A method for constructing a soft rock creep damage model

Abstract

The present invention discloses a method for constructing a soft rock creep damage model, which belongs to the field of geotechnical technology and includes the following steps: S1: classifying soft rock creep damage and establishing various types of damage equations; S2: dividing the soft rock creep curve into a stable creep stage and an unstable creep stage, constructing viscoelastic elements, viscoplastic elements and a creep model; S3: establishing creep equations for the stable creep stage and the unstable creep stage; S4: establishing a three-dimensional creep damage model. The soft rock creep damage model constructed by the present invention can better characterize the nonlinear creep characteristics of soft rock under the action of dry-wet cycles, the physical meaning of the parameters is clear, and it can accurately reflect the influence of the number of dry-wet cycles, axial pressure and time coupling on the soft rock creep damage.

Description

Technical Field

[0001] The invention belongs to the field of rock and soil technology, and specifically relates to a method for constructing a soft rock creep damage model. Background Art

[0002] Soft rock is a complex rock mechanical medium with significant plastic deformation under specific conditions. With the long-term changes in the external atmosphere, soft rock will produce time-dependent deformation, that is, the deformation increases with time, and different degrees of deformation correspond to different degrees of soft rock damage. For example, carbonaceous mudstone is a type of soft rock, which is widely distributed in the Permian strata in southwest my country. Under the action of atmospheric dry-wet cycles and continuous loads, the problem of creep damage of carbonaceous mudstone slopes is very prominent. Constructing a constitutive model that can accurately characterize the creep damage characteristics of carbonaceous mudstone under the action of dry-wet cycles is of great significance for the deformation prediction and stability analysis of carbonaceous mudstone and soft rock slopes.

[0003] At present, the methods for constructing creep models mainly include: empirical method, phenomenological theory and component model method. Both empirical method and phenomenological theory obtain empirical equations of creep models by numerically fitting the test results, and the physical meaning of the model parameters is difficult to clarify. The component model connects Hooke body, Newton body and Coulomb body in series or in parallel to form a creep model. It has the characteristics of simple form and clear physical meaning of parameters, so it is widely used by researchers. Typical component models include Maxwell model, Kelvin model, Burgers model and Nishihara model. Scholars have achieved good results in describing rock creep characteristics using the above component models. Since the component model is composed of linear components, the constructed model can only represent linear creep characteristics. However, rock mass is affected by multiple factors such as engineering environment, geological structure and construction activities, and its deformation often shows complex nonlinear characteristics. If the traditional component model is continued to be used, it is difficult to accurately represent the time-dependent deformation characteristics of rock. In order to enable the component model to better represent the nonlinear characteristics of rock, researchers have tried to use nonlinear components instead of traditional basic components. However, the entire creep process of soft rock has obvious nonlinearity. The existing methods mainly consider the nonlinearity of the accelerated creep stage of rock, while the attenuation creep stage and the steady creep stage are still linear equations. Some researchers have modified the component model parameters by introducing damage variables. However, most of the creep models established in the past only considered the influence of single damage factors such as dry-wet cycles, axial pressure, and time, and empirically used damage variables to uniformly modify the model parameters. However, in fact, the creep of slope rock mass should be affected by the coupling of dry-wet cycles, axial pressure (i.e. stress) and time, and the damage effects of different influencing factors in each creep stage are significantly different. It is impossible to modify all component model parameters with the same damage variables. At present, there is still a lack of constitutive models that can accurately characterize the time-dependent deformation of soft rock under the coupling of dry-wet cycles, axial pressure (i.e. stress) and time. Summary of the invention

[0004] In view of the above problems existing in the prior art, the purpose of the present invention is to provide a method for constructing a soft rock creep damage model. Based on the component model theory, a soft rock creep model is established by constructing a viscoelastic element and a viscoplastic element in series, and the coupled damage variables of initial damage and time-dependent damage are used to correct the viscoelastic element parameters. The crack extension damage is introduced to correct the viscoplastic element parameters, and a new soft rock creep damage model is constructed. The model can better characterize the nonlinear creep characteristics of soft rock under the action of dry-wet cycles, the physical meaning of the parameters is clear, and it can accurately reflect the influence of the number of dry-wet cycles, axial pressure and time coupling on the creep damage of soft rock.

