A damage relation calculation method for expressing the tensile properties of rock after high temperature

Abstract

The present invention discloses a damage relationship calculation method for expressing the tensile properties of rock after high temperature action, which includes defining a thermal damage variable D T , used to characterize the influence of temperature on the mechanical properties of rock; define the micro-element strength F of rock material to obey Weibull distribution, and construct the probability density function P(F) of rock material; according to the probability density function P(F) of rock material, obtain the number N of micro-element used to characterize the damage under stress state F The ratio of the total number of micro-elements N is defined as the load statistical damage D M ; According to the thermal damage variable D T The damage relationship σ of rock under tensile load is obtained. The present invention can reflect the tensile stress-strain relationship, reflect the rationality of the model, and reveal the evolution law of coupled damage variables with strain.

Description

Technical Field

[0001] The invention relates to the technical field of rock damage statistics, and in particular to a damage relationship calculation method for expressing the tensile properties of rocks after high temperature action. Background Art

[0002] With the increasing number of tunnel construction projects in my country, the possibility of fire inside them is also gradually increasing. During the operation of the tunnel, there are many vehicles on the road, and the risk and probability of fire are extremely high, which will cause varying degrees of damage to the surrounding rock support system, deteriorate the mechanical properties, and greatly reduce the safety of the bearing structure. Therefore, it is necessary to analyze the mechanical properties of rock after high temperature in order to study the evolution mechanism of fire damage to the surrounding rock support structure.

[0003] At the same time, the statistical damage constitutive model can reasonably describe the defects of the rock damage evolution process and can better reflect the mechanical mechanism of rock damage under high temperature. However, in the application of statistical damage mechanics to study the rock damage constitutive model, the existing model has not been combined with tensile tests for analysis. Summary of the invention

[0004] The present invention provides a damage relationship calculation method for expressing the tensile properties of rock after high temperature action, so as to overcome the technical problems that the existing rock damage constitutive model cannot be combined with tensile experiments for analysis.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A damage relationship calculation method for expressing the tensile properties of rock after high temperature action includes the following steps:

[0007] Step 1: Define the thermal damage variable D T , used to characterize the effect of temperature on the mechanical properties of rock;

[0008] Step 2: Define the rock material microelement strength F to obey Weibull distribution, and construct the probability density function P(F) of the rock material;

[0009] Step 3: Obtain the number of micro-elements N used to characterize the damage under stress state according to the probability density function P(F) of the rock material. F The ratio of the total number of micro-elements N is defined as the load statistical damage D M ;

[0010] Step 4: According to the thermal damage variable D T The damage relation σ of rock under tensile load is obtained.

[0011] Furthermore, the thermal damage variable D in step 1 T The specific formula is:

[0012]

[0013] Among them, E T E is the tensile elastic modulus of the rock sample after the temperature T acts; 0 is the tensile elastic modulus of the rock sample after exposure to 20°C.

[0014] Furthermore, the specific formula for constructing the probability density function P(F) of the rock material in step 2 is:

[0015]

[0016] Among them, F represents the strength of rock microelement, m, F 0 are the shape parameter and scale parameter of the Weibull distribution function respectively.

[0017] Furthermore, in step 3, the load statistical damage D is obtained. M The specific formula is:

[0018]

[0019] According to Weibull's distribution function, formula (3) is transformed into:

[0020]

[0021] Here, ε represents the strain.

[0022] Furthermore, the specific formula of the damage relationship σ of rock under tensile load obtained in step 4 is:

[0023] σ=E T ε(1-D M )(5)

[0024] Substituting formula (1) into formula (5), we get:

[0025] σ=E 0 (1-D T )ε(1-D M )=E 0 ε(1-D)(6)

[0026] Where D is the coupled damage variable of rock subjected to tensile load after high temperature, D = D M +D T -D M D T ; E 0 Represents the elastic modulus at 20°C.

