A method for constructing a nonlinear elastic constitutive model of rock considering porosity

Abstract

The present invention discloses a method for constructing a nonlinear elastic constitutive model of rock that takes porosity into account. The method comprises: conducting an indoor uniaxial compression test on rock to obtain a stress-strain curve for the rock's elastic deformation; constructing a hyperbolic stress-strain model for the rock's elastic deformation based on the stress-strain curve, and determining the parameters of the hyperbolic stress-strain model; obtaining a quantitative relationship between the model parameters and physical and mechanical indices using the parameters of the hyperbolic stress-strain model; and establishing a nonlinear elastic constitutive model of rock that takes porosity into account based on the quantitative relationship between the model parameters and the physical and mechanical indices. This method achieves a unified quantitative description of the compaction and linear elastic stages of the rock's elastic deformation process, significantly contributing to the improvement of the theoretical system of nonlinear elastic rock mechanics.

Description

Technical Field

[0001] The present invention relates to the field of geotechnical engineering technology, and in particular to a method for constructing a rock nonlinear elastic constitutive model taking porosity into consideration. Background Art

[0002] Deep hard rock tunnels are widely used in hydropower, transportation, mining, nuclear waste disposal, and national defense. Deep hard rock failure differs from shallow conditions in that the intact brittle rock mass is cut by parallel cracks, forming layers of rock slabs (sheets) approximately parallel to the excavation surface. This failure phenomenon is known as slab cracking. Slab cracking is closely related to the propagation and penetration of tensile cracks within the surrounding rock. It is a typical failure mode of deep hard rock. It not only poses many adverse factors to the construction, support, and maintenance of tunnels in deep hard rock mining, seriously affecting the long-term stability of the tunnels, but also exhibits a clear correlation and essential connection with the occurrence of rockburst hazards, and is considered a precursor to rockbursts. With increasing depth, the rock slabs formed by slab cracking break and suddenly separate from the surrounding rock, causing rockbursts. The resulting dynamic disasters often cause casualties, equipment damage, and project delays, posing a significant challenge to the safe, efficient, and sustainable development of deep hard rock tunnels and shafts. Deep rock slab cracking is closely related to nonlinear rock deformation. The key to calculating nonlinear rock stress in deep tunnels is to rationally construct a nonlinear elastic constitutive model for rock. This is also an important foundation for developing strategies to prevent and control deep rock slab cracking.

[0003] At present, there have been many studies on the nonlinear elastic constitutive equation of rock. Rock is regarded as a nonlinear elastic body. Based on the double-strain Hooke model, the rock mass composed of "soft body" (pores and cracks) and "hard body" (the complete skeleton without pores and cracks) is characterized by two different parts of Hooke's law. Some scholars believe that the pores of rock cannot be completely compacted, but rather infinitely approach a constant value, and propose the concept of compaction factor. The existing technology proposes the concept of void strain ratio K, establishes an exponential function to represent the nonlinear elastic constitutive model, and proposes a hyperbolic nonlinear elastic constitutive model of rock, see formula (32), which is obtained by translating the inverse proportional function. Although these models reflect the nonlinear characteristics of rock compaction stage to a certain extent, there are still some problems, which are mainly reflected in the essential connection between the pores of rock and the nonlinear deformation of rock, and the previous models lack parameters related to rock pores.

[0004]

[0005] Incorporating parameters reflecting rock porosity (such as porosity) into the constitutive model can establish a more reasonable nonlinear constitutive model of rock. Therefore, it is urgent to establish a nonlinear constitutive model of rock with porosity and other rock physical and mechanical indicators as the main parameters. Summary of the Invention

[0006] The purpose of the present invention is to address the deficiencies in the prior art and propose a method for constructing a nonlinear elastic constitutive model of rock taking porosity into consideration. A nonlinear elastic constitutive model of rock is established with porosity and elastic modulus of rock elastic medium as basic parameters. The model parameters have clear physical meanings and can all be obtained based on experiments, and have wide applicability.

