Construction method of rock creep constitutive model considering moisture content influence

Abstract

The invention discloses a method for constructing a rock creep constitutive model considering the influence of water content. The method comprises the following steps: constructing a rock creep constitutive model corresponding to mechanical behaviors in attenuation and stable creep stages in rock creep; obtaining a rock creep constitutive model based on a memory-dependent derivative; constructing a nonlinear creep constitutive model reflecting the mechanical characteristics of the accelerated creep stage; obtaining a damage variable; obtaining a nonlinear creep constitutive model considering the mechanical characteristics of the rainfall damage in the accelerated creep stage; and constructing a nonlinear creep constitutive model which considers rainfall damage and describes the whole rock creep process. According to the method, after a rock creep constitutive model based on a memory-dependent derivative and a nonlinear creep constitutive model considering mechanical properties in an accelerated creep stage of rainfall damage are fused, the nonlinear creep constitutive model considering the rainfall damage and describing the whole rock creep process is obtained; therefore, the constitutive model has higher prediction precision.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering structures, and in particular to a method for constructing a rock creep constitutive model taking into account the influence of water content. Background Art

[0002] In the field of rock creep mechanics, constitutive models are an effective theoretical research tool. Constitutive models are used to describe the relationship between stress, strain and time during the creep process. They include two main forms: empirical models and component combination models.

[0003] Empirical models, which mathematically describe experimental curves, are simple and practical, and were a hot topic in early rock creep research. Common types include exponential, power, logarithmic, and hybrid models. However, because these models are usually developed for specific experiments, their applicability is limited.

[0004] The component combination model is usually composed of elastic elements, viscous elements and plastic elements. Through different combinations, a variety of rock creep models can be established, which can vividly describe the creep behavior of rocks and have clear physical meanings and simple mechanical parameters, such as Figures 1 to 4 As shown in Figure 2, the parameters of the component combination model have clear physical and mechanical significance, allowing for deeper investigation of rock creep mechanical properties. Although the component combination model has certain limitations due to the complexity of rock properties, it can reflect rock creep properties in most cases. Therefore, the component combination model is a major research direction in the construction of creep constitutive models.

[0005] Traditional constitutive models include Nishihara model, Kelvin model, Maxvell model, Burgers model, Bingham model, etc. [1] These models are composed of linearly constant parameters and cannot well study the accelerated creep behavior with significant nonlinear characteristics. Moreover, studies have shown that in rock creep, the parameters of the model change continuously during the creep process and are related to factors such as stress, time, and temperature. [2,3] The nonlinearity in the creep process is not only reflected in the accelerated creep stage, but also exists in the attenuation and stable creep stages. In order to accurately reflect the nonlinear behavior of rock creep, the current research hotspots of creep constitutive models focus on the nonlinear improvement of traditional component combination models and the construction of new nonlinear creep models. Tang, H et al. [4] Based on memory-dependent derivatives and continuum damage mechanics, a four-element creep model capable of simulating three creep stages was established. Wang, JB et al. [5] By using effective stress instead of apparent stress in the creep equation, the axial creep damage equation of the Burgers model is obtained; Yang, XB et al. [6]Based on the assumption that damage is a function of stress level and time, a nonlinear damage creep model of coal rock based on the Kelvin model was established; Zhou, HW et al. [7] The Newton damper in the classic Nishihara model is replaced by an Abelian damper with memory-dependent derivatives, and a creep model based on time-memory-dependent derivatives is proposed. SP Jia et al. [8] Based on the damage mechanics theory, a nonlinear elastic-viscoplastic damage model based on the improved Mohr-Coulomb criterion was proposed. Yang, L et al. [9] By adopting memory-dependent calculus and replacing the viscous elements in the Nishihara model with new elements, a nonlinear Nishihara model describing rock creep was established.

[10] From the perspective of microstructural evolution, a full stress-strain creep model considering multiple factors was established.

