A method for calculating the porosity of rock based on the stress-strain curve

Abstract

The present invention discloses a method for calculating the porosity of rock based on the stress-strain curve, which includes: obtaining information on the elastic deformation process of the rock; constructing a stress-strain model of the rock to be measured based on the information on the elastic deformation process of the rock; using the stress-strain model to obtain the pore strain information of the rock to be measured; constructing a relationship model between pore strain and rock porosity based on the pore strain information of the rock to be measured; and obtaining the porosity of the rock to be measured based on the relationship model between pore strain and rock porosity. The present invention establishes a hyperbolic model of the rock stress-strain curve, demonstrates the relationship between the model parameters and the rock porosity, and realizes the calculation of the porosity of the rock sample only by using the stress-strain curve of the uniaxial loading elastic deformation process of the rock, without the need to conduct additional tests to measure the porosity of the rock sample, which can greatly reduce the labor intensity and improve the efficiency of calculating the rock porosity.

Description

Technical Field

[0001] The present invention belongs to the technical field of measuring the permeability of rock and soil masses, and particularly relates to a method for measuring the porosity of rock based on a stress-strain curve. Background Art

[0002] As shallow mineral resources are gradually depleted, resource development is continuously moving towards the deep part of the earth. Deep well and tunnel excavation has become the new normal for water conservancy, transportation, mining, and geothermal development. During the deep excavation process, deep rock mechanics phenomena such as slab cracking of tunnel surrounding rock are becoming increasingly prominent, posing a severe challenge to the safe construction of deep-buried well and tunnel projects. Through research, it has been found that after hundreds of millions of years of geological action, the stress-strain relationship of the microscopic pores and cracks widely distributed inside the rock also exhibits strong non-linear characteristics; the slab cracking of the surrounding rock of deep-buried tunnels is closely related to the non-linear mechanical properties of the surrounding rock, and the non-linearity of the mechanical properties of the surrounding rock mainly comes from the pores inside the rock. The more pores there are, the higher the porosity, and the more obvious the non-linearity of the mechanical properties of the rock. Porosity is an important basic index for understanding the non-linear mechanical properties of rock. How to conveniently, quickly, and accurately measure the porosity of rock is of great significance for understanding the mechanism of slab cracking of the surrounding rock of deep-buried tunnels.

[0003] The porosity of rock refers to the percentage of the volume of pores in a rock specimen to the total volume of the specimen. At present, the rock porosity testing methods are mainly divided into destructive testing methods and non-destructive testing methods. The destructive testing methods mainly include: weighing method, density method, adsorption method, mercury intrusion method, and metallographic test method, etc. The non-destructive testing methods include: acoustic emission detection technology, industrial detection technology, microwave detection technology, and ultrasonic detection technology, etc. However, the measurement time often takes several hours, and the measurement cost is high. Since the porosity of rock affects the mechanical properties of rock, can the porosity of rock be deduced based on the mechanical properties of rock? When conducting conventional mechanical tests, if the porosity of rock can be measured simultaneously, the workload will be further reduced, time will be saved, and efficiency will be improved. Therefore, the present invention provides a method for measuring the porosity of rock based on a stress-strain curve. Summary of the Invention

[0004] The purpose of the present invention is to provide a simple and effective method for testing the porosity of rock, to explore new applications in the conventional rock stress-strain test data, measure the porosity, realize the full utilization of test data, reduce the labor intensity, and improve the efficiency.

[0005] To achieve the above purpose, the present invention provides a method for measuring the porosity of rock based on a stress-strain curve, including:

[0006] Obtaining information on the elastic deformation process of the rock;

[0007] Based on the information on the elastic deformation process of the rock, constructing a stress-strain model of the rock to be measured;

[0008] Use the stress-strain model to obtain the pore strain information of the rock to be measured;

[0009] Based on the pore strain information of the rock to be measured, construct a relationship model between pore strain and rock porosity;

[0010] Based on the relationship model between pore strain and rock porosity, obtain the porosity of the rock to be measured.

[0011] Optionally, using the stress-strain model to obtain the pore strain information of the rock to be measured includes:

[0012] Based on the stress-strain model, construct a stress-strain hyperbolic model of the rock to be measured;

[0013] Based on the stress-strain hyperbolic model, obtain the pore strain information of the rock to be measured.

[0014] Optionally, based on the stress-strain model, constructing the stress-strain hyperbolic model of the rock to be measured includes:

[0015] Based on the downward convex characteristic of the stress-strain model curve, use a hyperbola to fit the stress-strain hyperbolic model of the rock to be measured to obtain the stress-strain hyperbolic model of the rock to be measured.

[0016] Optionally, after constructing the stress-strain hyperbolic model of the rock to be measured, it further includes:

[0017] Based on the least squares method, perform nonlinear fitting on the stress-strain hyperbolic model of the rock to be measured to obtain the undetermined coefficients in the stress-strain hyperbolic model of the rock to be measured.