[0007] To achieve the above objectives, the present invention provides a method for constructing a nonlinear elastic constitutive model of rock considering porosity, comprising:

[0008] Conduct indoor uniaxial compression tests on rocks to obtain rock elastic deformation stress-strain data;

[0009] constructing a rock elastic deformation stress-strain hyperbola model based on the rock elastic deformation stress-strain data, and determining parameters of the rock elastic deformation stress-strain hyperbola model;

[0010] Obtaining the quantitative relationship between the model parameters and the physical and mechanical indicators through the parameters of the rock elastic deformation stress-strain hyperbola model;

[0011] Based on the quantitative relationship between the model parameters and physical and mechanical indicators, a nonlinear elastic constitutive model of rock considering porosity is established.

[0012] Preferably, constructing the rock elastic deformation stress-strain hyperbola model includes:

[0013] Analyze the changing characteristics of the hyperbola and the similarity between the hyperbola and the stress-strain curve of the rock elastic deformation process, and obtain the hyperbola equation and its asymptote after translation;

[0014] A nonlinear constitutive model of rock based on hyperbola is established, and a nonlinear elastic constitutive model of rock based on hyperbola and the asymptotes of the constitutive equation are obtained.

[0015] Preferably, determining the parameters of the rock elastic deformation stress-strain hyperbola model includes:

[0016] The parameters of the hyperbolic nonlinear elastic constitutive model of rock are determined by fitting the stress and strain data obtained from the indoor rock uniaxial compression test according to the least squares method.

[0017] Preferably, obtaining the quantitative relationship between the model parameters and the physical and mechanical indicators includes:

[0018] Abstract the rock into a porous elastic body, introduce the concept of porous elastic body, and obtain the PE properties;

[0019] Through the hyperbolic nonlinear constitutive model of rock, the quantitative relationship between the model parameters and the elastic modulus of the rock elastic medium, as well as the quantitative relationship between the model parameters and the rock porosity are constructed.

[0020] Preferably, the PE properties include:

[0021] PE has infinite strength; under infinite stress, PE approaches a completely compacted state infinitely; the limiting tangent modulus of PE is equal to the elastic modulus of the elastic medium; and the deformation of PE has nonlinear elasticity.

[0022] Preferably, constructing a quantitative relationship between the model parameters and the elastic modulus of the rock elastic medium includes:

[0023] Derivative the hyperbolic nonlinear constitutive model of rock with respect to strain to obtain a tangent elastic modulus model;

[0024] Based on the tangent elastic modulus model, the stress magnitude is changed, and when the stress tends to infinity, the strain tends to infinity, thereby obtaining a limiting tangent elastic modulus model;

[0025] According to the property that the PE limiting tangent elastic modulus is equal to the elastic modulus of the PE elastic medium, a quantitative relationship between the model parameters and the elastic modulus of the rock elastic medium is obtained.

[0026] Preferably, constructing a quantitative relationship between the model parameters and rock porosity includes:

[0027] Setting stress increase conditions, obtaining PE deformation and PE length before deformation, and calculating a total strain increment, wherein the total strain increment includes an elastic medium strain increment and a pore strain increment;

[0028] Obtaining a reduction in pore volume through the pore strain increment;

[0029] Obtaining a porosity reduction model through the pore strain increment and the pore volume reduction;

[0030] Based on the porosity reduction model, a hyperbola-based nonlinear elastic constitutive model of rock is obtained;

[0031] According to the hyperbolic nonlinear elastic constitutive model of rock, the stress is increased, and when the rock is close to a fully compressed state, a quantitative relationship between the model parameters and the rock porosity is obtained.

[0032] Preferably, establishing the nonlinear elastic constitutive model of rock considering porosity includes:

[0033] Obtain rock elastic deformation stress-strain data through experiments and construct a rock elastic deformation stress-strain hyperbola model;

[0034] Based on the rock elastic deformation stress-strain hyperbola model, the physical meanings of the parameters in the rock nonlinear constitutive equation are obtained, porosity is introduced into the hyperbola-based rock nonlinear elastic constitutive model, and a general form of the rock nonlinear elastic constitutive model characterized by the elastic modulus of the rock elastic medium and the rock porosity is obtained;

[0035] Based on the elastic modulus and porosity of the rock elastic medium, the nonlinear elastic constitutive model of the rock considering the porosity is obtained.

