Preparation method of natural joint-containing rock standard piece for test

Abstract

The present application belongs to the technical field of rock mechanics and geological engineering, and aims to solve the problems of insufficient simulation accuracy, low preparation efficiency and high cost of natural joint topography. A preparation method of rock standard parts for natural joint test is provided, which comprises the following steps: collecting rock blocks to be tested, cutting to obtain rock test blocks for standby; constructing point cloud data based on wavelet basis function and random phase; generating standard grid points in the point cloud data, calculating the height value corresponding to each grid point, and obtaining a grid file; testing whether the simulated natural rough joint surface has the statistical characteristics of natural joint fluctuation topography based on normal distribution test; importing the grid file into a rock carving machine to generate a carving path, performing rough carving and fine carving, and obtaining a rock standard part for test. The present application can efficiently and accurately simulate the multi-scale roughness and anisotropy of natural joints, and provide high-quality standardized test pieces for rock mechanics tests.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of rock mechanics and geological engineering, and particularly relates to a preparation method of a rock standard piece for a natural joint-containing test. BACKGROUND

[0002] Rock mass is a complex geological structure composed of rock blocks and joint networks. The shear slip of joint surfaces is one of the main causes of engineering geological disasters. Studies have shown that the topographic features of joint surfaces have a significant impact on the strength, mechanical properties, and hydraulic characteristics of rock mass. Therefore, in-depth research on the topography of joint surfaces and its influence mechanism on the mechanical behavior of rock mass is of great significance in the field of rock mass engineering.

[0003] The topography of natural joint surfaces is formed under the combined action of tectonic stress, weathering, and erosion during geological evolution, and usually exhibits complex characteristics such as irregular shape, multi-scale undulation, and anisotropy. In order to study the influence of joint surface topography on the mechanical properties of rock mass, obtaining rock specimens with natural joint topography and conducting indoor tests is an important means. However, the existing joint surface simulation methods have many shortcomings in terms of accuracy and practicality, making it difficult to meet the needs of scientific research and engineering practice.

[0004] Currently, there are many difficulties in the preparation of natural joint-containing rock specimens, which limit the accuracy and reliability of the test. The main defects are as follows:

[0005] (1) Many studies use regular zigzag joint specimens to simulate the shear behavior of natural joint surfaces. However, the topography of such specimens is too regular and cannot fully reflect the complexity and randomness of natural joint surfaces, leading to large deviations in interpreting the true mechanical behavior of rock mass.

[0006] (2) The artificial splitting method can directly obtain natural joint surfaces, but the generated joint surfaces lack repeatability and the roughness is difficult to accurately control, limiting its application in systematic research.

[0007] (3) The method of obtaining point cloud data of natural joint surfaces through three-dimensional laser scanning or unmanned aerial vehicle photogrammetry technology and reconstructing the joint surface using reverse modeling technology is costly, complex to operate, and has high requirements for the experimental environment, making it difficult to be widely promoted. SUMMARY

[0008] The present application provides a preparation method of a rock standard piece for a natural joint-containing test to solve at least one of the above technical problems in the prior art.

[0009] The application adopts the technical scheme as follows: a preparation method of a rock standard piece with natural joints for testing, comprising the following steps: S1: collecting a rock block to be tested, and obtaining a rock test block after cutting, the rock test block having a flat joint surface; S2: constructing point cloud data based on a wavelet base function and a random phase, the point cloud data forming a natural rough joint surface with natural joint undulating topography; S3: dividing points in the point cloud data to generate standard grid points, calculating a height value corresponding to each grid point by an interpolation method, and obtaining a grid file of the natural rough joint surface with simulation; S4: testing whether the natural rough joint surface with simulation has statistical characteristics of natural joint undulating topography based on a normal distribution, if not, returning and repeatedly executing steps S2-S3, and if yes, sequentially executing steps S5 and S6; S5: calculating a roughness coefficient of the natural rough joint surface with simulation; and S6: importing the grid file into a rock carving machine to generate a carving path, and coarsely carving and finely carving the rock test block based on the carving path to obtain a rock standard piece for testing with natural joint topography.

