卸荷条件下岩石平行偏置双裂隙的扩展规律研究

周子涵; 陈忠辉; 王建明; 年庚乾; 陈帅; 包敏

doi:10.11779/CJGE202004015

卸荷条件下岩石平行偏置双裂隙的扩展规律研究 English Version

中国矿业大学（北京）力学与建筑工程学院,北京　100083

基金项目:

国家重点研发计划项目 2016YFC0801602

国家重点研发计划项目 2017YFC1503103

详细信息

作者简介:
周子涵(1995—),男,博士研究生,主要从事边坡灾变机理与岩石断裂力学等方面的研究。E-mail: 18813027369@163.com

中图分类号: TU452
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出版历程
- 收稿日期: 2019-05-23
- 网络出版日期: 2022-12-07
- 刊出日期: 2020-03-31

Propagation of offset parallel cracks in rock under unloading conditions

School of Mechanics & Civil Engineering, China University of Mining and Technology, Beijing 100083, China

摘要

摘要: 岩质边坡中存在着大量的非贯通断续节理,对于开挖扰动下的边坡岩体强度及破坏模式起着重要的控制作用。为了研究边坡岩体在开挖扰动下内部节理裂隙的细观扩展规律,基于叠加原理与Kachanov法,推导了卸荷条件下平行偏置双裂隙的尖端应力强度因子表达式并从理论上分析了多种因素对裂隙间相互作用的影响规律,最后对含平行偏置裂隙的类岩试件进行了卸荷试验,结果表明：①主次裂隙间的裂隙错距或岩桥长度愈小、主裂隙长度愈大,裂隙尖端处的相互作用变化愈剧烈；②随着裂隙倾角的增大,裂隙尖端张拉破坏的趋势愈发明显,而剪切破坏趋势减弱；③裂隙间的岩桥长度越大,应力强度因子放大系数受裂隙倾角的影响越敏感。通过对比理论上不同试件在侧向卸荷条件下的裂隙轴向起裂应力与试验测得的实际起裂应力发现,两者相对误差均在4.7%以内,证明了利用提出的理论方法计算裂隙的临界起裂应力是合理可行的。通过本研究揭示的卸荷条件下平行偏置双裂隙的扩展规律,可对露天矿节理岩质边坡在开挖过程中的细观破坏机制提供一定的理论依据。
- 断续节理 /
- 叠加原理 /
- Kachanov法 /
- 应力强度因子 /
- 卸荷试验
Abstract: The numerous non-penetrating intermittent joints in rock slopes play an important role in controlling the strength and failure mode of rock mass under excavation disturbance. In order to determine the meso-influence laws of intermittent joint interaction in the slope under the action of excavation, using the superposition principle and the Kachanov method, the stress intensity factor of parallel offset double cracks at the tip in rock mass under unloading conditions is calculated, the influences of many factors on the interaction between cracks are theoretically analyzed, and the unloading tests on rock-like specimens with parallel offset cracks are conducted. The results show that: (1) The interaction at the crack tips becomes more severe and sensitive if the length of the main crack larger or the staggered distance between the cracks or the length of rock bridge is shorter. (2) As the inclination angle of cracks increases, the tensile failure gradually increases but shear failure weakens. (3) The sensitivity of the amplification factors of the stress intensity factor affected by the angle is positively correlated with the length of rock bridge. In addition, the axial-initiation stresses of cracks in different specimens theoretically calculated under unloading conditions are compared with the measured ones by tests, and it is found that the relative error between them are all less than 4.7%, revealing that the proposed theoretical formula is a reasonable and feasible method to calculate the axial-initiation stresses of cracks. The propagation laws of the offset parallel cracks in rock under unloading conditions are revealed and are conducive to the studies on meso-failure mechanism of jointed rock slopes in open-pit mines under the action of excavation.
- intermittent joint /
- superposition principle /
- Kachanov method /
- stress intensity factor /
- unloading test

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图 1 边坡中不同部位应力分布示意图

Figure 1. Sketch of stress in different parts of a slope

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图 2 边坡中“关键块体”开挖前后力学模型示意图

Figure 2. Sketch of mechanical models for "key block" in slope before and after excavation

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图 3 卸荷条件下含双裂隙岩体应力状态二次叠加

Figure 3. Superposition method of stress state of rock mass with double cracks under unloading condition

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图 4 单轴拉伸作用下的平行偏置裂隙力学模型

Figure 4. Mechanical model for a pair of offset parallel cracks

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图 5 裂隙面力的分解（i=1,2）

Figure 5. Decomposition of crack force (i=1,2) under uniaxial tension

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图 6 单轴压缩作用下的平行偏置裂隙力学模型及面力等效示意图