[0018] Optionally, performing nonlinear fitting on the hyperbolic model of the stress-strain curve of the rock to be measured includes:

[0019] Obtain the stress-strain data in the information of the elastic deformation process of the rock, and based on the stress-strain data, perform nonlinear fitting on the stress-strain data.

[0020] Optionally, the stress-strain hyperbolic model of the rock to be measured is:

[0021]

[0022] Wherein, σ is the stress, ε is the strain; a and b are the undetermined coefficients of the model.

[0023] Optionally, the pore strain ε of the rock to be measured , , , g ,

[0024] ,

[0023] ,

[0022] (σ) The calculation method is:

[0024]

[0025] Optionally, the relationship model between pore strain and rock porosity is:

[0026]

[0027] Where η is the porosity of rock.

[0028] Technical Effects of the Invention: This invention establishes a hyperbolic model of rock stress-strain curves, demonstrates the relationship between model parameters and rock porosity, and enables the porosity of rock samples to be calculated using only the stress-strain curve of the rock's elastic deformation process under uniaxial loading, eliminating the need for separate experimental porosity measurements. This significantly reduces labor intensity and improves the efficiency of rock porosity calculations. Furthermore, the concept of porosity is introduced into the established hyperbolic model of rock stress-strain curves, which is of great significance for the subsequent study of nonlinear rock mechanical properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0030] Figure 1 This is a flowchart of a method for calculating rock porosity based on a stress-strain curve according to an embodiment of the present invention;

[0031] Figure 2 is the stress-strain curve of the rock elastic deformation process in an embodiment of the present invention;

[0032] Figure 3 A comparison chart of the rock stress-strain curve measured results and the hyperbola fitting results in an embodiment of the present invention;

[0033] Figure 4 This is a curve showing the change of rock pore strain with stress in an embodiment of the present invention. DETAILED DESCRIPTION

[0034] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0035] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0036] like Figure 1As shown in the figure, in this embodiment, a method for calculating the porosity of rock based on the stress-strain curve is provided, including:

[0037] Step 1: Conduct an elastic deformation test on a standard rock specimen under uniaxial loading, measure the stress and strain data during the elastic deformation process of the rock, and draw the stress-strain curve of the rock to be measured. In order to ensure that the measured stress and strain of the rock are in the elastic deformation stage (i.e., after the load is removed, the rock deformation can be completely restored, including the compaction stage and the linear elastic stage), it is appropriate to set the maximum load during the loading process to half of the peak load of the rock loading failure.

[0038] Step 2: Establish a hyperbolic model of the rock stress-strain curve, and determine the undetermined coefficients of the hyperbolic model of the rock stress-strain curve based on the least squares method.

[0039] First, according to the characteristic that the stress-strain curve of the rock specimen under uniaxial compression is mostly convex downward, establish a mathematical model for fitting the stress-strain nonlinear curve with a hyperbola, that is:

[0040]

[0041] In the formula, σ is the stress, ε is the strain; a and b are the undetermined coefficients of the model.

[0042] The basis for establishing this model is as follows: There are various pores in the rock. After the rock is compressed, the pores will be compacted, and the solid particles will also deform. The total strain of the rock comes from these two parts. At the initial stage of loading, the pore deformation is more obvious and makes a greater contribution to the total deformation of the rock; as the load increases, the pores are gradually compacted, and the contribution of pore deformation to the rock deformation becomes smaller and smaller, but it will not completely disappear; theoretically, when the rock strength is large enough and the load approaches infinity, the pores are infinitely close to the completely compacted state, and this process is similar to the process of a hyperbola approaching the asymptote infinitely. Moreover, comparing the stress-strain curve of the rock elastic deformation process with the hyperbola has similar morphological change characteristics. Therefore, it is reasonable to use a hyperbola to fit the stress-strain curve of the rock elastic deformation process.

[0043] Then, use the MATLAB nonlinear fitting method to fit the measured (ε, σ) data points to obtain the optimal undetermined coefficients a and b.

[0044] Step 3: Calculate the pore strain of the rock using the hyperbolic model. There is a close relationship between the pore strain and the porosity of the rock. In essence, this invention uses the pore strain to infer the porosity of the rock, so it is crucial to calculate the pore strain. The pore strain ε g (σ) calculation formula is:

[0045]

[0046] Step 4: Establish a relationship model between pore strain and rock porosity. According to the definitions of rock porosity and pore strain, the relationship between the two is derived as follows: when the stress approaches infinity, the pores tend to be completely compacted, and the limit of pore strain is the rock porosity. The relationship model is:

[0047]

[0048] It can be seen from Equation (3) that the porosity of the rock is equal to the undetermined coefficient b of the hyperbolic model of the stress-strain curve. By determining the parameter b, the porosity of the rock can be measured.

