Method for establishing rock elastic-plastic damage constitutive model considering freeze-thaw strength and compaction effect

Abstract

The invention belongs to the technical field of rock mechanical property research, and discloses a rock elastic-plastic damage constitutive model establishment method considering freeze-thaw strength and compaction effect, and the method comprises the following steps: proposing a concept of freeze-thaw strength to comprehensively reflect the freeze-thaw damage degrees of rock at different freeze-thaw temperatures and durations; performing a freeze-thaw test and a triaxial compression test on the rock test piece, recording test data in the triaxial compression test process, drawing a stress-strain curve based on the test data, and constructing a yield function and a hardening rule of the rock test piece based on the strength characteristic parameters of the freeze-thaw rock; establishing a rock elastic-plastic damage constitutive equation considering the freeze-thaw effect and the compaction effect; and determining a parameter expression of the rock elastic-plastic damage constitutive model based on an elastic-plastic theory in combination with freeze-thaw rock triaxial compression test data. According to the technical scheme, the compaction stage and the volume deformation of the frozen-thawed rock can be reflected, and the method has the advantages of being wide in application range and high in prediction precision.

Description

Technical Field

[0001] The invention belongs to the technical field of rock mechanical property research, and in particular relates to a method for establishing a rock elastic-plastic damage constitutive model taking into account freeze-thaw strength and compaction effects. Background Art

[0002] Freeze-thaw is a powerful weathering process that can cause a rapid decline in rock mechanical properties, seriously threatening the safe operation, stability, and durability of rock mass engineering projects in cold regions. The mechanical properties of rock under harsh climatic conditions are key indicators of the stability and safety of rock mass engineering projects. Rocks are commonly found with numerous pores and microcracks. When water in these pores freezes into ice, it expands by approximately 9%, generating frost heave pressure within the rock. This pressure gradually dissipates as the ice melts into water. Freeze-thaw exposure to rock in cold climates can cause internal damage. Repeated freeze-thaw cycles gradually accumulate this damage, leading to a rapid deterioration in rock strength and severely impacting the safety, stability, and durability of rock mass engineering and structures. Therefore, developing a freeze-thaw rock mechanics model to predict the mechanical and deformation properties of frozen-thawed rock is of vital engineering significance for the construction and stability assessment of rock mass engineering projects in cold regions.

[0003] In recent years, with the continuous development of indoor test equipment and theoretical analysis, some progress has been made in the study of the constitutive model theory of freeze-thaw rock. Many scholars have proposed statistical damage models for freeze-thaw rock based on experimental stress-strain curves and combined with statistical damage theory. However, they all have certain limitations, which are mainly reflected in the following aspects:

[0004] (1) The existing model only fits some model parameters into the equation of the number of freeze-thaw cycles, without considering the effect of freeze-thaw cycles on the initial yield and hardening process; and does not consider the effect of different freeze-thaw temperatures and freeze-thaw durations on the freeze-thaw damage of rocks;

[0005] (2) These models can only reflect the elasticity, yielding and post-peak failure stages of rocks, ignoring the initial compaction stage of rocks, resulting in large errors between the predicted values ​​of theoretical models and experimental values ​​in the initial stage;

[0006] (3) These models can only predict the axial strain-deviatoric stress relationship of rocks, but cannot predict the volume deformation of rocks, which is one of the important indicators reflecting rock failure.

[0007] Therefore, it is necessary to propose a method for establishing a constitutive model of freeze-thaw rock that considers the influence of freeze-thaw strength on the initial yield and hardening stage of rock, and can reflect the compaction stage and volume deformation of freeze-thaw rock, has a wide range of applicability, and has high prediction accuracy. Summary of the Invention

[0008] The purpose of the present invention is to provide a method for establishing a rock elastic-plastic damage constitutive model taking into account freeze-thaw strength and compaction effects, so as to solve the problems existing in the above-mentioned prior art.

[0009] To achieve the above objectives, the present invention provides a method for establishing a rock elastic-plastic damage constitutive model taking into account freeze-thaw strength and compaction effects, comprising:

[0010] Step S1: The concept of freeze-thaw intensity is proposed to comprehensively reflect the freeze-thaw damage degree of rocks under different freeze-thaw conditions;

[0011] Step S2: preparing a number of rock specimens;

[0012] Step S3: performing a freeze-thaw test on each of the rock specimens;

[0013] Step S4: performing a triaxial compression test on each of the rock specimens that have undergone the freeze-thaw test, and recording test data during the triaxial compression test, wherein the test data includes the axial stress, axial strain, and radial strain of the rock specimen;

[0014] Step S5: plotting a deviatoric stress-strain curve based on the test data, and constructing a yield function and hardening law of the rock specimen based on the strength characteristic parameters of the freeze-thaw rock;

[0015] Step S6: Based on the elastic-plastic mechanics theory, combined with the yield function and the hardening law, a rock elastic-plastic damage constitutive equation is established that takes into account freeze-thaw and compaction effects;

[0016] Step S7: Based on the elastic-plastic theory and the triaxial compression stress-strain data of rock, the parameter expression of the elastic-plastic damage constitutive model of freeze-thaw rock is determined.

