Prediction method for irreversible deformation of salt rock creep fatigue under complex loading and unloading paths

Abstract

The present invention discloses a prediction method for irreversible deformation of salt rock creep fatigue under complex loading and unloading paths, which includes establishing a constitutive equation describing the deceleration stage and the steady state stage of salt rock fatigue creep: establishing a constitutive equation for predicting the accelerated deformation stage of salt rock: predicting the three stages of salt rock fatigue creep behavior through the established constitutive equation. The present invention can accurately describe and predict the irreversible deformation of salt rock creep fatigue under complex loading and unloading paths, especially the third stage, i.e., the accelerated deformation stage before critical failure, and can obtain more practical results for practical engineering applications such as the long-term stability evaluation and life assessment of salt cavern gas storage.

Description

Technical Field

[0001] The present invention relates to the technical field of rock mechanics, and particularly to a prediction method for the creep-fatigue failure behavior of salt rock under complex loading and unloading paths. Background Art

[0002] Salt rock has characteristics such as dense structure, low porosity, low permeability, and good damage self-recovery, and is an ideal surrounding rock for underground storage chambers. Different engineering environments make the stress state and environment of salt rock surrounding rock complex and changeable, and the creep-fatigue interaction is a typical characteristic of salt cavern surrounding rock. Salt cavern natural gas storage reservoirs are affected by seasonal gas injection and production, and the surrounding rock is in a typical slow cyclic loading state; compressed air energy storage makes the surrounding rock under rapid high-frequency fatigue loading due to high-frequency rapid air pressure fluctuations; the radioactive heat of low-level radioactive nuclear waste causes salt rock to bear long-term high-temperature creep.

[0003] However, due to the diverse complexity of actual projects and the continuous change of the loading history, when the rock and soil mass is subjected to fatigue creep interaction, there may also be the influence of the loading and unloading history, such as being affected by surrounding mining activities in long-term underground mine roadways, being disturbed by frequent gas injection and production activities in underground salt rock gas storage reservoirs, and the concrete dam body being subjected to the combined action of long-term rheological stress and cyclic stress. The long-term creep interaction and loading and unloading actions of these projects are coupled and related, influencing each other, increasing the difficulty of recognizing and evaluating the engineering stability. Therefore, describing the long-term creep interaction characteristics of salt rock and establishing a model that can scientifically and accurately predict the creep interaction behavior of salt rock have always been the key to evaluating whether the salt rock cavity can operate stably for a long time.

[0004] Both the creep process and the fatigue process have stage characteristics of deformation, which can be roughly divided into three stages, the first stage (decelerated deformation), the second stage (steady-state deformation), and the third stage (accelerated deformation). In order to accurately describe the behavior of the fatigue-creep interaction of rocks, a constitutive model adapted to the test results needs to be established. However, in the prior art, the constitutive models used to predict the fatigue-creep interaction characteristics of rocks do not fully consider the unloading and loading history of rocks, and the fitting degree of the constitutive model with creep experimental data is not good enough. Therefore, the accuracy of predicting the fatigue-creep interaction failure behavior of salt rock using the existing constitutive model needs to be improved. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a prediction method considering the irreversible deformation of salt rock creep fatigue under complex loading and unloading paths to solve the technical problem of accurately predicting the creep fatigue behavior of salt rock.

[0006] The prediction method of the present invention considering the irreversible deformation of salt rock creep fatigue under complex loading and unloading paths includes the following steps:

[0007] 1) The constitutive equations describing the first-stage decelerated deformation and the second-stage steady-state deformation of salt rock creep fatigue are established as follows:

[0008]

[0009] In the above formula, ε represents the strain of salt rock varying with time, and ε 0 represents the initial strain of salt rock, σ 0 represents the initial stress of salt rock, t represents time, v represents the stress loading rate, a represents the stress-deformation rate relationship factor in the steady-state deformation stage of salt rock, b represents the stress-deformation rate relationship factor in the decelerated deformation stage of salt rock, c represents the comprehensive control coefficient of strain rate attenuation, k represents the time sensitivity coefficient of strain rate attenuation; m represents the stress sensitivity coefficient of strain rate attenuation, U 1 represents the variable-speed creep unloading factor, and U 2 represents the steady creep unloading factor; where:

[0010]

[0011] In the above formula represents the initial hardening degree related to the dislocation density inside the salt rock, and σ represents the stress of salt rock varying with time;

[0012] Predict the first stage and the second stage of the salt rock creep fatigue behavior through the established constitutive equations describing the decelerated deformation and the steady-state deformation of salt rock creep fatigue;

[0013] 2) The constitutive equation describing the third-stage accelerated deformation of salt rock creep fatigue is established as follows:

[0014]

[0015] In the above formula is the effective stress, which is obtained through the following formula:

[0016]

[0017] d is the crack propagation relationship factor, and λ represents the dynamic friction coefficient of the crack surface;

[0018] Predict the third stage of the salt rock creep fatigue behavior through the established constitutive equation describing the accelerated deformation stage.

[0019] Furthermore, based on step 1), the viscoelastic-plastic constitutive equation describing the decelerated deformation and the steady-state deformation of salt rock creep fatigue is established as:

[0020]

[0021] In the above formula, σ ijThe stress components in different directions of the three-dimensional space are represented, F represents the yield function, i.e., the starting condition for the creep of salt rock; E is the elastic modulus of salt rock;

[0022] In the above formula, γ 1 represents the kinematic function of the decelerated deformation of salt rock creep fatigue, γ 2 represents the kinematic function of the steady-state deformation stage of salt rock creep fatigue, and the kinematic function γ 1 and γ 2 characterize the kinematic relationship between deformation and stress. The kinematic functions γ 1 and γ 2 both adopt the constitutive equations established in step 1) to describe the decelerated deformation in the first stage and the steady-state deformation in the second stage of salt rock creep fatigue;

[0023] In the above formula, Q 1 represents the plastic potential function in the attenuation stage of salt rock fatigue creep, Q 2 represents the plastic potential function in the steady-state stage of salt rock creep fatigue. The general expression forms of the plastic potential functions Q 1 and Q 2 are as follows:

[0024]

[0025] The partial derivative of the plastic potential function Q with respect to time characterizes the direction of plastic flow. J 2 is the second invariant of the stress deviator, α is a material parameter, and I 1 is the first invariant of the stress tension.

[0026] Predict the first stage and the second stage of the salt rock creep fatigue behavior through the established viscoelastic-plastic constitutive equation.

[0027] Advantages of the present invention:

[0028] The present invention considers a prediction method for the irreversible deformation of salt rock creep fatigue under complex loading and unloading paths. This method can: (1) perform fitting and prediction for the entire three stages of creep fatigue, especially the acceleration deformation stage before critical failure in the third stage; (2) fully consider the viscoplastic deformation during the loading and unloading process, which is more in line with the experimental results; (3) the established constitutive equation can well predict and fit the irreversible deformation characteristics under common complex loading and unloading paths such as conventional creep experiments, cyclic loading and unloading fatigue experiments, lower limit interval cyclic loading and unloading experiments, trapezoidal wave creep cyclic loading and unloading experiments, ascending gradient graded creep experiments, and descending gradient graded creep experiments, and can better characterize the mutual influence between constant load creep and cyclic loading and unloading. More practical results can be obtained for practical engineering applications such as the long-term stability evaluation and life assessment of salt cavern gas storage. Description of the Drawings

[0029] Figure 1 It is a model prediction diagram for a conventional creep experiment using a constitutive equation;

[0030] Figure 2 It is a model prediction diagram for a cyclic loading and unloading fatigue experiment using a constitutive equation;

[0031] Figure 3 It is a model prediction diagram for a lower limit interval cyclic loading and unloading experiment using a constitutive equation;

[0032] Figure 4 It is a model prediction diagram for a trapezoidal wave creep cyclic loading and unloading experiment using a constitutive equation;

[0033] Figure 5 It is a model prediction diagram for a rising gradient stepwise creep experiment using a constitutive equation;

[0034] Figure 6 It is a model prediction diagram for a falling gradient stepwise creep experiment using a constitutive equation. Specific implementation manner

[0035] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0036] The prediction method for the irreversible deformation of salt rock creep fatigue under complex loading and unloading paths in this embodiment includes the following steps:

[0037] 1) Establish the following constitutive equations for describing the decay stage and the steady state stage of salt rock creep fatigue:

[0038]

[0039] In the above formula, ε represents the strain of salt rock varying with time, ε 0 represents the initial strain of salt rock, σ 0 represents the initial stress of salt rock, t represents time, v represents the stress loading rate, a represents the stress-deformation rate relationship factor in the steady state deformation stage of salt rock, b represents the stress-deformation rate relationship factor in the decelerated deformation stage of salt rock, c represents the comprehensive control coefficient of strain rate decay, k represents the time sensitivity coefficient of strain rate decay; m represents the stress sensitivity coefficient of strain rate decay, U 1 represents the variable speed creep unloading factor, U 2 represents the steady creep unloading factor; a, b, c, n, m, k, U 1 and U 2 are design parameters, and their values are set by the experimenter himself, where:

[0040]

[0041] In the above formula represents the initial hardening degree related to the dislocation density inside the salt rock, and σ represents the stress of the salt rock varying with time;

[0042] Predict the first and second stages of the creep-fatigue behavior of salt rock through the established constitutive equations describing the decelerated deformation and stage-steady deformation of salt rock creep-fatigue.

[0043] The constitutive equations describing the decelerated deformation and creep-fatigue steady deformation stages of salt rock are as follows:

[0044] For the steady-state process of salt rock, the power of the strain rate and stress shows a linear relationship.

[0045]

[0046] For the decelerated process of salt rock, that is, the first-stage deformation, the power of strain and stress and time show a hyperbolic relationship.

[0047]

[0048] Combining equations (1) and (2), the following relationship is obtained

[0049]

[0050] The state variable is defined by the stress-strain relationship, characterizing the hardening degree σ related to the dislocation density inside the salt rock * . The state variable can be written as

[0051]

[0052]

[0053] The strain equation can be rewritten as:

[0054]

[0055] The state variable can characterize the influence of the magnitude of stress and its acting time on the creep-fatigue of salt rock. Assume that when a new stress acts on the rock, the initial state of the state variable Then the new state variable can be expressed as

[0056]

[0057]

[0058] The strain equation can be further rewritten as:

[0059]

[0060] Taking the first derivative of equations (7) and (8) with respect to time, the state rate is obtained as

[0061]

[0062] The strain rate obtained is

[0063]

[0064] It can be seen from the above formula that when the stress changes, the strain rate changes accordingly. When in the loading state, if the stress loading rate is v, the state variable can be obtained by integrating the following formula:

[0065]

[0066] Then the strain during the loading process can be obtained by the following formula

[0067]

[0068] When in the unloading state, it is possible that the external force is less than the state variable. At this time, the state variable is

[0069]

[0070] Since during unloading, the internal structure adjustment depends entirely on internal forces and the adjustment rate is slow, a variable-speed unloading factor (state variable unloading factor) U 1 is introduced. Taking the first derivative with respect to time, the state rate obtained is

[0071]

[0072]

[0073] The steady-state deformation rate will also be affected. A steady-state creep fatigue unloading factor U 2 is introduced, and the strain formula can be rewritten as:

[0074]

[0075] 2) Establish the constitutive equation describing the third-stage accelerated deformation of salt rock creep fatigue as follows:

[0076]

[0077] In the above formula is the effective stress, which is obtained through the following formula:

[0078]

[0079] d is the crack propagation relation factor, and λ represents the dynamic friction coefficient of the crack surface; d and λ are design parameters, and their values are set by the experimenter himself.

[0080] Predict the third stage of the creep-fatigue behavior of salt rock through the established constitutive equation describing the accelerated deformation stage.

[0081] The construction process of the constitutive equation describing the accelerated deformation stage of salt rock is as follows:

[0082] The main reason for the acceleration characteristics in the third stage of salt rock creep-fatigue is crack propagation. Introduce the crack propagation relation factor d. Crack formation is mainly caused by the accumulation of dislocations. The stress field generated by the accumulation of a large number of dislocations and the external stress field are superimposed to form an intensity factor that reaches the fracture toughness, that is, cracks (or crack nucleation) are generated. The nucleation of cracks is a rapid instantaneous process. The relevant evolution process has not been directly observed in rock experiments. Assume that the initial nucleation length is d 0 , and it is formed instantaneously. Its formation time is related to the externally applied stress and the accumulated plastic deformation.