[0010] Preferably, the rock block to be tested is obtained after two cutting processes, wherein the first cutting process is to cut the rock block to be tested into an original test block, and the second cutting process is to cut the original test block into two identical rock test blocks along the height center line of the original test block.

[0011] Preferably, the step of constructing point cloud data based on the wavelet base function and the random phase comprises:

[0012] S21: defining a wavelet base function for reconstructing multi-scale characteristics of a joint surface;

[0013] S22: generating a multi-scale wave-shaped surface function based on the wavelet base function;

[0014] S23: generating a random phase field for each scale of the wave-shaped surface function;

[0015] S24: combining the multi-scale wave-shaped surface function and the random phase field to generate point cloud data with natural joint undulating topography.

[0016] Preferably, the step of obtaining the grid file of the natural rough joint surface with simulation comprises:

[0017] S31: reading the point cloud data with natural joint undulating topography, and performing denoising and smoothing processing;

[0018] S32: defining a resolution of an interpolation grid, generating regular grid points, and determining the number of the grid points based on the range of the point cloud data and the resolution of the interpolation grid;

[0019] S33: calculating the height value corresponding to each grid point using cubic spline interpolation method;

[0020] S34: generating grid data based on the grid points and the height values corresponding to the grid points, performing smoothing processing on the grid data, and simultaneously performing clipping or extension on the boundary of the grid data to obtain a grid file with a simulated natural rough joint surface, and exporting the grid file in STL format and saving.

[0021] Preferably, the step of calculating the height value corresponding to each grid point using cubic spline interpolation method comprises:

[0022] S331: finding 16 nearest neighboring points around each grid point;

[0023] S332: representing the height value corresponding to the grid point as a bicubic polynomial;

[0024] S333: solving the coefficients of the bicubic polynomial by least squares method based on the point cloud data of the 16 nearest neighboring points around the grid point;

[0025] S334: bringing the grid point into the bicubic polynomial to obtain the height value corresponding to the grid point.

[0026] Preferably, the step of checking whether the simulated natural rough joint surface has the statistical characteristics of natural joint undulating topography based on normal distribution comprises:

[0027] S41: equally dispersing the grid data in the grid file for generating a natural rough joint surface into new point cloud data;

[0028] S42: randomly selecting N points in the new point cloud data, and extracting a profile line passing through any point in the N points, and the profile line is parallel to the X-axis or the Y-axis;

[0029] S43: calculating the climbing angle N and the projection length of the continuously rising or falling segment of the two profile lines corresponding to each point in all points;

[0030] S44: fitting the climbing angle and the projection length of the continuously rising or falling segment of the extracted profile line in the simulated natural rough joint surface based on normal distribution;

[0031] S45: verifying the climbing angle of the extracted profile line based on chi-square test​​ and the projected length of the continuously rising or falling segment whether it obeys normal distribution.

[0032] Preferably, the step of calculating the roughness coefficient of the simulated natural rough joint surface comprises:

[0033] Setting a sampling interval, extracting 100-200 joint profile lines along the shear direction, calculating the slope root mean square of each profile line;

[0034] Based on the slope root mean square, the roughness coefficient of each profile line is calculated;

[0035] The roughness coefficients of all profile lines are averaged to obtain the roughness coefficient of the simulated natural rough joint surface.

[0036] Preferably, when the rock test block is engraved, if the rock test block has obvious corners, the corners of the rock test block are engraved first, and then the middle part of the rock test block is engraved; meanwhile, a large-diameter engraving tool is selected to coarsely engrave the rock test block, and a small-diameter engraving tool is selected to finely engrave the rock test block.

[0037] Compared with the prior art, the present application has the following beneficial effects:

[0038] The present application provides a simple, efficient, high-precision and batch-reproducible method for preparing rock standard pieces with natural joints for testing. The method generates multi-scale wave-shaped surfaces through wavelet basis functions, simulates the complex topographic features of natural joint surfaces by combining random phase fields, converts point cloud data into high-precision grid data using interpolation method, and ensures the consistency of the simulated joint surface and the natural joint through geometric similarity test and roughness quantification. Finally, the rock standard pieces with natural joint topography are prepared in batches through high-precision engraving technology.

