CN104849276A - Granite three-dimensional microstructure re-building method based on pixel statistics - Google Patents

Abstract

The invention provides a granite three-dimensional microstructure re-building method based on pixel statistics. The method comprises the following steps that the geometrical information of various minerals (quartz, feldspars and mica) in a granite surface image is counted; a digital rock sample with a two-dimensional or three-dimensional microstructure is constructed by utilizing a specific mineral growth mode and the growth probability distribution principle. For the three-dimensional condition, the mineral growth modes include three modes of the point, the line and the surface, and each growth mode has different growth positions. Proper probabilities are distributed for different growth positions. In order to reflect the mutual influence of same or different kinds of mineral group growth processes, two principles including an embezzlement forbidding principle and an embezzlement allowing principle are set. When the embezzlement forbidding principle is used, the merging of the same kind of mineral groups can be avoided, and the iteration convergence can be ensured. The method provided by the invention obtains the granite surface image, and is totally realized through computer programming. Compared with a CT (computed tomography) method or a machining method, the granite three-dimensional microstructure re-building method has the advantages of high precision, high efficiency, low manufacturing cost and wide application range.

Description

A 3D Mesostructure Reconstruction Method of Granite Based on Pixel Statistics

technical field

The invention relates to the field of three-dimensional internal structure reconstruction, in particular, the invention relates to a method for reconstructing the three-dimensional mesoscopic structure of granite based on pixel statistics.

Background technique

Natural rock is composed of minerals, pores, fluids, cements and other media arranged according to certain rules in space. Granite is an igneous rock whose minerals mainly include feldspar, quartz and mica. Although it can be regarded as approximately uniform rock material on the macroscopic scale, it also has material heterogeneity and even anisotropy on the mesoscopic scale (0.1-10.0mm). The inhomogeneity of rock on the mesoscopic scale has an important impact on the macroscopic mechanical behavior of rock (stress, strain distribution and fracture propagation path, etc.).

For quite a long time in the past, due to limited technical conditions and research level, rock materials were often regarded as a homogeneous material, which brought about the difficulty of determining the basic mechanical parameters of rocks, and a large number of more and more researches emerged. Increasingly complex constitutive models. Some complex constitutive models contain a large number of parameters, and the physical meaning of some parameters and how to measure them are difficult to explain clearly, so it is not easy to apply. The root of the above problems lies in the neglect of rock mesostructure. Since the late 1990s, the importance of rock mesostructure has been gradually recognized. In some numerical models, by considering the heterogeneity of element strength parameters, more studies have been carried out on the influence of rock mesostructure on its macroscopic response. Research (Chen Sha, Yue Zhongqi, Tan Guohuan. Three-dimensional numerical analysis method of geotechnical engineering materials based on real mesostructure. Journal of Rock Mechanics and Engineering, 2006, 25(10): 1951-1959; Yu Qinglei, Yang Tianhong, Zheng Chao, etc. . Numerical analysis of the influence of rock mesostructure on its deformation evolution. Rock and Soil Mechanics, 2011, 32(11): 3468-3472). However, the mesoscopic structure in these models is virtual, unlike the mesoscopic structure of any rock material, and does not take into account the spatial distribution of various mineral components in rocks. The extent to which this virtual mesostructure truly reflects rock heterogeneity is unclear. No matter what material is analyzed, it is difficult to convincing people to use a similar virtual microstructure. Some people even think that it is difficult to obtain the real mechanical properties of materials based on the analysis based on the virtual mesoscopic structure, and the real mesoscopic structure must be considered in the analysis in order to obtain targeted and correct results (Yue Zhongqi. Geotechnical Mesoscopic The method, application and progress of digital representation of medium spatial distribution and related mechanical numerical analysis. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(5): 875-888).

Introducing the real mesostructure of rock materials into numerical models begins with the introduction of digital image technology into rock mechanics. In the rock surface images taken, different mineral components can be distinguished due to the difference in color, by establishing the relationship between the smallest unit (pixel) in the image and the unit in the numerical model, and further establishing the grayscale of the pixel and the mechanics of the unit The correlation between parameters makes it possible to consider the real mesostructure of rocks in numerical models. However, since the captured images are all two-dimensional, mechanical analysis can only be performed on two-dimensional digital rock samples, which cannot meet the needs of three-dimensional research.

