三维微观孔隙结构与岩石变形机制及输运特性
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摘要
岩石是一种有着复杂内部结构的非均匀材料。在较小的尺度上，岩石含有各种不同的矿物颗粒、胶结物、孔隙和微裂纹等微观特征。孔隙是岩石微观结构重要组分之一，是岩石微观非均匀性的重要体现。孔隙对岩石的力学性质、输运性质和其他岩石物理性质有重要的影响。
因此：1，应该在岩石力学和岩石物理学中描述孔隙的几何特性如孔隙大小、形状、弯曲度以及孔隙空间结构与连通性；2，定量的讨论孔隙结构如何从微观的尺度控制了岩石的宏观力学行为，将提高对岩石物理性质的认识。
微CT作为一种新的三维成像技术为研究岩石孔隙结构的复杂性提供了新的视角，这对理解岩石的孔隙结构及其对岩石的物理性质的影响，岩石破坏的演化及其与破裂微观力学的关系有极大的帮助。将新技术与传统经典的岩石实验力学方法相结合，我们开展了以下几方面的工作：
（1）传统的岩石微观构造的研究是基于二维薄片的，通过利用光学显微镜和SEM，可以对岩石样品的二维薄片进行不同尺度的综合观察；目前绝大多数微CT岩石研究的对象是两相砂岩，对于微观结构更为复杂的灰岩，尚没有任何工作开展。我们首次利用三维微CT成像研究了印第安纳灰岩完整样品和变形样品中的孔隙结构；并创新性的将三维CT图像分为三个组分：固体颗粒，宏孔隙和以微孔隙为主要成分的中间域；在此基础上，给出了每一个独立宏孔隙的三维形态，得到了球形度和等效直径两个几何参数的统计分布，并定量比较了变形对孔隙结构的影响。
我们的研究指出两个与灰岩力学和输运特性有关的重要问题：与完整样品相比，在变形样品中，宏孔隙的数目显著的减少；中间域（微孔隙）保持了整体骨架的连通性，非弹性压缩不仅导致微孔隙骨架的体积减少，也导致微孔隙骨架厚度的减少；对于印第安纳灰岩，宏孔隙并不是内部连通的，仅仅依靠宏孔隙并不能组成流体通道。因此，为了穿过样品，流体必须流经部分渗透率较低的微孔隙。
（2）我们用类似的方法分析了Majella灰岩完整样品的三维微观结构，给出了Majella灰岩宏孔隙与微孔隙的定量描述。然后，我们获得了不同围压条件下的Majella灰岩样品在变形前后的三维X光成像，通过三维数字图像相关分析，首次获得了灰岩样品的不可逆变形位移场和三维应变张量场；进一步，我们运用数字图像处理和形态学分析对样品的三维应变场进行了详细的分析，分析了不同围压条件下多孔灰岩的破坏机制，以及Majella灰岩中的脆韧性转换的破裂形态。
我们的研究指出，对于Majella灰岩样品，在低围压条件下样品很快达到了差应力峰值，并进入应变软化阶段，具有典型的脆性破坏特征，高应变区在三维空间中体现为较窄的应变局部化带；对于高围压样品，在进入非弹性变形阶段后，样品一直处于应变硬化的状态，高应变区在三维空间中的分布更为分散，有典型的碎屑流特征。当围压介于两者之间时，变形曲线比较平直、斜率接近0，没有显著的应变硬化或者应变软化的趋势；即使在较大轴向应变的情况下，也没有出现差应力峰值；高应力区不是单条窄剪切带，而是由多个不同角度的层状结构叠加而成剪切区域，宽度约为9mm；即使在同一层状结构内部，应变的分布也是不均匀的；同时具备分散式和局部化的特征，其破坏过程是脆性破裂和碎屑流共同作用的结果。
（3）局部化离散压缩带是一种介于脆性和韧性之间的特殊破坏模式。这是一种平面结构压缩带，垂直于平面方向的缩短导致了平面内的碎裂压缩，伴随着非常少量的剪切。这种压缩带的首次报道见于野外研究中，后来在实验室得到了系统的研究。其变形机制尚无定论。Fortin等人(Fortin et al.(2006))发现在Bleuswiller砂岩中有局部的孔隙块存在。并推测，这些孔隙块体的塌缩造成了某种程度上的应力扰动，应力扰动最终导致了压缩带的成核聚集。此假设有一定影响力，并已经被用于实际研究中。
我们对Bleuswiller砂岩变形后的样品进行X光CT扫描，并在此基础上给出了孔隙块体的数学定义，从而能够分析孔隙块体的特征及其在三维空间里的几何分布；进一步我们利用COV算法抽象出样品的应变局部化带的在三维空间里的分布；最后我们将这两者在空间里的位置进行比较，并直观的观察到：孔隙块是一系列尺度在毫米量级、局部孔隙度相对较低的空间区域；其形状近似为椭球形（长轴约为3mm至5mm），在三维空间中的位置是相对随机的。通过比较孔隙块与应变局部化带的空间位置，我们认为：应变局部化带在三维空间里的位置与孔隙块并没有直接关系，也就是说Fortin等人关于孔隙块导致了离散压缩带的假设可能是不成立的。
（4）数据分类是所有岩石CT研究工作的基础。为了能够更准确的对岩石样品的微观结构进行定量分析，我们需要一种稳定的、不依赖个人经验的、能获得全局最优解的多层分类算法。虽然大津算法可以基本满足要求，但是当将其推广至高灰度分辨率CT图像的多层分类问题是，计算效率非常低，而且占用了过量的内存，导致计算无法进行。
为此我们提出了一个改进的基于查找表的大津算法。在内存控制方面，通过对灰度分布的裁剪，和分步输出H查找表，有效的控制了内存占用；在运算速度方面，通过逐级搜索，将低层数分类的最优阈值的结果用作高维分类阈值的限制条件，从而实现了在大幅降低运算量的同时，保证得到全局最优的阈值。这种改进方案可以将计算时间减少为之前的约1/50。之后利用递归的思想，我们的算法可以很自然的升级到多层分类。