[0017] Optionally, the step S1 specifically includes:

[0018] Taking the freeze-thaw damage caused by specific indoor freeze-thaw temperature and duration as the benchmark, according to the damage equivalence principle and cumulative damage theory, the equivalent relationship between the freeze-thaw damage under other freeze-thaw temperatures and durations and the benchmark freeze-thaw damage is established.

[0019] Optionally, step S2 specifically includes:

[0020] Obtaining a plurality of rock blocks, and processing each of the rock blocks based on a preset size and a preset shape to obtain a plurality of initial test pieces;

[0021] A homogeneity inspection is performed on each of the initial test pieces, and rock test pieces that pass the inspection are selected.

[0022] Optionally, step S3 specifically includes:

[0023] Step S31: saturating the rock specimen with water;

[0024] Step S32: performing a freeze-thaw cycle test on the rock specimen after saturation treatment based on the set time and temperature;

[0025] Repeat step S31 to step S32 until the preset number of freeze-thaw cycles is reached, completing the freeze-thaw test.

[0026] Optionally, a triaxial compression test is performed on each of the rock specimens that have undergone the freeze-thaw test, specifically including:

[0027] The rock specimens that have undergone the freeze-thaw test are placed at the bottom of the triaxial chamber of a rock mechanics testing machine, displacement meters are arranged, and the triaxial chamber is lowered and filled with silicone oil;

[0028] First, lateral stress and axial stress are applied at a set rate, then the lateral stress is kept constant and the axial displacement is applied at a set rate until the rock specimen is destroyed;

[0029] The axial stress, axial strain and radial strain during the test were recorded.

[0030] Optionally, drawing a stress-strain curve based on the test data specifically includes:

[0031] Deviatoric stress-axial strain and deviatoric stress-radial strain curves are constructed with the axial strain and the radial strain as abscissas and the deviatoric stress as ordinates.

[0032] Optionally, the yield function and hardening law of rock materials are constructed based on the strength characteristic parameters of freeze-thaw rock, including:

[0033] The construction process of the yield function:

[0034] determining the initial yield strength of the rock specimen based on the deviatoric stress-strain curve;

[0035] Calculating a first principal stress invariant and a second invariant of the deviatoric stress tensor of the rock specimen based on the test data and the initial yield strength;

[0036] Using the first principal stress invariant as the abscissa and the second invariant of the deviatoric stress tensor as the ordinate, plotting a yield curve of the rock specimen on a meridian plane, wherein the yield curve includes an initial yield curve and a critical yield curve;

[0037] Determine the yield function based on the shape of the yield curve in the meridian plane;

[0038] The construction process of hardening law:

[0039] Based on the deviatoric stress-strain curve, a relationship curve of equivalent plastic shear strain-deviatoric stress tensor second invariant in the rock hardening stage under different confining pressures with the same freeze-thaw times is drawn;

[0040] The second invariant of the deviatoric stress tensor corresponding to the same equivalent plastic shear strain value is plotted on the meridian plane, and the freeze-thaw rock hardening trajectory under different confining pressures with the same freeze-thaw times is obtained.

[0041] The hardening law of the freeze-thaw rock specimen is determined based on the hardening trajectory of the freeze-thaw rock.

[0042] Optionally, step S6 specifically includes:

[0043] Based on the yield function, elastic-plastic mechanics theory and associated flow law, the elastic-plastic damage constitutive equation of rock considering freeze-thaw and compaction effects is derived.

[0044] Optionally, step S7 specifically includes:

[0045] The parameters of the elastic-plastic damage constitutive model of freeze-thaw rock are determined based on the deviatoric stress-axial strain curve, the first principal stress invariant-deviatoric stress tensor second invariant curve, and the equivalent plastic shear strain-deviatoric stress tensor second invariant deviatoric stress relationship curve of freeze-thaw rock.

[0046] The technical effects of the present invention are:

[0047] This paper provides a new method for accurately theoretically predicting the stress-strain response of frozen-thaw rock. This method constructs an incremental stress-strain relationship and an elastic-plastic stiffness matrix that considers freeze-thaw intensity. Furthermore, it introduces correction coefficients and damage factors to reflect the compaction and softening characteristics of the frozen-thaw rock deformation curve. This model has few parameters and clear physical meaning, and can be obtained through triaxial compression tests on frozen-thaw rock.

[0048] The present invention considers the effects of freeze-thaw cycles on rock mechanical characteristics and constitutive equations, introduces freeze-thaw strength parameters into the yield equation, and reflects the effects of freeze-thaw on the initial yield and hardening process of rock. The present invention also introduces a damage factor to describe the post-peak softening phenomenon of freeze-thaw rock and can quantitatively determine the macroscopic damage evolution law of freeze-thaw rock under load.

[0049] Moreover, the theoretical values ​​calculated by the rock elastic-plastic damage constitutive model constructed by the present invention, which takes into account freeze-thaw strength and compaction effects, are basically close to the experimental values, fully reflecting the influence trend of freeze-thaw cycles on rock mechanics and deformation characteristics, and can better predict the peak strain, compressive strength and stress-strain response of rocks under different freeze-thaw times.