In order to obtain the three-dimensional mesoscopic structure of rocks, there are two commonly used methods (Wang Yuanyin, Ma Shaopeng, Ma Qinwei, etc. Small slice type three-dimensional structure reconstruction system. Chinese invention patent, publication number: CN 102175175 A, publication date: 2011.09. 07): 1) CT scan method; 2) Machining method. The CT scanning method obtains the three-dimensional internal structure of the entire specimen by scanning the specimen layer by layer with X-rays. However, CT scanning equipment costs a lot, occupies a large area, requires professionals to operate and maintain, and cannot detect components with the same X-ray absorption rate but different colors or structures. In addition, the spatial resolution of images obtained by conventional CT equipment is low , it is difficult to perform fine detection of complex structures. The machining method obtains images on multiple layers of the specimen by grinding or cutting the specimen layer by layer, and taking pictures layer by layer, and then splicing them into the three-dimensional internal structure of the specimen. The advantages of this method are mainly reflected in the accuracy and resolution of 3D reconstruction, and also have certain advantages in terms of equipment miniaturization and cost reduction. However, the disadvantages of this method are mainly reflected in: 1) damage to the specimen, after obtaining the three-dimensional mesoscopic structure of the specimen, the specimen disappears, and the mechanical behavior of the specimen on the testing machine cannot be compared with the numerical results of the specimen, that is, given It is inconvenient to examine the correctness of the numerical results of the specimen, and it is not suitable for the situation where the specimen is not allowed to be damaged or the specimen is not allowed to be made; 2) The operation of the equipment is complicated, the process of obtaining the mesoscopic structure is time-consuming and laborious, the slight vibration of the mechanical system, and the light conditions Minor changes will affect the accuracy of 3D reconstruction. For example, if the thickness of one grinding or cutting is 1mm, if you want to remove the specimen thickness of 10cm, you need to process 100 times. May cause some mineral particles to fall off prematurely. More importantly, it is necessary to keep the distance between the lens and the surface of the specimen constant every time the camera is used to take pictures. In fact, this is difficult to achieve, because it is difficult to control the camera to move forward by 1mm each time. In addition, there can only be one pixel in the thickness direction of 1 mm instead of multiple pixels, which will affect the accuracy of 3D reconstruction. If the thickness of one grinding is reduced, it will not be conducive to the efficiency of 3D reconstruction.

Contents of the invention

In order to solve the problems of low precision, low efficiency, high price and damaged samples in the existing three-dimensional microstructure reconstruction method of granite, the present invention provides a three-dimensional microstructure reconstruction method of granite based on pixel statistics. Digital image technology obtains images of the granite surface and counts the distribution of various mineral components. Based on this, the three-dimensional mesoscopic structure of granite is realized, which greatly improves the accuracy and efficiency of the reconstruction of the mesoscopic structure, and significantly reduces the cost.

In order to solve the above problems, the present invention provides a method for reconstructing the three-dimensional mesostructure of granite based on pixel statistics (Figure 1), which is characterized in that it includes: using digital image technology to distinguish different minerals in the image of the surface of the granite , to obtain the statistical laws of various mineral components; according to the above statistical laws, use the specified mineral growth mode and growth probability distribution principles to construct digital rock specimens with two-dimensional or three-dimensional mesoscopic structures.

Further, wherein, the digital image technology is used to distinguish different minerals in the image of the granite surface taken, and the statistical law of obtaining various mineral components is further as follows:

Firstly, use the shooting equipment to obtain images of the granite surface; then, use the edge detection and segmentation algorithms in digital image technology to distinguish various mineral components; finally, make statistics on the geometric information of various mineral components to obtain the Area percentage, maximum radius and equivalent (equivalent) radius information for any mineral cluster. in:

The various mineral components are mica, quartz and feldspar (Fig. 2).

The mineral group is an isolated irregular aggregate composed of pixels belonging to the same substance, and the pixels forming the aggregate are connected to each other. There are two types of connection: line connection and point connection. Line connection means that two pixels share a line segment (Figure 3-b), and point connection means that two pixels share a point (Figure 3-a).

The area percentage of the mineral is the ratio of the sum of the number of each pixel in a certain mineral in an image to the overall pixel in the image.

The maximum radius of the mineral group is the distance from the center of the pixel farthest from the center of the mineral group in a certain mineral group to the center. Wherein, the mineral group center is obtained by the coordinates of each pixel in the mineral group, which specifically includes: treating any pixel as a square, obtaining the coordinates and area of the center point of any square, and using the geometric center formula of a plane figure to obtain The coordinates of the center of the complex geometric shape composed of squares are the geometric center coordinates of the mineral group.

