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黄金科学技术 ›› 2020, Vol. 28 ›› Issue (3): 430-441.doi: 10.11872/j.issn.1005-2518.2020.03.151

• 采选技术与矿山管理 • 上一篇    下一篇

基于核磁共振T2谱图的裂隙砂岩疲劳损伤分析

毛思羽(),曹平(),李建雄,欧传景   

  1. 中南大学资源与安全工程学院，湖南 长沙 410083
  • 收稿日期:2019-09-06 修回日期:2020-02-26 出版日期:2020-06-30 发布日期:2020-07-01
  • 通讯作者: 曹平 E-mail:632776568@qq.com;pcao_csu@sina.com
  • 作者简介:毛思羽（1993-），男，安徽黄山人，硕士研究生，从事岩石力学方面的研究工作。632776568@qq.com
  • 基金资助:
    国家自然科学基金项目“开挖卸载诱导下的硬岩断裂破坏机理与尺寸效应研究”(11772358);中南大学自主创新项目“非贯通不同节理倾角的砂岩在不同加载方式下的强度和损伤特性及其裂纹扩展研究”(2019zzts982)

Fatigue Damage Analysis of Fractured Sandstone Based on Nuclear Magnetic Resonance T2 Spectrum

Siyu MAO(),Ping CAO(),Jianxiong LI,Chuanjing OU   

  1. School of Resources and Safety Engineering，Central South University，Changsha 410083，Hunan，China
  • Received:2019-09-06 Revised:2020-02-26 Online:2020-06-30 Published:2020-07-01
  • Contact: Ping CAO E-mail:632776568@qq.com;pcao_csu@sina.com

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摘要：

岩石工程中岩体经常处于周期性的力学行为作用下，研究裂隙岩体在疲劳加载下的损伤变化具有重要的工程意义。选取了5种裂隙倾角的黄砂岩试样进行疲劳试验，采用核磁共振仪器分别测得各倾角裂隙砂岩在不同疲劳上限应力作用下30个疲劳循环前后其内部的孔隙变化情况，发现大孔隙数量随疲劳上限应力的增加呈指数增长，是造成裂隙砂岩疲劳加载后孔隙度增大的主要因素。定义了2种基于大孔隙占总孔隙比值的损伤变量来研究疲劳上限应力对各裂隙倾角砂岩的疲劳损伤影响，均能较好地反映损伤变量随疲劳上限应力的变化情况，得出损伤变化趋于平缓的裂隙岩样最终破坏时的强度大于损伤变量陡增的裂隙岩样。最后从理论角度分析得出孔隙与轴向应变之间存在正相关关系，即用孔隙反映砂岩疲劳损伤是合理的。

关键词: 裂隙砂岩, 疲劳加载, 核磁共振, 微观损伤, 疲劳强度, 损伤变量

Abstract:

In the process of underground mining and tunnel construction，the rock is mostly in the process of repeated loading and unloading，and the macro-cracks and micro-defects in the rock mass itself will continue to expand under fatigue loading and eventually lead to many accidents.Therefore，it is of great engineering significance to study the micro-defects of fractured rock masses under fatigue loading.In the previous studies, acoustic emission and CT scanning technology were mainly used to reflect the change of microscopic damage through AE number or CT number, which obtained good results.The porosity measured by nuclear magnetic resonance technology can also be used to show the damage of rock samples，but it is currently mainly used in uniaxial compression loading.In this experiment，yellow sandstone specimens with five fracture inclination angles （0°，15°，30°，45°，60°） were selected.Firstly，uniaxial compression experiments were performed to measure the uniaxial compressive strength of fractured sandstone at various angles.Then carry out fatigue loading experiments，and select the upper limit fatigue loading stresses based on the measured uniaxial compressive strength to be 19.1 MPa,25.6 MPa and 30.3 MPa，respectively.The internal porosity of each fractured sandstone before and after 30 fatigue cycles under each upper limit stress was measured with nuclear magnetic resonance instruments.Combined with the analysis of T2 spectrum measured by nuclear magnetic resonance instrument，it is found that with the increase of the upper limit stress，the total area of T2 spectrum and the accumulation of porosity in fractured sandstone have increased significantly.This shows that its internal damage increases with the increase of the upper limit stress，and then combined with the T2 spectral area for quantitative analysis，it was found that the spectral area of the small pores in the T2 spectrum changed only slightly with the increase of the upper limit stress，while the spectral area of large pores increases exponentially with the increase of the upper limit stress.No matter from the angle of the change of the ratio of large pores (to the total pores) to the fatigue upper limit stresses under different inclination angles，or from the angle of the change of the ratio of large pores under different fatigue upper limit stresses to the angle of fracture inclination，similar rules are obtained.Therefore，it can be concluded that the change of large pores is the main factor that causes the total porosity of fractured sandstones to increase after fatigue loading，and then the curve of the ratio of the proportion of large holes to the upper limit fatigue stress ratio after fatigue loading at various inclination cracks is fitted.The fitting coefficients of sandstones at various inclination angles are very high，which shows that the change law of internal damage can be well displayed.Considering the effect of initial damage of rock samples on fatigue loading，two types of damage variables based on the ratio of large pores to total pores were defined to study the impact of fatigue upper limit stress on the fatigue damage of sandstones with different fracture inclination angles.According to the relationship curves between the two damage variables，the upper limit stress ratio and the upper limit stress，the change of the defined damage variable can be well projected. Further analysis can show the intensity change of the sandstones with different fracture inclination angles，that is，the damage intensity of the fractured rock sample that tends to be gentle will eventually be greater than that of the fractured rock sample with a sharp increase in damage. Finally，combining the probability density function of Weibull distribution and generalized Hook’s law，it is deduced from the theoretical formula that it is reasonable to use pores to study sandstone fatigue damage.Combining the results of previous studies and this experiment，it was found that the porosity can well reflect the microscopic damage of rock samples in both uniaxial compression experiments and fatigue loading experiments.