Rock is a typical inhomogeneous material. The inhomogeneities of rock may becaused by its complex microstructure, including grains, pores, and cements. Porespace is one of the most important part of microstructure and will influence thebehaviors of rock on a macroscale. The mechanical and transport behaviors of a rockare sensitively dependent on its pore geometry. Hence it is of fundamentalimportance in rock physics to characterize the pore space and its geometricattributes, including pore size, shape, tortuosity and connectivity.
Therefore, quantitative characterization of pore geometry of rocks is of greatsignificance to both rock mechanics and rock physics; and being able to interpret themacro behaviors of rocks from a microstructure perspective can advance rock studyto a higher level.
Recent advances in3-dimensional imaging techniques such as X-raymicrocomputed tomography (microCT) have provided enhanced perspective on poregeometry complexity, which has contributed to useful insights into the preexistingpore space and how it influences rock physical properties, as well as damageevolution and its relation to the micromechanics of failure. With a combination ofconventional rock mechanics experiments and an advanced technology such asmicroCT, a few approaches have been made.
First of all, this thesis studied the pore structure in intact and inelasticallycompacted Indiana limestone using microCT imaging. Guided by detailedmicrostructural observations and using the Otsu’s global thresholding method, the3D images acquired at voxel resolution of4m were segmented into three domains:solid grains, macropores and an intermediate zone dominated by microporosity. Themacropores were individually identified by morphological processing and their shapequantified by their sphericity and equivalent diameter. The new data revealed asignificant reduction of the number of macropores in hydrostatically and triaxiallycompressed samples with respect to the intact material, in agreement with previousmicrostructural analysis. The intermediate (microporosity) domains remained interconnected in compacted samples. The data suggest that the inelasticcompaction in Indiana limestone is manifested by not only a decrease in the volumefraction of the microporosity backbone, but also a corresponding decrease in itsthickness.