The equivalent radius of any mineral group is the square root of the ratio of the sum of the areas of each pixel in the mineral group to π.

Further, wherein, according to the above statistical laws, constructing digital rock specimens with two-dimensional or three-dimensional mesoscopic structures by using the specified mineral growth mode and growth probability distribution principle is further as follows: first, according to research needs and computer computing power, set Determine the size of the granite specimen to be reconstructed, and estimate the maximum number of pixels that can be accommodated in the specimen to be reconstructed; after that, divide the specimen to be reconstructed into several square or cubic cells (Figure 4), one cell and one pixel or voxels (three-dimensional pixels); after that, one of the three minerals is used as the background without reconstruction, and the other two minerals are selected for reconstruction, and several cells are randomly selected among all cells as the first 1. Seeds of two kinds of minerals to be reconstructed (Figure 5); after that, given the statistical laws to be followed when the two minerals are reconstructed and the end conditions of the reconstruction, according to the specified growth law, make the two minerals near the seeds Grow until the reconstruction is over; finally, review the reconstruction results, if the current statistical results of one or two reconstructed mineral clusters are significantly different from the set statistical laws, make appropriate adjustments to the current statistical results. fix. Wherein: the square cell is suitable for two-dimensional microstructure reconstruction, and the cube cell is suitable for three-dimensional.

The end conditions of the reconstruction include two kinds: the conditions for stopping the growth of a single mineral group and the conditions for ending the reconstruction of the whole specimen. The conditions for stopping the growth of a single mineral group include: the maximum radius or equivalent radius of the mineral group has exceeded the allowable range; the end conditions for the overall reconstruction of the specimen include: the maximum number of iterations allowed is reached, the maximum number of iterations allowed is not reached but the iteration result Already stabilized, the area percentages of the two mineral clusters have exceeded the allowable range.

The growth law includes the growth method and the distribution principle of growth probability. For the two-dimensional case, there are two types of growth methods: point growth and line growth (Figure 6); for the three-dimensional case, there are three types of growth methods: point growth, line growth and surface growth. (Figure 7). Point growth means that the cell as the mother and the growing cell share a point; line growth means that the cell as the mother and the growing cell share a line segment; surface growth means that the cell as the mother and the growing cell The cells of share a face. The principle of growth probability distribution refers to how to carry out probability distribution among various growth modes. The probability distribution among point growth, line growth, and surface growth can be the same or different. In the same growth mode, it can be further divided into different types. Growth direction, they equally share the probability of the growth mode. A simple and efficient approach can be taken to obtain the number of independent potential growth orientations around the parent body (Figure 8), among which the growth probabilities are evenly distributed.

The growth of the two minerals near the seeds is a process of nibbling the background or other minerals, following two principles: the principle of prohibiting encroachment and the principle of allowing encroachment. The principle of prohibiting encroachment means that only the background cells around a parent have the opportunity to become minerals (Figure 9-a, Figure 9-c); the principle of allowing encroachment means that any cell around a parent has the opportunity to become Minerals (Fig. 9-a, Fig. 9-b). If the principle of prohibiting encroachment is not further restricted, adjacent mineral groups of the same type may be connected (Fig. 10-a, Fig. 10-b), so that the size of the mineral group will change suddenly, which is not conducive to the statistics of the reconstruction results. It is also possible that the growth of the mineral clusters stops due to the size of the mineral clusters exceeding the set range. Therefore, it is necessary to further restrict the background cells around the parent body, and the background cells can become minerals without the same kind of minerals besides the parent body (Fig. 10-a, Fig. 10-c).

The checking of the reconstruction results refers to comparing the geometric information of the two minerals in the reconstructed digital granite specimen with the set reconstruction range. If the refactoring results are in good agreement with the refactoring requirements, it means that the refactoring is successful. If the refactoring results are not in good agreement, one or two refactoring results need to be corrected. When correcting, enable the principle of allowing encroachment, or change the probability distribution of different growth methods.

A method for reconstructing the three-dimensional mesoscopic structure of granite based on pixel statistics described in the present invention can realize the reconstruction of the mesoscopic structure of granite, except for obtaining images of the surface of the granite, all of which are realized by computer programming, with high precision and high efficiency , low cost, wide applicability, not limited to the laboratory, even do not need to make granite samples, only need to have a smooth granite surface for shooting images, especially suitable for working granite components or granite historical relics microstructural reconstruction.

