基于CT图像处理的冻结岩石细观结构及损伤力学特性研究
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摘要
低温下冻结岩石的损伤是影响寒区岩石工程、地下低温贮存库以及冻结法施工的矿井建设等工程安全稳定的重要因素。论文以寒区岩石工程和人工冻结岩石工程为背景，针对低温状态下的冻结岩石损伤问题，以岩石的细观结构为切入点，以损伤力学、细观力学、体视学、冰力学作为理论依据，以CT扫描实验为研究基础，采用CT图像处理技术、损伤理论分析和细观数值计算相结合的方法，对低温环境下冻结岩石的细观结构及损伤力学特性进行研究，主要内容和成果如下：
（1）进行了陕西红砂岩和灰砂岩两种岩石在常温、-2℃、-5℃、-10℃、-20℃、-30℃的CT扫描实验，获得了不同低温下岩石CT扫描图像。冻结岩石CT图像很好地反映了冻结过程中岩石的细观结构、各相组分分布（水、冰、岩石矿物颗粒）及损伤变化情况。低温作用下岩石内部产生新的孔隙和裂隙，同时伴有裂隙、孔隙贯通现象。岩石内部初始损伤随着温度的降低扩展增大，当温度降低至-20℃后，岩石内部细观结构不再变化。
（2）将数字图像处理理论应用于冻结岩石CT图像处理中，实现了CT图像的伪彩色增强；获得了不同冻结温度下岩石的CT数直方图；将最大类间方差法和遗传算法相结合，对冻结岩石CT图像进行双阈值分割，实现了冻结岩石CT图像的三值化分割技术；运用Canny算子对冻结岩石CT图像进行边缘检测，获得了冻结岩石细观结构的二值图像。冻结岩石CT图像的伪彩色增强能够提高CT图像的分辨率，减少视觉上的判断误差，根据伪彩色增强图像颜色的变化、CT数直方图可定量分析冻结过程中岩石细观结构、水冰含量以及损伤分布随温度的变化情况。冻结岩石CT图像的三值化分割技术，将冻结岩石内部的水、冰、岩石三相介质区分开，明确地给出了水、冰、岩石空间位置及含量的数字表述。
（3）将体视学原理引入到冻结岩石细观结构特性研究中，结合冻结岩石CT图像，分析了冻结岩石细观结构的构成及其相互关系，给出了冻结岩石细观结构参数计算公式。对冻结过程中岩石内部裂隙、孔隙的长度、周长、面积、宽度、圆形度等细观结构参数及水冰含量进行定量计算。细观结构参数能够显示冻结过程中损伤大小及形态的变化情况。冻结岩石内部水和冰含量定量计算结果表明：岩石内部水、冰含量随温度的变化而改变，两者处于动态平衡状态中。
引入未冻水含量作为内变量，从与内变量功共轭的相变潜热出发，利用连续介质热力学理论推导出冻结岩石中未冻水、冰含量与冻结温度关系的理论公式。所给出的公式能描述冻结过程中岩石内部未冻水和冰含量的变化情况，同时可预测给定含水量的冻结岩石的纯冰点。
（4）根据冻结岩石的细观结构组构及特性，从岩石细观力学机理出发，用混合律方法将含孔隙的冻结岩石视为各向同性介质，将含裂隙的冻结岩石视为横观各向同性介质，推导出不同冻结温度下的等效弹性模量计算公式。
针对冻结作用对岩石力学性能的影响，提出“冻结负损伤”的概念，用冻结损伤、荷载损伤描述冻结和荷载两种不同作用下岩石损伤过程，拓展损伤变量内涵。基于连续介质热力学方法，以岩石的初始损伤状态为基准状态，应用推广后的应变等价原理及损伤力学理论，建立荷载作用下冻结岩石的宏—细观损伤本构模型。对模型进行了验证，理论曲线与实验曲线比较接近，所建立的模型能够描述荷载作用下冻结岩石损伤演化规律。
（5）提出了冻结岩石数字图像数值分析方法（DIP-FEM），建立不同低温环境、不同荷载作用下岩石破坏过程的有限元数值计算格式。通过CT图像的三维重建技术，获得冻结岩石真实细观结构数字化模型，对其进行矢量化转化，并导入至有限元软件ANSYS中，进行冻结过程中温度场及冰膨胀力分布规律的数值模拟试验研究，分析含裂隙或孔隙岩石在低温环境下的损伤特性，该方法弥补了低温冻结岩石物理实验的不足，为实现冻结岩石的破坏过程研究从细观尺度向宏观尺度过渡提供新的研究途径。
Frozen rock problems exist in many projects in different degree, including the rockengineering in cold regions, the reservoir pool at low temperature of liquefied natural gas andthe construction using frozen methods in mine building projects, etc. The research on frozenrock problems has extensive engineering background and practical significance. The damageon frozen rock at low temperature has a significant effect on the security and stability of therock engineering in cold region. Aiming at the engineering demands for practical problemsoccurred in frozen rock engineering, based on the computed tomography (CT) scanningexperiment of frozen rock at different minus temperature, and guided by the theories ofDamage Mechanics, Continuous Media of Thermodynamics, Meso-mechanics, Stereology,Ice mechanics, and taking the meso-structure of frozen rock as cut-in point, meso-structureand mechanical characteristics of frozen rock were investigated by the method combiningwith CT image processing technology and damage theoretical analysis and mesoscopicnumerical calculation. The following conclusions have been gotten:
(1) CT scanning images of red and gray sandstones at different low temperature areobtained by carrying out the CT scanning experiment at room temperature20℃,0℃,-5℃,-10℃,-20℃and-30℃. CT scanning images can well show the change of themeso-structure and damage of the frozen rock, and the composition distribution whichincludes water, ice and mineral particles during process of freezing. Under low temperature,the new internal rock pore and crack are generated also accompany with the phenomenon ofcrack propagation and coalescence. Rock damage increases with the temperature dropping.When the temperature drops to-20℃, the rock meso-structure keep stable and almost changeno more.