Secondly, this thesis analyzed the pore structure of the intact sample of Majellalimestone following the same routine, and the quantitative characterization of themacro pore and micro pore was presented. Besides, CT scan was applied to eachsample before and after deformation, and then the TOMOWARP code was used toperform3D volumetric DIC on the two images to derive the permanent displacementfield and the full3D strain tensor field of each sample. Furthermore, a detailedanalysis of the3D strain field has been made with the help of image processing andmorphological methods.
Thirdly, this study tried to gain some insight of how the localized discretecompaction band would develop. The discrete compaction band is an intermediatefailure mode between the two end-members of brittle faulting and compactivecataclastic flow. So far, there are only three sandstones that have been observed todevelop discrete compaction bands in the lab, which are Bleuswiller sandstone,Bentheim sandstone and Diemelstadt sandstone. The mechanism of the compactionband is still under debate. This work applied CT scan on each Bentheim sandstonesample before and after deformation. Based on the CT images, the porosity patchwas defined and the strain localization band was recognized. Both porosity patch andstrain localization were plotted together in3D space, which led to a conclusion thatthe locations of these patches did not coincide with where the compaction bandsformed.
Finally, a fast algorithm for multi-level thresholding is presented. Rock is atypical multi-phase medium on a microscale, with the participation of different grains,pores, micro cracks and so on. To quantitatively study the behavior of rock on amicroscale, a reliable way of segmenting the CT images of rock is required. The Otsus method of image segmentation selects an optimum threshold by maximizing the between-class variance in a gray image. However, this method becomes verytime-consuming and resource-consuming when applied to a multi-level thresholdproblem due to the fact that a huge number of iterations are required for computingthe cumulative probability and the mean of a class, and a great amount of RAM isrequired to restore the look-up table. To improve the efficiency of Otsu's method, anew fast multi-level algorithm is proposed, which can greatly reduce computing timewith mush less RAM and produce the global optimum in the mean time.
因此：1，应该在岩石力学和岩石物理学中描述孔隙的几何特性如孔隙大小、形状、弯曲度以及孔隙空间结构与连通性；2，定量的讨论孔隙结构如何从微观的尺度控制了岩石的宏观力学行为，将提高对岩石物理性质的认识。