[0039] Based on wavelet basis functions and random phase field theory, the multi-scale roughness characteristics and anisotropy of natural joint surfaces can be accurately simulated to ensure the geometric consistency and mechanical similarity of the simulated joint surface and the natural joint. Through digital modeling and high-precision engraving technology, rock standard pieces with natural joint characteristics can be prepared in batches and quickly, significantly reducing the preparation cost and time. Through geometric similarity test and roughness quantification, the prepared rock standard pieces have high consistency and repeatability, providing reliable standardized test pieces for rock mechanics testing. The present application is suitable for rock mechanics testing, geological engineering simulation and teaching research, and provides scientific basis and technical support for solving complex rock mass engineering problems. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed in the embodiments. Obviously, the drawings described below only illustrate some of the embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without any creative effort.

[0041] Figure 1 Flow chart of the method of the present application.

[0042] Figure 2 Schematic diagram of the generation of natural rough joint surface in the present application.

[0043] Figure 3 Schematic diagram of the extraction of section line in the present application.

[0044] Figure 4 Illustration diagram for the calculation of the projection length of the climbing angle and the continuous rising or falling section of the section line in the present application.

[0045] Figure 5 Flow chart of the geometric similarity inspection method of the simulated natural rough joint surface in the present application.

[0046] Figure 6 Statistical analysis result diagram of the geometric similarity inspection of the simulated natural rough joint surface in the present application. DETAILED DESCRIPTION

[0047] The technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without any creative effort fall within the scope of the present application.

[0048] It should be noted that the structures, proportions, sizes, etc. shown in the drawings of the present specification are only used to cooperate with the content disclosed in the present specification, to be understood and read by those skilled in the art, and do not have technical substantive significance, and any modification of the structure, change of the proportion relationship or adjustment of the size, without affecting the effects and purposes that can be achieved by the present application, should fall within the scope of the technical content disclosed by the present application. It should be noted that in the present specification, relationship terms such as first and second are only used to distinguish one entity from another entity, and do not necessarily require or imply any actual relationship or order between the entities.

[0049] The present application provides an embodiment:

[0050] As Figures 1 to 6As shown, a preparation method of a natural joint-containing test rock standard part, comprising the following steps:

[0051] S1: Collecting a rock block to be tested, and obtaining a rock test block after cutting, the rock test block having a flat joint surface.

[0052] Collecting a rock block to be tested with a certain scale at an engineering site, and obtaining a rock test block after two cutting processes, wherein the first cutting process is to cut the rock block to be tested into a raw test block, and the second cutting process is to cut the raw test block into two identical rock test blocks along the height center line of the raw test block. The raw test block is a cuboid test block with a length of 100 mm, a width of 100 mm, and a height of 100± mm, the maximum fluctuation difference of the natural rough joint surface.

[0053] S2: Constructing point cloud data based on a wavelet basis function and a random phase, and the point cloud data constitutes a natural rough joint surface with natural joint fluctuation topography.

[0054] The step of constructing point cloud data based on a wavelet basis function and a random phase comprises:

[0055] S21: Defining a wavelet basis function for reconstructing the multi-scale features of the joint surface; selecting a suitable wavelet basis function (such as a Daubechies wavelet basis function, a Haar wavelet basis function, etc.), in this embodiment, the expression of the wavelet basis function is shown in formula (1):

[0056] (1)

[0057] In the formula, is a scale parameter for controlling the wavelength of the wavelet, the larger the scale parameter is, the longer the corresponding wavelength is, and the slower the fluctuation is; is a translation parameter for controlling the position of the wavelet; and are coordinates in a two-dimensional space, representing the position of the joint surface in the horizontal direction; is a mother wavelet function, which can be selected from different types such as Daubechies (Daubechies) and Haar (Haar), for generating local fluctuations.

[0058] S22: Generating a multi-scale wave surface based on the wavelet basis function; the expression of each scale of the wave surface is shown in formula (2):

[0059] (2)

[0060] In the formula, is the th wave surface; For the first The amplitude of each waveform surface is used to control the height of the fluctuations; For the first The scale parameters of the waveform surface are used to control the wavelength of the undulations; For the first The translation parameters of the waveform surface are used to control the position of the undulations.