[11] In order to study the creep instability law of frozen red sandstone under triaxial conditions, triaxial static compression tests and triaxial creep tests were carried out on sandstone with different joint inclinations, and a triaxial creep model considering the freezing factor was established.

[12] The uniaxial creep test of sandstone with different freeze-thaw creep times was carried out, and a nonlinear damage evolution equation considering the effects of freeze-thaw and time was established. After introducing the classic Nishihara model, a creep constitutive model considering the effects of freeze-thaw was established.

[13] By introducing the GTN model, the traditional West original body was improved, and a joint rock shear creep model considering anchoring was established. The rationality and effectiveness of the model were verified by comparing the model calculation values ​​with the test curves.

[14] Based on the uniaxial creep test of salt rock and the characteristics of acoustic emission, a damage evolution model was established, and the rationality of the model was verified by fitting the calculated values ​​with the experimental values.

[15] The elastic element in the Nishihara model is replaced by the Abel viscosity pot based on the memory-dependent calculus equation, and a nonlinear creep model based on the memory-dependent derivative is obtained. The rationality of the model is verified by the agreement between the experimental curve and the model calculation curve.

[0006] Despite the numerous constitutive model studies mentioned above, they primarily focus on conditions such as high temperature, freeze-thaw, and pH. There are relatively few studies that consider moisture content in creep models, particularly those that consider the relationship between long-term strength and moisture content. Given that landslides are often caused by rainfall-induced creep failure in key locations, it is necessary to develop a rock creep constitutive model that considers moisture content.

[0007] [1]Peng Y,Zhao J,Li Y.A wellbore creep model based on the fractionalviscoelastic constitutive equation[J].Petroleum Exploration and Development,2017,44(6):1038-1044.

[0008] [2]Liu L,Wang G-m,Chen J-h,et al.Creep experiment and rheologicalmodel of deep saturated rock[J].Transactions of Nonferrous Metals Society ofChina,2013,23(2):478-483.

[0009] [3]Zhao J,Feng X-T,Zhang X,et al.Time-dependent behaviour andmodeling of Jinping marble under true triaxial compression[J].InternationalJournal of Rock Mechanics and Mining Sciences,2018,110:218-230.

[0010] [4]Tang H,Wang D,Huang R,et al.A new rock creep model based onvariable-order fractional derivatives and continuum damage mechanics[J].Bulletin of Engineering Geology and the Environment,2017,77(1):375-383.

[0011] [5]Wang J B,Liu X R,Liu X J,et al.Creep properties and damage modelfor salt rock under low-frequency cyclic loading[J].Geomech Eng,2014,7(5):569-587.

[0012] [6]Yang X B,Li Y,Guan H H,et al.Nonlinear damage creep model of coalor rock containing gas[J].Appl Mech Mater,2012,20208:289-296.

[0013] [7]Zhou H W,Wang C P,Han B B,et al.A creep constitutive model forsalt rock based on fractional derivatives[J].International Journal of RockMechanics and Mining Sciences,2011,48(1):116-121.

[0014] [8]Jia S P,Zhang L W,Wu B S,et al.A coupled hydro-mechanical creepdamage model for clayey rock and its application to nuclear waste repository[J].Tunnelling and Underground Space Technology,2018,74:230-246.

[0015] [9]Yang L,Li Z-d.Nonlinear Variation Parameters Creep Model of Rockand Parametric Inversion[J].Geotechnical and Geological Engineering,2018,36(5):2985-2993.

[0016]

[10] Shao J F,Zhu Q Z,Su K.Modeling of creep in rock materials interms of material degradation[J].Computers and Geotechnics,2003,30(7):549-555.

[0017]

[11] Shan Renliang, Bai Yao, Sun Pengfei, et al. Study on triaxial creep characteristics and constitutive model of frozen layered red sandstone [J]. Journal of China University of Mining and Technology, 2019, 48(1): 12-22.