[0027] Furthermore, it also includes obtaining the statistical damage constitutive model of rock under different temperatures and tensile loads according to the damage relationship σ of rock under tensile load Obtaining the statistical damage constitutive model of rock under different temperatures and tensile loads The specific formula is:

[0028]

[0029] Substituting equation (7) into equation (6), the statistical damage constitutive model of rock under different temperatures and tensile loads is obtained:

[0030]

[0031] Furthermore, it also includes:

[0032] Step 5: Obtain the stress-strain curve fitting and determine the model parameter F according to the statistical damage constitutive model σ of rock under different temperatures and tensile loads. 0 .

[0033] Furthermore, the stress-strain curve obtained in step 5 is fitted to determine the model parameter F 0 The specific steps are:

[0034] Step 5.1. Take the logarithm of both sides of equation (8) and obtain:

[0035]

[0036] Step 5.2, take the logarithm of both sides of equation (9) again and obtain:

[0037]

[0038] Step 5.3: Simplify equation (14) to obtain:

[0039]

[0040] Step 5.4, order X = lnε, then formula (11) is:

[0041] Y=m(X-lnF 0 )=mX-B(12)

[0042] Given B = mlnF 0 , where Y represents the ordinate of the fit, X represents the abscissa, and B represents the intercept;

[0043] Step 5.5: Perform linear fitting to obtain stress-strain curve fitting and determine model parameters F 0 , obtain the stress-strain curve fitting to determine the model parameter F 0The specific formula is:

[0044]

[0045] Beneficial effects: The present invention establishes a square sandstone statistical damage constitutive model considering high temperature and tensile effects, and clarifies the determination method and significance of each parameter of the model. In addition, the parameters required by the model can be calculated from the direct tensile test results, and are all conventional mechanical parameters, which are easy to apply, can better reflect the tensile stress-strain relationship, can reflect the rationality of the model, and reveal the evolution law of coupled damage variables with strain. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0047] Figure 1 This is the flow chart of the direct tensile test of square sandstone after high temperature action;

[0048] Figure 2 It is the graph of mechanical parameter changes in the test;

[0049] Figure 3 It is a comparison chart between the test value and the theoretical curve;

[0050] Figure 4 This is a flow chart of the statistical damage calculation method of the present invention;

[0051] Figure 5 is the parameter F in the constitutive model 0 = 0.0017 when m affects the curve;

[0052] Figure 6 This is the evolution law diagram of the coupled damage variable D. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] This embodiment provides a damage relationship calculation method for expressing the tensile properties of rock after high temperature action.

[0055] like Figure 1 As shown in the figure, after high temperature heating, the rock will be affected by medium softening and thermal stress, and a large number of micro cracks will be generated inside it. When the tensile stress condition exceeds the rock cracking point, the cracks inside the rock begin to germinate, and the mechanical parameters change significantly. Therefore, the tensile elastic modulus is used as the damage variable to describe the damage caused by high temperature to the rock, such as Figure 2-6 As shown, the following steps are included:

[0056] Step 1: Define the thermal damage variable D T , used to characterize the effect of temperature on the mechanical properties of rock;

[0057] Step 2. Under the action of external tensile load, the stress level of the micro-element inside the rock material exceeds a certain strength and will cause rupture. The original micro-cracks inside it will gradually expand and evolve, resulting in continuous damage to the rock. Considering that the development of cracks in rocks has the characteristics of random distribution, this paper introduces statistical damage theory. First, it is assumed that the rock material satisfies the isotropic condition macroscopically. Since the Weibull probability distribution is easy to integrate and has a simple form, it meets the statistical characteristics of rock tensile failure. Define the micro-element strength F of the rock material to obey the Weibull distribution, and construct the probability density function P(F) of the rock material;

[0058] Step 3: At a microscopic level, rock materials are composed of randomly distributed microelement particles. Under axial tension, when the microelement strength F exceeds a certain strength, the rock gradually breaks inside and eventually forms macroscopic damage. According to the probability density function P(F) of the rock material, the number of microelement N used to characterize the damage under stress is obtained. F The ratio of the total number of micro-elements N is defined as the load statistical damage D M ;

[0059] Step 4: According to the Lemaitre strain equivalence principle, the strain produced by the damaged rock under the stress condition (nominal stress) measured in the test is equal to the effective strain produced by the damaged rock under the effective stress condition. According to the test steps, a heating test was carried out before the tensile test on the rock, which shows that thermal damage has occurred before the load damage. Therefore, the thermal damage of the rock should be regarded as the first damage state, and the load effect on the rock after the high temperature is regarded as the second damage state. According to the thermal damage variable D T The damage relation σ of rock under tensile load is obtained.

