Rock elastic medium elastic modulus measurement method and system

Abstract

The present application relates to a kind of rock elastic medium elastic modulus measurement method and system, comprising: obtaining rock elastic deformation process data information;Based on the rock elastic deformation process data information generation rock stress-strain curve;Based on the rock stress-strain curve the hyperbolic model of rock stress-strain curve is established;Based on the hyperbolic model of rock stress-strain curve rock elastic medium elastic modulus is measured.The present application realizes only with rock uniaxial loading elastic deformation process stress-strain curve, i.e. rock elastic medium elastic modulus can be measured, and it has important promoting effect to the improvement of deep nonlinear rock mechanics system.

Description

Technical Field

[0001] This invention relates to the field of elastic modulus calculation technology, and in particular to a method and system for calculating the elastic modulus of rock elastic media. Background Technology

[0002] As is well known, the elastic modulus of rock is a fundamental mechanical indicator characterizing the elastic deformation of rocks. However, after hundreds of millions of years of geological processes, the widespread micropores and cracks within rocks cause their stress-strain relationships to exhibit strong nonlinear characteristics; such rocks are called "nonlinear elastic rocks." Conventional methods for determining the elastic modulus of rocks often rely on the tangential slope of the linear elastic stage of the rock's stress-strain curve. Using this method, the measured elastic modulus of the rock exhibits significant dispersion, causing considerable inconvenience in engineering applications. The reason for this is that even for the same lithology, differences in occurrence conditions and geological processes result in varying porosities within the rock. Porosity is the tangential modulus E of the rock's linear elastic deformation stage. t A key influencing factor. Generally, the greater the porosity, the higher the tangential modulus E of the rock during the linear elastic deformation stage. t The smaller the tangential modulus E of the linear elastic deformation stage of rock, the greater the tangential modulus E; conversely, the larger the tangential modulus E, the greater the tangential modulus E. t The elastic modulus is the result of the combined effects of the elastic medium and porosity in the rock. Using the tangential modulus Et of the linear elastic deformation stage to measure the deformation characteristics of nonlinear elastic rocks is not accurate enough. Therefore, there is an urgent need for a method to calculate the elastic modulus that is unaffected by porosity and has engineering or scientific significance. Summary of the Invention

[0003] The purpose of this invention is to address the aforementioned technical problems by proposing a method and system for calculating the elastic modulus of rock elastic media, accurately calculating the elastic modulus of rock elastic media, and promoting the construction of deep nonlinear rock mechanics systems.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A method for calculating the elastic modulus of rock elastic media, comprising:

[0006] Obtain data on the elastic deformation process of rocks;

[0007] Based on the data information of the rock elastic deformation process, a rock stress-strain curve is generated;

[0008] A hyperbolic model of the rock stress-strain curve is established based on the rock stress-strain curve.

[0009] The elastic modulus of the rock elastic medium is calculated based on the hyperbolic model of the rock stress-strain curve.

[0010] Furthermore, generating the stress-strain curve of the rock includes:

[0011] A rock elastic deformation test under uniaxial loading was conducted to measure the stress and strain data of the rock during the elastic deformation process, and the stress-strain curve of the rock was obtained based on the stress and strain data.

[0012] Furthermore, during the rock elastic deformation test under uniaxial loading, the maximum load during loading is half of the peak load at which the rock fails, in order to ensure that the measured rock stress and strain data are in the elastic deformation stage.

[0013] Furthermore, establishing a hyperbolic model of the rock stress-strain curve includes:

[0014] Based on the characteristic that the stress-strain curve of the rock under uniaxial compression is convex downward, the undetermined coefficients of the hyperbolic mathematical model of the stress-strain curve of the rock are obtained by fitting the hyperbolic model of the stress-strain curve of the rock, and the hyperbolic model of the stress-strain curve of the rock is obtained.

[0015] Furthermore, the hyperbolic mathematical model of the rock stress-strain curve is as follows:

[0016]

[0017] Where σ is stress, ε is strain, and a and b are undetermined coefficients of the model.

[0018] Furthermore, the least squares method is used to obtain the undetermined coefficients of the hyperbolic mathematical model of the rock stress-strain curve.

[0019] Furthermore, the undetermined coefficients of the hyperbolic mathematical model for obtaining the stress-strain curve of the rock include:

[0020] An asymptote model of the hyperbolic mathematical model of the rock stress-strain curve is constructed. A nonlinear fitting method is used to fit the measured strain and stress data, and the undetermined coefficients of the hyperbolic mathematical model of the rock stress-strain curve are calculated.