[0018]

[12] Chen Guoqing, Wan Yi, Pei Bencan, et al. Study on creep characteristics and damage model of sandstone under freeze-thaw creep[J]. Journal of Engineering Geology, 2020, 28(1): 19-28.

[0019]

[13] Song Yang, Li Yongqi, Wang Weiyi, et al. Analysis of shear creep characteristics and constitutive model of anchored jointed rock[J]. Journal of China Coal Society, 2020, 45(4): 1357-1366.

[0020]

[14] Liu Di, Zhou Hongwei, Zhao Yang, et al. Study on creep constitutive model of salt rock based on acoustic emission characteristics [J]. Rock and Soil Mechanics, 2017, 38(7): 1951-1958.

[0021]

[15] He Zhilei, Zhu Zhende, Zhu Mingli, et al. Research on unsteady creep constitutive model based on memory-dependent derivatives[J]. Rock and Soil Mechanics, 2016, 37(3): 737-744+775. Summary of the Invention

[0022] Based on this, the purpose of the present invention is to provide a method for constructing a rock creep constitutive model taking into account the influence of water content, which demonstrates high prediction accuracy and practical application value.

[0023] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0024] The present invention provides a method for constructing a rock creep constitutive model taking into account the influence of water content, which comprises the following steps:

[0025] S1. Construct a rock creep constitutive model ε that describes the mechanical behavior of the decay and stable creep stages in rock creep. eve =ε e +ε ve ; where ε e Characterized as the strain in the instantaneous loading stage, ε ve Characterized as the strain corresponding to the decay and stable creep stages;

[0026] S2. Introducing memory-dependent derivatives Memory-dependent derivatives Substitute into the rock creep constitutive model ε corresponding to the mechanical behavior of the attenuation and stable creep stages in rock creep eve In the paper, the rock creep constitutive model ε based on memory-dependent derivatives is obtained. eve ;

[0027] S3. Construct a nonlinear creep constitutive model ε that reflects the mechanical properties of the accelerated creep stage vp ;

[0028] S4. Obtain the damage variable D after coupling the rainfall damage caused by rainfall infiltration into the rock and the rock microscopic damage m =D ma +D mi -D ma D mi Among them, D ma is rainfall damage, D mi It is microscopic damage;

[0029] S5. Based on the strain equivalence theory, the damage variable D m The nonlinear creep constitutive model ε is introduced to reflect the mechanical characteristics of the accelerated creep stage. vp The nonlinear creep constitutive model ε of the mechanical characteristics of the accelerated creep stage considering rainfall damage is obtained. vp ;

[0030] S6. Combining steps S2 and S5, a nonlinear creep constitutive model ε is constructed to describe the entire rock creep process taking rainfall damage into consideration.

[0031] In summary, the present invention provides a method for constructing a rock creep constitutive model that takes into account the influence of water content. By integrating the rock creep constitutive model based on memory-dependent derivatives with the nonlinear creep constitutive model of the mechanical properties of the accelerated creep stage that takes into account rainfall damage, a nonlinear creep constitutive model that describes the entire rock creep process that takes into account rainfall damage is obtained, so that the constitutive model has higher prediction accuracy than the traditional Nishihara model. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 A schematic diagram of a creep element assembly provided by an embodiment of the present invention;

[0033] Figure 2 Provide a typical rock creep curve for the embodiment of the present invention;

[0034] Figure 3 A nonlinear creep model based on memory-dependent derivatives provided in an embodiment of the present invention;

[0035] Figure 4 A nonlinear creep model for the accelerated creep stage provided by an embodiment of the present invention;

[0036] Figure 5 Schematic diagram of coupled damage of rock mass caused by rainfall and creep provided by an embodiment of the present invention;

[0037] Figure 6The nonlinear creep constitutive model provided by the embodiment of the present invention reflects the mechanical behavior of the entire rock creep process;