[0050] The freeze-thaw rock elastic-plastic damage model constructed by the present invention can be written as a subroutine and embedded in commercial finite element software to simulate the mechanical and deformation characteristics of freeze-thaw rocks. It can also be used to simulate and analyze the stability of rock mass engineering in cold regions. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] 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. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0052] 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:

[0053] Figure 1 This is a flow chart of a method for establishing a freeze-thaw rock constitutive model in an embodiment of the present invention;

[0054] Figure 2 A triaxial compression testing machine for rock materials required in the embodiments of the present invention;

[0055] Figure 3 Schematic diagram of a sandstone sample in an embodiment of the present invention;

[0056] Figure 4 : is a graph showing deviatoric stress-axial strain and deviatoric stress-radial strain curves of freeze-thaw rock in an embodiment of the present invention, Figure 4 (a) is the deviatoric stress-axial strain and deviatoric stress-radial strain curve of freeze-thaw rock under confining pressure of σ3 = 0 MPa. Figure 4 (b) is the deviatoric stress-axial strain and deviatoric stress-radial strain curve of freeze-thaw rock under confining pressure of σ3 = 1 MPa. Figure 4 (c) is the deviatoric stress-axial strain and deviatoric stress-radial strain curve of freeze-thaw rock under confining pressure of σ3 = 3 MPa. Figure 4 (d) is the deviatoric stress-axial strain and deviatoric stress-radial strain curves of freeze-thaw rock under confining pressure of σ3 = 5 MPa;

[0057] Figure 5 is the initial yield curve of the freeze-thaw rock on the meridian plane in the embodiment of the present invention;

[0058] Figure 6 is the critical yield curve of the freeze-thaw rock in the meridian plane in the embodiment of the present invention;

[0059] Figure 7 Schematic diagram of the hardening stage selection in the equivalent plastic shear strain-deviatoric stress space of freeze-thaw rock in an embodiment of the present invention (freeze-thaw intensity Q=120);

[0060] Figure 8 : is a hardening trajectory diagram of the yield surface of freeze-thaw rock on the meridian plane in an embodiment of the present invention (freeze-thaw intensity Q=120);

[0061] Figure 9 is the variation law of the hardening parameter K in the embodiment of the present invention;

[0062] Figure 10 is the variation law of the hardening parameter k in the embodiment of the present invention;

[0063] Figure 11 is the variation law of the compaction coefficient R in the embodiment of the present invention;

[0064] Figure 12 is a flow chart of the constitutive equation algorithm in an embodiment of the present invention;

[0065] Figure 13 Schematic diagram showing the comparison between the constitutive model simulation results and the test results in the embodiment of the present invention, wherein: Figure 10 (a) is a schematic diagram showing the comparison between the constitutive model simulation results and the test results under σ3 = 0 MPa. Figure 10 (b) is a schematic diagram comparing the simulation results of the constitutive model and the test under σ3 = 3MPa.

[0066] Explanation of reference numbers: 1. Triaxial chamber oil drain pipe; 2. Axial displacement gauge fixture; 3. First axial displacement gauge; 4. Triaxial chamber chamber; 5. Triaxial chamber oil inlet pipe; 6. Load loading rod; 7. Load loader; 8. Loading rod displacement gauge; 9. Rigid upper pressure head; 10. Second axial displacement gauge; 11. Circumferential strain gauge; 12. Rock specimen; 13. Rigid lower pressure head. DETAILED DESCRIPTION

[0067] Various exemplary embodiments of the present invention will now be described in detail. This detailed description should not be considered as limiting the present invention, but rather as a more detailed description of certain aspects, features, and embodiments of the present invention.

[0068] 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.

[0069] like Figure 1 - Figure 13As shown, this embodiment provides a method for establishing a rock elastic-plastic damage constitutive model that takes into account freeze-thaw strength and compaction effects, including: preparing a number of rock specimens; performing a freeze-thaw test on each of the rock specimens; performing a triaxial compression test on each of the rock specimens that has undergone the freeze-thaw test, and recording the test data during the triaxial compression test, wherein the test data includes the axial stress, axial strain and radial strain of the rock specimen; drawing a stress-strain curve based on the test data, and constructing a yield function and hardening law of the rock specimen based on the freeze-thaw rock mechanics parameters; based on the elastic-plastic mechanics theory, combined with the yield function and the hardening law, establishing a rock elastic-plastic damage constitutive equation that takes into account freeze-thaw action and compaction effects; based on the elastic-plastic theory combined with the freeze-thaw rock triaxial compression test data, determining the parameter expression of the rock elastic-plastic damage constitutive model.