(2) Applying digital image processing theory to CT image, pseudo-color enhancement technique of CT image of frozen rock has been implemented. Histogram of frozen rock basedon CT value has been obtained. The double thresholds segmentation that based on geneticalgorithm is realized and the three-valued segmentation of frozen rock CT images iscompleted. By Canny operator's edge detection, the binary images of frozen rockmeso-structure are gotten. Using CT image processing technology can improve the resolutionof frozen rock CT images, and reduce the error of visual judgment. According with thechanges of colors in pseudo-color enhancement image of frozen rock CT images andhistogram of frozen rock based on CT value, meso-structure, unfrozen water, ice, and damagedistribution can be analyzed quantitatively dependent on temperature during freezing process.he three-valued segmentation of frozen rock CT images is employed to distinguish water andice from rock in the internal of frozen rock. Digital expression of spatial location and thecontent of water, ice and rock are given definitely by the three-valued segmentation.
(3) The stereology theory is introduced to the study of the characteristics of freeze rockmeso-structure. Combined with the CT images of frozen rock, the meso-structure compositionand their mutual relations are analyzed and the parameter calculation formulations ofmeso-structure of frozen rock are put forward. The meso-structure parameters are calculatedquantitatively, such as length, perimeter, area, width and circularity of pore and crack. Thecalculation results of unfrozen water and ice content shows that unfrozen water and icecontent in rock interior varied with the changes of temperature, and both are in a state ofdynamic balance.
In frozen rock, the unfrozen water content is considered as an internal variable and thework conjugated with the internal variable is the latent heat of phase change of unfrozen rock.The continuum thermodynamic theory is employed to deduce the formula of the relationshipbetween the unfrozen water and ice content depends on temperature. The experimental resultsof CT scanning agree well with the result predicted by deduced formula. The changes ofunfrozen water and ice content in the process of freezing can be described by deducedformula, and the pure frozen point of frozen rock can be predicted.
(4) Based on composition and characteristics of mesoscopic structure of frozen rock,from the idea of the rock mesoscopic mechanics, using mixed law methods to consider frozenrock with pore as isotropic medium, and frozen rock with crack as the transversely isotropicmedium, calculation formulas of equivalent elastic modulus of frozen rock under differentfrozen temperature were deduced.
In view of the influence of frozen action on the properties of rock mechanics, the conceptof frozen negative damage was put forward. Damage variable was proposed with more new meaning to frozen and loaded rock, three new conceptions were put forward, which werefrozen damage, loaded damage and total damage. Proposed damage variable can describedifferent damage process of rock under the two different actions,one is low temperaturefrozen and another is load.Based on the continuum thermodynamics method, and takeing theinitial damage state as reference state, macro-mesoscopic damaged constitutive model offrozen rock was build under the load action according to the generalized principle of strainequality and theory of damage mechanics.
(5) The CT image of frozen rock can be extended to be applicable to research frozenrock damage. The new method (DIP-FEM), Digital Image Processing—Finite ElementMethod was put forward. By the proposed method, the finite numerical analysis fomat of rockdamage process has been established under different low temperature environment and loadaction. The real mesoscopic structure digital model of frozen rock is obtained bythree-dimesion reconstruction technology of CT image. Vectorization algorithm ofmesoscopic structure digital model of frozen rock is presented, which can convert imageformat to graphics format. Then real meso-structure of frozen rock is imported into finiteelement software ANSYS to analysis damage characteristics of rock with pore or crack in lowtemperature environment. The proposed method can make up for the deficiencies of lowtemperature frozen rock physical experiment, and provide a new research avenues to realizedamage process research of frozen rock from the meso-scale to macro-scale.