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

[0006] A method for constructing a soft rock creep damage model comprises the following steps:

[0007] Step S1: Classify the soft rock creep damage and establish various damage equations, and classify the soft rock creep damage into three categories: initial damage, aging damage and crack extension damage;

[0008] Step S2: Divide the soft rock creep curve into a stable creep stage and an unstable creep stage, construct viscoelastic elements, viscoplastic elements and a creep model, and the creep model is composed of a viscoelastic element and a viscoplastic element connected in series;

[0009] Step S3: Using the damage equation of step S1 and the creep model of step S2, the creep equations of the stable creep stage and the unstable creep stage are established, the coupled damage variables of initial damage and aging damage are used to correct the viscoelastic component parameters, the crack extension damage is introduced to correct the viscoplastic component parameters, and a new soft rock creep damage model is constructed;

[0010] Step S4: Establish a three-dimensional creep damage model.

[0011] As a further improvement of the above technical solution:

[0012] In step S1, the initial damage Mesoscopic structural damage caused by the development of pores in soft rock due to dry-wet cycles; time-dependent damage Changes in rock mechanical properties caused by the directional flow of rock particles over time; crack extension damage It is the damage and deterioration of rock structure caused by the expansion and connection of rock cracks under load.

[0013] Preferably,

[0014] ;

[0015] ;

[0016] ;

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] in, is the total cross-sectional area, is the pore area, is the rock porosity, For the Wet-dry cycle under stage axial pressure The instantaneous elastic modulus, When time approaches infinity Wet-dry cycle under stage axial pressure The elastic modulus, Is related to the number of dry and wet cycles and axial pressure Related functions, It's time. is with , , Related functions, is with , , Related functions, yes The adaptation of the moment, and is the material parameter, , , They are the three principal stresses of soft rock in three mutually perpendicular directions in space, is the crack initiation angle, is the Poisson's ratio of the rock, is the crack radius, is the stress intensity factor of rock, According to the energy reciprocity theorem, is a parameter related to axial pressure. The least square method is used to calculate the soft rock under the action of dry-wet cycles. , , Fitting is performed to establish a functional relationship with the axial pressure.

[0024] In step S2, during the stable creep stage, < , soft rock only undergoes transient elastic and viscoelastic strains under load; in the unstable creep stage, ≥ , soft rock undergoes instantaneous elastic, viscoelastic and viscoplastic strains under load, among which, is the axial pressure, Long-term strength of rock.

[0025] In step S2, the viscoelastic element is composed of a spring and a damper, and the viscoplastic element is composed of a friction plate and a nonlinear damping element in parallel.

[0026] In step S3, during the stable creep stage, the damage of soft rock during the stable creep stage under the action of dry-wet cycles is Initial damage Time-related damage Coupling effect.

[0027] In step S3, during the stable creep stage, the damage equation of soft rock under the action of dry-wet cycles is:

[0028] .

[0029] In step S3, during the unstable creep stage, the time-dependent elastic modulus damage is the coupling effect of initial damage and time-dependent damage. , the viscoplastic viscosity coefficient damage is the crack extension damage .

[0030] In step S3, the creep equation in the unstable creep stage is:

[0031] ;

[0032] = ;

[0033] in, For strain, is the initial viscosity coefficient, is the initial elastic modulus.

[0034] when < When , the creep damage equation is:

[0035] ;

[0036] when ≥ When , the creep damage equation is:

[0037] ;

[0038] in, is the strain in the axial compression direction, , is the shear modulus, the bulk modulus .

[0039] The beneficial effects of the present invention are:

[0040] (1) The creep deformation mechanism of soft rock under the action of dry-wet cycles is analyzed from a microscopic perspective. The porosity, time-dependent elastic modulus and crack extension parameters are proposed as damage variables. The initial, time-dependent and crack extension damage equations of soft rock are established, which can accurately reflect the damage evolution law of soft rock under the action of dry-wet cycles, axial pressure and time factors.

[0041] (2) Based on fracture mechanics and the energy reciprocity theorem, it is proposed to use the viscoplastic creep rate to characterize the crack growth rate. A quantitative characterization relationship between rock microcrack growth parameters and damage is established, which provides a new idea for the quantitative study of rock crack growth damage evolution.

[0042] (3) It is proposed to use viscoelastic elements and elastoplastic elements to characterize the nonlinear characteristics of soft rock creep. Specifically, based on the element model theory, a soft rock creep model is established by constructing viscoelastic elements and viscoplastic elements in series. The coupled damage variables of initial damage and time-dependent damage are used to correct the parameters of the viscoelastic elements. Crack extension damage is introduced to correct the parameters of the viscoplastic elements. A new soft rock creep damage model is constructed. This model can better characterize the nonlinear creep characteristics of soft rock under the action of dry-wet cycles, and the physical meaning of the parameters is clear.

