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• CN 62-1112/TF
• ISSN 1005-2518
• 创刊于1988年

## Plastic Strain Analysis of Mineral Particles in Red Sandstone

FENG Chundi,, HUANG Rendong,

School of Resources and Safety Engineering，Central South University，Changsha 410083，Hunan，China

 基金资助: 国家重点研发计划项目“深部金属矿集约化连续采矿理论与技术”.  2017YFC0602901中南大学贵重仪器设备开放共享基金项目“多尺度下砂岩的内部结构的四维时空演化模型及其应用”.  CSUZC201802

Received: 2019-02-02   Revised: 2019-04-15   Online: 2019-08-08

Abstract

Seldom scholars have investigated the strain and stress state of mineral particles in the rock on the microscopic scale in experiment.At the same time，due to the complex shape of the internal particles of the rock，it is necessary to find suitable research methods and high-precision research instruments.Therefore，for quantitative research on the plastic strain and stress of mineral grains in sandstone under uniaxial compression，X-ray CT was used to scan three-dimensional structure for sandstone (spatial resolution of 4.6 micrometers) to investigate the movement behavior，and put forward the method of deformation gradient tensor calculation of mineral particles to investigate the plasticity of the grains and conduct statistical analysis of the results.Firstly，the displacement of sandstone mineral particles is extracted.At the same time，non-local means filtering algorithm is used to denoise images of sandstone.Then，based on the three-dimensional structure of sandstone，different mineral components are segmented.The principle strains and stress are obtained by and the deformation gradient of sandstone mineral particles.The results show that the filtering algorithm has a significant improvement effect on the CT image of sandstone.In addition，based on the X-ray CT in-situ test results of sandstone，there are relatively complex strain behaviors and stress responses in the sandstone，and significant differences in the deformation behaviors between the fracture zone and the non-fracture zone.Rock grains in Z axis direction experience compressive stress，and in the XY plane are under the effect of tensile stress.At the same time，mineral grains exist larger plastic strain，and the internal grains test of strain and stress is greater than strain and stress the sample at macro-scale.The grain plastic strain in the fracture zone and the non-fracture zone is about 30 times and 5 times bigger than on the macroscopic strain of the sample respectively，which indicate that the deformation behavior in in the microscopic of red sandstone is significantly different from that in the macroscopic sample.This method plays an important role in revealing the internal structure of rock mass and the evolution process of stress and strain state.

Keywords： rock mechanics ; X-ray computed tomography ; plastic strain of grains ; strain components ; stress components ; image filter ; grain strength

FENG Chundi, HUANG Rendong. Plastic Strain Analysis of Mineral Particles in Red Sandstone[J]. Gold Science and Technology, 2019, 27(4): 557-564 doi:10.11872/j.issn.1005-2518.2019.04.557

### 图1

Fig.1   Test devive of X ray computed tomography

### 1.2 试样特征和试验方案

（1）试样特征。试验选用的砂岩试样产自云南，呈红色，弱胶结，颗粒直径约为0.1 mm，如图2所示。为保证试样内部结构的完整性，未对试样进行干燥处理。采用聚焦离子束技术（FIB）将试样切割成直径为2.8 mm、高7.4 mm的圆柱形试样，其端面不平整度小于0.001 mm。采用X射线衍射（XRD）分析矿物粉末，主要成分为石英（80%）、白云母（7%）、钠长石（7%）、方解石（3%）和赤铁矿（1%），密度分别为2.65，2.81，2.61，2.75，4.40 g/cm3

### 图2

Fig.2   Image before and after processing by using Non Local Means algorithm

(a)和(b)分别为单矿物颗粒经过滤波处理前后的三维几何形态示意图；(c)和(d)分别为X射线岩石图像经滤波处理前后的二维灰度图像示意图；(e)和(f)分别为岩石图像经滤波前后中心位置红线的灰度值分布示意图

（2）试验步骤。采用蔡司显微CT和MTS伺服控制系统进行砂岩试验原位单轴压缩试验，试验过程如下：①采用FIB将自然状态下的砂岩切割成圆柱形，并对试样上下端面进行抛光以消除摩擦，同时采用薄膜对试样进行包裹，以保持破裂后试样的完整性；②调整显微CT与MTS单轴压缩仪的试验装置和系统，并对砂岩进行第一次扫描。采用速率为0.003 mm/min位移控制方式对试样进行加载，记录应力—应变曲线，并在峰值后对样品进行第二次扫描。③对于试样破裂前后的投影数据进行三维重构，以获得其内部组分三维结构数据，并采用Non Local Means算法对其三维重构进行图像去噪。④将去噪后的图像进行梯度分割，同时提取赤铁矿颗粒像素点，以对其进行三维重构。⑤通过提取变形梯度，对砂岩矿物颗粒的应力、应变进行计算。

### 2.1 Non Local Means滤波算法

$NL[v](i)=∑j∈Iv(j)w(i,j)$

$w(i,j)=1Z(i)exp-v(Ni)-v(Nj)2,a2h2$

$Z(j)=∑jexp-v(Ni)-v(Nj)2,a2h2$

### 2.2 矿物颗粒应力—应变提取方法

$A0jiei=EjAjiei=Ej$

$Aji=FjiA0li$

$εji=Fji-δji$
$σij=λεllδij+2μεij$

### 图3

Fig.3   Average strain components of grains as a function of normalized height (z) after unloading

### 图4

Fig.4   Average stress components of grains as a function of normalized height (z) after unloading

### 图5

6,7,8为3个主应变分量在空间的分布情况。εxxεyyεzz的数值分布范围在-0.5~0.5之间，主要集中在-0.1~0.1之间，如图所示应变区间跨度较大。由图6,7,8可知，应变负值区域即压缩应变构成倾角约为45°的斜面，该斜面即为砂岩卸载后的断裂面。卸载后，断裂带内的应变分量远远高于其他区域的应变分量，约为其他区域应变的5~10倍，且断裂带内主要显示为压缩应变；同时试样顶部的应变分量普遍大于试样底部的应变分量，其中Z轴方向最为明显。试样整体呈现压缩变形，其中非断裂带压缩应变数值主要集中在0~0.1之间，断裂带内压缩应变数值主要集中在-0.2~-0.4之间；但是局部区域的应变行为显示为拉伸，其中拉伸应变数值集中在0.2附近。由此表明，砂岩内部存在较为复杂的应变行为和应力响应。图9为赤铁矿颗粒主应变之和的概率密度分布，由图9可知，颗粒主应变之和范围为-1.5~1.5，其中70%的应变和集中在-0.5~0.5之间。

### 图9

Fig.9   Probability distribution of the sum of strain components for three main axes

### 图10

Fig.10   Probability distribution of strain components

### 图11

Fig.11   Probability distribution of stress components

## 4 结论

（1）提出的Non Local Means算法对矿相边界提取和降低射束硬化现象具有显著效果，基于CT的砂岩内部塑性应变计算方法能够成功提取出单颗粒变形梯度和应变分布等信息。

（2）主应变分量的空间分布特征表明，砂岩内部存在较为复杂的应变行为和应力响应，且在断裂带和非断裂区域变形行为有显著差异。

（3）砂岩内部矿物颗粒应变分量在xxyy方向明显小于zz方向，同时xxyy方向的波动程度小于zz方向。颗粒在Z轴方向受到压应力，而在XY平面受到拉伸应力的作用。

（4）断裂带和非断裂带区域内部颗粒塑性应变分别约为试样宏观应变的30倍和5倍，表明砂岩内部的变形行为与宏观试样的变形行为之间存在显著差异。

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