Description of drawings

Fig. 1 is a flow chart of a method for reconstructing the three-dimensional mesoscopic structure of granite based on pixel statistics according to the present invention.

Figure 2 is the distribution map of three minerals in the granite surface image (1 is mica; 2 is quartz; 3 is feldspar).

Fig. 3 is a schematic diagram of two connection methods of pixels, Fig. 3-a is a diagram of a point connection method; Fig. 3-b is a diagram of a line connection method. 4 is a pixel; 5 is a pixel of a certain mineral; 6 is a common point of the same mineral; 7 is a common edge of the same mineral.

Fig. 4 is a schematic diagram of a sample divided into cells and cell numbers, Fig. 4-a is a three-dimensional sample; Fig. 4-b is a two-dimensional sample.

Fig. 5 is a schematic diagram of the seed distribution of two reconstructed minerals (taking two dimensions as an example).

Figure 6 is a schematic diagram of each growth orientation of two-dimensional cells, Figure 6-a is the four growth orientations of point growth; Figure 6-b is the four growth orientations of line growth, 8 is the two-dimensional growth orientation; 9 is the two-dimensional growth orientation matrix.

Figure 7 is a schematic diagram of each growth orientation of a three-dimensional cell, Figure 7-a is 8 growth orientations of point growth; Figure 7-b is 12 growth orientations of line growth; Figure 7-c is 6 growth orientations of plane growth , 10 is the three-dimensional growth orientation; 11 is the three-dimensional matrix.

FIG. 8 is a schematic diagram of a potential growth orientation of a parent body or a mineral group (taking two dimensions as an example), and FIG. 12 is a two-dimensional potential growth orientation.

Figure 9 is a schematic diagram of the application effect of the principle of allowing encroachment and the principle of prohibiting encroachment (take two-dimensional as an example), Figure 9-a is the current form of the mineral cluster; Figure 9-b is a possible effect after the principle of allowing encroachment is applied; Fig. 9-c is a possible effect of the application of the principle of non-appropriation.

Figure 10 is a schematic diagram of the disadvantages and improvement effects of the principle of prohibiting encroachment (taking two-dimensional as an example). Figure 10-a shows the current form of mineral groups; The effect of the further restriction of background cells on the potential growth orientation.

Fig. 11 is the mesoscopic structure of the three-dimensional granite specimen obtained by the method of the present invention, Fig. 11-a is the mesoscopic structure of the surface of the specimen; Fig. 11-b and Fig. 11-c are the mesoscopic structures of some sections of the specimen.

Detailed ways

The technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings.

A method for reconstructing the three-dimensional mesoscopic structure of granite based on pixel statistics (Fig. 1) according to the present invention comprises steps:

Step 1, using digital image technology to distinguish different minerals in the acquired granite surface image, and obtain the statistical laws of various mineral components;

The implementation of this step is as follows: First, use the shooting equipment to obtain the image of the granite surface. Before taking the image, a layer of water or oil can be applied on the granite surface to make the mineral color on the granite surface bright and easy to distinguish, which is beneficial to subsequent statistical work; then, use the edge detection and segmentation algorithms in digital image technology to scientifically distinguish various mineral components; finally, perform statistics on the geometric information of various mineral components to obtain the area percentage of various minerals, any mineral The maximum radius and the equivalent (equivalent) radius of the blob.

The various minerals include mica, quartz and feldspar. The colors of the three minerals are different. Usually, mica is black, quartz is gray, and feldspar is white, and the gray values of the three are from small to large (Figure 2).

The mineral group is an isolated irregular aggregate composed of pixels belonging to the same mineral, and its shapes are different. In a mineral cluster, the pixels should be connected to each other. On the image, there are two connection methods (Figure 3-a and Figure 3-b): line connection and point connection, line connection means that two pixels share a line segment (Figure 3-b), and point connection means two Pixels share a single point (Fig. 3-a). For a pixel, in general, there are 4 situations for its line connection and point connection respectively. For line connection, there are four specific situations of up, down, left, and right; for point connection, there are four specific situations of upper left, upper right, lower left, and lower right. Certain cases are not covered if a pixel lies on the border of the image. The edge detection and segmentation algorithm can be realized by Matlab software.