[0043] (4) The established creep damage model can better characterize the nonlinear creep characteristics of soft rock under the action of dry-wet cycles, and can accurately reflect the influence of the number of dry-wet cycles, axial pressure and time coupling on the creep damage of soft rock. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1(a) is the experimental result of triaxial creep curve of soft rock when the number of dry-wet cycles is 0.

[0045] Figure 1(b) is the experimental result of triaxial creep curve of soft rock when the number of dry-wet cycles is 3.

[0046] Figure 1(c) is the experimental result of triaxial creep curve of soft rock when the number of dry-wet cycles is 6.

[0047] Figure 1(d) is the experimental result of triaxial creep curve of soft rock when the number of dry-wet cycles is 9.

[0048] Figure 2 This is a schematic diagram of the mesostructure evolution of soft rock.

[0049] Figure 3 Instantaneous elastic modulus of soft rock under dry-wet cycles.

[0050] Figure 4(a) shows the elastic modulus of soft rock at 0 dry-wet cycles.

[0051] Figure 4(b) shows the elastic modulus of soft rock after three dry-wet cycles.

[0052] Figure 4(c) shows the elastic modulus of soft rock after 6 dry-wet cycles.

[0053] Figure 4(d) shows the elastic modulus of soft rock after 9 dry-wet cycles.

[0054] Figure 5(a) is a viscoelastic element model.

[0055] FIG5( b ) is a curve showing the change of the elastic modulus of the viscoelastic element over time.

[0056] Figure 6(a) is the nonlinear damping element model.

[0057] FIG6( b ) is a curve showing the variation of the viscosity coefficient of the nonlinear damping element with time.

[0058] Figure 7(a) is the friction plate model.

[0059] Figure 7(b) is the stress and strain relationship diagram of the friction plate model.

[0060] Figure 8 It is a creep model.

[0061] Figure 9(a) shows the soft rock creep test results and model calculation results when the number of dry-wet cycles is 0.

[0062] Figure 9(b) shows the soft rock creep test results and model calculation results when the number of dry-wet cycles is 3.

[0063] Figure 9(c) shows the soft rock creep test results and model calculation results when the number of dry-wet cycles is 6.

[0064] Figure 9(d) shows the soft rock creep test results and model calculation results when the number of dry-wet cycles is 9. DETAILED DESCRIPTION

[0065] The specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the present invention, and is not used to limit the present invention.

[0066] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used here to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0067] A method for constructing a soft rock creep damage model comprises the following steps:

[0068] Step S1: Classify the soft rock creep damage and establish the damage equations of each category;

[0069] Step S2: Divide the soft rock creep curve into a stable creep stage and an unstable creep stage, and construct viscoelastic elements, viscoplastic elements and a creep model;

[0070] Step S3: using the damage equation of step S1 and the creep model of step S2 to establish creep equations of the stable creep stage and the unstable creep stage;

[0071] Step S4: Establish a three-dimensional creep damage model.

[0072] The obtained creep damage model can be used to calculate the strain of soft rock at different times, so as to calculate the deformation of soft rock at different times according to the strain, that is, the time-dependent deformation, and evaluate the damage of soft rock according to the strain and / or time-dependent deformation. Among them, strain is a dimensionless parameter, and deformation is a dimensional absolute value. The conversion between the two is a technology well known to those skilled in the art. As for the evaluation of rock damage, different evaluation methods have different classifications of damage levels, which will not be introduced in detail here, but all methods for evaluating damage are based on the strain and / or time-dependent deformation of soft rock.

[0073] In this embodiment, the soft rock used is carbonaceous mudstone.

[0074] The following is a detailed analysis of this plan.