[0038] Figure 7 Comparison of the calculated values ​​of the model provided by the embodiment of the present invention with the experimental values ​​and the calculated values ​​of the traditional model (no damage): (a) W-0-S; (b) W-117-S; (c) W-228-S; (d) W-326-S; (e) W-463-S;

[0039] Figure 8 Comparison of the calculated values ​​of the model provided by the embodiment of the present invention with the experimental values ​​and the calculated values ​​of the traditional model (damage occurs): (a) W-0-F; (b) W-117-F; (c) W-228-F; (d) W-326-F; (e) W-463-F;

[0040] Figure 9 A schematic flow chart of a method for constructing a rock creep constitutive model taking into account the influence of water content provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0041] In order to further understand the features, technical means, specific objectives and functions achieved by the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0042] Figure 9 FIG. 1 is a flow chart of a method for constructing a rock creep constitutive model taking into account the influence of water content provided by an embodiment of the present invention. Figure 9 As shown in FIG, a method for constructing a rock creep constitutive model considering the influence of water content specifically includes the following steps:

[0043] S1. Construct a rock creep constitutive model ε that describes the mechanical behavior of the decay and stable creep stages in rock creep. eve =ε e +ε ve ; where ε e Characterized as the strain in the instantaneous loading stage, ε ve Characterized as the strain corresponding to the decay and stable creep stages.

[0044] Furthermore, the strain ε in the instantaneous loading stage e , the strain corresponding to the decay and stable creep stages ε ve Satisfies the following formula:

[0045]

[0046] Among them, σ represents the upper limit stress of loading, E MT is a Hooke body, which is characterized by the deformation modulus corresponding to the instantaneous strain generated under load; E KCharacterized as the deformation modulus corresponding to the strain in the decay and stable creep stages under creep loading; η K is the viscosity element parameter, which represents the strain rate during creep loading; is the deformation modulus E K The corresponding strain, is the viscosity element parameter η K The corresponding strain, Characterized as model strain ε ve The first derivative with time reflects the growth rate of strain with time.

[0047] S2. Introducing memory-dependent derivatives Memory-dependent derivatives Substitute into the rock creep constitutive model ε corresponding to the mechanical behavior of the attenuation and stable creep stages in rock creep eve In the paper, the rock creep constitutive model ε based on memory-dependent derivatives is obtained. eve .

[0048] in, γ is the time delay coefficient; the weight function K(st) is an m-order continuous function, which indicates the degree of memory dependence.

[0049] Specifically, the method of step S2 includes the following steps:

[0050] Introducing memory-dependent derivatives to describe the constitutive model ε eve The parameter η in K , combined with the formula The constitutive equation is rewritten as:

[0051]

[0052] Among them, σ ηK and ε ηk (t) represent stress and creep deformation respectively, Represents ε ηk The second-order memory-related derivative of (t), ε″ ηk (s) represents ε ηk The second derivative of (t).

[0053] Set the weight function as follows:

[0054]

[0055] Substituting formula (3) into formula (2), we can get formula (4):

[0056]

[0057] Divide both sides of equation (4) by Further deduction yields:

[0058]

[0059] Solving formula (5), we can get:

[0060]

[0061] Substituting the conclusion that t∈[-γ,0], ε(t)=0 into equation (6), we can get the strain ε ηk Expressed as:

[0062]

[0063] According to formula (7) and formula (1), the following formula is obtained:

[0064]

[0065] According to formula (8), the strain ε corresponding to the decay and stable creep stages based on the memory-dependent derivative can be obtained: ve The expression is:

[0066]

[0067] Combined formula and the constitutive equation ε of the rock mass creep constitutive model eve =ε e +ε ve , obtain the rock creep constitutive model ε based on memory-dependent derivatives eve Strain expression

[0068] S3. Construct a nonlinear creep constitutive model ε that reflects the mechanical properties of the accelerated creep stage vp .