[0070] This embodiment discloses a method for establishing a rock elastic-plastic damage constitutive model considering freeze-thaw strength and compaction effects, which is used to theoretically predict the strength and deformation characteristics of rock after freeze-thaw effects, and includes the following steps: preparing rock specimens, performing freeze-thaw cycle tests in a freeze-thaw testing machine, until the number of freeze-thaw cycles of the rock specimen meets the set value; conducting conventional triaxial compression tests on freeze-thaw rocks, measuring and recording the axial, radial strains and axial stresses of the freeze-thaw rocks, and drawing the axial strain-deviatoric stress relationship and the radial strain-deviatoric stress relationship of the freeze-thaw rocks; obtaining the initial yield strength and compressive strength of the freeze-thaw rocks based on the deviatoric stress-axial strain curve of the freeze-thaw rocks, and establishing the yield criterion and hardening criterion of the freeze-thaw rocks; based on the theory of elastic-plastic mechanics, combined with the yield criterion and hardening criterion of the freeze-thaw rocks, deriving the rock elastic-plastic damage constitutive equation considering the freeze-thaw strength and compaction effects; using the elastic-plastic theory, combined with the deviatoric stress-axial strain curve, initial yield strength and critical yield strength of the freeze-thaw rocks, obtaining the parameter expression of the elastic-plastic constitutive model of the freeze-thaw rocks, and determining the constitutive model. The model proposed in this embodiment has clear physical meaning, a wide range of applications, and a high degree of consistency with the experimental curve, fully reflecting the initial compaction, strain hardening, and post-peak failure characteristics of rock after freeze-thaw.

[0071] The method of this embodiment proposes a yield function that takes into account the freeze-thaw effect, constructs a stress increment expression and an elastic-plastic matrix in the elastic-plastic deformation stage, introduces a compaction coefficient and a damage factor, and establishes a mechanical constitutive model that can reflect the freeze-thaw effect and post-peak softening phenomenon. The proposed constitutive equation expression is unique, the model parameters are few and are all determined through experiments, and each parameter has a clear physical meaning, thereby ensuring the uniqueness and accuracy of the solution, and at the same time having wide applicability.

[0072] The specific technical solutions are as follows:

[0073] (1) Taking the freeze-thaw damage caused by specific indoor freeze-thaw temperature and duration as the benchmark, based on the damage equivalence principle and cumulative damage theory, an equivalent relationship between the freeze-thaw damage at other freeze-thaw temperatures and durations and the benchmark freeze-thaw damage is established.

[0074] (2) According to the standards of the International Society for Rock Mechanics, cylindrical rock specimens were prepared and then subjected to multiple freeze-thaw cycle tests in a freeze-thaw testing machine until the number of freeze-thaw cycles of the rock specimens met the set value.

[0075] (3) Carry out conventional triaxial compression tests on rock specimens that meet the freeze-thaw cycle number, measure and record the axial, radial strain and axial stress of rock specimens under different freeze-thaw cycles,

[0076] (4) Draw the axial strain-deviatoric stress relationship and radial strain-deviatoric stress relationship of the frozen-thawed rock, obtain the initial yield strength and compressive strength of the rock under different freeze-thaw times and confining pressures, and establish the yield function and hardening criterion of the frozen-thawed rock material respectively.

[0077] (5) Based on the theory of elastic-plastic mechanics, combined with the yield function and hardening criterion of freeze-thaw rock, the elastic-plastic damage constitutive equation of rock considering the freeze-thaw action and compaction effect is established.

[0078] (6) Using the elastic-plastic theory, combined with the deviatoric stress-axial strain curve, initial yield strength and critical yield strength of freeze-thaw rock, the parameter expression of the elastic-plastic constitutive model of freeze-thaw rock is obtained and the constitutive model is determined.

[0079] The method can also include step (7), using the back-reflection algorithm to numerically implement the constitutive equation, comparing the test and simulation results under different freeze-thaw times, verifying the rationality of the constitutive equation and improving the model.

[0080] The freeze-thaw strength expression in step (1) is Q=NQ0, where Q is the total freeze-thaw strength, N is the number of freeze-thaw cycles, and Q0 is the unit freeze-thaw strength. α1 and α0 are the rock mechanical property degradation indices under other freeze-thaw temperature and time conditions and unit freeze-thaw times under fixed freeze-thaw temperature and time, respectively. Their values ​​can be macroscopic mechanical indices such as peak strength and elastic modulus, or other microscopic characteristic parameters such as longitudinal wave velocity, porosity and other indicators.

[0081] The cylindrical rock specimen in step (2) should be a complete specimen without obvious defects such as cracks and holes. The ratio of the height to the diameter of the cylindrical rock specimen in step (2) should be 2.0 to 2.5, and the non-parallelism error of the two end surfaces of the cylindrical specimen shall not be greater than 0.05 mm.

[0082] The freeze-thaw method of the rock specimen in step (2) is as follows: the rock specimen is placed in a saturated container with water, the water level in the container is always higher than the rock specimen, the vacuum pressure gauge reading is 0.1 MPa, and air is pumped until no gas overflows, but the pumping time shall not be less than 4 hours. The forced saturated rock specimen is wrapped with plastic wrap and placed in a freeze-thaw machine at an ambient temperature of -20°C for freezing. After 4 hours, the frozen rock specimen is taken out and placed in water at 20°C for thawing. The thawing time is 4 hours. The above steps are a freeze-thaw cycle process, and the above steps are repeated until the number of freeze-thaw cycles meets the target value.