[0075] Firstly, the creep characteristics are analyzed and the triaxial creep test results of soft rock under dry-wet cycle are obtained by using the Boltzmann superposition principle. Figure 1(a)~1(d) In the figure, For axial compression, multiple or multi-level axial compression loading is performed under the same number of dry-wet cycles. The loading levels are 8 or 7, as follows: The triaxial rheological tester RLW-2000 is used to conduct triaxial compression rheological tests on the samples that have completed the dry-wet cycle. The confining pressure is set to 2MPa, and a graded incremental loading method is used. The first level of creep test loading is designed to be 40% of the uniaxial compressive strength, that is, 14.26MPa. The graded loading increment is 3MPa. Each level of axial compression loading lasts for 48 hours, and then the next level of loading is performed until the rock sample is destroyed. Figure 1(a)~1(d) It can be seen that the axial strain of soft rock increases with the increase of dry-wet cycles and axial pressure. Under the same axial pressure, the strain of soft rock increases with the increase of dry-wet cycles; the axial strain of soft rock samples with 0, 3, 6 and 9 dry-wet cycles under axial pressure of 17.26 MPa after creep for 20 hours is 0.606×10 -3 , 0.958×10 -3 , 1.168×10 -3 and 1.340×10 -3 The average axial strain increases by 9.75×10-5 Under the same number of dry-wet cycles, the axial strain of soft rock increases with the increase of axial pressure; the axial strain of soft rock with 6 dry-wet cycles at level 1 to 7 creep for 20h is 1.168×10 -3 , 1.468×10 -3 , 1.786×10 -3 , 2.144×10 -3 , 2.538×10 -3 , 2.978×10 -3 and 3.364×10 -3 The average axial strain increases by 3.34×10 -4 In addition, soft rock has a low axial pressure ( < , is the long-term strength of rock), only attenuation creep occurs, and the strain increases with time first and then remains stable; when the axial pressure is high ( ≥ ), first decay creep occurs, then the strain gradually increases with time, and finally creep failure occurs. When the dry-wet cycle is 0 and 3 times, the soft rock only undergoes decay creep in the first four levels of loading (23.26MPa), and accelerated creep failure occurs at the eighth level of loading (35.26MPa); when the dry-wet cycle is 6 and 9 times, the soft rock only undergoes decay creep in the first three levels of loading (20.26MPa), and accelerated creep failure occurs at the seventh level of loading (32.26MPa).

[0076] From the above, we can see that the number of dry-wet cycles, axial pressure and time are important factors affecting the creep of soft rock.

[0077] The creep damage mechanism is as follows: The schematic diagram of the microstructure evolution of the soft rock creep damage process under the action of dry-wet cycles is shown in Figure 2 Soft rock is affected by geological structures, resulting in tiny pores inside it. After the dry-wet cycle, the internal pores gradually develop and increase in number. Under the load, the pores in the soft rock are first compressed and elastically deformed. As time goes by, the soft rock particles flow in a directional manner, causing the development of internal microcracks, and the soft rock undergoes viscoelastic strain. ; When the axial pressure is greater than the long-term strength of the rock When the load continues, the crack gradually expands and the plastic strain of the soft rock Gradually develop; when the cracks continue to expand for a certain period of time, the cracks accelerate and connect, the plastic strain of the soft rock increases sharply, and finally deformation and failure occur. The value of can be 70-80% of the uniaxial compressive strength, or refer to other solutions in the prior art.

[0078] In step S1, according to Figure 2 The evolution law of the microstructure and macroscopic mechanical damage characteristics of soft rock creep damage process under the action of medium-wet-dry cycle. The creep damage of soft rock can be divided into initial damage , Time-dependent damage and crack extension damage Category 3. Initial damage Mesoscopic structural damage caused by the development of pores in soft rock due to dry-wet cycles; time-dependent damage Changes in rock mechanical properties caused by the directional flow of rock particles over time; crack extension damage It is the damage and deterioration of rock structure caused by the expansion and connection of rock cracks under load.

[0079] The following equations are established for the three types of damage.

[0080] 1. Initial damage equation

[0081] Under the action of dry-wet cycles, soft rock pores develop, resulting in a reduction in the stress-bearing area of ​​the rock mesostructure. According to the geometric damage theory, rock damage is defined by the stress-bearing area of ​​the rock:

[0082] (1)

[0083] in, For the initial damage, is the total cross-sectional area, is the pore area, is the rock porosity.

[0084] 2. Time-dependent damage equation

[0085] Under continuous load, soft rock particles flow in a directional manner over time, which causes changes in its macroscopic mechanical properties. According to the Lemaitre strain equivalence principle, the rock damage equation is expressed as:

[0086] (2-1)

[0087] in, and are the matrix form and strain vector of axial pressure, respectively, \left [ {C} \right ] is the material elastic matrix, is the rock damage variable. The deformation of rock under nominal axial pressure is equivalent to the deformation under effective axial pressure, then:

[0088] (2-2)

[0089] In the formula, , , and They are the nominal axial pressure, nominal elastic modulus, effective axial pressure and effective elastic modulus respectively.

