Method for fast prediction of strength of marine porous reef limestone

Abstract

The application discloses a kind of marine porous reef limestone strength fast prediction method.It includes the following steps: selecting the porous reef limestone rock sample of construction site, obtaining the pore geometry characteristic quantization parameter of rock sample surface;Calculate the density of rock sample;Pore geometry characteristic quantization parameter and density are substituted into formula, and the strength of porous reef limestone is calculated, wherein σ is the strength of porous reef limestone, ρ is the density of rock sample, is the pore geometry characteristic quantization parameter of rock sample surface, C1 is constant, C2 is constant.The marine porous reef limestone strength fast prediction method of the application can obtain the strength of porous reef limestone more accurately and quickly under the condition that the required calculation parameters are less, so that the strength of the stratum to be constructed can be quickly judged by the on-site construction personnel whether it meets the construction requirements, the rock sample is avoided to be sent to land for detection, the engineering construction progress is accelerated, and the cost of offshore engineering construction is reduced.

Description

Technical Field

[0001] This invention relates to the field of island and reef engineering construction technology, specifically to a method for rapid prediction of the strength of porous marine reef limestone. Background Technology

[0002] The ocean contains abundant natural resources, but the land area above sea level is extremely limited. Efficient and safe island and reef engineering construction facilitates better human production and living activities in the open ocean. Reef limestone strata, as the main geological component of islands and reefs, have a crucial strength indicator in engineering construction, affecting both progress and safety. Because reef limestone strata are primarily formed from biological remains through complex sedimentary and metamorphic processes, they exhibit significant spatial variability. The geological properties discovered during actual construction often differ considerably from preliminary survey data. Numerous accidents, such as pile slippage, have occurred in domestic and international engineering projects due to misjudgments of the bearing capacity of reef limestone strata, severely impacting construction progress. Therefore, rapid and accurate assessment of the bearing capacity of reef limestone strata during actual construction is of paramount importance.

[0003] In existing technologies, strength testing of porous reef limestone requires various specialized equipment such as pressure testing machines. However, strength testing using pressure testing machines has the following drawbacks: First, if the specialized equipment used for strength testing is placed at a construction site with high temperature, high humidity, and high salinity, it is easy to reduce the service life of the equipment. Therefore, porous reef limestone samples need to be sent to a specialized laboratory on land for testing, which not only delays the progress of engineering construction but also increases the cost of offshore engineering construction. Second, processing the rock into standard samples is a time-consuming and labor-intensive process. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a rapid method for predicting the strength of porous reef limestone in marine environments. This method enables construction personnel to accurately and quickly determine whether the strength of porous reef limestone meets construction requirements at the construction site.

[0005] To achieve the above objectives, the present invention provides a rapid prediction method for the strength of porous marine reef limestone, characterized by the following steps:

[0006] Step 1: Select porous reef limestone samples from the construction site and obtain quantitative parameters of the pore geometry characteristics on the sample surface.

[0007] Step 2: Calculate the density ρ of the rock sample;

[0008] Step 3: Quantify the pore geometry parameters Substituting the density ρ into formula (1), the strength of porous reef limestone is calculated. Formula (1) is as follows:

[0009]

[0010] In the formula,

[0011] σ represents the strength of porous reef limestone.

[0012] ρ is the density of the rock sample.

[0013] Quantify the pore geometry characteristics of the rock sample surface using parameters.

[0014] C1 is a constant.

[0015] C2 is a constant.

[0016] Furthermore, in step one, the quantification parameters of the pore geometric features Quantification is achieved through the following steps.

[0017] Step 1) Take a picture of the surface of the porous reef limestone sample and import the picture into the image processing software on the computer. The image processing software should have grayscale conversion function, image segmentation function, and automatic area calculation function.

[0018] Step 2), set the image scale bar;

[0019] Step 3): Select the analysis area of ​​the photo in the image processing software, and use the grayscale function in the image processing software to convert the analysis area into a grayscale image.

[0020] Step 4): Using the image segmentation function in the image processing software, the pores and solid skeleton in the grayscale image are segmented to make the grayscale image a binary image. The grayscale values ​​of the pore pixels and the solid skeleton pixels in the binary image are two values.