[0061] S23: Generate a random phase field for the waveform surface at each scale; the random phase field can be generated based on a uniform distribution or a Gaussian distribution, as shown in equations (3) and (4):

[0062] (3)

[0063] (4)

[0064] In the formula, For the first The random phase field corresponding to each waveform surface; Indicates uniform distribution in interval; The mean is The variance is The Gaussian distribution.

[0065] S24: By combining multi-scale waveform surfaces with random phase fields, point cloud data with natural joint undulations is generated. The expression for the point cloud data is shown in equation (5):

[0066] (5)

[0067] In the formula, For the first Point cloud data corresponding to each waveform surface; The number of waveform surfaces; Used to introduce random phases and enhance the natural randomness of joint surfaces.

[0068] S25: Generate point cloud data Coordinates can be saved in a common format such as .txt or .xyz.

[0069] S3: Divide the points in the point cloud data to generate standard grid points, and calculate the height value corresponding to each grid point through interpolation to obtain a grid file with simulated natural rough joint surfaces.

[0070] The steps to obtain a mesh file with simulated natural rough joint surfaces include:

[0071] S31: reading point cloud data with natural joint relief topography, pre-processing the point cloud data, using statistical filtering or radius filtering method for denoising, using Gaussian filtering or moving least squares method (MLS) for smoothing the point cloud data;

[0072] S32: defining the resolution of the interpolation grid , generating regular grid points , the number of grid points is determined based on the range of the point cloud data and the resolution of the interpolation grid;

[0073] S33: for each grid point , using cubic spline interpolation method to calculate the height value corresponding to the grid point ; Cubic interpolation is based on bicubic polynomial fitting, which can provide higher precision interpolation results.

[0074] The step of calculating the height value corresponding to the grid point using cubic spline interpolation method includes:

[0075] S331: find 16 nearest neighboring points around each grid point;

[0076] S332: express the height value corresponding to the grid point as a bicubic polynomial, as shown in equation (6):

[0077] (6)

[0078] In the formula, is the polynomial coefficient, and is the coordinate value of the grid point in the two-dimensional plane;

[0079] S333: based on the point cloud data of the 16 nearest neighboring points around the grid point, solve the coefficients of the bicubic polynomial by least squares method ;

[0080] S334: put the grid point into the bicubic polynomial to get the height value corresponding to the grid point .

[0081] S34: generate grid data based on the grid points and the height values corresponding to the grid points, smooth the grid data, and clip or extend the boundary of the grid data to get a grid file with simulated natural rough joint surface. Export the grid file as.STL format and save.

[0082] S4: Based on the normal distribution test, whether the simulated natural rough joint surface has the statistical characteristics of natural joint fluctuation topography, if not, return and repeat steps S2-S3, if yes, execute steps S5 and S6 in turn.

[0083] The step of testing whether the simulated natural rough joint surface has the statistical characteristics of natural joint fluctuation topography based on the normal distribution includes:

[0084] S41: Equidistantly scatter the grid data of the generated natural rough joint surface in the grid file into new point cloud data;

[0085] S42: Randomly select 100 points in the new point cloud data, and extract a profile line passing through any point of the 100 points, and the profile line is parallel to the X axis or the Y axis;

[0086] S43: Calculate the climbing angle of the two profile lines corresponding to each of the 100 points and the projection length of the continuous rising or falling segment ;

[0087] S44: Based on the normal distribution fitting, the climbing angle and the projection length of the continuous rising or falling segment of the extracted profile line in the simulated natural rough joint surface are fitted, as shown in formula (7):

[0088] (7)

[0089] In the formula, A represents the climbing angle , the projection length of the continuous rising or falling segment ; is the standard deviation; is the probability density function of A , and is the natural logarithm.

[0090] S45: Based on the chi-square test, whether the climbing angle and the projection length of the continuous rising or falling segment of the extracted profile line conform to the normal distribution. In this embodiment, the chi-square test is a prior art, which will not be described here.