[0060] In a specific embodiment, the thermal damage variable D in step 1 T The specific formula is:

[0061]

[0062] Among them, E T E is the tensile elastic modulus of the rock sample after the temperature T acts; 0 is the tensile elastic modulus of the rock sample after exposure to 20°C.

[0063] In a specific embodiment, the specific formula for constructing the probability density function P(F) of the rock material in step 2 is:

[0064]

[0065] Among them, F represents the strength of rock microelement, m, F 0 They are the shape parameter and scale parameter of the Weibull distribution function, respectively, and both correspond to the mechanical characteristics of rocks.

[0066] In a specific embodiment, the load statistical damage D is obtained in step 3. M The specific formula is:

[0067]

[0068] According to Weibull's distribution function, formula (3) is transformed into:

[0069]

[0070] Here, ε represents the strain.

[0071] In a specific embodiment, the specific formula for obtaining the damage relationship σ of rock under tensile load in step 4 is:

[0072] σ=E T ε(1-D M )(5)

[0073] Substituting formula (1) into formula (5), we get:

[0074] σ=E 0 (1-D T )ε(1-D M )=E 0 ε(1-D)(6)

[0075] Where D is the coupled damage variable of rock subjected to tensile load after high temperature, D = D M +D T -D M D T ; E 0 Represents the elastic modulus at 20°C.

[0076] In a specific embodiment, it also includes obtaining a statistical damage constitutive model of rock under different temperatures and tensile loads according to the damage relationship σ of rock under tensile load Obtaining the statistical damage constitutive model of rock under different temperatures and tensile loads The specific formula is:

[0077]

[0078] Substituting equation (7) into equation (6), the statistical damage constitutive model of rock under different temperatures and tensile loads is obtained:

[0079]

[0080] In a specific embodiment, it also includes:

[0081] Step 5: Obtain the stress-strain curve fitting and determine the model parameter F according to the statistical damage constitutive model σ of rock under different temperatures and tensile loads. 0 .

[0082] In a specific embodiment, the stress-strain curve is obtained in step 5 to fit the model parameter F. 0 The specific steps are:

[0083] Step 5.1. Take the logarithm of both sides of equation (8) and obtain:

[0084]

[0085] Step 5.2, take the logarithm of both sides of equation (9) again and obtain:

[0086]

[0087] Step 5.3: Simplify equation (14) to obtain:

[0088]

[0089] Step 5.4, order X = lnε, then formula (11) is:

[0090] Y=m(X-lnF 0 )=mX-B(12)

[0091] Given B = mlnF 0 , where Y represents the ordinate of the fit, X represents the abscissa, and B represents the intercept;

[0092] Step 5.5: Perform linear fitting to obtain stress-strain curve fitting and determine model parameters F 0 , obtain the stress-strain curve fitting to determine the model parameter F0 The specific formula is:

[0093]

[0094] The specific application process is:

[0095] In order to verify the rationality of the rock statistical damage constitutive model considering high temperature and tensile action, the tensile test data of square sandstone is substituted into the expressions (9) to (13) of each parameter to obtain the parameters of the constitutive model. In order to verify the rationality of the model in this paper, the tensile test results of square sandstone under different heating temperature conditions are selected for verification, and the parameters of the statistical damage constitutive model are shown in Table 1.

[0096] Temperature / ℃ m <![CDATA[F 0 / 10 -5 ]]> Correlation coefficient R 20 10.91 90.50 0.95 200 11.45 98.42 0.96 600 9.49 114.05 0.93 1000 10.95 118.04 0.93

[0097] Table 1: Statistical damage constitutive model parameters

[0098] The parameters m and F in Table 1 0 Substituting into formula (8), we can obtain the calculated value curve of tensile stress-strain of square sandstone under different temperatures and the comparison chart of experimental value, as shown in Figure 3 shown.