[0083] The method for carrying out a conventional triaxial compression test on the frozen-thawed rock in step (3) is as follows: wrap the rock specimen with a heat shrink tube and arrange axial and circumferential displacement meters around the rock, place the rock specimen to be tested at the bottom of the triaxial chamber of the rock mechanics testing machine and insert the sensor data interface into the corresponding socket on the base, lower the triaxial chamber and fill it with silicone oil. Apply lateral stress σ3 and axial stress σ1 synchronously at a loading speed of 0.05 MPa per second to a predetermined lateral stress value σ3. The lateral stress value is always maintained at a predetermined value during the test. The loading process adopts a continuous single loading method, applying axial displacement at a loading rate of 0.1 mm / min until the rock is destroyed. During the test, the axial stress value σ1, axial strain ε1, and radial strain ε3 of the rock specimen are recorded at intervals of 0.1 seconds.

[0084] In the step (4), the method for drawing the axial strain-deviatoric stress relationship and the radial strain-deviatoric stress relationship of the freeze-thaw rock is as follows: using ε1 and ε3 as the horizontal coordinates and q=σ1-σ3 as the vertical coordinate to draw the axial strain-deviatoric stress relationship and the radial strain-deviatoric stress relationship of the freeze-thaw rock.

[0085] The method for establishing the yield criterion in step (4) is: based on the q=σ1-σ3 curve, determine the initial yield strength σ of the frozen-thaw rock q , the first principal stress invariant of the rock specimen I1=σ q +2σ3, the second invariant of the deviatoric stress tensor As the horizontal and vertical coordinates, plot the initial yield stress of the freeze-thaw rock corresponding to relationship curve, and according to the Based on the shape of the curve in the meridian plane, a yield equation suitable for describing the initial yield curve of freeze-thaw rocks is proposed.

[0086] The method for establishing the hardening law in step (4) is: based on the q = σ1-σ3 ~ ε1 curve, the equivalent plastic shear strain of the rock hardening stage under different confining pressures at the same freeze-thaw times is plotted. Relationship curve, in the rock hardening stage Let γ on the relationship curve p Take different values ​​and set γ pWhen the same value is taken, the corresponding stress value is plotted on In the meridian plane, the hardening trajectory of rock under the same number of freeze-thaw cycles and different confining pressures can be obtained. Based on the above hardening trajectory, the hardening law of freeze-thaw rock can be determined.

[0087] The specific method for deriving the rock elastic-plastic damage constitutive equation considering freeze-thaw action and compaction effect in step (5) is as follows: the total strain ε during rock deformation ij Can be decomposed into elastic strain and plastic strain Based on the yield criterion and elastic-plastic mechanics theory considering freeze-thaw cycles proposed above and the associated flow law, the elastic-plastic constitutive equation of rock considering freeze-thaw effects is derived. On this basis, the damage factor is introduced to establish an elastic-plastic constitutive equation that can reflect the softening phenomenon of freeze-thaw rock. Furthermore, the elastic modulus in the initial stage is multiplied by the compaction coefficient R to correct it, and an elastic-plastic damage constitutive model of rock considering freeze-thaw effects and compaction effects is established.

[0088] Based on the σ1-σ3~ε1 curve of freeze-thaw rocks, Curve, hardening stage curve, determine the parameter expression of the constitutive equation, and finally use FORTRAN language to digitize the constitutive model to verify and improve the constitutive equation.

[0089] This example provides a new method for accurately theoretically predicting the stress-strain response of frozen-thawed rock. This method constructs an incremental stress-strain relationship and an elastic-plastic stiffness matrix that account for freeze-thaw effects. It also introduces correction coefficients and damage factors to reflect the compaction and softening characteristics of the frozen-thaw rock deformation curve. This model has few parameters and clear physical meaning, and can be obtained through triaxial compression tests on frozen-thawed rock.

[0090] This example considers the effects of freeze-thaw cycles on rock mechanical properties and constitutive equations, introduces the number of freeze-thaw cycles into the yield equation, and reflects the effect of freeze-thaw on the initial yield and hardening process of rock. This example also introduces a damage factor to describe the post-peak softening phenomenon of freeze-thawed rock, and can quantitatively determine the macroscopic damage evolution law of freeze-thawed rock under load.

[0091] Moreover, the theoretical values ​​calculated by the rock elastic-plastic damage constitutive model constructed in this embodiment, which takes into account freeze-thaw and compaction effects, are basically close to the experimental values, fully reflecting the influence trend of freeze-thaw cycles on rock mechanics and deformation characteristics, and can better predict the peak strain, compressive strength, and stress-strain response of rock under different freeze-thaw cycles.

[0092] The freeze-thaw rock elastoplastic damage model constructed in this embodiment can be written as a subroutine and embedded in commercial finite element software to simulate the mechanical and deformation characteristics of freeze-thaw rocks. It can also be used to simulate and analyze the stability of rock mass engineering in cold regions.