[0083] K c = Γ(σ, ε p ) (16)

[0084] K c is the fracture toughness of the material, which is a natural property of the material. After that, the formation of each new crack is related to the deformation development rate.

[0085]

[0086] In the formula: μ d is the crack propagation factor.

[0087]

[0088] Effective stress can be obtained by the following formula

[0089]

[0090] Equation (25) can be rewritten as,

[0091]

[0092] λ is the dynamic friction coefficient of the crack surface. After entering the third stage, the deformation of salt rock is calculated by the following formula:

[0093]

[0094] As an improvement to the above embodiment, on the basis of step 1), establish a viscoelastic-plastic constitutive equation describing the decelerated deformation and steady-state deformation of salt rock creep-fatigue as:

[0095]

[0096] In the above formula, σ ijThe stress components in different directions of the three-dimensional space are denoted as, and F represents the yield function, i.e., the initiation condition for the creep of salt rock; E is the elastic modulus of salt rock;

[0097] In the above formula, γ 1 represents the kinematic function of the decelerated deformation of salt rock creep fatigue, and γ 2 represents the kinematic function of the steady-state deformation stage of salt rock creep fatigue. The kinematic functions γ 1 and γ 2 characterize the kinematic relationship between deformation and stress. The kinematic functions γ 1 and γ 2 both adopt the constitutive equations established in step 1) to describe the decelerated deformation in the first stage and the steady-state deformation in the second stage of salt rock creep fatigue;

[0098] In the above formula, Q 1 represents the plastic potential function in the attenuation stage of salt rock fatigue creep, and Q 2 represents the plastic potential function in the steady-state stage of salt rock creep fatigue. The general expression forms of the plastic potential functions Q 1 and Q 2 are as follows:

[0099]

[0100] The partial derivative of the plastic potential function Q with respect to time characterizes the direction of plastic flow; J 2 is the second invariant of the stress deviator, α is a material parameter, and I 1 is the first invariant of the stress tension.

[0101] Predict the first stage and the second stage of the salt rock creep fatigue behavior through the established viscoelastic-plastic constitutive equation.

[0102] The construction process of the viscoelastic-plastic constitutive equations describing the attenuation stage and the steady-state stage of salt rock creep fatigue is as follows:

[0103] In the plastic constitutive model, the potential function is usually used to characterize the direction of plastic flow. If the potential function has a similar form to the yield function, it is called the associated criterion; if it is different, it is called the non-associated criterion. In most cases, the measured flow direction in the experiment has little connection with the yield function. Therefore, the non-associated criterion is adopted here.

[0104]

[0105] F represents the yield function, i.e., the initiation condition for creep fatigue. Q represents the plastic potential function, and its partial derivative with respect to time characterizes the direction of plastic flow. γ characterizes the kinematic relationship between creep fatigue deformation and stress and can be calculated by Equation (15).

[0106] When the salt rock is in a steady-state deformation, the internal dislocation force and the external force reach a dynamic equilibrium. Dislocations mainly slip along the direction of the easiest slip system, that is, the direction of the maximum shear stress, and the plastic deformations formed are proportional in all directions. In the first stage, the external force is significantly greater than the internal force, and dislocations proliferate and slip rapidly. During this process, a "supersaturated" state of dislocations may occur, leading to the emergence of new slip systems for dislocation slip, such as climbing and other behaviors, thus causing changes in the proportion of plastic deformations in all directions. Therefore, a "double potential function" constitutive model is established for the plastic potential in the two stages respectively.

[0107]

[0108] Its viscoelastic-plastic constitutive equation is:

[0109]

[0110] γ 1 and γ 2 respectively represent the kinematic functions in the first and second stages of salt rock creep fatigue. Q 1 and Q 2 respectively represent the plastic potential functions in the first and second stages of salt rock creep fatigue. The F activation condition is shared by the first and second stages, and E is the elastic modulus. Here, the plastic potential function Q adopts the form of the D-P criterion, and the general expression forms of Q 1 and Q 2 are as follows:

[0111]

[0112] The D-P criterion is described in detail in "Research on the Integration of Ideal Elastic-Plastic Constitutive Relations Based on the D-P Criterion" published in the 4th issue of the 22nd volume of "Engineering Mechanics".