[0021] Step 5): Using the automatic area calculation function in the image processing software, automatically calculate the pore area in the binarized image and export it as the original pore area dataset.

[0022] Step 6) Effectively process the original pore area dataset to obtain a high-precision effective pore area dataset.

[0023] Step 7): Substitute the effective pore area dataset into formula (2) to calculate the quantification parameters of pore geometric features. Formula (2) is as follows

[0024]

[0025] In the formula,

[0026] n is the number of pores in the effective pore area dataset.

[0027] S i Let i be the area of ​​the i-th pore.

[0028] Quantify the pore geometry characteristics of the rock sample surface using parameters.

[0029] Furthermore, in step 1), when taking a picture of the surface of the porous reef limestone sample, the shooting angle should be perpendicular to the shooting surface, and the flash should be turned on at the same time.

[0030] Furthermore, in step 1), the image processing software is MATLAB or ImageJ.

[0031] Furthermore, in step 2), the method for setting the image scale is to place a graduated ruler on the surface of the shooting area, measure the length of the graduated ruler in the image, and combine it with the actual length of the graduated ruler to obtain the image scale according to the formula: scale = actual length / length in the image.

[0032] Furthermore, in step 2), the method for setting the image scale is to place a line segment of a certain length on the surface of the shooting area, measure the length of the line segment in the image, and combine it with the actual length of the line segment to obtain the image scale according to the formula: scale = actual length / length in the image.

[0033] Furthermore, in step 3), the analysis area refers to the region in the image that has no obvious distortion and has a clear pore structure.

[0034] Furthermore, in step 6), the steps for effectively processing the original pore area dataset are as follows:

[0035] Step a: Divide all data within the pore area distribution range into first-level statistical intervals according to their order of magnitude;

[0036] Step b: Divide each primary statistical interval into several secondary statistical intervals proportionally;

[0037] Step c: Select the first-level statistical interval with the largest proportion of the total pore area to the total pore area and the pore area of ​​each of the secondary statistical intervals within it being non-zero as the effective interval, and use the dataset within this effective interval as the effective pore area dataset.

[0038] Further, in step two, the density ρ is obtained by first weighing the rock sample after drying, then placing the rock sample into a bucket filled with water, and the volume of the overflowing liquid is the volume of the rock sample. Finally, the density of the rock sample is calculated using formula (3), which is as follows:

[0039]

[0040] In the formula,

[0041] ρ is the density of the rock sample.

[0042] m is the mass of the rock sample.

[0043] v represents the volume of the rock sample.

[0044] Furthermore, in step three, the determination of C1 and C2 in formula (1) is as follows: after the porous reef limestone sample is made into a standard size, the weight, volume, and pore geometric characteristics are measured and quantitative parameters are determined. Then, a pressure test is carried out to obtain the strength of the sample. The sample strength data is then imported into computer software for fitting, and the values ​​of C1 and C2 are obtained.

[0045] The advantages of this invention are:

[0046] 1. This invention can conveniently identify the pore geometry of porous reef limestone, quantify the pore geometry features of porous reef limestone, and apply the quantified pore geometry features parameters to the strength prediction formula of porous reef limestone.

[0047] 2. This invention has low requirements for instruments, equipment, and operators. It can quickly process data on the construction site using simple equipment, avoiding the need to send rock samples to land for testing, thus speeding up the construction progress and reducing the cost of offshore engineering construction.

[0048] 3. This invention can obtain the strength of porous reef limestone relatively accurately and quickly with fewer required calculation parameters, which makes it easier for on-site construction personnel to quickly determine whether the strength of the stratum being constructed meets the construction requirements.

[0049] The present invention provides a rapid prediction method for the strength of porous reef limestone in the ocean. It can accurately and quickly obtain the strength of porous reef limestone with fewer required calculation parameters. This allows on-site construction personnel to quickly determine whether the strength of the strata under construction meets the construction requirements, avoids sending rock samples to land for testing, speeds up the construction progress, and reduces the cost of offshore engineering construction. Attached Figure Description

[0050] Figure 1 This is a flowchart of the rapid prediction method for the strength of porous marine reef limestone according to the present invention;

[0051] Figure 2 This is a flowchart of the method for quantifying the pore geometry of porous reef limestone in this invention.