[0069] Among them, the nonlinear creep constitutive model ε that reflects the mechanical characteristics of the accelerated creep stage vp The corresponding constitutive equation satisfies:

[0070]

[0071] In formula (9), σ represents the upper limit stress of loading, η vp Characterized by the viscosity element coefficient, D m Characterized as damage variable, Characterized as model strain ε vp The first derivative with time reflects the growth rate of strain with time, σ S It is characterized by the threshold stress value at which the rock mass enters the accelerated creep stage.

[0072] S4. Obtain the damage variable D after coupling the rainfall damage caused by rainfall infiltration into the rock and the rock microscopic damage m =D ma +D mi -D ma D mi Among them, D ma is rainfall damage, D mi It is microscopic damage.

[0073] The method of step S4 comprises the following steps:

[0074] like Figure 5 As shown in the figure, during rainfall, the infiltration of rainwater not only weakens the bonding between internal particles, but also reduces the friction between particles, seriously affecting the mechanical properties of the rock mass. When studying the mechanical properties of rock mass under rainfall conditions, it is necessary to consider both rainfall damage and microscopic damage caused by creep. Therefore, based on the strain equivalence theory, the coupled damage of rock mass caused by rainfall and microscopic damage can be expressed as:

[0075] D m =D ma +D mi -D ma D mi (10)

[0076] Among them, D ma is rainfall damage, D mi It is microscopic damage. From expression (10), we can see that when there is only microscopic damage in the rock mass, that is, rainfall damage D ma = 0, the coupling damage D m =D mi ; When the rock mass is only damaged by rainfall, that is, microscopic damage D mi = 0, the coupling damage D m =D ma , indicating that the coupled damage expression (10) can be well adapted to the study of mechanical properties under coupled conditions.

[0077] In addition, rainfall damage ma The following formula can be obtained:

[0078]

[0079] Among them, E CW is the elastic modulus after rainfall, E CO is the elastic modulus under dry conditions.

[0080] The present invention adopts Kachanov damage law in creep to describe micro damage D mi The relationship between time N, where the Kachanov damage law equation is:

[0081]

[0082] Where A and δ are material constants determined by experiments, ω is the applied load, is the micro damage variable D mi The first derivative with respect to time t.

[0083] From the definition of formula (12), it can be seen that when time t = 0, the sample is not subjected to creep, and at this time D mi =0, combined with the rainfall condition, and integrating formula (12), we can get D mi The expression is:

[0084]

[0085] When the rock mass is completely destroyed, D mi =1, the corresponding complete damage time t C for:

[0086] t C =[A(δ+1)ω δ ] -1 (14)

[0087] Combining equations (12) and (13), the rock damage evolution equation under creep conditions can be obtained as follows:

[0088]

[0089] Since the constitutive model corresponding to the damage evolution equation under creep conditions describes the mechanical behavior of the rock mass in the accelerated creep stage, it is assumed that when the damage begins to occur in Equation (14), t = t S , therefore, the true damage time of formula (14) is The actual total damage time is: Under this creep condition, Equation (14) is changed to:

[0090]

[0091] Among them, t S is the time when the rock mass enters the accelerated creep stage, t F The time when the rock mass is completely destroyed, that is, the creep life, when t = t S When D mi =0; t=t F When D mi =1.

[0092] Substituting equations (11) and (16) into equation (10), the rock damage expression considering rainfall damage can be obtained as follows:

[0093]

[0094] S5. Based on the strain equivalence theory, the damage variable D m The nonlinear creep constitutive model ε is introduced to reflect the mechanical characteristics of the accelerated creep stage. vp The nonlinear creep constitutive model ε of the mechanical characteristics of the accelerated creep stage considering rainfall damage is obtained. vp .