[0091] S46: If the climbing angle and the projection length of the continuous rising or falling segment of the extracted profile line conform to the normal distribution or approximately conform to the normal distribution, it indicates that the simulated joint surface has good geometric consistency with the natural rough joint surface. Figure 6 ​is the mean value of the climbing angle; is the variance of the climbing angle; is the mean value of the projected length of the continuous ascending or descending segment; is the variance of the projected length of the continuous ascending or descending segment.

[0092] S5: Calculate the roughness coefficient of the simulated natural rough joint surface. In this application, the roughness coefficient of the simulated natural rough joint surface is a theoretical calculation before carving, which has no explicit connection with the subsequent rough carving and fine carving of the rock test block based on the carving path. Only before carving, the operator needs to know the roughness coefficient, but the roughness coefficient does not participate in the subsequent actual carving.

[0093] The step of calculating the roughness coefficient of the simulated natural rough joint surface includes:

[0094] Set the sampling interval, extract 100-200 joint profile lines along the shear direction, and calculate the slope root mean square of each profile line As shown in equation (8):

[0095] (8)

[0096] In the formula, is the x-coordinate of the i-th discrete point on the profile line; is the y-coordinate of the i-th discrete point on the profile line; is the z-coordinate of the i-th discrete point on the profile line, i.e. the relief height at the discrete point; is the sampling number of the profile line discrete points. Based on the slope root mean square, calculate the roughness coefficient of each profile line; Take the average of the roughness coefficients of all profile lines to obtain the roughness coefficient of the simulated natural rough joint surface. S6: Import the grid file into the rock carving machine to generate a carving path, and perform rough carving and fine carving on the rock test block based on the carving path to obtain a test rock standard part containing natural joint topography. When carving the rock test block, if the rock test block has obvious corners, carve the corners of the rock test block first, and then carve the middle part of the rock test block; At the same time, select a large-diameter relief knife to perform rough carving on the rock test block, and then select a small-diameter relief knife to perform fine carving on the rock test block.

[0097] S6: Import the grid file into the rock carving machine to generate a carving path, and perform rough carving and fine carving on the rock test block based on the carving path to obtain a test rock standard part containing natural joint topography. When carving the rock test block, if the rock test block has obvious corners, carve the corners of the rock test block first, and then carve the middle part of the rock test block; At the same time, select a large-diameter relief knife to perform rough carving on the rock test block, and then select a small-diameter relief knife to perform fine carving on the rock test block.

[0098] S6: Import the grid file into the rock carving machine to generate a carving path, and perform rough carving and fine carving on the rock test block based on the carving path to obtain a test rock standard part containing natural joint topography. When carving the rock test block, if the rock test block has obvious corners, carve the corners of the rock test block first, and then carve the middle part of the rock test block; At the same time, select a large-diameter relief knife to perform rough carving on the rock test block, and then select a small-diameter relief knife to perform fine carving on the rock test block.

[0099] S6: Import the grid file into the rock carving machine to generate a carving path, and perform rough carving and fine carving on the rock test block based on the carving path to obtain a test rock standard part containing natural joint topography. When carving the rock test block, if the rock test block has obvious corners, carve the corners of the rock test block first, and then carve the middle part of the rock test block; At the same time, select a large-diameter relief knife to perform rough carving on the rock test block, and then select a small-diameter relief knife to perform fine carving on the rock test block.