[0036] Compared with the prior art, the present invention has the following advantages and technical effects:

[0037] (1) In order to accurately describe the nonlinear mechanical behavior of rocks, the present invention constructs a nonlinear elastic constitutive model of rocks based on hyperbolas, and introduces two important physical and mechanical parameters, "rock porosity" and "elastic modulus of rock elastic medium", into the model; establishes a more essential quantitative relationship between the nonlinear deformation of rocks and their main influencing factors, and realizes a unified quantitative description of the compaction stage and the linear elastic stage of the rock elastic deformation process, which plays an important role in promoting the improvement of the theoretical system of nonlinear elastic rock mechanics.

[0038] (2) The constitutive model constructed by the present invention has a simple structure and clear physical meanings of the model parameters. In particular, the physical meanings of the model parameters have important application value. A simple uniaxial compression test of rock can be performed and two important physical and mechanical indicators of the rock's elastic medium, the elastic modulus and porosity, can be measured simultaneously, thus opening up a new path for the determination of these two indicators. In addition, based on the established nonlinear constitutive model of rock, the quantitative relationship between the rock's shear modulus and secant modulus and stress can be obtained, providing an important theoretical basis for the calculation of the nonlinear elastic modulus distribution and nonlinear stress distribution of the surrounding rock in deep buried tunnels. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] 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:

[0040] Figure 1 This is a flowchart of the steps of a method for constructing a nonlinear elastic constitutive model of rock taking porosity into consideration in an embodiment of the present invention;

[0041] Figure 2 is a stress-strain curve diagram of the rock elastic deformation process according to an embodiment of the present invention;

[0042] Figure 3Schematic diagram of a hyperbola and asymptotes according to an embodiment of the present invention, (a) is the standard equation of the hyperbola and its asymptotes, (b) is the hyperbola and its asymptotes in the first quadrant after translation;

[0043] Figure 4 This is a schematic diagram of the rock in an embodiment of the present invention being equivalent to a porous elastic body under pressure;

[0044] Figure 5 This is a comparison chart of the measured results of the rock stress-strain curve and the constructed constitutive equation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0045] 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.

[0046] 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.

[0047] like Figure 1 As shown in FIG, a method for constructing a nonlinear elastic constitutive model of rock considering porosity includes the following steps:

[0048] Step 1: Conduct indoor rock uniaxial compression test

[0049] The present invention is mainly about the elastic deformation process of rock, and there are some special requirements for the indoor rock uniaxial compression test carried out. The rock used in the test of this embodiment is granite, and its peak strength is 240MPa. The specimen is a standard cylindrical specimen with a diameter of 50mm and a height of 100mm, and the non-parallelism of the upper and lower end faces must be controlled within 0.01mm. During the loading process, polytetrafluoroethylene plates cannot be placed between the upper and lower end faces of the specimen and the pressure plate of the press. The standard specimen is placed in the press chamber, and a deformation test of the standard rock specimen under uniaxial loading is carried out. The load is loaded from 0MPa to 120MPa, and the loading is stopped and unloaded. This process records and saves stress and displacement data in real time.

[0050] Step 2: Obtain the rock elastic deformation stress-strain relationship curve

[0051] According to the displacement data measured in step 1, calculate the strain data of the rock loading process. According to the stress and strain data, draw the stress-strain curve of the rock elastic deformation process as shown in Figure 2 As shown. Figure 2It can be seen that the elastic deformation process of rock can be divided into two stages, the compaction stage and the linear elastic stage; in the compaction stage, the stress-strain curve of rock presents a convex nonlinear characteristic; in the linear elastic stage, the stress-strain curve of rock presents a linear characteristic.

[0052] Step 3: Establish rock elastic deformation stress-strain hyperbola model

[0053] Step 3.1 Analyze the characteristics of hyperbolic changes

[0054] Generally, there are two forms of the standard equation of a hyperbola: one with the focus on the horizontal axis and the other with the focus on the vertical axis. Considering the downward convex variation of stress-strain, the latter should be chosen, and the standard equation of the hyperbola is:

[0055]

[0056] Where σ is stress, ε is strain, and a and b are parameters of the model.