（1）进行了陕西红砂岩和灰砂岩两种岩石在常温、-2℃、-5℃、-10℃、-20℃、-30℃的CT扫描实验，获得了不同低温下岩石CT扫描图像。冻结岩石CT图像很好地反映了冻结过程中岩石的细观结构、各相组分分布（水、冰、岩石矿物颗粒）及损伤变化情况。低温作用下岩石内部产生新的孔隙和裂隙，同时伴有裂隙、孔隙贯通现象。岩石内部初始损伤随着温度的降低扩展增大，当温度降低至-20℃后，岩石内部细观结构不再变化。
（2）将数字图像处理理论应用于冻结岩石CT图像处理中，实现了CT图像的伪彩色增强；获得了不同冻结温度下岩石的CT数直方图；将最大类间方差法和遗传算法相结合，对冻结岩石CT图像进行双阈值分割，实现了冻结岩石CT图像的三值化分割技术；运用Canny算子对冻结岩石CT图像进行边缘检测，获得了冻结岩石细观结构的二值图像。冻结岩石CT图像的伪彩色增强能够提高CT图像的分辨率，减少视觉上的判断误差，根据伪彩色增强图像颜色的变化、CT数直方图可定量分析冻结过程中岩石细观结构、水冰含量以及损伤分布随温度的变化情况。冻结岩石CT图像的三值化分割技术，将冻结岩石内部的水、冰、岩石三相介质区分开，明确地给出了水、冰、岩石空间位置及含量的数字表述。
（3）将体视学原理引入到冻结岩石细观结构特性研究中，结合冻结岩石CT图像，分析了冻结岩石细观结构的构成及其相互关系，给出了冻结岩石细观结构参数计算公式。对冻结过程中岩石内部裂隙、孔隙的长度、周长、面积、宽度、圆形度等细观结构参数及水冰含量进行定量计算。细观结构参数能够显示冻结过程中损伤大小及形态的变化情况。冻结岩石内部水和冰含量定量计算结果表明：岩石内部水、冰含量随温度的变化而改变，两者处于动态平衡状态中。
引入未冻水含量作为内变量，从与内变量功共轭的相变潜热出发，利用连续介质热力学理论推导出冻结岩石中未冻水、冰含量与冻结温度关系的理论公式。所给出的公式能描述冻结过程中岩石内部未冻水和冰含量的变化情况，同时可预测给定含水量的冻结岩石的纯冰点。
（4）根据冻结岩石的细观结构组构及特性，从岩石细观力学机理出发，用混合律方法将含孔隙的冻结岩石视为各向同性介质，将含裂隙的冻结岩石视为横观各向同性介质，推导出不同冻结温度下的等效弹性模量计算公式。
针对冻结作用对岩石力学性能的影响，提出“冻结负损伤”的概念，用冻结损伤、荷载损伤描述冻结和荷载两种不同作用下岩石损伤过程，拓展损伤变量内涵。基于连续介质热力学方法，以岩石的初始损伤状态为基准状态，应用推广后的应变等价原理及损伤力学理论，建立荷载作用下冻结岩石的宏—细观损伤本构模型。对模型进行了验证，理论曲线与实验曲线比较接近，所建立的模型能够描述荷载作用下冻结岩石损伤演化规律。
（5）提出了冻结岩石数字图像数值分析方法（DIP-FEM），建立不同低温环境、不同荷载作用下岩石破坏过程的有限元数值计算格式。通过CT图像的三维重建技术，获得冻结岩石真实细观结构数字化模型，对其进行矢量化转化，并导入至有限元软件ANSYS中，进行冻结过程中温度场及冰膨胀力分布规律的数值模拟试验研究，分析含裂隙或孔隙岩石在低温环境下的损伤特性，该方法弥补了低温冻结岩石物理实验的不足，为实现冻结岩石的破坏过程研究从细观尺度向宏观尺度过渡提供新的研究途径。
Frozen rock problems exist in many projects in different degree, including the rockengineering in cold regions, the reservoir pool at low temperature of liquefied natural gas andthe construction using frozen methods in mine building projects, etc. The research on frozenrock problems has extensive engineering background and practical significance. The damageon frozen rock at low temperature has a significant effect on the security and stability of therock engineering in cold region. Aiming at the engineering demands for practical problemsoccurred in frozen rock engineering, based on the computed tomography (CT) scanningexperiment of frozen rock at different minus temperature, and guided by the theories ofDamage Mechanics, Continuous Media of Thermodynamics, Meso-mechanics, Stereology,Ice mechanics, and taking the meso-structure of frozen rock as cut-in point, meso-structureand mechanical characteristics of frozen rock were investigated by the method combiningwith CT image processing technology and damage theoretical analysis and mesoscopicnumerical calculation. The following conclusions have been gotten:
(1) CT scanning images of red and gray sandstones at different low temperature areobtained by carrying out the CT scanning experiment at room temperature20℃,0℃,-5℃,-10℃,-20℃and-30℃. CT scanning images can well show the change of themeso-structure and damage of the frozen rock, and the composition distribution whichincludes water, ice and mineral particles during process of freezing. Under low temperature,the new internal rock pore and crack are generated also accompany with the phenomenon ofcrack propagation and coalescence. Rock damage increases with the temperature dropping.When the temperature drops to-20℃, the rock meso-structure keep stable and almost changeno more.