[0100] ​​​The above merely describes preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto, any changes or replacements within the technical scope disclosed by the present application, which can be easily thought by those skilled in the art, should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for preparing a standard rock specimen for testing with natural joints, characterized in that, Includes the following steps: S1: Collect the rock block to be tested, cut it to obtain a rock test block for later use. The rock test block has a straight joint surface. S2: Constructing point cloud data based on wavelet basis functions and random phase, wherein the point cloud data constitutes a natural rough joint surface with natural joint undulations; the steps of constructing point cloud data based on the wavelet basis functions and random phase include: S21: Defining wavelet basis functions for reconstructing multi-scale features of the joint surface; S22: Generating multi-scale waveform surface functions based on the wavelet basis functions; S23: Generating a random phase field for each scale of the waveform surface function; S24: Combining the multi-scale waveform surface functions with the random phase field to generate point cloud data with natural joint undulations; the expression for the point cloud data is shown in the following formula: In the formula, For the first Point cloud data corresponding to each waveform surface; The number of waveform surfaces; For the first The amplitude of each waveform surface is used to control the height of the fluctuations; These are wavelet basis functions; Used to introduce random phases and enhance the natural randomness of joint surfaces; S3: Divide the points in the point cloud data to generate standard grid points, and calculate the height value corresponding to each grid point by interpolation to obtain a grid file with simulated natural rough joint surface; S4: Based on the normal distribution, test whether the simulated natural rough joint surface possesses the statistical characteristics of natural joint undulation morphology. If it does not possess the statistical characteristics of natural joint undulation morphology, return and repeat steps S2-S3. If it possesses the statistical characteristics of natural joint undulation morphology, execute steps S5 and S6 sequentially. The steps for testing whether the simulated natural rough joint surface possesses the statistical characteristics of natural joint undulation morphology based on the normal distribution include: S41: Divide the mesh data of the generated natural rough joint surface in the mesh file into new point cloud data at equal intervals; S42: Randomly select from the new point cloud data... N Points, and extract the data. N S43: Calculate the profile line at any point among the points, and the profile line is parallel to the X-axis or Y-axis; N The ascent angle of the two profile lines corresponding to each point in the data. and the projected length of continuous rising or falling segments S44: The ascent angle of the profile line extracted from the simulated natural rough joint surface based on the normal distribution fitting. θ i and the projected length of continuous rising or falling segments S45: Verify the ascent angle of the extracted profile line based on the chi-square test. and the projected length of continuous rising or falling segments Does it follow a normal distribution? S5: Calculate the roughness coefficient of the simulated natural rough joint surface; S6: Import the mesh file into the rock carving machine to generate a carving path, and perform rough carving and fine carving on the rock test block based on the carving path to obtain a test rock standard with natural joint morphology.

2. The method for preparing a standard rock specimen for testing containing natural joints according to claim 1, characterized in that: The rock block to be tested is cut into a rock test block after two cutting processes. The first cutting process is to cut the rock block to be tested into an original test block, and the second cutting process is to cut the original test block into two identical rock test blocks along its own height center line.

3. The method for preparing a standard rock specimen for testing containing natural joints according to claim 1, characterized in that: The steps to obtain the simulated mesh file with naturally rough jointed surfaces include: S31: Read the point cloud data with natural joint undulations and perform noise reduction and smoothing processing; S32: Define the resolution of the interpolation grid and generate regular grid points. The number of grid points is determined based on the range of the point cloud data and the resolution of the interpolation grid. S33: For each grid point, the height value corresponding to the grid point is calculated using cubic spline interpolation; S34: Generate grid data based on the grid points and their corresponding height values, smooth the grid data, and trim or extend the boundaries of the grid data to obtain a grid file with simulated natural rough joint surfaces. Export the grid file as an .STL file and save it.

4. The method for preparing a standard rock specimen for testing containing natural joints according to claim 3, characterized in that: The steps for calculating the height values ​​corresponding to grid points using cubic spline interpolation include: S331: Find the 16 nearest neighboring points around each of the grid points; S332: Represent the height value corresponding to the grid point as a bicubic polynomial; S333: Based on the point cloud data of the 16 nearest neighboring points around the grid point, solve the coefficients of the bicubic polynomial using the least squares method; S334: Substitute the grid points into the bicubic polynomial to obtain the height value corresponding to the grid points.

5. The method for preparing a standard rock specimen for testing containing natural joints according to claim 4, characterized in that: The steps for calculating the roughness coefficient of the simulated natural rough joint surface include: Set the sampling interval, extract 100-200 joint profile lines along the shear direction, and calculate the root mean square of the slope of each profile line; The roughness coefficient of each profile line is calculated based on the root mean square of the slope. The roughness coefficient of the simulated natural rough joint surface is obtained by averaging the roughness coefficients of all the cross-sectional lines.

6. The method for preparing a standard rock specimen for testing containing natural joints according to claim 1, characterized in that: When carving the rock specimen, if the rock specimen has sharp edges, carve the sharp edges first, and then carve the middle part of the rock specimen; at the same time, select a large-diameter relief carving tool to rough carve the rock specimen, and then select a small-diameter relief carving tool to fine carve the rock specimen.

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