[0057] The asymptotes of the standard equation hyperbola are:

[0058]

[0059] Step 3.2 Analyze the similarity between the hyperbola and the stress-strain curve of the rock elastic deformation process

[0060] Figure 3 (a) is a diagram of the standard equation of the hyperbola and its asymptotes. Figure 3 (a) and Figure 2 It can be seen that in the first quadrant, the stress-strain curve of the nonlinear elastic deformation process of rock is similar to the trend of the hyperbola, except that the hyperbola does not pass through the origin. Therefore, it is necessary to appropriately transform the standard equation of the hyperbola, that is, to shift it downward by a unit. The equation of the hyperbola and its asymptote after the shift are:

[0061]

[0062] The asymptotes of the standard equation hyperbola are:

[0063]

[0064] In the first quadrant of the coordinate system, the hyperbola after translation is as follows Figure 3 (b) shows the comparison. Figure 2 and Figure 3 (b) It can be seen that the translated hyperbola is highly similar to the rock stress-strain curve in terms of starting point, curve shape, and change trend. Therefore, the translated hyperbola can be used to quantitatively describe the nonlinear stress-strain curve of rock.

[0065] Step 3.3 Establish a nonlinear constitutive model of rock based on hyperbola

[0066] By transforming formula (5), we can obtain the nonlinear elastic constitutive model of rock based on hyperbola, namely:

[0067]

[0068] The asymptote of this constitutive equation is:

[0069]

[0070] Formula (5) is a nonlinear elastic constitutive model for rock based on a hyperbola, but the physical meaning of the parameters in this equation is unclear. To establish a constitutive model with porosity and other rock physical and mechanical indicators as the main parameters, it is necessary to further demonstrate the physical meaning of the model parameters a and b and establish a quantitative relationship between a and b and the rock porosity and other physical and mechanical indicators. Since there are two model parameters, the following will first demonstrate the relationship between the model parameters and the elastic modulus E0 of the rock elastic medium using PE property 3 to establish the first relationship; then discuss the relationship between the model parameters and porosity η0 to establish the second relationship. The combination of these two relationships can achieve the replacement of model parameters a and b by E0 and η0, thereby achieving the purpose of introducing "porosity" into the constitutive model.

[0071] Step 4: Determine the parameters of the rock elastic deformation stress-strain hyperbola model

[0072] The parameters a and b of the hyperbola-based nonlinear elastic constitutive model for rock (see Formula 5) can be determined by fitting the stress and strain data obtained from the experiment in Step 1 using the least squares method. The fitting results yield a = 125.0133 and b = 0.1048%.

[0073] Step 5: Construct a quantitative relationship between model parameters and physical and mechanical indicators

[0074] In order to facilitate the construction of quantitative relationships between model parameters and physical and mechanical indicators, the present invention introduces the concept of porous elastic bodies. Rocks are abstracted as porous elastic bodies to establish quantitative relationships between model parameters and physical and mechanical indicators.

[0075] Step 5.1 Introducing the concept of porous elastomers

[0076] Rock porosity is a crucial factor in its nonlinear elastic deformation. In the past, the influence of porosity was typically ignored, and the rock was treated as a linear elastic body, with a single elastic modulus assigned to the rock mass, for simulation and calculation of the rock mass structural stress field. While this greatly simplifies the computational model and approach, as geotechnical engineering excavation depths increase, deep rock mechanical phenomena such as rockbursts, slab cracking, and zonal fractures are becoming increasingly common, and are difficult to explain using conventional elastic-plastic mechanics theory. Ignoring the influence of porosity effectively treats the rock as a physical model of a non-porous linear elastic body. This physical model possesses only linear elasticity, but not porosity. Therefore, constitutive equations based on elastic bodies struggle to incorporate parameters characterizing porosity. Introducing porosity into these constitutive equations requires the establishment of a new physical model, one that incorporates both porosity and elasticity. Therefore, to facilitate the description of the nonlinear elastic deformation characteristics of rock, the present invention introduces the concept of a "porous elastic body."