[0095] Specifically, the method of step S5 includes the following steps:

[0096] Substituting Equation (17) into Equation (9), the constitutive equation of the nonlinear creep model considering rainfall damage is obtained as follows:

[0097] Further deduction through formula (18) yields:

[0098]

[0099] Combined with the initial condition t = t S , ε vp = 0, solving Equation (18) can obtain the nonlinear creep constitutive model ε of the mechanical characteristics of the accelerated creep stage considering rainfall damage vp The expression:

[0100]

[0101] S6. Combine steps S2 and S5 to construct a nonlinear creep constitutive model that describes the entire rock creep process taking into account rainfall damage. Specifically, the memory-dependent derivative is used to Rock creep constitutive model ε eve (t) and the nonlinear creep constitutive model of mechanical characteristics in the accelerated creep stage considering rainfall damageε vp By connecting them in series, the nonlinear creep constitutive model ε is obtained, which describes the whole process of rock creep considering rainfall damage.

[0102] The nonlinear creep model based on memory-dependent derivatives and Figure 4 By connecting the acceleration stage nonlinear creep model in series, we can obtain a nonlinear constitutive model that reflects the three-stage mechanical behavior of rock mass under creep conditions, such as Figure 6 shown.

[0103] Specifically, the method of step S6 includes the following steps:

[0104] Construct the constitutive equation corresponding to the nonlinear creep constitutive model that describes the entire creep process taking rainfall damage into account:

[0105] ε=ε e +ε ve +ε vp(twenty one),

[0106] Combining equations (8) and (20), the threshold stress value σ at which the rock mass enters the accelerated creep stage is S As the dividing point, the expression corresponding to the nonlinear constitutive model reflecting the three-stage mechanical behavior of rock mass under creep conditions is substituted into Equation (21) to obtain the nonlinear creep constitutive model describing the entire rock creep process considering rainfall damage:

[0107]

[0108] In order to verify the rationality of the nonlinear creep constitutive model that describes the whole process of rock creep considering rainfall damage in the present invention, the test results are processed to obtain the mechanical test parameters required by formula (22), as shown in Table 1; then formula (22) is used to fit the creep test results. The comparison results of the model calculation values ​​proposed in the present invention with the test values ​​and the calculated values ​​of the traditional Nishihara model are shown in Figure 1. Figure 7 and Figure 8 As shown, from Figure 7 and Figure 8 It can be seen from the results that the creep constitutive model proposed in the present invention is in good agreement with the experimental curve, with the highest prediction accuracy and R2 exceeding 0.98, which verifies the rationality and superiority of the model proposed in the present invention.

[0109] Table 1 Mechanical parameters of creep test

[0110]

[0111] Compared with the traditional Nishihara model, the model proposed in this paper can accurately reflect the changes in rock mass characteristics after rainfall damage, such as Figure 8 As shown in the figure, the model proposed in the present invention also shows high accuracy, indicating that the model proposed in the present invention can effectively reflect the mechanical properties of rock mass during the damage process.

[0112] like Figure 9 As shown, in order to make the technical solution of the present invention clearer, the preferred embodiments are described below.

[0113] S1. Construct a rock creep constitutive model ε that describes the mechanical behavior of the decay and stable creep stages in rock creep. eve =ε e +ε ve ; where ε e Characterized as the strain in the instantaneous loading stage, ε ve Characterized as the strain corresponding to the decay and stable creep stages;

[0114] S2. Introducing memory-dependent derivatives Memory-dependent derivatives Substitute into the rock creep constitutive model ε corresponding to the mechanical behavior of the attenuation and stable creep stages in rock creep eve In the paper, the rock creep constitutive model ε based on memory-dependent derivatives is obtained. eve ;

[0115] S3. Construct a nonlinear creep constitutive model ε that reflects the mechanical properties of the accelerated creep stage vp ;

[0116] S4. Obtain the damage variable D after coupling the rainfall damage caused by rainfall infiltration into the rock and the rock microscopic damage m =D ma +D mi -D ma D mi Among them, D ma is rainfall damage, D mi It is microscopic damage;

[0117] S5. Based on the strain equivalence theory, the damage variable D m The nonlinear creep constitutive model ε is introduced to reflect the mechanical characteristics of the accelerated creep stage. vp The nonlinear creep constitutive model ε of the mechanical characteristics of the accelerated creep stage considering rainfall damage is obtained. vp ;

[0118] S6. Combining steps S2 and S5, a nonlinear creep constitutive model ε is constructed to describe the entire rock creep process taking rainfall damage into consideration.