[0049] The following further describes the present invention by taking granite with a peak strength of 240 MPa as an example in conjunction with the attached drawings:

[0050] Step 1: Taking granite with a peak strength of 240 MPa as an example, conduct a deformation test on the standard rock specimen under uniaxial loading. The load is applied from 0 MPa to 120 MPa, and the stress and strain data during the elastic deformation process of the rock are measured. Draw the stress-strain curve of the elastic deformation process of the rock to be measured, as Figure 2 shown.

[0051] Step 2: Establish and solve the hyperbolic model of the rock stress-strain curve. It can be seen from Figure 2 that the relationship between stress and strain presents a downward-convex non-linear curve, approximately following a hyperbolic relationship.

[0052] Based on the least squares method, perform non-linear fitting on the rock stress-strain curve. The fitting results are shown in Figure 3 shown. It can be seen from Figure 3 that the correlation coefficient between the measured results and the fitting curve can reach 0.9999, and the two are highly correlated, and the fitting results are reasonable. The undetermined coefficients a and b of the hyperbolic model determined by non-linear fitting are respectively:

[0053]

[0054] Step 3: Calculate the pore strain of the rock using the hyperbolic model. Substitute Equation (4) into Equation (2) to obtain the expression of the pore strain ε g (σ) of the rock:

[0055]

[0056] As Figure 4 shown, as the stress σ increases, the pore strain does not increase indefinitely, but approaches a fixed value infinitely; when the stress σ approaches infinity, the limit of ε g (σ) converges.

[0057] Step 4: Construct a relationship model between pore strain and rock porosity, and calculate the rock porosity. The rock porosity can be calculated using formula (3):

[0058] η = b = 0.1048% (6)

[0059] Therefore, as calculated, the porosity of the measured rock sample is η = 0.1048%.

[0060] By looking up the table, it can be known that the porosity of granite generally ranges from 0.04% to 2.80%. The calculated porosity of the granite is within this range, which is relatively reasonable.

[0061] The greatest advantage of the present invention is that a hyperbolic model of the rock stress-strain curve is established, the relationship between the model parameters and the rock porosity is demonstrated, and it is realized that the porosity of the rock sample can be measured only by using the stress-strain curve of the uniaxial loading elastic deformation process of the rock, without the need to conduct additional tests to measure the porosity of the rock sample, which can greatly reduce the labor intensity and improve the efficiency of measuring the rock porosity. Moreover, the concept of porosity is introduced into the established hyperbolic model of the rock stress-strain curve, which is of great significance for the research on the subsequent nonlinear mechanical properties of rocks.

[0062] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by 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 calculating the porosity of rock based on the stress-strain curve, characterized in that, Including: Obtaining information on the elastic deformation process of the rock; Based on the information on the elastic deformation process of the rock, constructing a stress-strain model of the rock to be measured; Using the stress-strain model to obtain information on the pore strain of the rock to be measured, including: Based on the stress-strain model, constructing a stress-strain hyperbolic model of the rock to be measured; Based on the stress-strain hyperbolic model, obtaining information on the pore strain of the rock to be measured; Based on the information on the pore strain of the rock to be measured, constructing a relationship model between pore strain and rock porosity; Based on the relationship model between pore strain and rock porosity, obtaining the porosity of the rock to be measured.

2. The method for calculating the porosity of a rock based on a stress-strain curve according to claim 1, wherein , constructing the stress-strain hyperbolic model of the rock to be measured based on the stress-strain model includes: Based on the downward convex characteristic of the stress-strain model curve, using a hyperbola to fit the stress-strain hyperbolic model of the rock to be measured to obtain the stress-strain hyperbolic model of the rock to be measured.

3. The method for calculating the porosity of rock based on the stress-strain curve according to claim 1, wherein, After constructing the stress-strain hyperbolic model of the rock to be measured, it further includes: Based on the least squares method, performing nonlinear fitting on the stress-strain hyperbolic model of the rock to be measured to obtain the undetermined coefficients in the stress-strain hyperbolic model of the rock to be measured.

4. The method for calculating the porosity of rock based on the stress-strain curve according to claim 3, wherein, Performing nonlinear fitting on the hyperbolic model of the stress-strain curve of the rock to be measured includes: Obtaining the stress-strain data in the information on the elastic deformation process of the rock, and based on the stress-strain data, performing nonlinear fitting on the stress-strain data.

5. A method for calculating the porosity of a rock based on a stress-strain curve according to claim 1, characterized in that, The stress-strain hyperbolic model of the rock to be measured is: where σ is stress, ε is strain; a and b are undetermined coefficients of the model.

6. The method for calculating the porosity of rock based on the stress-strain curve according to claim 5, characterized in that The pore strain information ε of the rock to be measured g (σ) The calculation method is as follows:

7. The method for calculating the porosity of rock based on the stress-strain curve according to claim 6, wherein, The relationship model between pore strain and rock porosity is: where η is rock porosity.

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