[0021] Furthermore, the calculation of the elastic modulus of the rock elastic medium based on the hyperbolic model of the rock stress-strain curve includes:

[0022] The slope of the asymptote model is calculated based on the undetermined coefficients of the hyperbolic mathematical model of the rock stress-strain curve. This slope is the elastic modulus E0 of the rock's elastic medium, calculated using the following formula:

[0023]

[0024] To further optimize the technical solution, the present invention also provides a system for calculating the elastic modulus of rock elastic media, comprising:

[0025] The data acquisition module is used to acquire stress and strain data of the rock elastic deformation process based on rock elastic deformation tests;

[0026] The model building module is used to plot the rock stress-strain curve based on the stress and strain data of the rock elastic deformation process, and to construct a hyperbolic model of the rock stress-strain curve based on the rock stress-strain curve.

[0027] The calculation module is used to calculate the elastic modulus of the rock elastic medium based on the hyperbolic model of the rock stress-strain curve.

[0028] The beneficial effects of this invention are as follows:

[0029] This invention views rock as an elastic body composed of two parts: pores and an elastic medium. Since the elastic medium is independent of the pores, its elastic modulus is not affected by porosity and can more accurately reflect the elastic mechanical properties of rock. Therefore, a new concept of "elastic modulus of rock elastic medium" is proposed. Based on the established hyperbolic model of rock stress-strain curve and the quantitative relationship between model parameters and the elastic modulus of rock elastic medium, the elastic modulus of rock elastic medium can be calculated using only the stress-strain curve of the rock's uniaxial loading elastic deformation process. This has an important promoting effect on the construction of deep nonlinear rock mechanics systems. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a flowchart of a method for calculating the elastic modulus of rock elastic media according to an embodiment of the present invention;

[0032] Figure 2 This is a stress-strain curve diagram of the elastic deformation process of rock according to an embodiment of the present invention;

[0033] Figure 3 This is a comparison chart of the measured results of the rock stress-strain curve and the hyperbola fitting results in an embodiment of the present invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] Example 1

[0037] This embodiment provides a method for calculating the elastic modulus of rock elastic media, such as... Figure 1 As shown, it includes:

[0038] S1. Conduct elastic deformation tests on standard rock specimens under uniaxial loading, measure the stress and strain data of the rock during the elastic deformation process, and plot the stress-strain curve of the rock to be tested.

[0039] In order to ensure that the measured rock stress and strain are in the elastic deformation stage (i.e., the rock deformation can be fully recovered after the load is removed, including the compaction stage and the linear elastic stage), the maximum load during the loading process is set to half of the peak load of rock loading failure.

[0040] S2. 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.

[0041] Based on the characteristic that the stress-strain curves of rock specimens under uniaxial compression conditions are mostly convex downwards, a mathematical model is established to fit the nonlinear stress-strain curve using a hyperbola, namely:

[0042]

[0043] Where σ is stress, ε is strain, and a and b are undetermined coefficients of the model.

[0044] The asymptotes of the hyperbola are:

[0045]

[0046] Then, using a nonlinear fitting method, the measured (ε, σ) data points are fitted to obtain the optimal undetermined coefficients a and b.

[0047] S3. Calculate the elastic modulus of rock elastic medium using a hyperbolic model.

[0048] As stress approaches infinity, the pores tend to be fully compacted. At this point, the rock can be considered an elastic body composed only of elastic media, with a porosity of 0. The stress-strain hyperbola of the rock approaches its asymptote, and the limiting tangential elastic modulus of the rock is equal to the elastic modulus of the elastic media, which is equal to the slope of the asymptote, i.e.:

[0049]

[0050] As can be seen from the above formula, the elastic modulus of rock elastic medium is related to the undetermined coefficients a and b of the stress-strain curve hyperbolic model. The elastic modulus E0 of rock elastic medium can be calculated by using a and b.

[0051] Example 2

[0052] This embodiment uses granite with a peak strength of 240 MPa as an example.

[0053] S1. Conduct deformation tests on standard rock specimens under uniaxial loading, with the load increasing from 0 MPa to 120 MPa. Measure the stress and strain data during the elastic deformation process of the rock, and plot the stress-strain curves of the elastic deformation process of the rock. Figure 2 As shown.

[0054] S2. Establish and solve a hyperbolic model of the rock stress-strain curve. Figure 2 It can be seen that the stress-strain relationship presents a downward-convex nonlinear curve, approximately conforming to a hyperbolic relationship.

[0055] Nonlinear fitting of rock stress-strain curves based on the least squares method, such as... Figure 3 As shown, the correlation coefficient between the measured results and the fitted curve reaches 0.9999, indicating a high correlation and reasonable fitting results. The undetermined coefficients a and b of the hyperbolic model determined by nonlinear fitting are as follows:

[0056]

[0057] S3. Using the hyperbolic model to calculate the elastic modulus of the rock elastic medium, the elastic modulus of the rock elastic medium is obtained as follows:

[0058]

[0059] Therefore, the elastic modulus of the rock sample can be obtained as E0 = 11.924 × 10⁻⁶. 4 MPa, according to conventional methods, the tangential modulus of the rock sample in the linear elastic deformation stage is calculated as E. t =9.6534×10 4 MPa. The calculation of E0 has eliminated the influence of rock porosity and represents the elastic modulus when the rock sample porosity is 0. It is generally higher than E... tThe calculated result (due to the influence of porosity) is too large, so the calculated result of E0 is reasonable.