[0052] Figure 3a To capture the original image;

[0053] Figure 3b Convert the image to grayscale;

[0054] Figure 3c Image binarization;

[0055] Figure 3dTo automatically collect pore data;

[0056] Figure 4 for Figure 3d A schematic diagram showing the data distribution curves of the original pore area in image recognition and the original pore area in manual recognition in existing technologies. Detailed Implementation

[0057] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] In the description of this invention, it should be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention.

[0059] like Figure 1 As shown, the rapid prediction method for the strength of marine porous reef limestone of the present invention includes the following steps:

[0060] Step 1: Select porous reef limestone samples from the construction site and obtain quantitative parameters of the pore geometry characteristics on the sample surface.

[0061] Step 2: Calculate the density ρ of the rock sample;

[0062] Step 3: Quantify the pore geometry parameters Substituting the density ρ into formula (1), the strength of porous reef limestone is calculated. Formula (1) is as follows:

[0063]

[0064] In the formula,

[0065] σ represents the strength of porous reef limestone.

[0066] ρ is the density of the rock sample.

[0067] Quantify the pore geometry characteristics of the rock sample surface using parameters.

[0068] C1 is a constant.

[0069] C2 is a constant.

[0070] In step one above, the pore geometric feature quantification parameters Quantification is achieved through the following steps, such as Figure 2 As shown:

[0071] Step 1) Take a picture of the surface of the porous reef limestone sample and import the picture into image processing software on the computer. The image processing software should have grayscale conversion function, image segmentation function, and automatic area calculation function.

[0072] Specifically, a relatively flat, porous reef limestone sample surface is selected as the photographing surface. High-definition imaging equipment is used for imaging, ensuring that the pore structure of the sample surface is clearly visible in the captured image. To ensure the image meets the requirements, the photographing angle should be perpendicular to the photographing surface, and a flash should be used. High-definition imaging equipment can be a digital camera with a flash, or a mobile phone with a high-definition camera and flash, etc.

[0073] In this embodiment, a digital camera equipped with a 28-200mm focal length lens is used. The standard cylindrical specimen was photographed. A camera tripod and built-in flash were used during the photographing process. The photos are as follows: Figure 3a As shown.

[0074] The image processing software is MATLAB, ImageJ, or other software with image processing functions. The model and type of image processing software are not considered as limitations of this invention.

[0075] In this embodiment, the captured photos are imported into the open-source image processing software ImageJ on the computer.

[0076] Step 2), set the image scale.

[0077] Specifically, the method for setting the image scale is as follows: Place a graduated ruler on the surface of the shooting area, measure the length of the graduated ruler in the image, and combine this with the actual length of the ruler to obtain the image scale using the formula: Scale = Actual Length / Length in Image; or place a line segment of a certain length on the surface of the shooting area, measure the length of the line segment in the image, and combine this with the actual length of the line segment to obtain the image scale using the formula: Scale = Actual Length / Length in Image. Based on this image scale, subsequent length measurements, automatic area calculations, and other operations will yield the actual length and actual area.

[0078] In this embodiment, the diameter of the sample in the image was measured to be 3000 pixels using the line tool and measurement function in the software. Comparing this to the actual size (diameter of 50 mm), the scale bar was found to be 60:1.

[0079] Step 3): Select the analysis area of ​​the photo in the image processing software, and use the grayscale function in the image processing software to convert the analysis area into a grayscale image.

[0080] Specifically, the analysis area refers to the region in the image without obvious distortion and with a clear pore structure. The analysis area with good image quality is selected using the selection tool in the image processing software, and the remaining image areas are deleted using the inverse selection-delete function.

[0081] In this embodiment, the software's "8-bit" function is used to convert the image into a grayscale image, such as... Figure 3b As shown.

[0082] Step 4): Using the image segmentation function in the image processing software, the pores and solid skeleton in the grayscale image are segmented to make the grayscale image a binary image. The grayscale values ​​of the pore pixels and the solid skeleton pixels in the binary image are two values.