[0093] Specific implementation examples:

[0094] (1) Introduction of the concept of freeze-thaw strength. When establishing freeze-thaw damage evolution equations or constitutive models for rocks, only the relationship between rock mechanical parameters and the number of freeze-thaw cycles under fixed temperature freeze-thaw is considered, ignoring the effects of freeze-thaw temperature amplitude changes and different freeze-thaw durations on the degree of rock freeze-thaw damage. In actual rock mass engineering, freeze-thaw damage is usually caused by variable amplitude freeze-thaw temperatures. Therefore, the application of theoretical models established based on indoor freeze-thaw tests (usually carried out in a fixed freeze-thaw temperature range (-20℃~+20℃)) in actual engineering is limited. Therefore, it is urgent to establish the relationship between freeze-thaw damage intensity under fixed temperature freeze-thaw and freeze-thaw damage intensity under other freeze-thaw conditions, so as to further expand the application scope of experimental and theoretical research results under fixed temperature freeze-thaw.

[0095] Based on this, this patent proposes the concept of freeze-thaw intensity to comprehensively reflect the degree of rock damage caused by different freeze-thaw temperatures and durations. Its expression is as follows:

[0096] Q=NQ0

[0097] Where: Q is the total freeze-thaw strength, N is the number of freeze-thaw cycles, Q0 is the unit freeze-thaw strength, and its expression is as follows:

[0098]

[0099] Where α1 and α0 are rock mechanical property degradation indices under other freeze-thaw conditions and per freeze-thaw cycle at a fixed freeze-thaw temperature, respectively. These values ​​can be macroscopic mechanical indices such as peak strength and elastic modulus, or other microscopic characteristic parameters such as longitudinal wave velocity and porosity. In this patent, only freeze-thaw tests were conducted at a fixed freeze-thaw temperature, so Q0 = 1.

[0100] (2) Rock block collection and rock specimen preparation. Rock blocks were collected from a slope of a certain project in western my country. According to the recommended standards of the International Society for Rock Mechanics, the rock blocks were processed into cylindrical specimens with a diameter of 50 mm and a height of 100 mm. Figure 3 As shown;

[0101] (3) Rock specimen homogeneity inspection. First, visually inspect all cylindrical specimens and remove those with obvious cracks or cavities. Second, perform ultrasonic testing on all specimens that pass the visual inspection. Place ultrasonic probes at both ends of the cylindrical specimen, with one end stimulating the ultrasonic wave and the other end receiving the ultrasonic wave. Record the ultrasonic wave velocity of all rock specimens and remove those with ultrasonic wave velocity that significantly deviates from the average value.

[0102] (4) Freeze-thaw test of rock specimens. Place the rock specimen in a saturated container with water. The water level in the container is always higher than the rock specimen. The vacuum pressure gauge reads 0.1 MPa. Pump air until no gas overflows, but the pumping time must not be less than 4 hours. Wrap the forced saturated rock specimen with plastic wrap and place it in a freeze-thaw machine at an ambient temperature of -20°C for freezing. After 4 hours, take out the frozen rock specimen and place it in water at 20°C for thawing. The thawing time is 4 hours. The above steps are a freeze-thaw cycle process. Repeat the above steps until the number of freeze-thaw cycles meets the target value.

[0103] (5) Rock triaxial compression test. Wrap the rock specimen with heat shrink tubing and arrange axial and circumferential displacement meters around the rock. Place the rock specimen to be tested at the bottom of the triaxial chamber of the rock mechanics testing machine and insert the sensor data interface into the corresponding socket on the base. Lower the triaxial chamber and fill it with silicone oil. Apply lateral stress σ3 and axial stress σ1 simultaneously at a loading rate of 0.05 MPa per second to the predetermined lateral stress value σ3. The lateral stress value is always maintained at the predetermined value during the test. The loading process adopts a continuous single loading method, applying axial displacement at a loading rate of 0.1 mm / min until the rock is destroyed. During the test, the axial stress value σ1, axial strain ε1, and radial strain ε3 of the rock specimen are recorded at intervals of 0.1 seconds.

[0104] (6) Calculate the volume strain ε based on the axial strain ε1 and radial strain ε3 obtained from the test records v , volume strain ε v =ε1+2ε3, where ε1 is a positive value and ε3 is a negative value. With axial strain ε1 and radial strain ε3 as the abscissa and deviatoric stress q=σ1-σ3 as the ordinate, the deviatoric stress-axial and radial stress-strain curves are plotted, as shown in Figure 4 According to the initial yield stress and peak compressive strength of the frozen-thaw rock material under different confining pressures σ3, the frozen-thaw rock material in the meridian plane under the initial yield and critical state is obtained. Relationship curve; for cylindrical specimens, I1=σ q +2σ3, according to The shape of the curve in the meridian plane, such as Figure 5-Figure 6 As shown in the figure, a linear yield equation is proposed to describe the initial yield state and critical yield state of freeze-thaw rock:

[0105]

[0106] I1=σ ii , J2=S ij S ij / 2

[0107] S ij =σ ij -σ ii δ ij / 3

[0108]

[0109] Where α(Q) is the slope of the yield curve, K(γ p , Q) is the hardening parameter, which reflects the change of the yield line slope, β is the hardening coefficient, which reflects the expansion of the yield surface in the hardening stage, ω is the damage factor, which reflects the reduction of the yield surface in the softening stage, and k(Q) is the intercept in the meridian plane of the yield curve.