[0060] Example 3

[0061] This embodiment provides a system for calculating the elastic modulus of rock elastic media, including:

[0062] The data acquisition module is used to acquire stress and strain data of the rock elastic deformation process based on rock elastic deformation tests;

[0063] The model building module is used to plot the stress-strain curve of rock based on the stress and strain data of the rock elastic deformation process, and to build a hyperbolic model of the rock stress-strain curve based on the rock stress-strain curve.

[0064] The calculation module is used to calculate the elastic modulus of rock elastic media based on the hyperbolic model of rock stress-strain curve;

[0065] The data acquisition module, model building module, and calculation module are connected sequentially.

[0066] This invention views rock as an elastic body composed of two parts: pores and an elastic medium. Since the elastic medium is independent of the pores, its elastic modulus is not affected by porosity and can more accurately reflect the elastic mechanical properties of rock. Therefore, a new concept of "elastic modulus of rock elastic medium" is proposed. Based on the established hyperbolic model of rock stress-strain curve and the quantitative relationship between model parameters and the elastic modulus of rock elastic medium, the elastic modulus of rock elastic medium can be calculated using only the stress-strain curve of the rock's uniaxial loading elastic deformation process. This has an important promoting effect on the construction of deep nonlinear rock mechanics systems.

[0067] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for calculating the elastic modulus of rock elastic media, characterized in that, include: Obtain data on the elastic deformation process of rocks; Based on the data information of the rock elastic deformation process, a rock stress-strain curve is generated; A hyperbolic model of the rock stress-strain curve is established based on the rock stress-strain curve. The elastic modulus of the rock elastic medium is calculated based on the hyperbolic model of the rock stress-strain curve. The hyperbolic mathematical model of the rock stress-strain curve is as follows: Where σ is stress, ε is strain, and a and b are undetermined coefficients of the model.

2. The method for calculating the elastic modulus of rock elastic media according to claim 1, characterized in that, Generating the stress-strain curve of the rock includes: A rock elastic deformation test under uniaxial loading was conducted to measure the stress and strain data of the rock during the elastic deformation process, and the stress-strain curve of the rock was obtained based on the stress and strain data.

3. The method for calculating the elastic modulus of rock elastic media according to claim 2, characterized in that, When conducting the rock elastic deformation test under uniaxial loading, the maximum load during the loading process is half of the peak load at which the rock fails, in order to ensure that the measured rock stress and strain data are in the elastic deformation stage.

4. The method for calculating the elastic modulus of rock elastic media according to claim 1, characterized in that, Establishing the hyperbolic model of the rock stress-strain curve includes: Based on the characteristic that the stress-strain curve of the rock under uniaxial compression is convex downward, the undetermined coefficients of the hyperbolic mathematical model of the stress-strain curve of the rock are obtained by fitting the hyperbolic model of the stress-strain curve of the rock, and the hyperbolic model of the stress-strain curve of the rock is obtained.

5. The method for calculating the elastic modulus of rock elastic media according to claim 4, characterized in that, The least squares method is used to obtain the undetermined coefficients of the hyperbolic mathematical model of the rock stress-strain curve.

6. The method for calculating the elastic modulus of rock elastic media according to claim 4, characterized in that, The undetermined coefficients of the hyperbolic mathematical model for obtaining the stress-strain curve of the rock include: An asymptote model of the hyperbolic mathematical model of the rock stress-strain curve is constructed. A nonlinear fitting method is used to fit the measured strain and stress data, and the undetermined coefficients of the hyperbolic mathematical model of the rock stress-strain curve are calculated.

7. The method for calculating the elastic modulus of rock elastic media according to claim 6, characterized in that, The calculation of the elastic modulus of rock elastic medium based on the hyperbolic model of the rock stress-strain curve includes: The slope of the asymptote model is calculated based on the undetermined coefficients of the hyperbolic mathematical model of the rock stress-strain curve. This slope is the elastic modulus E0 of the rock's elastic medium, calculated using the following formula:

8. A calculation system based on the method for calculating the elastic modulus of rock elastic media according to claim 1, comprising: The data acquisition module is used to acquire stress and strain data of the rock elastic deformation process based on rock elastic deformation tests; The model building module is used to plot the rock stress-strain curve based on the stress and strain data of the rock elastic deformation process, and to construct a hyperbolic model of the rock stress-strain curve based on the rock stress-strain curve. The calculation module is used to calculate the elastic modulus of the rock elastic medium based on the hyperbolic model of the rock stress-strain curve.

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