The maximum radius of any mineral group describes the largest scale of the mineral group, which should be determined by the distance from the pixel farthest from the center of the mineral group to the center of the mineral group, and the center of the mineral group is determined by the geometric center of the plane figure The formula is obtained. Any pixel can be regarded as a square, so an irregularly shaped aggregate composed of several pixels can be regarded as a plane figure composed of several squares. The area of any square and the coordinates of its central point are easy to determine, so that the geometric center of the plane figure can be determined, and this center is the geometric center of the mineral mass.

The equivalent radius of any mineral group is the square root of the ratio of the sum of the areas of all pixels in the mineral group to π. That is to say, the irregularly shaped mineral group is assumed to be a circle with an equivalent area, and the radius of the circle is the equivalent radius. The ratio of the equivalent radius to the maximum radius describes the shape of the mineral cluster. If the ratio is close to 1, it means that the shape of the mineral cluster is relatively round. If the shape of the mineral cluster is elliptical, the ratio will be less than 1.

The area percentage of a certain mineral is the percentage of the number of all pixels of the mineral in an image to the number of all pixels in the image. The higher the percentage, the greater the proportion of the mineral in the granite. When reconstructing the three-dimensional mesoscopic structure of granite based on two-dimensional statistical results, it is very effective if the area percentage can be extended to the volume percentage. However, this relationship is not easy to obtain and there is no conclusion. Two-dimensional porosity and three-dimensional porosity are quite different, and there is no unified expression. For this reason, the present invention randomly checks the area percentage of each layer by performing three mutually perpendicular slices on the core of the three-dimensional digital granite sample.

Step 2, according to the above statistical laws, use the specified mineral growth mode and growth probability distribution principle to construct a digital rock specimen with a two-dimensional or three-dimensional mesoscopic structure;

The implementation of this step is as follows: First, according to the research needs and computer computing power, set the size of the granite specimen to be reconstructed, and estimate the maximum number of pixels that can be accommodated in the specimen according to the conversion relationship between pixels and length measurement units ; After that, divide the specimen to be reconstructed into several square (two-dimensional reconstruction) or cube (three-dimensional reconstruction) cells of equal size and number them (Figure 4-a and Figure 4-b), one cell and one pixel or voxels (three-dimensional pixels); after that, one of the three minerals is used as the background cell without reconstruction. For example, the feldspar with the most content can be selected as the background cell, and only mica and quartz The two minerals are reconstructed, and a number of non-repeating random numbers are randomly selected between 1 and the total number of cells as the initial positions (seeds) of mica and quartz minerals (Figure 5); after that, according to the actual statistical results, set Statistical laws to be followed when each mineral is reconstructed and the conditions for the end of reconstruction, specify the growth mode and growth probability distribution principle of the two minerals, so that they grow near the seeds until the reconstruction is completed; finally, the reconstruction results are analyzed Review, if there is a large difference between the statistical results of the current digital rock specimens and the set statistical rules, the current statistical results need to be properly corrected until they are satisfied.

The simple steps for determining the conversion relationship between the pixel and the length measurement unit are as follows: before taking pictures of the granite surface, place or fix a steel ruler on the granite surface, and on the acquired image, determine that there are How many pixels, in this way, how many centimeters one pixel is equivalent to can be determined.

The computing power of the computer depends on the performance of hardware and software. On a microcomputer with common configuration, the reconstruction of a granite specimen with millions of cells can be realized. However, it is generally difficult to simulate the deformation and destruction process of such specimens on computers with common configurations. Considering that the computer with ordinary configuration can only simulate the mechanical process of the calculation model with no more than 400,000 units, the size of the specimen to be reconstructed should not be too large. If you want to reconstruct a cube containing about 400,000 units Granite specimens have about 74 units in three mutually perpendicular directions. According to the literature (Wang Xuebin, Du Yazhi, Pan Yishan. 2012. The strain distribution and Experimental study on strain gradient [J]. Acta Geotechnical Engineering, 34(11): 2050-2057), 1 pixel corresponds to about 0.11mm, so the side length of the cubic granite specimen is about 8.14mm. Such specimens are too small for practical application. Therefore, we can choose to reconstruct the mesoscopic structure of granite on a computer with ordinary configuration, and simulate the mechanical process of specimens with equivalent directions in three directions on a server with high configuration.

The random selection of several non-repeating random numbers between 1 and the total amount of cells can be realized by Matlab software. If the selected random numbers are allowed to repeat, it will cause the previous seeds to be covered by the latter seeds.