[0110] (7) The freeze-thaw rock hardening law is proposed. Based on the σ1-σ3~ε1 curve, the equivalent plastic shear strain of the rock hardening stage under different confining pressures at the same freeze-thaw times is plotted. Relationship curve, in the rock hardening stage Let γ on the relationship curve p Take different values, such as Figure 7 As shown, and γ p When the same value is taken, the corresponding stress value is plotted on In the meridian plane, Figure 8 As shown in , the hardening trajectory of rock under different confining pressures with the same number of freeze-thaw cycles can be obtained. Based on the above hardening trajectory, the hardening law of freeze-thaw rock can be determined, as shown in Figure 9-10 As shown in Figure 2, the hardening parameter K increases nonlinearly with the increase of equivalent plastic shear strain, and the intercept k decreases nonlinearly with the increase of equivalent plastic shear strain. Both can be expressed by the following equations:

[0111]

[0112] k=k0(1+β)

[0113] Where Δ is the difference between the slope of the critical yield surface and the slope of the initial yield surface, k0 is the initial intercept of the yield surface, and A, B, and β are model parameters.

[0114] (8) Derivation of the elastoplastic constitutive model of freeze-thaw rock. The total strain ε of freeze-thaw rock ij Including elastic strain and plastic strain The expression is as follows:

[0115]

[0116] According to Hooke's law, the stress increment dσ of frozen-thawed rock is ij It can be expressed as the following formula:

[0117]

[0118] Where, is the elastic stiffness matrix, is the plastic strain increment.

[0119] Using the associated flow law, the plastic strain increment can be written as follows:

[0120]

[0121] During plastic loading, the stress state of the rock is always on the yield surface, with the following consistency conditions:

[0122]

[0123] Where, Substituting dK, dω, and dβ into the consistency conditions, we have:

[0124]

[0125] Where,

[0126] From this, the plastic multiplier dλ can be calculated as:

[0127]

[0128] Where,

[0129] From this, the stress-strain relationship in the form of freeze-thaw rock increments can be obtained:

[0130]

[0131] Where,

[0132] (9) Considering the freeze-thaw strength and compaction effect, an elastic-plastic damage model is established. Based on the elastic-plastic constitutive model of freeze-thaw rock, the elastic modulus E of the model is modified to reflect the compaction characteristics of freeze-thaw rock. The compaction coefficient change law is as follows: Figure 11 As shown, its definition is as follows:

[0133]

[0134] Where ε is the axial strain, ε1c is the peak strain, χ,n is the compaction coefficient, which can be determined based on experiments.

[0135] (10) Numerical implementation of constitutive model. The above constitutive model is numerically implemented using FORTRAN language. The basic process of the numerical algorithm is as follows: Figure 12 As shown in the figure, there are three main parts: elastic prediction, plastic correction and damage correction. The first part, elastic prediction: the elastic prediction formula is as follows:

[0136]

[0137] Where, t k+1 Predicted stress at time D e is the elastic stiffness matrix; σ k t k The calculated stress at the moment; Δε is the strain increment in the current iteration step. Substitute the predicted stress into Substituting the yield criterion, if f k+1 <0, then t k+1 The stress at the moment is updated as follows

[0138]

[0139] Where, σ k+1 t k+1 Calculated stress at time.

[0140] If there is f k+1 ≥0, then enter the plastic correction stage. The second part is plastic correction. According to the plastic increment theory, the Newton-Raphson iterative equation is established to solve the update formula until f is satisfied. k+1 <0, the expression formula is as follows:

[0141]

[0142] Where, is the return vector, and dλ is the plasticity multiplier.

[0143] Most of the constitutive model parameters can be obtained through triaxial compression tests of rocks. Among them, Young's modulus E and Poisson's ratio v can be determined by the straight line part of the deviatoric stress-strain curve of freeze-thaw rock; the yield parameter α can be obtained by Figure 5 The yield surface in the hardening parameter K can be determined by A, B, Δ Figure 9 The changing law of K in the equation is determined; β can be determined by Figure 10 The variation law of k in the compaction coefficient R is determined by fitting the variation law of R; the damage parameter b cannot be obtained directly through experiments and is determined by trial and error.

[0144] The constitutive model parameters determined by the above method are shown in Table 1.

[0145] Table 1 Parameters of the elastic-plastic damage constitutive model of freeze-thaw sandstone

[0146]

[0147]

[0148] The above constitutive model and parameters were used to numerically simulate the mechanical and deformation characteristics of freeze-thaw sandstone. The results are as follows: Figure 13 As shown, the simulation results are generally consistent with the test results, confirming that the constitutive model constructed in this example can accurately describe the mechanical and deformation characteristics of sandstone under different freeze-thaw cycles. Therefore, it is believed that the method for establishing the freeze-thaw rock elastic-plastic damage constitutive model based on triaxial compression tests proposed in this example is accurate, reliable, simple to operate, and has clear physical significance.

[0149] This method is based on the mechanical characteristics of deformation and failure of freeze-thaw rocks, proposes a yield function and hardening law considering the freeze-thaw effect, and establishes an elastic-plastic damage constitutive model of freeze-thaw rocks. Comparison with experimental results shows that this method has high accuracy and can be used to predict the strength and stress-strain response of freeze-thaw rocks. It can also be applied to the deformation and stability analysis of actual rock engineering in cold regions.