[0119] In summary, the damage statistical constitutive model of water-bearing rock considering compaction deformation of the present invention is obtained by integrating the rock creep constitutive model based on memory-dependent derivatives with the nonlinear creep constitutive model of the mechanical properties of the accelerated creep stage considering rainfall damage, so as to obtain a nonlinear creep constitutive model that describes the entire rock creep process considering rainfall damage, so that this constitutive model has higher prediction accuracy than the traditional Nishihara model.

[0120] The above-described embodiments merely illustrate several embodiments of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make various modifications and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A method for constructing a rock creep constitutive model considering the influence of water content, characterized in that: The following steps are included: S1. Construct a rock creep constitutive model ε that describes the mechanical behavior of the decay and stable creep stages in rock creep. eve =ε e +ε ve ; where ε e Characterized as the strain in the instantaneous loading stage, ε ve Characterized as the strain corresponding to the decay and stable creep stages; S2. Introducing memory-dependent derivatives Memory-dependent derivatives Substitute into the rock creep constitutive model ε corresponding to the mechanical behavior of the attenuation and stable creep stages in rock creep eve In the paper, the rock creep constitutive model ε based on memory-dependent derivatives is obtained. eve ; S3. Construct a nonlinear creep constitutive model ε that reflects the mechanical properties of the accelerated creep stage vp ; S4. Obtain the damage variable D after coupling the rainfall damage caused by rainfall infiltration into the rock and the rock microscopic damage m =D ma +D mi -D ma D mi Among them, D ma is rainfall damage, D mi It is microscopic damage; S5. Based on the strain equivalence theory, the damage variable D m The nonlinear creep constitutive model ε is introduced to reflect the mechanical characteristics of the accelerated creep stage. vp The nonlinear creep constitutive model ε of the mechanical characteristics of the accelerated creep stage considering rainfall damage is obtained. vp ; S6. Combining steps S2 and S5, a nonlinear creep constitutive model ε is constructed to describe the entire rock creep process taking rainfall damage into consideration.

2. The method for constructing a rock creep constitutive model considering the influence of water content according to claim 1, characterized in that: The strain ε in the transient loading stage e , the strain corresponding to the decay and stable creep stages ε ve Satisfies the following formula: Among them, σ represents the upper limit stress of loading, E MT is a Hooke body, which is characterized by the deformation modulus corresponding to the instantaneous strain generated under load; E K Characterized as the deformation modulus corresponding to the strain in the decay and stable creep stages under creep loading; η K is the viscosity element parameter, which represents the strain rate during creep loading; is the deformation modulus E K The corresponding strain, is the viscosity element parameter η K The corresponding strain, Characterized as model strain ε ve The first derivative with time reflects the growth rate of strain with time.