The position of the seed is the initial position of mineral growth. When a new background cell changes into mica or quartz, both the seed and the newly generated mineral will be used as the parent body, and the new mineral will be produced near the parent body. As the size of minerals increases, the chance of growing minerals from seeds decreases.

The end condition of the reconstruction includes two kinds: the condition that a single mineral group stops growing and the condition that the overall reconstruction of the specimen ends. After a single mineral grows to a certain extent, once its growth stop condition is met, it will no longer grow. After all the mineral clusters grow to a certain extent, once the respective stop conditions are met, the overall reconstruction conditions of the specimen will inevitably be achieved. Even if some minerals have not grown to maturity, the conditions for the end of the overall reconstruction of the specimen may be achieved.

The conditions for the completion of the overall reconstruction of the specimen specifically include: 1) the maximum number of iterations allowed is reached, and one calculation cycle is one iteration; 2) the result of the iteration has reached stability, although the maximum number of iterations allowed has not yet been reached The results of this iteration no longer cause the background cells to transform into mica or quartz; 3) The area percentages of mica and quartz minerals have exceeded the allowable range on many different levels. As long as any one of the above three conditions is met, the overall reconstruction of the specimen will be completed.

The conditions for the unit mineral group to stop growing specifically include: 1) the maximum radius of the mineral group has exceeded the allowable range; 2) the equivalent radius of the mineral group has exceeded the allowable range. In order to improve the reconstruction efficiency and avoid the impact on the reconstruction results caused by the difference in the growth order of mineral clusters, no sub-iterations are set during the growth of a single mineral cluster. One overall iteration corresponds to one growth of all mineral clusters. During one overall iteration, some mineral clusters will get a substantial increase (the size of the mineral clusters increases), while the size of some mineral clusters may not change (affected by cannot grow due to the restriction of other mineral clusters). 

The growth mode and growth probability distribution principle of the minerals directly determine the morphology and reconstruction efficiency of each mineral group. For the two-dimensional case, there are two types of mineral cluster growth: point growth and line growth; for the three-dimensional case, there are three types of mineral growth: point growth, line growth and surface growth. Point growth means that the growing cell and the grown mineral share a point. For the two-dimensional case, a cell as the parent can grow new minerals in up to four orientations (upper left, lower left, upper right, and lower right) (Fig. 6-a); for the three-dimensional case, a cell as the parent New minerals can be grown in up to 8 orientations (front up left, front up right, back up left, back up right, front down left, front down right, back down left, back down right) (Figure 7-a ). Line growth means that the cell as the parent and the grown mineral share a line segment. For the two-dimensional case, a cell as a parent can grow new minerals in up to four directions (up, down, left, and right) (Fig. 6-b); for a three-dimensional case, a cell as a parent can at most New minerals can be grown in 12 orientations (Fig. 7-b), because 1 space cell has 12 edges. Plane growth is a unique growth mode in the three-dimensional situation. A cell as a parent can grow new minerals in up to 6 directions (Fig. 7-c). This is because a space cell has 6 faces.

For the two-dimensional case, there are at most 8 growth directions; for the three-dimensional case, there are at most 26 directions. If a parent cell is on the surface of a granite specimen, some growth orientations will be outside the specimen, so there are not so many effective growth orientations. In addition, some growth orientations will be occupied by the mother body, or occupied by other adjacent mother bodies, so the effective growth direction will be reduced, especially when the mother body develops to a certain extent or the mother body is surrounded by other mother bodies.

The growth probability distribution principles include uniform distribution and non-uniform distribution principles. A simple and efficient method is (Figure 8): the potential growth orientations of all the cells as the mother can be collected together, the overlapping orientations can be eliminated, and only the number of independent potential growth orientations can be obtained, and each potential growth orientation can be analyzed. Numbering, and then between 1 and the number of potential growth orientations, random numbers are drawn according to the principle of uniform distribution. In one iteration, only the numbered positions corresponding to the random numbers are allowed to grow minerals. In order to construct various granite mesostructures, different growth probabilities can be assigned to different growth modes. For example, for the two-dimensional case, the probability of point growth is specified as 1/4, and the probability of line growth is specified as 3/4. Assume that point growth and line growth each have 4 growth orientations. In this way, the 4 orientations of point growth The growth probability of any of the 4 orientations is 1/16, and the growth probability of any of the 4 directions of line growth is 3/16. Therefore, the parent body tends to grow in line growth, which will significantly change the shape of the mineral cluster. Similarly, the growth probability can be increased in one or some growth orientations, so that the growth of mineral clusters will have a dominant direction.