[0077] "Porous elastomer" (PE) is an idealized model. As the name suggests, its basic meaning is an elastomer containing many small pores. PE is essentially an elastomer, composed of pores and an elastic medium. Unlike elastomers, it possesses both porosity and elasticity. These two basic properties lead to four important properties of PE:

[0078] Property 1: PE has infinite strength

[0079] Because PE is elastic, no matter how high the stress is, it remains in a state of elastic deformation, without damage or failure. Once the load is removed, the deformation disappears instantly and completely, returning to its original state. This property provides theoretical support for limit calculations under infinite stress conditions.

[0080] Property 2: Under infinite stress, PE approaches a completely compressed state

[0081] Because there is no plastic deformation, the pores cannot be completely compacted. As stress increases, the pores within PE are continuously compressed, and the PE porosity decreases. However, it will never be completely compacted, and will only approach a completely compacted state infinitely. The completely compacted state refers to the ideal state where the PE porosity is zero. This property provides theoretical support for limiting calculations under infinite stress conditions.

[0082] Property 3: The PE limiting tangent modulus is equal to the elastic modulus of the elastic medium

[0083] A porous elastic body consists of two parts: pores and an elastic medium. Assume the elastic modulus of the elastic medium is E0. When the stress is infinite, the pores are nearly completely compressed, and the stress-strain curve in this section approaches a straight line. Its slope is the rock's limiting tangent modulus. At this point, the porous elastic body approximates an elastic body, and the limiting tangent modulus of the porous elastic body is equal to that of the elastic medium, which is equal to E0. This property provides theoretical support for exploring the physical significance of constitutive model parameters.

[0084] Property 4: PE deformation has nonlinear elasticity

[0085] Due to the presence of pores, the deformation of PE under load comes from two sources: pore deformation and deformation of the elastic medium. Initially, the pores are rapidly compressed, and the PE stress-strain curve exhibits distinct nonlinear deformation. Because PE is elastic, its deformation is nonlinear elastic. This property suggests that porous, nonlinear elastic rocks can be viewed as a series of porous elastic bodies with varying porosity and elastic modulus of the elastic medium.

[0086] Therefore, when analyzing the nonlinear mechanical behavior of rocks, rocks can be abstracted as "porous elastic bodies".

[0087] Step 5.2 Construct the quantitative relationship between the model parameters and the elastic modulus E0 of the rock elastic medium

[0088] By taking the derivative of the strain from formula (5), we can get the expression of the tangent elastic modulus:

[0089]

[0090] When the stress approaches infinity, the strain approaches infinity, and the limiting tangent modulus is calculated as:

[0091]

[0092] According to PE Property 3, the PE limit tangent modulus is equal to the elastic modulus of the PE elastic medium, that is,

[0093]

[0094] Combining (8) and (9) we can get:

[0095]

[0096] Formula (10) is the quantitative relationship between the model parameters and the elastic modulus E0 of the rock elastic medium. It is also the first relationship in which the model parameters a and b are replaced by E0 and η0. Next, we establish the second relationship between E0, η0 and a and b from the perspective of porosity η0.

[0097] Step 5.3: Construct a quantitative relationship between model parameters and rock porosity η0

[0098] Assuming that the stress increase is dσ, the PE deformation is dl, and the PE length before deformation is l, see Figure 4 Based on this, the total strain increment can be calculated as:

[0099]

[0100] Since PE is composed of two parts, elastic medium and pores, when the stress increases by dσ, the pores will be compressed, resulting in a strain increment, and the elastic medium will also deform and produce a strain increment. Therefore, the deformation of PE dl can be divided into two parts. One part is the equivalent deformation of the pores, recorded as dl p The other part is the deformation of the elastic medium, denoted as dl m ,like Figure 4 As shown. Substituting the two into formula (11) we get:

[0101]

[0102] make

[0103] dε m 、dε p are the elastic medium strain increment and the pore strain increment respectively. Formula (12) can be rewritten as:

[0104] dε=dε m +dε p (13)

[0105] It is known that the deformation of elastic media obeys Hooke's law:

[0106]

[0107] In formula (14), E0 is the elastic modulus of the elastic medium. p , multiply the numerator and denominator by the PE cross-sectional area S to obtain:

[0108]

[0109] In formula (15), S×dl m The meaning is: when the stress increases by dσ, the pore volume decreases by dV m , which can be expressed as:

[0110] dV m =S×dl m (16)

[0111] The relationship between pore strain increment and porosity reduction:

[0112] Assume that the porosity of PE is very small. When the pores are in a completely compacted state, the volume of the rock remains basically unchanged compared to the initial state. If the volume of the initial rock is V, then:

[0113] V=S×l (17)

[0114] Combining formulas (15), (16), and (17), we can obtain:

[0115]

[0116] It means the decrease in porosity when the stress increases by dσ.

[0117] The cumulative reduction of porosity during PE loading is defined as When the stress increases by dσ, The increment is is also the reduction in porosity, then the following relationship holds:

[0118]

[0119] Combining formulas (18) and (19), we can obtain:

[0120]

[0121] Substituting formulas (14) and (20) into (13), we can obtain:

[0122]

[0123] By transforming formula (21), we can get:

[0124]

[0125] Integrating dσ on both sides of the equation (22) yields:

[0126]

[0127] According to the initial conditions, when the stress is 0, the reduction in porosity is 0, resulting in C=0.

[0128]

[0129] By transforming formula (5), we can get:

[0130]

[0131] Substituting formula (5) and (25) into formula (24), we can obtain

[0132]

[0133] When the stress approaches infinity, the rock approaches a completely compacted state, and the reduction in porosity is equal to the initial porosity η0 of the rock itself.

[0134]

[0135] Step 6: Establish a nonlinear elastic constitutive model of rock considering porosity

[0136] In order to introduce “porosity” into the hyperbola-based nonlinear elastic constitutive model of rock (see Formula 5), ​​the simultaneous solution of Formula (10) and Formula (27) can be obtained:

[0137]

[0138] It can be seen from formula (28) that the physical meanings of parameters a and b in the nonlinear constitutive equation of rock are the product of porosity and elastic modulus of elastic medium and porosity, respectively.

[0139] Substituting formula (28) into formula (5), we can obtain the general form of the nonlinear elastic constitutive model of rock:

[0140]

[0141] Where E0 and η0 are the elastic modulus and porosity of the rock elastic medium, respectively.

[0142] The model parameters a and b obtained in step 4, as well as formulas (10) and (27), can be used to obtain the elastic modulus and porosity of the rock elastic medium:

[0143]

[0144] Substituting formula (30) into (29) yields:

[0145]

[0146] The nonlinear elastic constitutive model of granite established is shown in formula (31). In order to evaluate the effect of the model, a comparison chart of the measured rock stress-strain curve and the constitutive equation curve constructed by the present invention is made, as shown in the figure. Figure 5 As shown. Figure 5 It can be seen that the measured results basically coincide with the constructed constitutive equation curve, and the two are highly correlated, with a correlation coefficient of up to 0.9999, indicating that the constructed model is reasonable.

[0147] The rock constitutive equation is one of the three fundamental conditions for calculating nonlinear surrounding rock stress in tunnels, along with the geometric equation and the equilibrium equation. This method is a fundamental method for studying rockburst mechanisms. Introducing porosity into the rock constitutive equation quantitatively describes the nonlinear elastic deformation process of rock, laying an important foundation for calculating stress in nonlinear elastic surrounding rock.