[0099] The determination of the damage constitutive model parameters needs to be linked to the macroscopic mechanical test parameters of the rock, so that the physical meaning of the model parameters can be clarified and the model has a certain applicability. 0 The influence of tensile stress-strain curve on Figure 5 The data analysis shows that as F 0 The shape of the stress-strain curve does not change significantly, but its peak strain gradually increases, and the overall curve moves to the right, indicating that the parameter F 0 Mainly reflects the strain characteristics of rocks, F 0 The larger the value, the greater the peak strain. Figure 5 It can be seen that with the continuous increase of m, the post-peak stage of the stress-strain curve becomes steeper, the failure rate is accelerated, and obvious brittle failure phenomenon will occur accordingly.

[0100] The continuous accumulation of internal damage in the material is the main reason for the reduction of material strength. In order to further reveal the mechanical damage mechanism of square sandstone after different temperatures, the coupled damage variable D of sandstone under tensile load after high temperature is calculated according to formula (7), and the relationship between D and strain is obtained as follows: Figure 6 shown.

[0101] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A damage relationship calculation method for expressing the tensile properties of rock after high temperature, characterized by: The following steps are involved: Step 1: Define the thermal damage variable D T , used to characterize the effect of temperature on the mechanical properties of rock; Step 2: Define the rock material microelement strength F to obey Weibull distribution, and construct the probability density function P(F) of the rock material; Step 3: Obtain the number of micro-elements N used to characterize the damage under stress state according to the probability density function P(F) of the rock material. F The ratio of the total number of micro-elements N is defined as the load statistical damage D M ; Step 4: According to the thermal damage variable D T The damage relation σ of rock under tensile load is obtained; the thermal damage variable D described in step 1 is T The specific formula is: Among them, E T is the tensile elastic modulus of the rock sample after the temperature T acts; E0 is the tensile elastic modulus of the rock sample after the temperature 20°C acts; the specific formula for constructing the probability density function P(F) of the rock material in step 2 is: Where F represents the strength of the rock microelement, m and F0 are the shape parameter and scale parameter of the Weibull distribution function respectively; the load statistical damage D is obtained in step 3 M The specific formula is: According to the Weibull distribution function, equation (3) is transformed into: Where ε represents strain; the specific formula of the damage relationship σ of rock under tensile load obtained in step 4 is: σ=E T e(1-D M (5) Substituting formula (1) into formula (5), we get: σ=E0(1-D T )e(1-D M )=E0ε(1-D)(6) Where D is the coupled damage variable of rock subjected to tensile load after high temperature, D = D M +D T -D M D T ; E0 represents the elastic modulus at 20℃; the method also includes obtaining the statistical damage constitutive model of rock under different temperatures and tensile loads according to the damage relationship σ of rock under tensile load Obtaining the statistical damage constitutive model of rock under different temperatures and tensile loads The specific formula is: Substituting equation (7) into equation (6), the statistical damage constitutive model of rock under different temperatures and tensile loads is obtained:

2. A damage relationship calculation method for expressing the tensile properties of rock after high temperature as claimed in claim 1, characterized in that: Also includes: Step 5: Statistical damage constitutive model of rock under different temperatures and tensile loads The stress-strain curve was fitted to determine the model parameter F0.

3. A damage relationship calculation method for expressing the tensile properties of rock after high temperature as claimed in claim 2, characterized in that: The specific steps for obtaining the stress-strain curve fitting and determining the model parameter F0 in step 5 are: Step 5.

1. Take the logarithm of both sides of equation (8) and obtain: Step 5.2, take the logarithm of both sides of equation (9) again and obtain: Step 5.3: Simplify equation (14) to obtain: Step 5.4, order X = lnε, then formula (11) is: Y=m(X-lnF0)=mX-B(12) Given B = mlnF0, where Y represents the ordinate of the fit, X represents the abscissa, and B represents the intercept; Step 5.5, perform linear fitting to obtain stress-strain curve fitting to determine model parameter F0. The specific formula for obtaining stress-strain curve fitting to determine model parameter F0 is:

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