微CT作为一种新的三维成像技术为研究岩石孔隙结构的复杂性提供了新的视角，这对理解岩石的孔隙结构及其对岩石的物理性质的影响，岩石破坏的演化及其与破裂微观力学的关系有极大的帮助。将新技术与传统经典的岩石实验力学方法相结合，我们开展了以下几方面的工作：
（1）传统的岩石微观构造的研究是基于二维薄片的，通过利用光学显微镜和SEM，可以对岩石样品的二维薄片进行不同尺度的综合观察；目前绝大多数微CT岩石研究的对象是两相砂岩，对于微观结构更为复杂的灰岩，尚没有任何工作开展。我们首次利用三维微CT成像研究了印第安纳灰岩完整样品和变形样品中的孔隙结构；并创新性的将三维CT图像分为三个组分：固体颗粒，宏孔隙和以微孔隙为主要成分的中间域；在此基础上，给出了每一个独立宏孔隙的三维形态，得到了球形度和等效直径两个几何参数的统计分布，并定量比较了变形对孔隙结构的影响。
我们的研究指出两个与灰岩力学和输运特性有关的重要问题：与完整样品相比，在变形样品中，宏孔隙的数目显著的减少；中间域（微孔隙）保持了整体骨架的连通性，非弹性压缩不仅导致微孔隙骨架的体积减少，也导致微孔隙骨架厚度的减少；对于印第安纳灰岩，宏孔隙并不是内部连通的，仅仅依靠宏孔隙并不能组成流体通道。因此，为了穿过样品，流体必须流经部分渗透率较低的微孔隙。
（2）我们用类似的方法分析了Majella灰岩完整样品的三维微观结构，给出了Majella灰岩宏孔隙与微孔隙的定量描述。然后，我们获得了不同围压条件下的Majella灰岩样品在变形前后的三维X光成像，通过三维数字图像相关分析，首次获得了灰岩样品的不可逆变形位移场和三维应变张量场；进一步，我们运用数字图像处理和形态学分析对样品的三维应变场进行了详细的分析，分析了不同围压条件下多孔灰岩的破坏机制，以及Majella灰岩中的脆韧性转换的破裂形态。
我们的研究指出，对于Majella灰岩样品，在低围压条件下样品很快达到了差应力峰值，并进入应变软化阶段，具有典型的脆性破坏特征，高应变区在三维空间中体现为较窄的应变局部化带；对于高围压样品，在进入非弹性变形阶段后，样品一直处于应变硬化的状态，高应变区在三维空间中的分布更为分散，有典型的碎屑流特征。当围压介于两者之间时，变形曲线比较平直、斜率接近0，没有显著的应变硬化或者应变软化的趋势；即使在较大轴向应变的情况下，也没有出现差应力峰值；高应力区不是单条窄剪切带，而是由多个不同角度的层状结构叠加而成剪切区域，宽度约为9mm；即使在同一层状结构内部，应变的分布也是不均匀的；同时具备分散式和局部化的特征，其破坏过程是脆性破裂和碎屑流共同作用的结果。
（3）局部化离散压缩带是一种介于脆性和韧性之间的特殊破坏模式。这是一种平面结构压缩带，垂直于平面方向的缩短导致了平面内的碎裂压缩，伴随着非常少量的剪切。这种压缩带的首次报道见于野外研究中，后来在实验室得到了系统的研究。其变形机制尚无定论。Fortin等人(Fortin et al.(2006))发现在Bleuswiller砂岩中有局部的孔隙块存在。并推测，这些孔隙块体的塌缩造成了某种程度上的应力扰动，应力扰动最终导致了压缩带的成核聚集。此假设有一定影响力，并已经被用于实际研究中。
我们对Bleuswiller砂岩变形后的样品进行X光CT扫描，并在此基础上给出了孔隙块体的数学定义，从而能够分析孔隙块体的特征及其在三维空间里的几何分布；进一步我们利用COV算法抽象出样品的应变局部化带的在三维空间里的分布；最后我们将这两者在空间里的位置进行比较，并直观的观察到：孔隙块是一系列尺度在毫米量级、局部孔隙度相对较低的空间区域；其形状近似为椭球形（长轴约为3mm至5mm），在三维空间中的位置是相对随机的。通过比较孔隙块与应变局部化带的空间位置，我们认为：应变局部化带在三维空间里的位置与孔隙块并没有直接关系，也就是说Fortin等人关于孔隙块导致了离散压缩带的假设可能是不成立的。
（4）数据分类是所有岩石CT研究工作的基础。为了能够更准确的对岩石样品的微观结构进行定量分析，我们需要一种稳定的、不依赖个人经验的、能获得全局最优解的多层分类算法。虽然大津算法可以基本满足要求，但是当将其推广至高灰度分辨率CT图像的多层分类问题是，计算效率非常低，而且占用了过量的内存，导致计算无法进行。
为此我们提出了一个改进的基于查找表的大津算法。在内存控制方面，通过对灰度分布的裁剪，和分步输出H查找表，有效的控制了内存占用；在运算速度方面，通过逐级搜索，将低层数分类的最优阈值的结果用作高维分类阈值的限制条件，从而实现了在大幅降低运算量的同时，保证得到全局最优的阈值。这种改进方案可以将计算时间减少为之前的约1/50。之后利用递归的思想，我们的算法可以很自然的升级到多层分类。
Rock is a typical inhomogeneous material. The inhomogeneities of rock may becaused by its complex microstructure, including grains, pores, and cements. Porespace is one of the most important part of microstructure and will influence thebehaviors of rock on a macroscale. The mechanical and transport behaviors of a rockare sensitively dependent on its pore geometry. Hence it is of fundamentalimportance in rock physics to characterize the pore space and its geometricattributes, including pore size, shape, tortuosity and connectivity.