[0148] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for constructing a nonlinear elastic constitutive model of rock considering porosity, characterized in that: include: Conduct indoor uniaxial compression tests on rocks to obtain rock elastic deformation stress-strain data; constructing a rock elastic deformation stress-strain hyperbola model based on the rock elastic deformation stress-strain data, and determining parameters of the rock elastic deformation stress-strain hyperbola model; Obtaining the quantitative relationship between the model parameters and the physical and mechanical indicators through the parameters of the rock elastic deformation stress-strain hyperbola model; Based on the quantitative relationship between the model parameters and physical and mechanical indicators, a nonlinear elastic constitutive model of rock considering porosity is established; The nonlinear elastic constitutive model of rock considering porosity is established, including: Obtain rock elastic deformation stress-strain data through experiments and construct a rock elastic deformation stress-strain hyperbola model; Based on the rock elastic deformation stress-strain hyperbola model, the physical meanings of the parameters in the rock nonlinear constitutive equation are obtained, porosity is introduced into the hyperbola-based rock nonlinear elastic constitutive model, and a general form of the rock nonlinear elastic constitutive model characterized by the elastic modulus of the rock elastic medium and the rock porosity is obtained; Based on the elastic modulus and porosity of the rock elastic medium, the nonlinear elastic constitutive model of the rock considering the porosity is obtained.

2. The method for constructing a nonlinear elastic constitutive model of rock considering porosity according to claim 1, characterized in that: Constructing the rock elastic deformation stress-strain hyperbola model includes: Analyze the changing characteristics of the hyperbola and the similarity between the hyperbola and the stress-strain curve of the rock elastic deformation process, and obtain the hyperbola equation and its asymptote after translation; A nonlinear constitutive model of rock based on hyperbola is established, and a nonlinear elastic constitutive model of rock based on hyperbola and the asymptotes of the constitutive equation are obtained.

3. The method for constructing a nonlinear elastic constitutive model of rock considering porosity according to claim 2, characterized in that: Determining the parameters of the rock elastic deformation stress-strain hyperbola model includes: The parameters of the hyperbolic nonlinear elastic constitutive model of rock are determined by fitting the stress and strain data obtained from the indoor rock uniaxial compression test according to the least squares method.

4. The method for constructing a nonlinear elastic constitutive model of rock considering porosity according to claim 1, characterized in that: Obtaining the quantitative relationship between the model parameters and the physical and mechanical indicators includes: Abstract the rock into a porous elastic body, introduce the concept of porous elastic body, and obtain the PE properties; Through the hyperbolic nonlinear constitutive model of rock, the quantitative relationship between the model parameters and the elastic modulus of the rock elastic medium, as well as the quantitative relationship between the model parameters and the rock porosity are constructed.

5. The method for constructing a nonlinear elastic constitutive model of rock considering porosity according to claim 4, characterized in that: The PE properties include: PE has infinite strength; under infinite stress, PE approaches a completely compacted state infinitely; the limiting tangent modulus of PE is equal to the elastic modulus of the elastic medium; and the deformation of PE has nonlinear elasticity.

6. The method for constructing a nonlinear elastic constitutive model of rock considering porosity according to claim 5, characterized in that: Constructing a quantitative relationship between the model parameters and the elastic modulus of the rock elastic medium includes: Derivative the hyperbolic nonlinear constitutive model of rock with respect to strain to obtain a tangent elastic modulus model; Based on the tangent elastic modulus model, the stress magnitude is changed, and when the stress tends to infinity, the strain tends to infinity, thereby obtaining a limiting tangent elastic modulus model; According to the property that the PE limiting tangent elastic modulus is equal to the elastic modulus of the PE elastic medium, a quantitative relationship between the model parameters and the elastic modulus of the rock elastic medium is obtained.

7. The method for constructing a nonlinear elastic constitutive model of rock considering porosity according to claim 5, characterized in that: Constructing a quantitative relationship between the model parameters and rock porosity, including: Setting stress increase conditions, obtaining PE deformation and PE length before deformation, and calculating a total strain increment, wherein the total strain increment includes an elastic medium strain increment and a pore strain increment; Obtaining a reduction in pore volume through the pore strain increment; Obtaining a porosity reduction model through the pore strain increment and the pore volume reduction; Based on the porosity reduction model, a hyperbola-based nonlinear elastic constitutive model of rock is obtained; According to the hyperbolic nonlinear elastic constitutive model of rock, the stress is increased, and when the rock is close to a fully compressed state, a quantitative relationship between the model parameters and the rock porosity is obtained.

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