Key words: fractured sandstone, fatigue loading, nuclear magnetic resonance, microscopic damage, fatigue strength, damage variable

中图分类号: 

  • TU443

图1

黄砂岩试样与试验设计流程图（a）5种倾角的黄砂岩；（b）部分裂隙砂岩；（c）试验设计步骤及部分步骤作用"

图2

单轴压缩加载试验示意图及试验结果"

图3

疲劳加载曲线示意图"

图4

所有试样核磁共振图谱（a）试样T2谱分布曲线； （b）试样孔隙度的累积曲线"

图5

砂岩疲劳加载前后T2谱分布曲线和孔隙度累积曲线注：岩样代号以A-B形式标注，A为裂隙角度（°），B为疲劳上限应力（MPa）"

表1

0°裂隙岩样疲劳加载前后核磁共振谱面积对比"

岩样代号编号小孔谱面积疲劳加载后增幅大孔谱面积疲劳加载后增幅
疲劳前疲劳后疲劳前疲劳后
0-1917 765.157 865.13+1.29%6 088.456 530.75+7.26%
27 562.448 187.28+8.26%1 420.061 969.82+38.71%
37 209.697 990.78+10.83%5 592.666 159.69+10.14%
0-2618 025.266 854.49-14.59%2 408.643 473.45+44.21%
28 205.958 446.64+2.93%2 653.975 242.45+97.53%
36 612.318 041.24+21.61%2 721.096 020.57+121.26%
0-3118 019.327 611.89-5.08%2 626.235 901.92+124.73%
28 022.078 509.59+6.08%1 850.364 751.84+156.81%
37 888.177 936.17+0.61%2 687.425 587.12+107.90%

图6

不同裂隙倾角下大孔占比随疲劳上限应力的变化注：岩样代号以A-B形式标注，A为裂隙倾角（°），B为疲劳上限应力（MPa）"

图7

各疲劳上限应力下大孔占比随裂隙倾角的变化情况注：岩样代号以A-B形式标注，A为裂隙倾角（°），B为疲劳上限应力（MPa）"

图8

各倾角裂隙砂岩大孔占比随疲劳上限应力比的拟合曲线"

表2

大孔占比随疲劳上限应力比的拟合方程特性"

裂隙倾角/（°）拟合曲线方程拟合系数R2X=0.96的拟合数值
0y=0.15421+0.58142*x3.338360.972900.66156
15y=0.14508+0.44167*x10.392120.972410.43406
30y=0.15864+0.50032*x5.4260.999700.55955
45y=0.17174+0.34557*x3.101330.935110.47622
60y=0.13469+0.55907*x6.468360.998310.56402

表3

各倾角裂隙砂岩的损伤变量D的相关方程"

裂隙倾角/（°）D与上限应力比的关系D与上限应力（σmax）的关系
0D0=1.14599*x3.33836D0=1.14599*（σmax/39.58）3.33836
15D15=1.52838*x10..39212D15=1.52838*（σmax/33.66）10..39212
30D30=1.24796*x5.426D30=1.24796*（σmax/35.75）5.426
45D45=1.13495*x3.10133D45=1.13495*（σmax/37.72）3.10133
60D60=1.30219*x6.46836D60=1.30219*（σmax/36.51）6.46836

图9

各倾角裂隙砂岩损伤变量曲线（a）D与疲劳上限应力比的曲线；（b）D与疲劳上限应力的曲线；（c）D′与疲劳上限应力比的曲线；（b）D′与疲劳上限应力的曲线"

表4

各倾角裂隙砂岩的损伤变量D′的相关方程"

裂隙角度/（°）D′与上限应力比的关系D′与上限应力（σmax）的关系
0D0′=0.2331+0.8789*x3.33836

D0′=0.2331+0.8789*

（σmax/39.58）3.33836

15D15′=0.3342+1.0175*x10.39212

D15′=0.3342+1.0175*

（σmax/33.66）10..39212

30D30′=0.2835+0.8941*x5.426

D30′=0.2835+0.8941*

（σmax/35.75）5.426

45D45′=0.3606+0.7257*x3.10133

D45′=0.3606+0.7257*

（σmax/37.72）3.10133

60D60′=0.2388+0.9912*x6.46836

D60′=0.2388+0.9912*

（σmax/36.51）6.46836

图10

大孔占比随孔隙度的变化曲线"

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