Figure 6. Mechanical model for a pair of offset parallel cracks under uniaxial compression and equivalent sketch of crack force

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图 7 卸荷条件下含单裂隙岩体应力状态二次叠加

Figure 7. Superposition method for stress state of rock mass with a single crack under unloading conditions

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图 8 卸荷条件下应力强度因子放大系数随裂隙错距比的变化规律（ $s = - a$ ）

Figure 8. Variation of amplification factors of SIF with staggered distance ratio between cracks（ $s = - a$ ）

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图 9 卸荷条件下应力强度因子放大系数随岩桥长度比的变化规律（ $h = a$ ）

Figure 9. Variation of amplification factors of SIF with length ratio of rock bridge between the cracks under unloading conditions

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图 10 卸荷条件下应力强度因子放大系数随裂隙长度比的变化规律

Figure 10. Variation of amplification factors of SIF with crack length ratio under unloading conditions

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图 11 卸荷条件下应力强度因子放大系数随裂隙倾角α的变化规律

Figure 11. Variation of amplification factors of SIF with crack angle α under unloading conditions

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图 12 试件尺寸示意图

Figure 12. Sketch of specimen dimensions

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图 13 试验装置

Figure 13. Experimental devices

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图 14 试验应力路径示意图

Figure 14. Sketch of experimental stress path

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图 15 试件1的裂隙扩展过程

Figure 15. Crack propagation process of specimen 1

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图 16 试件3的裂隙扩展过程

Figure 16. Crack propagation process of specimen 3

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图 17 试件4的裂隙扩展过程

Figure 17. Crack propagation process of specimen 4

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图 18 试件7的裂隙扩展过程

Figure 18. Crack propagation process of specimen 7

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表 1 应力强度因子放大系数误差分析

Table 1 Error analysis of amplification factors of SIF

s/a	本文（B）		手册（C）		相对误差值
s/a	$K_{Ι} (- b) / K_{Ι}_{0} (- b)$	$K_{Ι} (b) / K_{Ι}_{0} (b)$	$K_{Ι} (- b) / K_{Ι}_{0} (- b)$	$K_{Ι} (b) / K_{Ι}_{0} (b)$	$K_{Ι} (- b) / K_{Ι}_{0} (- b)$	$K_{Ι} (b) / K_{Ι}_{0} (b)$
-0.5	0.8577	1.1237	0.8700	1.1380	0.0623	0.0143
-0.25	0.9966	1.1287	1.0100	1.1400	0.0534	0.0113
0	1.1098	1.1214	1.1210	1.1320	0.0182	0.0106
0.25	1.1662	1.1063	1.1700	1.1120	0.0138	0.0057
0.5	1.1715	1.0891	1.1730	1.0900	0.0015	0.0009
注：相对误差 $W_{1} = \| C - B \|$ , $s / a$ 为负值代表裂隙之间有重叠。

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表 2 砂岩与试件的力学参数对照表

Table 2 Mechanical properties of sandstone and specimens

材料	密度/(kg·m^-3)	单轴抗压强度/MPa	单轴抗拉强度/MPa	弹性模量/GPa	泊松比
砂岩	2000~2600	20 ~ 200	4 ~ 25	10 ~ 100	0.2 ~ 0.3
试件	2350	52.32	5.06	15.21	0.23

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表 3 试件中裂隙的相关几何参数

Table 3 Geometric parameters of cracks in specimens

试件编号	裂隙倾角α/(°)	裂隙1长度2a/ mm	裂隙2长度2b/mm	岩桥长度s/mm	裂隙错距h/mm
1	45	12	24	-12	6
2	45	12	24	-12	12
3	45	12	24	-12	24
4	45	12	24	12	6
5	45	12	36	12	6
6	30	12	24	12	6
7	75	12	24	12	6
注：s为负值时代表裂隙之间存在搭接部分。

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表 4 卸荷条件下不同试件的裂隙轴向起裂应力

Table 4 Axial-initiation stresses of cracks in different specimens under unloading conditions

试件编号	起裂位置	理论轴向起裂应力σ_1t/kN	实际轴向起裂应力σ_1s/ kN	相对误差W₂/%
1	主裂隙外尖端	89.03	85.17	4.5
2	主裂隙内尖端	93.16	89.71	3.8
3	主裂隙内尖端	96.11	92.13	4.3
4	次裂隙外尖端	85.64	83.52	2.5
5	次裂隙内尖端	83.25	79.68	4.5
6	主裂隙内尖端	86.22	82.33	4.7
7	次裂隙内尖端	97.17	94.28	3.1
注： $W_{2} = \| σ_{1t} - σ_{1s} \| / σ_{1s}$ 。

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