[0113] Next, conventional creep experiments ( Figure 1 ), cyclic loading-unloading fatigue experiments ( Figure 2 ), lower-bound interval cyclic loading-unloading experiments ( Figure 3 ), trapezoidal-wave creep cyclic loading-unloading experiments ( Figure 4 ), ascending-gradient stepwise creep experiments ( Figure 5 ), and descending-gradient stepwise creep experiments ( Figure 6 ) are respectively used to fit the obtained experimental curves with the described constitutive equation, where formula (15) is used for fitting the first and second stages of creep fatigue deformation in each experiment. As can be seen from the figure, the experimental results and the model prediction results have a high degree of agreement and small errors, indicating that the prediction method considering the irreversible deformation of salt rock creep fatigue under complex loading-unloading paths in this embodiment can accurately predict the entire process of salt rock creep fatigue.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A prediction method for irreversible deformation of salt rock creep fatigue under complex loading and unloading paths, characterized in that: It includes the following steps: 1) Establish a constitutive equation to describe the first-stage decelerated deformation and the second-stage steady-state deformation of salt rock creep fatigue as follows: In the above formula, ε represents the strain of salt rock varying with time, ε 0 represents the initial strain of salt rock, σ 0 represents the initial stress of salt rock, t represents time, v represents the stress loading rate, a represents the stress-deformation rate relationship factor in the steady-state deformation stage of salt rock, b represents the stress-deformation rate relationship factor in the decelerated deformation stage of salt rock, c represents the comprehensive control coefficient of strain rate attenuation, k represents the time-sensitive coefficient of strain rate attenuation; m represents the stress-sensitive coefficient of strain rate attenuation, U 1 represents the variable-speed creep unloading factor, U 2 represents the steady-state creep unloading factor; where: In the above formula represents the initial hardening degree related to the dislocation density inside the salt rock, and σ represents the stress of the salt rock varying with time; Predict the first stage and the second stage of salt rock creep fatigue behavior through the established constitutive equation describing the decelerated deformation and the steady-state deformation of salt rock creep fatigue; 2) Establish a constitutive equation to describe the third-stage accelerated deformation of salt rock creep fatigue as follows: In the above formula is the effective stress, which is obtained by the following formula: d is the crack propagation relation factor, and λ represents the dynamic friction coefficient of the crack surface; Predict the third stage of salt rock creep fatigue behavior through the established constitutive equation describing the accelerated deformation stage.

2. The prediction method for irreversible deformation of salt rock creep fatigue under complex loading and unloading paths according to claim 1, characterized in that: Based on step 1), establish a viscoelastic-plastic constitutive equation to describe the decelerated deformation and steady-state deformation of salt rock creep fatigue as: In the above formula, σ ij represents the stress components in different directions of the three-dimensional space, F represents the yield function, that is, the starting condition for the creep of salt rock; E is the elastic modulus of salt rock; In the above formula, γ 1 represents the motion function of the decelerated deformation of the salt rock creep fatigue, and γ 2 represents the motion function of the steady-state deformation stage of the salt rock creep fatigue. The motion functions γ 1 and γ 2 characterize the motion relationship between the deformation and the stress. The motion functions γ 1 and γ 2 both adopt the constitutive equations established in step 1) to describe the decelerated deformation in the first stage and the steady-state deformation in the second stage of the salt rock creep fatigue; In the above formula, Q 1 represents the plastic potential function in the fatigue creep attenuation stage of salt rock, and Q 2 represents the plastic potential function in the steady state stage of salt rock creep fatigue. The general expression form of the plastic potential functions Q 1 and Q 2 is as follows: The partial derivative of the plastic potential function Q with respect to time characterizes the direction of plastic flow, J 2 is the second invariant of the stress deviator, α is a material parameter, I 1 is the first invariant of the stress tension; Predict the first stage and the second stage of salt rock creep fatigue behavior through the established viscoelastic-plastic constitutive equation.

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