03	0.188
10	60	50	30	10	105	4	0.32	0.35	0.276
11	70	10	40	20	120	4	2.54	2.05	0.141
12	70	20	10	50	105	5	2.58	1.73	0.141
13	70	30	30	30	90	1	1.64	1.52	0.115
14	70	40	50	10	75	2	1.74	0.62	0.110
15	70	50	20	40	60	3	1.56	1.24	0.113
16	80	10	30	50	75	3	3.74	2.21	0.146
17	80	20	50	30	60	4	2.74	1.95	0.134
18	80	30	20	10	120	5	1.47	0.53	0.078
19	80	40	40	40	105	1	2.59	1.58	0.123
20	80	50	10	20	90	2	2.19	0.68	0.101
21	90	10	20	30	105	2	2.94	2.05	0.141
22	90	20	40	10	90	3	2.15	1.12	0.083
23	90	30	10	40	75	4	2.70	1.44	0.106
24	90	40	30	20	60	5	2.31	1.10	0.081
25	90	50	50	50	120	1	2.53	1.77	0.125

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表 7 节理参数对岩体力学特征影响的显著性分析

Table 7. Significance analysis of joint parameter effect on mechanical properties of rock mass

Factor	10° ≤ $\, \beta $< 50°			50° ≤ $\, \beta $ ≤ 90°
Factor	${F}{_{ {\sigma }_{\rm u} }}$	${F}{_{E}}$	${F}{_{\nu }}$	${F}{_{ {\sigma }_{\rm u} }}$	${F}{_{E}}$	${F}{_{\nu }}$
$\,\beta$	40.69^**	25.98^**	0.06	13.43^*	0.51	4.03
${L}{_{\rm{j} }}$	77.84^**	27.42^**	0.40	18.48^**	17.39^**	0.55
L_r	11.28^*	2.67	0.63	1.05	2.03	0.67
$ d $	26.04^**	20.87^**	1.11	11.95^*	16.65^**	1.13
$ \gamma $	1.10	0.96	0.47	1.84	0.21	0.73
Note: Superscript “” and “*” represent significant and extremely significant, respectively.

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表 8 节理几何参数与岩体力学特征之间的回归方程

Table 8. Regression equations between joint geometrical parameters and rock mass mechanical properties

$\,\beta$/(°)	Fitting formula	${R}{^{2} }$
10−50	${\sigma }{_{\rm{u} }}$ = 3.257 − 0.345$ {\,\beta' } $ − 0.498${L'}{_{\rm{j} } }$ + 0.169${L'}{_{\rm{r} }}$ + 0.255$ {d'} $ + 0.021$ {\gamma '} $	0.841
10−50	E = 2.386 − 0.187$ {\,\beta '} $ − 0.208${L'}{_{\rm{j} } }$ + 0.059${L'}{_{\rm{r} } }$ + 0.154$ {d'} $ − 0.034$ {\gamma '} $	0.818
50−90	${\sigma }{_{\rm{u} }}$ = 2.103 + 0.017${\,\beta '}$ − 0.455${L'}{_{\rm{j} } }$ + 0.093${L'}{_{\rm{r} } }$ + 0.289$ {d'} $ − 0.067$ {\gamma '} $	0.799
50−90	E = 1.598 − 0.015${\,\beta '}$ − 0.269${L'}{_{\rm{j} } }$ + 0.064${L'}{_{\rm{r} } }$ + 0.189$ {d'} $ − 0.020$ {\gamma '} $	0.891
Note: The units of ${\sigma }{_{\rm{u} }}$ and E are MPa and GPa, respectively.

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