[0083] Specifically, each pixel in the grayscale image is represented by a grayscale value (also known as an intensity value or brightness value), with the grayscale value ranging from 0 to 255. Grayscale values ​​of 0 and 255 can be selected as pixels in the binarized image, where pixels with a grayscale value of 0 are black and pixels with a grayscale value of 255 are white. Generally, the pore areas in the binarized image are white and the skeleton areas are black, or vice versa.

[0084] In this step, the grayscale value range is selected by manual adjustment to make the pore area closer to reality, while keeping adjacent pores as disconnected as possible.

[0085] In this embodiment, after manually comparing the pore separation effect under different interval values, [25, 125] was selected as the gray value interval for image binarization, resulting in the binarized image as shown below. Figure 3c As shown in the figure, white represents pores and black represents the solid skeleton.

[0086] Step 5): Using the automatic area calculation function in the image processing software, automatically calculate the pore area in the binarized image and export it as the original pore area dataset.

[0087] In this embodiment, the "Analyze Particles" function of the software is used to automatically count the pore area in the image, obtaining the original pore area dataset, such as... Figure 3d As shown.

[0088] The image recognition raw pore area data distribution curve in this embodiment and the data distribution curve of manually recognized raw pore area in the prior art are as follows: Figure 4 As shown. By Figure 4It can be seen that, compared with the accurate results of manual recognition, the original data curve obtained in this image recognition study shows a better match in the middle section, but a poorer match at both ends of the curve. This is because, during the image recognition process, noise in the image is easily treated as pores in the statistics, and these noise points are generally small in area, thus causing the pores to appear smaller than 0.1mm. 2 Within the specified range, the image recognition result is greater than the manual recognition result.

[0089] In addition, during the image recognition process, if adjacent pores are close together, they may be identified as a single pore, which can cause the area data of some individual pores in the image recognition results to be too large.

[0090] The original pore area dataset is distorted due to the inclusion of noise and interconnected adjacent pores. Therefore, it is necessary to effectively process the original pore area dataset.

[0091] Step 6) Effectively process the original pore area dataset to obtain a high-precision effective pore area dataset.

[0092] Specifically, the steps for effectively processing the original pore area dataset are as follows:

[0093] Step a: Divide all data within the pore area distribution range into first-level statistical intervals according to their order of magnitude;

[0094] Step b: Divide each primary statistical interval into several secondary statistical intervals proportionally;

[0095] Step c: Select the first-level statistical interval with the largest proportion of the total pore area to the total pore area and the pore area of ​​each of the secondary statistical intervals within it being non-zero as the effective interval, and use the dataset within this effective interval as the effective pore area dataset.

[0096] The first-level statistical interval with the largest proportion of the total pore area within the interval is selected as the effective interval to eliminate numerous but small "noise" data. The second-level statistical interval with all non-zero pore areas is selected as the effective interval to eliminate data involving connected adjacent pores. Since connected adjacent pores are infrequent, even if the area of ​​a connected pore is an order of magnitude larger than the actual pore data, it is unlikely to be distributed throughout all second-level intervals within the first-level interval.

[0097] Depend on Figure 4 It can be seen that the pore area of ​​the samples identified in this study is mostly distributed in the range of [1*10]. -1 ,1) Within the interval. Using the above-mentioned method for effectively processing the original pore area dataset, the original pore area data is divided into: [1*10 -41*10 -3 ), [1*10 -3 1*10 -2 ), [1*10 -2 1*10 -1 ), [1*10 -1 ,1),[1,1*10 1 There are a total of 5 primary statistical intervals. Each primary statistical interval is further divided into 10 secondary statistical intervals, such as the primary statistical interval [1, 1*10]. 1 The secondary statistical intervals are [1,2), [2,3), [3,4), [4,5), [5,6), [6,7), [7,8), [8,9), [9,10), for a total of ten secondary statistical intervals. The results show that the primary statistical interval [1*10]... -1 If the total pore area within interval [1) is the largest and the pore area in the ten secondary statistical intervals below it is not zero, then the primary statistical interval [1*10] is taken. -1 The data in ,1) is the effective pore area dataset.

[0098] Step 7): Substitute the effective pore area dataset into formula (2) to calculate the quantification parameters of pore geometric features. Formula (2) is as follows

[0099]

[0100] In the formula,

[0101] n is the number of pores in the effective pore area dataset.