[0090] According to formula (2-1) and formula (2-2), we can get:

[0091] (3)

[0092] In the formula, Time-dependent damage to rocks.

[0093] The instantaneous elastic modulus of soft rock under the action of dry-wet cycles can be calculated by the following formula:

[0094] (4)

[0095] In the formula, is the number of dry-wet cycles, For the Wet-dry cycle under stage axial pressure The instantaneous elastic modulus, Creep time Approaching 0 Wet-dry cycle under stage axial pressure The axial pressure increment is For the Wet-dry cycle under stage axial pressure The instantaneous strain increment. It is a wet and dry cycle sequence The stress during level loading, corresponding to, It is a wet and dry cycle sequence The stress at level -1 loading. The instantaneous elastic modulus of soft rock calculated by formula (4) is: Figure 3 , in the figure is the elastic modulus value corresponding to the fitting curve obtained under fixed axial pressure, is the number of cycles, is the correlation coefficient.

[0096] The instantaneous elastic modulus of soft rock under the action of dry-wet cycles is fitted by the least squares method:

[0097] (5)

[0098] in, , is a parameter related to axial pressure. , The functional relationship with the axial pressure is:

[0099] (6)

[0100] (7)

[0101] Substituting equations (6) and (7) into equation (5), we can obtain the instantaneous elastic modulus equation of soft rock under the action of dry-wet cycles:

[0102] (8)

[0103] The elastic modulus of the soft rock under the first four loading levels of dry-wet cycles is shown in Figure 4 (a) to (d). The elastic modulus decreases rapidly with time, and then remains basically stable after 15 hours. The elastic modulus at stability decreases with the increase of the number of dry-wet cycles.

[0104] The relationship between the elastic modulus of soft rock under the action of dry-wet cycles is obtained by fitting the least square method:

[0105] (9)

[0106] For the Wet-dry cycle under stage axial pressure Second-rate The elastic modulus at the moment, parameter , and It is a function related to the number of dry-wet cycles and axial pressure. Through parameter fitting, we get:

[0107] (10)

[0108] (11)

[0109]

[0110] Analyzing formula (9), when =0:

[0111] (12)

[0112] when → hour:

[0113] (13)

[0114] Substituting equation (12) and equation (13) into equation (9), we get:

[0115] (14)

[0116] Substituting equation (14) into equation (3), we get the time-dependent damage equation of rock:

[0117] (15)

[0118] 3. Crack propagation damage equation

[0119] Under load, cracks in rocks gradually expand and connect, which leads to the degradation of rock mechanical properties. According to the prior art, the axial pressure at the crack tip of an open crack in a rock that expands in an airfoil shape is:

[0120] (16)

[0121] In the formula, is the stress intensity factor of rock, is the crack initiation angle, is the radius of the crack. , , They are radial axial pressure, annular axial pressure, and tangential axial pressure.

[0122] The axial pressure at the crack tip converted from the coordinate system to the rectangular coordinate system:

[0123] (17)

[0124] In formula 17, , , They are Axial pressure, Axial pressure, Tangential pressure of the coordinate system.

[0125] Assuming that the rock material fracture obeys the Mohr-Coulomb yield criterion, the calculation formula for the principal axial pressure is:

[0126] (18)

[0127] In the formula, , , They are the three principal stresses of rock in three mutually perpendicular directions in space. is the Poisson's ratio of the rock. The principal axial pressure of the rock is obtained from equations (17) and (18):

[0128] (19)

[0129] (20)

[0130] The axial compressive strength factor of rock is obtained by formula (19):

[0131] (twenty one)

[0132] According to the law of energy reciprocity, the total elastic strain energy that can be released by the unit under the action of external force is , which is equal to the elastic strain energy stored in the material and the change in elastic strain energy sum.

[0133] (twenty two)

[0134] According to the existing technology, the total elastic strain energy that can be released by the unit is :

[0135] (twenty three)

[0136] In the formula, is the damage in the crack extension stage, is the unit volume of rock.

[0137] Elastic strain energy stored in the material :

[0138] (twenty four)

[0139] In the false triaxial state = , then formula (24) is:

[0140] (25)

[0141] is the elastic modulus of rock, which can be taken as the elastic modulus in the linear elastic stage; For the initial damage, is the initial elastic modulus.

