Characteristics of Twinning in Marble with Stable Faulting Process
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摘要: 双晶滑移是大理岩产生塑性变形的微观机制之一.为探究剪切破裂时的双晶表现，首先在贺州大理岩试样中诱发不同发展程度的剪切破裂，接着对试样中双晶的发育特征进行了全断面观测与定量统计分析.结果显示：（1）剪切变形带范围内的双晶明显区别于外部双晶，具有局部化、扭折、增粗、分叉及尖灭的特征，具体表现受剪切方向与双晶面倾向之间的相对关系控制；（2）试样整体的双晶密度随加载略有增加，而双晶发生率则维持高位、无变化规律；（3）双晶平均宽度不受加载程度影响，而双晶最大宽度则随剪切破坏程度稳定增加约3倍.以上结果表明低围压受压条件下，贺州大理岩整体双晶增生并不明显，而是集中发育于剪切带内、主要体现为双晶宽度的增加，其表观特征受剪切方向与双晶面倾向之间的相对关系控制.Abstract: Twinning is one the micromechanisms of plastic deformation of marble. To investigate the twinning performance during faulting, shear ruptures with different deformations were induced in Hezhou marble. Microscopic observation and quantitative analysis were performed on twinning characteristics in cross sections perpendicular to faulting plane. The results show that the twinning in the faulting zone was obviously different from that outside of the zone, presenting the characteristics of localization, kinking, thickening, bifurcation and spiking out, which is largely controlled by the relation between the shear direction and twin plane dip. Twin density of the entire sample increased slightly after loading, while twin incidence fluctuated in high level. The average twin width was not affected by loading, however, the maximum twin width increased steadily up to three times with faulting deformation. The above results show that under low confining pressure, the twinning of Hezhou marble is unobvious overall, but concentrated in the shear zone, mainly manifested by the increase of the width of the twin. The apparent characteristics of twinning are controlled by the relative relationship between the shear direction and the inclination of the twin lamellae.
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Key words:
- marble /
- twinning /
- faulting /
- twin density /
- twin incidence /
- geotechnical engineering
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图 4 微观试样制备及观测流程图
蓝色面/线条示意剪切破裂带；红色线条表示切割位置；数字代表切割后小试块的序号；双晶的定量统计只对块1与块9中的绿色阴影部分进行
Fig. 4. Working flow of sample preparation for optical observation
图 5 贺州大理岩5 MPa围压下应力-应变曲线特征(a)及各试样卸载位置(b)(红点)
Fig. 5. Stress-strain curve(a) and specimen unloading locations (b) (red dots) of Hezhou marble under pressure of 5 MPa
图 6 贺州大理岩各阶段破坏照片及垂直破裂面的CT扫描剖面图
照片中箭头指向试样表面破裂面；CT图中深色区为裂隙发育密集区；试样3-T-8破坏程度浅，为提高扫描精度只对中间部分进行了CT扫描
Fig. 6. Photos of Hezhou marble at different damage stages and CT profiles perpendicular to the faulting surfaces
图 7 双晶分布局部化微观图
虚线指明双晶局部化发育的范围，箭头指向上下端裂隙，T.双晶
Fig. 7. Microphotographs of localized twinning which developed between the dotted lines
图 8 双晶扭折微观图
a.扭折处已发生破裂；b.颗粒A中双晶扭折，B内双晶增宽，虚线表示颗粒A边界；c.扭折处左下端已产生微裂隙；箭头指示相对位移方向；T.双晶
Fig. 8. Microphotographs of kinked twins.
图 9 双晶宽度差异及分叉现象微观图
a~c中箭头指向上、下端裂隙；d.中箭头指向两组不同的双晶面；e.中箭头指向双晶分叉点，上分叉点无裂隙，下分叉点处发育微裂隙.a中虚线为颗粒边界，该颗粒大部分面积都被双晶占据.
Fig. 9. Microphotographs of thickening and bifurcation of twins
图 14 双晶平均宽度与应变关系图
Fig. 14. Correlation between the average thickness of twins and strain
图 15 双晶最大宽度与应变关系图(a)和累计双晶最大宽度与应变关系(b)
Fig. 15. Correlation between the maximum thickness of twins and strain (a), and the accumulation of the maximum thickness of twins and strain (b)
表 1 双晶抽样测量误差
Table 1. Errors of sampling measurement of twin
双晶序号 宽度一(μm) 宽度二(μm) 绝对误(μm) 相对误差 1 2.15 2.56 -0.41 -16% 2 2.73 3.01 -0.28 -9% 3 14.76 14.46 0.30 2% 4 6.94 6.73 0.21 3% 5 5.89 5.99 -0.09 -2% 6 1.72 1.86 -0.14 -8% 7 3.29 3.75 -0.46 -12% 
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表 2 双晶密度$ {\mathit{N}}_{\mathit{L}} $统计及偏应力估算
Table 2. Statistics of twinning density$ {\mathit{N}}_{\mathit{L}} $ and estimation of deviatoric stress
试样 试块1
(mm-1)试块9
(mm-1)均值
(mm-1)偏应力一(MPa)*
$ \mathrm{\sigma }=-52.0+171.1\mathrm{l}\mathrm{g}{N}_{L} $偏应力二(MPa)**
$ \mathrm{\sigma }=21.86{{N}_{L}}^{0.57} $偏应力三(MPa)***
$ \mathrm{\sigma }=(19.5\pm 9.8){{N}_{L}}^{0.5} $3-S 3.13 5.59 4.36 / / / 3-T-8 9.86 7.18 8.52 159.2 74.1 56.9±28.6 3-T-7 7.18 7.63 7.40 148.7 68.4 53.0±26.7 3-T-6 5.23 5.02 5.13 121.5 55.5 44.2±22.2 3-T-5 5.23 6.34 5.79 130.5 59.5 46.9±23.6 3-T-4 8.57 6.63 7.60 150.7 69.5 53.8±27.0 注：* Rowe and Rutter (1990); ** Sakaguchi et al. (2011); *** Rybacki et al. (2013).
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表 3 各试样统计数据
Table 3. Statistic data of each sample
试样 测线长
(μm)颗粒数 平均粒径
(μm)双晶数 3-S 53 108 80 664 226 3-T-8 47 280 49 965 404 3-T-7 47 541 104 457 352 3-T-6 47 789 152 314 245 3-T-5 50 373 107 471 290 3-T-4 49 283 99 498 375 总计 29 5374 591 500 1 892
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