[0102] S i Let i be the area of ​​the i-th pore.

[0103] Quantify the pore geometry characteristics of the rock sample surface using parameters.

[0104] In this embodiment, the result of the quantification parameter of pore geometry is 0.2585.

[0105] To compare the effectiveness of the above processing, the original pore area data of the grayscale image was compared with the manually identified pore area data and the effective pore area data. The results are shown in Table 1 below.

[0106] Table 1 Comparison of Data

[0107]

[0108] As can be seen from Table 1, the software-automated identification of effective pore area data obtained by using the method of the present invention to effectively process the original pore area dataset is consistent with the results of manual identification.

[0109] Quantification parameters using the pore geometry features described above The quantitative method was used to obtain quantitative parameters of the pore geometry characteristics of five porous reef limestone samples. They are 0.424mm respectively. 2 0.417mm 2 0.394mm 2 0.03mm 2 0.033mm 2 .

[0110] In step two, the density ρ is obtained by first weighing the dried rock sample, then placing the rock sample into a bucket filled with water, and the volume of the overflowing liquid is the volume of the rock sample. Finally, the density of the rock sample is calculated using formula (3), which is as follows:

[0111]

[0112] In the formula,

[0113] ρ is the density of the rock sample.

[0114] m is the mass of the rock sample.

[0115] v represents the volume of the rock sample.

[0116] If the obtained porous reef limestone sample is relatively dry, its weight can be weighed directly; if the obtained porous reef limestone sample is relatively moist, it needs to be dried before weighing. The strong sunlight of tropical oceans can be used to dry the sample by exposing it to the sun, or simple equipment such as hair dryers, ovens, or ovens can be used to dehydrate and dry it.

[0117] The densities ρ of the five porous reef limestone samples mentioned above are 1.02 g / cm³. 3 0.96g / cm 3 1.35g / cm 3 0.94g / cm 3 0.94g / cm 3 .

[0118] In step three, the determination of C1 and C2 in formula (1) is as follows: In the geological exploration stage at the beginning of the project construction, after the porous reef limestone rock sample obtained from the exploration borehole is formulated into a standard size in the laboratory, the weight, volume, and pore geometric characteristics are measured and quantitative parameters are determined. Then, a pressure test is carried out to obtain the rock sample strength. The rock sample strength data is then imported into computer software for fitting, and the values ​​of C1 and C2 are obtained.

[0119] In this embodiment, based on the results of previous indoor tests, the values ​​of C1 and C2 are 2.88 and -9.32, respectively.

[0120] Quantify the pore geometry characteristics of the above five porous reef limestone samples. Substitute the corresponding density ρ into formula (1) to calculate the rock sample strength. The calculation results are compared with the laboratory test strength results, as shown in Table 2 below.

[0121] Table 2 Comparison of Formula-Predicted Strength and Tested Strength of Porous Reef Limestone Samples

[0122]

[0123] The difference in Table 2 above is the value of the predicted strength minus the experimental strength. Due to certain simplifications to the original pore area dataset, the results obtained by the rapid strength prediction method for marine porous reef limestone in this invention deviate somewhat from the strength values ​​measured in actual experiments. However, the actual engineering geological conditions are complex and variable, and this deviation is acceptable in engineering practice.

[0124] The present invention provides a rapid prediction method for the strength of porous reef limestone in the ocean. It can accurately and quickly obtain the strength of porous reef limestone with fewer required calculation parameters. This allows on-site construction personnel to quickly determine whether the strength of the strata under construction meets the construction requirements, avoids sending rock samples to land for testing, speeds up the construction progress, and reduces the cost of offshore engineering construction.