[0142] According to the prior art, the change in elastic strain energy caused by crack extension is :

[0143] (26)

[0144] In the formula, is the crack extension length. By integrating formula (26), we can get:

[0145] (27)

[0146] Assume that there is If there are cracks, the damage equation of the rock crack when it is not extended can be expressed as:

[0147] (28)

[0148] Substituting equations (24) to (28) into equation (22), we can obtain the rock crack propagation damage equation:

[0149] (29)

[0150] Where:

[0151] (30)

[0152] (31)

[0153] According to the existing technology, the functional relationship between the rock micro-crack extension length and the macro-strain is:

[0154] (32)

[0155] In the formula, and is the material parameter, It's strain. is the initial length of the crack. Generalize equation (32) to the time-dependent equation:

[0156] (33)

[0157] Substituting equation (33) into equation (29) yields the crack propagation damage equation for rock:

[0158] (34)

[0159] In step S2, according to Figure 1(a)~1(d) and Figure 2 The creep deformation law of soft rock under the action of medium-wet-dry cycle is used to divide the soft rock creep curve into stable creep stage and unstable creep stage. < ): Soft rock only undergoes transient elastic and viscoelastic strains under load; unstable creep stage ( ≥ ): Soft rock undergoes instantaneous elastic, viscoelastic and viscoplastic strains under load. To this end, this scheme constructs viscoelastic elements and viscoplastic elements, such as Figure 5(a) , 5(b) , 6(a), 6(b), 7(a), 7(b), 8. The viscoelastic element (Figure 5(a)) consists of a spring and a damper. When subjected to force, the spring undergoes instantaneous elastic deformation, and the elastic modulus of the element is As time goes by, the damper is gradually compressed, the elastic modulus of the element is gradually weakened, and the elastic strain is gradually increased. The viscoplastic element is composed of a friction plate (Figure 7 (a)) and a nonlinear damping element (Figure 6 (a)) in parallel. When the axial pressure is greater than the long-term strength of the rock (i.e. ≥ ), the friction plate starts to slide, the viscoplastic element starts to deform, and the rock plastic deformation increases with time. As the rock deformation increases, the viscosity coefficient of the nonlinear damping element The smaller the rock viscoplastic creep rate, the faster it increases. Based on the above understanding, this scheme uses viscoelastic elements and viscoplastic elements in series to form a creep model (see Figure 8 ), which can characterize the nonlinear characteristics of rocks.

[0160] In step S3, the process of establishing the creep equation in the stable creep stage is as follows:

[0161] When the axial pressure is less than the long-term strength of the rock ( < ), the elastic modulus deteriorates over time, and the rock undergoes viscoelastic creep. At this stage, the rock can remain stable for a long time, which is the stable creep stage. At this time, the friction plate in the model has not yet slipped, and the soft rock only undergoes transient elastic and viscoelastic strains, which is equivalent to Figure 8 The creep model shown has only viscoelastic elements in effect. According to Hooke's law, its creep equation can be expressed as:

[0162] (35)

[0163] In the stable creep stage, the time-dependent elastic modulus of rock Due to dry-wet cycles, axial pressure and gradual degradation over time, Figure 2 The cause of the damage in the middle stage can be considered that the damage in the stable creep stage of soft rock under the action of dry-wet cycles is the initial damage. Time-related damage Coupling effect. According to damage theory (35), it can be expressed as:

[0164] (36)

[0165] In the formula The damage is in the stable creep stage.

[0166] The initial damage As the first type of damage state, time-dependent damage It is the second type of damage state. According to the damage definition and Lemaitre strain equivalent equation, we have:

[0167] (37)

[0168] From equation (36) and equation (37), we get:

[0169] (38)

[0170] Substituting equations (1) and (15) into equation (38), the damage equation of the soft rock in the stable creep stage under the action of dry-wet cycles is obtained as follows:

[0171] (39)

[0172] The process of establishing the creep equation in the unstable creep stage is as follows:

[0173] When the axial pressure is greater than the long-term strength of the rock ( ≥ ), rock cracks gradually initiate, its elastic modulus and viscosity coefficient weaken over time, and the rock undergoes viscoelastic-plastic deformation. This stage increases with time and the rock eventually creeps and fails, which is the unstable creep stage. At this time, the friction plate in the model begins to slide, and the soft rock undergoes instantaneous elastic, viscoelastic and viscoplastic strains. Its creep equation can be expressed as:

[0174] (40)

[0175] is the viscosity coefficient of the nonlinear damper.