3. The method for constructing a rock creep constitutive model considering the influence of water content according to claim 2, characterized in that: The method of step S2 comprises the following steps: Introducing memory-dependent derivatives to describe the constitutive model ε eve The parameter η in K , combined with the formula The constitutive equation is rewritten as: in, γ is the time delay coefficient; the weight function K(st) is an m-order continuous function, indicating the degree of memory dependence, σ K and ε ηk (t) represent stress and creep deformation respectively, Represents ε ηk The second-order memory-related derivative of (t), ε″ ηk (s) represents ε ηk The second derivative of (t). Set the weight function as follows: Substituting formula (3) into formula (2), we can get formula (4): Divide both sides of equation (4) by Further deduction yields: Solving formula (5), we can get: Substituting the conclusion that t∈[-γ,0], ε(t)=0 into equation (6), we can get the strain ε ηk Expressed as: According to formula (7) and formula (1), the following formula is obtained: According to formula (8), the strain ε corresponding to the decay and stable creep stages based on the memory-dependent derivative can be obtained: ve The expression is: Combined formula and the constitutive equation ε of the rock mass creep constitutive model eve =ε e +ε ve , obtain the rock creep constitutive model ε based on memory-dependent derivatives eve Strain expression 4. The method for constructing a rock creep constitutive model considering the influence of water content according to claim 3, characterized in that: Nonlinear creep constitutive model ε reflecting the mechanical properties of the accelerated creep stage vp The corresponding constitutive equation satisfies: In formula (9), σ represents the upper limit stress of loading, ηvp represents the viscosity element coefficient, and D m Characterized as damage variable, Characterized as model strain ε vp The first derivative with time reflects the growth rate of strain with time, σ S It is characterized by the threshold stress value at which the rock mass enters the accelerated creep stage.

5. The method for constructing a rock creep constitutive model considering the influence of water content according to claim 4, characterized in that: The method of step S4 comprises the following steps: Based on the strain equivalence theory, the coupled damage of rainfall and microscopic damage to rock mass can be expressed as: D m =D ma +D mi -D ma D mi (10) Among them, D ma is rainfall damage, D mi It is microscopic damage; Rainfall damage D ma The following formula can be obtained: Among them, E CW is the elastic modulus after rainfall, E CO is the elastic modulus under dry conditions; Kachanov's damage law in creep is used to describe microscopic damage D mi The relationship between time N, where the Kachanov damage law equation is: Where A and δ are material constants determined by experiments, ω is the applied load, is the micro damage variable D mi The first derivative with respect to time t; From the definition of formula (12), we can know that when time t = 0, the sample is not subjected to creep, and at this time D mi =0, combined with the rainfall condition and integrating formula (12), we can get D mi The expression is: When the rock mass is completely destroyed, D mi =1, the corresponding complete damage time t C for: t C =[A(δ+1)ω δ ] -1 (14) Combining equations (12) and (13), the rock damage evolution equation under creep conditions can be obtained as follows: Since the constitutive model corresponding to the damage evolution equation under creep conditions describes the mechanical behavior of the rock mass in the accelerated creep stage, it is assumed that when the damage begins to occur in Equation (14), t = t S , therefore, the true damage time of formula (14) is The actual total damage time is: Under this creep condition, Equation (14) is changed to: Among them, t S is the time when the rock mass enters the accelerated creep stage, t F The time when the rock mass is completely destroyed, that is, the creep life, when t = t S When D mi =0; t=t F When D mi =1; Substituting equations (11) and (16) into equation (10), the rock damage expression considering rainfall damage can be obtained as follows:

6. The method for constructing a rock creep constitutive model considering the influence of water content according to claim 5, characterized in that: The method of step S5 is specifically performed as follows: Substituting Equation (17) into Equation (9), the constitutive equation of the nonlinear creep model considering rainfall damage is obtained as follows: Further deduction through formula (18) yields: Combined with the initial condition t = t S , ε vp = 0, solving Equation (18) can obtain the nonlinear creep constitutive model ε of the mechanical characteristics of the accelerated creep stage considering rainfall damage vp The expression:

7. The method for constructing a rock creep constitutive model considering the influence of water content according to claim 6, characterized in that: The method of step S6 comprises the following steps: Construct the constitutive equation corresponding to the nonlinear creep constitutive model that describes the entire creep process taking rainfall damage into account: e=e e +e ve +e vp (21), Combining equations (8) and (20), the threshold stress value σ at which the rock mass enters the accelerated creep stage is S As the dividing point, the expression corresponding to the nonlinear constitutive model reflecting the three-stage mechanical behavior of rock mass under creep conditions is substituted into Equation (21) to obtain the nonlinear creep constitutive model describing the entire rock creep process considering rainfall damage:

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