[0150] The above description is merely a preferred embodiment 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 the present 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 establishing a rock elastic-plastic damage constitutive model considering freeze-thaw strength and compaction effect, characterized in that: include: Step S1: The concept of freeze-thaw intensity is proposed to comprehensively reflect the freeze-thaw damage degree of rock under different freeze-thaw temperatures and durations; Step S2: preparing a number of rock specimens; Step S3: performing a freeze-thaw test on each of the rock specimens; Step S4: performing a triaxial compression test on each of the rock specimens that have undergone the freeze-thaw test, and recording test data during the triaxial compression test, wherein the test data includes the axial stress, axial strain, and radial strain of the rock specimen; Step S5: plotting a deviatoric stress-strain curve based on the test data, and constructing a yield function and hardening law of the rock specimen based on the strength characteristic parameters of the freeze-thaw rock; Step S6: Based on the elastic-plastic mechanics theory, combined with the yield function and the hardening law, a rock elastic-plastic damage constitutive equation is established that takes into account freeze-thaw and compaction effects; Step S7: Based on the elastic-plastic theory and the triaxial compression stress-strain data of rock, the parameter expression of the elastic-plastic damage constitutive model of freeze-thaw rock is determined.

2. The method according to claim 1, characterized in that The step S1 specifically includes: Taking the freeze-thaw damage caused by specific indoor freeze-thaw temperature and duration as the benchmark, according to the damage equivalence principle and cumulative damage theory, the equivalent relationship between the freeze-thaw damage under other freeze-thaw temperatures and durations and the benchmark freeze-thaw damage is established.

3. The method according to claim 1, characterized in that The step S2 specifically includes: Obtaining a plurality of rock blocks, and processing each of the rock blocks based on a preset size and a preset shape to obtain a plurality of initial test pieces; A homogeneity inspection is performed on each of the initial test pieces, and rock test pieces that pass the inspection are selected.

4. The method according to claim 1, wherein The step S3 specifically includes: Step S31: saturating the rock specimen with water; Step S32: performing a freeze-thaw cycle test on the rock specimen after saturation treatment based on the set time and temperature; Repeat step S31 to step S32 until the preset number of freeze-thaw cycles is reached, completing the freeze-thaw test.

5. The method according to claim 1, wherein A triaxial compression test is performed on each of the rock specimens that have undergone the freeze-thaw test, specifically including: The rock specimens that have undergone the freeze-thaw test are placed at the bottom of the triaxial chamber of a rock mechanics testing machine, displacement meters are arranged, and the triaxial chamber is lowered and filled with silicone oil; First, lateral stress and axial stress are applied at a set rate, then the lateral stress is kept constant and the axial displacement is applied at a set rate until the rock specimen is destroyed; The axial stress, axial strain and radial strain during the test were recorded.

6. The method according to claim 1, characterized in that Drawing a stress-strain curve based on the test data specifically includes: Deviatoric stress-axial strain and deviatoric stress-radial strain curves are constructed with the axial strain and the radial strain as abscissas and the deviatoric stress as ordinates.

7. The method according to claim 1, characterized in that The yield function and hardening law of rock materials are constructed based on the strength characteristic parameters of freeze-thaw rocks, including: The construction process of the yield function: determining the initial yield strength of the rock specimen based on the deviatoric stress-strain curve; Calculating a first principal stress invariant and a second invariant of the deviatoric stress tensor of the rock specimen based on the test data and the initial yield strength; Using the first principal stress invariant as the abscissa and the second invariant of the deviatoric stress tensor as the ordinate, plotting a yield curve of the rock specimen on a meridian plane, wherein the yield curve includes an initial yield curve and a critical yield curve; Determine the yield function based on the shape of the yield curve in the meridian plane; The construction process of hardening law: Based on the deviatoric stress-strain curve, a relationship curve of equivalent plastic shear strain-deviatoric stress tensor second invariant in the rock hardening stage under different confining pressures with the same freeze-thaw times is drawn; The second invariant of the deviatoric stress tensor corresponding to the same equivalent plastic shear strain value is plotted on the meridian plane, and the freeze-thaw rock hardening trajectory under different confining pressures with the same freeze-thaw times is obtained. The hardening law of the freeze-thaw rock specimen is determined based on the hardening trajectory of the freeze-thaw rock.

8. The method according to claim 1, characterized in that The step S6 specifically includes: Based on the yield function, elastic-plastic mechanics theory and associated flow law, the elastic-plastic damage constitutive equation of rock considering freeze-thaw and compaction effects is derived.

9. The method according to claim 1, characterized in that The step S7 specifically includes: The parameters of the elastic-plastic damage constitutive model of freeze-thaw rock are determined based on the deviatoric stress-axial strain curve, the first principal stress invariant-deviatoric stress tensor second invariant curve, and the equivalent plastic shear strain-deviatoric stress tensor second invariant deviatoric stress relationship curve of freeze-thaw rock.

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