[0176] Unstable creep stage, aging elastic modulus Under the influence of dry-wet cycles, axial pressure and time, the rock gradually deteriorates; under the influence of load, the rock yields locally, the internal cracks continue to expand and connect, and the viscoplastic viscosity coefficient gradually decreases due to the influence of crack expansion. Therefore, it can be considered that the damage of the time-dependent elastic modulus is the coupling effect of initial damage and time-dependent damage. , the viscoplastic viscosity coefficient damage is the crack extension damage According to the damage theory formula (40), it can be expressed as:

[0177] (41)

[0178] In the formula is the initial viscosity coefficient, = It can be obtained from (29).

[0179] In step S4, a three-dimensional creep damage model is established. Considering the actual stress state of the rock, the creep damage model of soft rock under the action of dry-wet cycles is extended to three dimensions, and then:

[0180] when < When , the creep model is:

[0181] (42)

[0182] when ≥ When , the creep model is:

[0183] (43)

[0184] in, 1~3, representing the three directions of three dimensions. 1~3, representing the three directions of three dimensions. ≠ . is the deviatoric stress, is the strain corresponding to the deviatoric stress. is the shear modulus.

[0185] (44)

[0186] is the stress tensor, is the Kronecker function.

[0187] Assuming that the sample is homogeneous and isotropic, a triaxial rheological test is performed at t=0. Under the pseudo triaxial condition, > = , its axial pressure state is:

[0188] (45)

[0189] In the Cartesian coordinate system, the coordinate axis 1 is along the axial direction, then:

[0190] (46)

[0191] From equation (44) to equation (46), we can get:

[0192] (47)

[0193] In the formula, .

[0194] Likewise for strain:

[0195] (48)

[0196] In the formula, ; is the spherical stress tensor.

[0197] Then we have:

[0198] (49)

[0199] Because the confining pressure is applied first in the triaxial test loading process, the rock has already undergone compression deformation at this time, and the measured axial stress (i.e. axial pressure) is:

[0200] (50)

[0201] Substituting equations (46), (48) and (49) into equations (36) and (41), we can obtain the creep damage equation of soft rock under triaxial compression conditions: < When , the creep damage equation is:

[0202] (51)

[0203] when ≥ When , the creep damage equation is:

[0204] (52)

[0205] In the formula, is the principal stress or strain in the axial compression direction, and the bulk modulus , shear modulus .

[0206] Next, we will determine the parameters and verify the model.

[0207] Based on the creep damage model proposed in this paper, the model parameters can be determined according to the macro and micro experiments of soft rock. = , Poisson's ratio It can be determined by triaxial compression test. =0.12; According to the prior art, the crack initiation angle of the opening crack is =0; initial crack length It can be determined by electron microscopy experiments. =0.2mm; parameters , It can be determined by formula (12) and (13) respectively. It can also be determined by the above formula; The long-term strength of rock can be determined by the isochronous curve method in the existing technology. It can be measured by low-field nuclear magnetic resonance method; and is a rock parameter, which can be determined according to existing methods in the prior art; The initial viscosity coefficient can be obtained from formula (52):

[0208] (53)

[0209] in is the rock viscoelastic strain, which can be obtained according to the method in the prior art. Other stable creep stage model parameters are shown in Table 1, and the unstable creep stage model parameters are shown in Table 2.

[0210] Table 1 Stable creep stage model parameters:

[0211]

[0212] Table 2 Unstable creep stage model parameters:

[0213]

[0214] The model is verified below. The creep of soft rock under different dry-wet cycles at different loading levels is calculated by equations (51) and (52). Figures 9(a) to 9(d) From the figure, we can see that the creep damage model proposed in this scheme can better reflect the attenuation, steady and accelerated creep stages of rock, and the creep model has a high degree of fit with the test data, which verifies the rationality of the soft rock creep damage model under the action of dry-wet cycles proposed in this scheme. From the creep model ( Figure 5(a) , 5(b) , 6(a), 6(b), 7(a), 7(b), 8) Analysis: When the axial pressure is less than the long-term strength of the rock, the friction plate in the model does not slide, and the creep model degenerates into a viscoelastic model. By introducing damage variables that consider dry-wet cycles and time effects, the attenuation creep stage of the rock can be better reflected. This model is equivalent to the typical Maxwell model, but the model form of this scheme is simple and can reflect the damage effects of dry-wet cycles and creep on the rock; when the axial pressure is greater than or equal to the long-term strength of the rock, rock cracks initiate and expand, and are locally damaged. The friction plate begins to slide, and the rock undergoes viscoelastic-plastic deformation. The model equation is relatively simple and can better reflect the accelerated creep stage of the rock. It also introduces crack extension damage, which can reveal the damage mechanism of the accelerated creep stage of the rock.