The growth process of the mineral near the seed is not an isolated process, and will inevitably be affected by other mineral groups, which can be the same mineral group or different mineral groups. The growth process of a certain mineral is essentially a process of encroaching, encroaching or replacing the background cell (or matrix) or other minerals. In the early stage of mineral growth, the mutual influence between mineral groups is usually small. However, when the mineral clusters grow to a certain size, the same or different mineral clusters will be close or in contact, which will cause some potential growth orientations of the parent cells to be occupied. At this time, the growth mode of the mineral needs to be further restricted, and there are two corresponding principles to choose from. One is the principle of prohibiting embezzlement, and the other is the principle of allowing embezzlement. The principle of no encroachment means that only the background cells around a parent body can have a chance to become minerals, that is to say, a background cell can only have one chance to become minerals. The principle of allowing encroachment means that any cell around a parent body has the opportunity to become a mineral, that is, the mineral properties of a cell that has become a mineral can be changed again.

The use of the principle of allowing encroachment will make the interface of heterogeneous mineral clusters constantly adjusted during the iterative process (Fig. It will cause a certain mineral group to be divided into several parts or partly disappear, and may also lead to the merger of the same kind of mineral group. The occurrence of the above phenomena is not conducive to the statistics of reconstruction results, the preservation of good reconstruction results, and the convergence of the iterative process. In contrast, the use of the principle of non-appropriation generally works better (Figure 9-a and Figure 9-c).

If the principle of prohibiting encroachment is not further restricted, adjacent mineral groups of the same type may be connected (Fig. 10-a and Fig. 10-b), so that the size of the mineral group will change suddenly, which is not conducive to the reconstruction results. Statistically, it is also possible that the growth of the mineral clusters stops due to the size of the mineral clusters exceeding the set range. Therefore, it is necessary to further restrict the background cells around the parent body, and the background cells can become minerals without the same kind of minerals besides the parent body (Fig. 10-a and Fig. 10-c).

It is necessary to check the reconstruction results by spot-checking the area percentages of the two reconstructed minerals in different layers. This is because there are mutual influences in the mineral growth process, which makes it difficult for some minerals to grow, and some minerals grow too much, or the number of iterations has been used up but has not yet reached convergence. Therefore, it is necessary to compare the geometric information of the two reconstructed minerals with the preset reconstruction range. If the reconstruction results are in good agreement with the reconstruction requirements, it means that the reconstruction is successful. fix. If the coincidence is not good, one or two reconstruction results need to be corrected, and usually the correction to one reconstruction result will naturally lead to the change of the other reconstruction result. Compared with the complete reconstruction of the mesoscopic structure of the specimen, it is undoubtedly more efficient and simple to correct the reconstruction results. The specific methods include: 1) changing the probability distribution scheme between different growth modes; Randomly arrange some mineral seeds at some positions, for example, at the background cell; 3) Enable the principle of allowing invasion; 4) Randomly remove some mineral clusters of a certain mineral, and turn them into background cells or another mineral cluster (Without causing the same kind of mineral groups to merge).

The mesoscopic structure of the three-dimensional granite specimen obtained by the method of the present invention is shown in Fig. 11-a, Fig. 11-b, and Fig. 11-c.

Claims (5)