[0125] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for rapid prediction of the strength of marine porous reef limestone, characterized in that, Includes the following steps: Step 1: Select porous reef limestone samples from the construction site and obtain quantitative parameters of the pore geometry characteristics on the sample surface. The quantification parameters of pore geometric features The calculation formula is as follows (2). In the formula, n is the number of pores in the effective pore area dataset. S i Let i be the area of ​​the i-th pore. Quantify the pore geometry characteristics of the rock sample surface; Step 2: Calculate the density ρ of the rock sample; Step 3: Quantify the pore geometry parameters Substituting the density ρ into formula (1), the strength of porous reef limestone is calculated. Formula (1) is as follows: In the formula, σ represents the strength of porous reef limestone. ρ is the density of the rock sample. Quantify the pore geometry characteristics of the rock sample surface using parameters. C1 is a constant. C2 is a constant; The method for determining C1 and C2 in the formula (1) is as follows: after the porous reef limestone sample is made into a standard size, the weight, volume and pore geometric characteristics are measured and quantitative parameters are determined. Then, a pressure test is carried out to obtain the strength of the sample. The strength data of the sample is then imported into computer software for fitting, and the values ​​of C1 and C2 are obtained.

2. The method for rapid prediction of the strength of marine porous reef limestone according to claim 1, characterized in that: In step one, the pore geometric feature quantification parameters Quantification is achieved through the following steps. Step 1) Take a picture of the surface of the porous reef limestone sample and import the picture into the image processing software on the computer. The image processing software should have grayscale conversion function, image segmentation function, and automatic area calculation function. Step 2), set the image scale bar; Step 3): Select the analysis area of ​​the photo in the image processing software, and use the grayscale function in the image processing software to convert the analysis area into a grayscale image. Step 4): Using the image segmentation function in the image processing software, the pores and solid skeleton in the grayscale image are segmented to make the grayscale image a binary image. The grayscale values ​​of the pore pixels and the solid skeleton pixels in the binary image are two values. Step 5): Using the automatic area calculation function in the image processing software, automatically calculate the pore area in the binarized image and export it as the original pore area dataset. Step 6) Effectively process the original pore area dataset to obtain a high-precision effective pore area dataset. Step 7): Substitute the effective pore area dataset into formula (2) to calculate the quantification parameters of pore geometric features.

3. The method for rapid prediction of the strength of marine porous reef limestone according to claim 2, characterized in that: In step 1), when taking a picture of the surface of the porous reef limestone sample, the shooting angle should be perpendicular to the shooting surface, and the flash should be turned on at the same time.

4. The method for rapid prediction of the strength of marine porous reef limestone according to claim 3, characterized in that: In step 1), the image processing software is MATLAB or ImageJ.

5. The method for rapid prediction of the strength of marine porous reef limestone according to claim 4, characterized in that: In step 2), the method for setting the image scale is to place a graduated ruler on the surface of the shooting area, measure the length of the graduated ruler in the image, and combine it with the actual length of the graduated ruler to obtain the image scale according to the formula: scale = actual length / length in the image.

6. The method for rapid prediction of the strength of marine porous reef limestone according to claim 4, characterized in that: In step 2), the method for setting the image scale is to place a line segment of a certain length on the surface of the shooting area, measure the length of the line segment in the image, and combine it with the actual length of the line segment to obtain the image scale according to the formula: scale = actual length / length in the image.

7. The method for rapid prediction of the strength of marine porous reef limestone according to claim 5 or 6, characterized in that: In step 3), the analysis area refers to the region in the image that has no obvious distortion and has a clear pore structure.

8. The method for rapid prediction of the strength of marine porous reef limestone according to claim 2, characterized in that: In step 6), the steps for effectively processing the original pore area dataset are as follows: Step a: Divide all data within the pore area distribution range into first-level statistical intervals according to their order of magnitude. Step b: Divide each primary statistical interval into several secondary statistical intervals proportionally; Step c: Select the first-level statistical interval with the largest proportion of the total pore area to the total pore area and the pore area of ​​each of the secondary statistical intervals within it being non-zero as the effective interval, and use the dataset within this effective interval as the effective pore area dataset.

9. The method for rapid prediction of the strength of marine porous reef limestone according to claim 1, characterized in that: In step two, the density ρ is obtained by first weighing the dried rock sample, then placing the rock sample into a bucket filled with water, and the volume of the overflowing liquid is the volume of the rock sample. Finally, the density of the rock sample is calculated using formula (3), which is as follows: In the formula, ρ is the density of the rock sample. m is the mass of the rock sample. v represents the volume of the rock sample.

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