(2) Applying digital image processing theory to CT image, pseudo-color enhancement technique of CT image of frozen rock has been implemented. Histogram of frozen rock basedon CT value has been obtained. The double thresholds segmentation that based on geneticalgorithm is realized and the three-valued segmentation of frozen rock CT images iscompleted. By Canny operator's edge detection, the binary images of frozen rockmeso-structure are gotten. Using CT image processing technology can improve the resolutionof frozen rock CT images, and reduce the error of visual judgment. According with thechanges of colors in pseudo-color enhancement image of frozen rock CT images andhistogram of frozen rock based on CT value, meso-structure, unfrozen water, ice, and damagedistribution can be analyzed quantitatively dependent on temperature during freezing process.he three-valued segmentation of frozen rock CT images is employed to distinguish water andice from rock in the internal of frozen rock. Digital expression of spatial location and thecontent of water, ice and rock are given definitely by the three-valued segmentation.
(3) The stereology theory is introduced to the study of the characteristics of freeze rockmeso-structure. Combined with the CT images of frozen rock, the meso-structure compositionand their mutual relations are analyzed and the parameter calculation formulations ofmeso-structure of frozen rock are put forward. The meso-structure parameters are calculatedquantitatively, such as length, perimeter, area, width and circularity of pore and crack. Thecalculation results of unfrozen water and ice content shows that unfrozen water and icecontent in rock interior varied with the changes of temperature, and both are in a state ofdynamic balance.
In frozen rock, the unfrozen water content is considered as an internal variable and thework conjugated with the internal variable is the latent heat of phase change of unfrozen rock.The continuum thermodynamic theory is employed to deduce the formula of the relationshipbetween the unfrozen water and ice content depends on temperature. The experimental resultsof CT scanning agree well with the result predicted by deduced formula. The changes ofunfrozen water and ice content in the process of freezing can be described by deducedformula, and the pure frozen point of frozen rock can be predicted.
(4) Based on composition and characteristics of mesoscopic structure of frozen rock,from the idea of the rock mesoscopic mechanics, using mixed law methods to consider frozenrock with pore as isotropic medium, and frozen rock with crack as the transversely isotropicmedium, calculation formulas of equivalent elastic modulus of frozen rock under differentfrozen temperature were deduced.
In view of the influence of frozen action on the properties of rock mechanics, the conceptof frozen negative damage was put forward. Damage variable was proposed with more new meaning to frozen and loaded rock, three new conceptions were put forward, which werefrozen damage, loaded damage and total damage. Proposed damage variable can describedifferent damage process of rock under the two different actions,one is low temperaturefrozen and another is load.Based on the continuum thermodynamics method, and takeing theinitial damage state as reference state, macro-mesoscopic damaged constitutive model offrozen rock was build under the load action according to the generalized principle of strainequality and theory of damage mechanics.
(5) The CT image of frozen rock can be extended to be applicable to research frozenrock damage. The new method (DIP-FEM), Digital Image Processing—Finite ElementMethod was put forward. By the proposed method, the finite numerical analysis fomat of rockdamage process has been established under different low temperature environment and loadaction. The real mesoscopic structure digital model of frozen rock is obtained bythree-dimesion reconstruction technology of CT image. Vectorization algorithm ofmesoscopic structure digital model of frozen rock is presented, which can convert imageformat to graphics format. Then real meso-structure of frozen rock is imported into finiteelement software ANSYS to analysis damage characteristics of rock with pore or crack in lowtemperature environment. The proposed method can make up for the deficiencies of lowtemperature frozen rock physical experiment, and provide a new research avenues to realizedamage process research of frozen rock from the meso-scale to macro-scale.
引文
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