1. A method for reconstructing the three-dimensional mesoscopic structure of granite based on pixel statistics, comprising: utilizing digital image technology to distinguish different minerals in the image of the surface of the granite taken, and obtaining statistical laws of various mineral components; The above statistical laws use the specified mineral growth mode and growth probability distribution principles to construct digital rock specimens with two-dimensional or three-dimensional mesoscopic structures. 2. the method for reconstructing the three-dimensional mesostructure of granite based on pixel statistics according to claim 1, characterized in that, said utilize digital image technology to distinguish different minerals in the image of the granite surface taken, and obtain 3 kinds of mineral components The statistical law of the method is further as follows: firstly, the image of the granite surface is obtained by using the shooting equipment; then, the edge detection and segmentation algorithms in digital image technology are used to distinguish various mineral components; finally, the geometric information of various mineral components is counted , to obtain the area percentage of the three minerals, the maximum radius and equivalent (equivalent) radius information of any mineral group. 3. the method for reconstructing the three-dimensional mesostructure of granite based on pixel statistics according to claim 2, wherein the three mineral components are mica, quartz and feldspar; the mineral clusters belong to the same mineral An isolated irregular aggregate composed of pixels. The pixels that make up the aggregate are connected to each other. There are two connection methods: line connection and point connection. Line connection means that two pixels in a mineral group share a line segment. Point connection is Refers to two pixels in a mineral group sharing one point; the area percentage of the mineral is the ratio of the sum of the number of pixels in a certain mineral in an image to the overall pixel in the image; the maximum radius of the mineral group is a certain The distance from the center of the pixel farthest from the center of the mineral group in the mineral group to the center; wherein, the center of the mineral group is obtained from the coordinates of each pixel in the mineral group, specifically including: treating any pixel as a square, Obtain the coordinates and area of the center point of any square, and use the formula of the geometric center of the plane figure to obtain the coordinates of the center of the complex geometric shape composed of multiple squares, which is the geometric center coordinates of the mineral group; the equivalent radius of any mineral group Take the square root of the ratio of the sum of the area of each pixel in the mineral cluster to π. 4. The method for reconstructing the three-dimensional mesoscopic structure of granite based on pixel statistics according to claim 1, characterized in that, according to the above-mentioned statistical laws, using the specified mineral growth mode and growth probability distribution principle to construct a two-dimensional or three-dimensional The digital rock specimen with mesoscopic structure is further as follows: First, according to the research needs and computer computing power, set the size of the granite specimen to be reconstructed, and estimate the maximum number of pixels that can be accommodated in the specimen to be reconstructed; The structural specimen is divided into several square or cubic cells, and one cell corresponds to one pixel or voxel (three-dimensional pixel); after that, one of the three minerals is used as the background, and the other two minerals are selected for reconstruction. Among all the cells, several cells are randomly selected as the seeds of the first and second minerals to be reconstructed; after that, given the statistical laws to be followed when the two minerals are reconstructed and the end conditions of the reconstruction, according to the specified growth law , make the two minerals grow near the seeds until the reconstruction is completed; finally, review the reconstruction results, if the current statistical results of one or two reconstructed mineral clusters have a large discrepancy with the set statistical law Make appropriate corrections to the current statistical results. 5. The method for reconstructing the three-dimensional microstructure of granite based on pixel statistics according to claim 4, wherein the square cell is suitable for two-dimensional microstructure reconstruction, and the cube cell is suitable for three-dimensional situation ; The end condition of the reconstruction includes two kinds: a single mineral mass stop growth condition and a specimen overall reconstruction end condition, and a single mineral mass stop growth condition includes: the maximum radius or equivalent radius of the mineral mass has exceeded the allowed range; The end conditions of the overall reconstruction of the specimen include: the maximum number of iterations allowed is reached, the maximum number of iterations allowed has not been reached but the iteration result has stabilized, and the area percentages of the two mineral clusters have exceeded the allowed range; the growth law includes the growth mode and growth rate. The principle of probability distribution includes two types of growth methods for two-dimensional cases: point growth and line growth; three types of growth methods for three-dimensional cases: point growth, line growth and surface growth; the point growth refers to the cell and The grown cells share a point; the line growth means that the parent cell and the grown cell share a line segment; the surface growth means that the parent cell and the grown cell share a plane The described growth probability distribution principle refers to how to carry out probability distribution between various growth modes, the probability distribution between point growth, line growth and surface growth can be the same or different, in the same growth mode, it can be further divided For different growth directions, they equally divide the probability of this growth mode; the growth of the two minerals near the seed is the process of eating away at the background or other minerals, following two principles: the principle of prohibiting encroachment and the principle of allowing encroachment; the prohibition of encroachment The principle means that only the cells around the parent body as the background have the opportunity to become minerals; the principle of allowing invasion means that any cells around a parent body have the opportunity to become minerals; The limitation of the same kind of mineral clusters can cause adjacent mineral clusters of the same kind to connect, so that the size of the mineral clusters changes suddenly, which is not conducive to the statistics of the reconstruction results, and may also cause the growth of the mineral clusters to stop due to the size of the mineral clusters exceeding the set range. , therefore, it is necessary to further restrict the background cells around the parent body. There is no same mineral around the background cells except the parent body to become a mineral; the review of the reconstruction results means that the reconstructed digital The geometric information of the two minerals in the granite specimen is compared with the set reconstruction range. If the reconstruction results are in good agreement with the reconstruction requirements, it means that the reconstruction is successful. If the agreement is not good, one or two Refactor the results to make corrections, enable the principle of allowing encroachment, or change the probability distribution of different growth modes.