Therefore, quantitative characterization of pore geometry of rocks is of greatsignificance to both rock mechanics and rock physics; and being able to interpret themacro behaviors of rocks from a microstructure perspective can advance rock studyto a higher level.
Recent advances in3-dimensional imaging techniques such as X-raymicrocomputed tomography (microCT) have provided enhanced perspective on poregeometry complexity, which has contributed to useful insights into the preexistingpore space and how it influences rock physical properties, as well as damageevolution and its relation to the micromechanics of failure. With a combination ofconventional rock mechanics experiments and an advanced technology such asmicroCT, a few approaches have been made.
First of all, this thesis studied the pore structure in intact and inelasticallycompacted Indiana limestone using microCT imaging. Guided by detailedmicrostructural observations and using the Otsu’s global thresholding method, the3D images acquired at voxel resolution of4m were segmented into three domains:solid grains, macropores and an intermediate zone dominated by microporosity. Themacropores were individually identified by morphological processing and their shapequantified by their sphericity and equivalent diameter. The new data revealed asignificant reduction of the number of macropores in hydrostatically and triaxiallycompressed samples with respect to the intact material, in agreement with previousmicrostructural analysis. The intermediate (microporosity) domains remained interconnected in compacted samples. The data suggest that the inelasticcompaction in Indiana limestone is manifested by not only a decrease in the volumefraction of the microporosity backbone, but also a corresponding decrease in itsthickness.
Secondly, this thesis analyzed the pore structure of the intact sample of Majellalimestone following the same routine, and the quantitative characterization of themacro pore and micro pore was presented. Besides, CT scan was applied to eachsample before and after deformation, and then the TOMOWARP code was used toperform3D volumetric DIC on the two images to derive the permanent displacementfield and the full3D strain tensor field of each sample. Furthermore, a detailedanalysis of the3D strain field has been made with the help of image processing andmorphological methods.
Thirdly, this study tried to gain some insight of how the localized discretecompaction band would develop. The discrete compaction band is an intermediatefailure mode between the two end-members of brittle faulting and compactivecataclastic flow. So far, there are only three sandstones that have been observed todevelop discrete compaction bands in the lab, which are Bleuswiller sandstone,Bentheim sandstone and Diemelstadt sandstone. The mechanism of the compactionband is still under debate. This work applied CT scan on each Bentheim sandstonesample before and after deformation. Based on the CT images, the porosity patchwas defined and the strain localization band was recognized. Both porosity patch andstrain localization were plotted together in3D space, which led to a conclusion thatthe locations of these patches did not coincide with where the compaction bandsformed.
Finally, a fast algorithm for multi-level thresholding is presented. Rock is atypical multi-phase medium on a microscale, with the participation of different grains,pores, micro cracks and so on. To quantitatively study the behavior of rock on amicroscale, a reliable way of segmenting the CT images of rock is required. The Otsus method of image segmentation selects an optimum threshold by maximizing the between-class variance in a gray image. However, this method becomes verytime-consuming and resource-consuming when applied to a multi-level thresholdproblem due to the fact that a huge number of iterations are required for computingthe cumulative probability and the mean of a class, and a great amount of RAM isrequired to restore the look-up table. To improve the efficiency of Otsu's method, anew fast multi-level algorithm is proposed, which can greatly reduce computing timewith mush less RAM and produce the global optimum in the mean time.
引文
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