[0215] In summary, the creep damage model proposed in this scheme, which combines the element model principle and damage theory, is highly consistent with the experimental results, has a simple structure, can better reveal the characteristics of the rock damage evolution mechanism, and has clear physical meanings of the parameters.

[0216] Finally, it is necessary to explain here that the above embodiments are only used to further illustrate the technical solution of the present invention in detail and cannot be understood as limiting the scope of protection of the present invention. Some non-essential improvements and adjustments made by technicians in this field based on the above content of the present invention all fall within the scope of protection of the present invention.

Claims

1. A method for constructing a soft rock creep damage model, characterized in that: The steps include: Step S1: Classify the creep damage of soft rock and establish damage equations of various types, and classify the creep damage of soft rock into three categories: initial damage, aging damage and crack extension damage; Step S2: Divide the soft rock creep curve into a stable creep stage and an unstable creep stage, construct viscoelastic elements, viscoplastic elements and a creep model, and the creep model is composed of a viscoelastic element and a viscoplastic element connected in series; Step S3: Using the damage equation of step S1 and the creep model of step S2, the creep equations of the stable creep stage and the unstable creep stage are established, the coupled damage variables of initial damage and aging damage are used to correct the viscoelastic component parameters, the crack extension damage is introduced to correct the viscoplastic component parameters, and a new soft rock creep damage model is constructed; Step S4: establishing a three-dimensional creep damage model; In step S1, the initial damage The mesostructure damage is caused by the development of pores in soft rock due to the dry-wet cycle. Time-related damage Changes in rock mechanical properties caused by the directional flow of rock particles over time; crack propagation damage It is the damage and deterioration of rock structure caused by the expansion and connection of rock cracks under load; ， ， ， ， ， ， ， ， ， in, is the total cross-sectional area, is the pore area, is the rock porosity, For the Wet-dry cycle under stage axial pressure The instantaneous elastic modulus, When time approaches infinity Wet-dry cycle under stage axial pressure The elastic modulus, is related to the number of dry-wet cycles n and the axial pressure The function is: t is the time, is with , , v Related functions, is with v、 , Related functions, is the strain at time t, and is the material parameter, , , They are the three principal stresses of soft rock in three mutually perpendicular directions in space, is the crack initiation angle, is the Poisson's ratio of the rock, is the crack radius, is the stress intensity factor of rock, According to the energy reciprocity theorem, is a parameter related to axial pressure. The least square method is used to calculate the soft rock under the action of dry-wet cycles. , , Perform fitting and establish a functional relationship with axial pressure; In step S3, during the stable creep stage, the damage of soft rock during the stable creep stage under the action of dry-wet cycles is Initial damage Time-related damage Coupling effect; In step S3, during the stable creep stage, the damage equation of soft rock under the action of dry-wet cycles is: ； In step S3, during the unstable creep stage, the time-dependent elastic modulus damage is the coupling effect of initial damage and time-dependent damage. , the viscoplastic viscosity coefficient damage is the crack extension damage ; In step S3, the creep equation in the unstable creep stage is: ， ， in, For strain, is the initial viscosity coefficient, is the initial elastic modulus; is the axial pressure, is the long-term strength of rock; when When , the creep damage equation is: ; when When , the creep damage equation is: , in, is the strain in the axial compression direction, , is the shear modulus, the bulk modulus .

2. The construction method according to claim 1, characterized in that: In step S2, during the stable creep stage, , soft rock only undergoes transient elastic and viscoelastic strains under load; in the unstable creep stage, , soft rock undergoes instantaneous elastic, viscoelastic and viscoplastic strains under load.

3. The construction method according to claim 2, characterized in that: In step S2, the viscoelastic element is composed of a spring and a damper, and the viscoplastic element is composed of a friction plate and a nonlinear damping element in parallel.

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