A method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption

Abstract

A method for establishing a full-stage constitutive model reflecting the softening effect of rock due to water absorption, the method comprising the steps of: establishing a pre-yield constitutive relationship expression of the rock; establishing a post-yield constitutive relationship expression of the rock; and establishing a full-stage constitutive model of the rock according to the pre-yield constitutive relationship expression and the post-yield constitutive relationship expression. The method for establishing a full-stage constitutive model reflecting the softening effect of rock due to water absorption provided in the present application is suitable for simulating situations where the nonlinear characteristics of the compaction section are obvious, and can provide technical support for the stability evaluation and optimization design of rock engineering.

Description

Technical Field

[0001] The invention belongs to the technical field of rock mechanics, and in particular relates to a method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption. Background Art

[0002] Rocks are composed of cemented mineral particles and countless randomly distributed micro-defects (such as pores and cracks), and their constitutive relations are very complex to describe. The presence of micro-defects not only affects the strength and heterogeneity of rocks, but also provides channels for the storage and transportation of groundwater. Due to complex physical and chemical interactions, when rocks encounter water, the mechanical properties of rocks will inevitably deteriorate. In fact, the water absorption and softening effect, as an important form of water-rock interaction, has been considered to be one of the main causes of natural or engineering geological disasters, such as landslides induced by rainfall or reservoir water level fluctuations, and groundwater exacerbating large deformations of surrounding rocks in tunnels or deep mines. Therefore, establishing a constitutive model that takes into account the water absorption and softening effect is crucial for the design and stability assessment of rock mass engineering.

[0003] Among the existing rock constitutive model results, there are few constitutive models that describe the softening effect of rock due to water absorption, and most of the constitutive models that consider the softening effect due to water absorption are established under uniaxial loading conditions. However, rocks are usually under triaxial stress conditions, and uniaxial loading conditions are too simplified for actual environmental conditions. The constitutive models under uniaxial loading conditions are not representative and have little application value in engineering. In addition, the stress-strain curves of a large number of constitutive models under uniaxial or triaxial loading conditions in the past usually consist of a linear elastic deformation stage, a yield stage, and a post-peak stage, and the compaction stage is usually ignored. In fact, due to the complexity of rock components, especially the widespread distribution of pores and cracks, rocks often exhibit significant nonlinear deformation characteristics in the early elastic deformation stage. If this nonlinear deformation characteristic is ignored, there will often be a serious deviation between the proposed constitutive model and the actual situation, resulting in the constitutive model being unable to describe the true deformation behavior of the rock.

[0004] On the other hand, the rock statistical damage constitutive model is one of the most widely used rock constitutive models, but there is a problem that the compaction stage of the rock stress-strain curve is difficult to describe accurately. Some scholars have proposed a two-strain Hooke model (TPHM) based on the traditional Hooke's law (Liu, et al., 2009; Zhao and Liu, 2012), which can describe the nonlinear deformation of the elastic section of the rock. However, TPHM is only applicable to the constitutive relationship of rock under triaxial stress conditions, and does not consider the damage effect of rock under complex environmental conditions (such as water absorption softening effect); in addition, TPHM can only characterize the stress-strain relationship in the elastic deformation stage, but cannot describe the deformation characteristics of the post-yield stage.

[0005] Therefore, the above two models each have obvious defects in describing the constitutive relationship of rock under the combined action of water absorption softening effect and triaxial loading. At present, there is a lack of a full-stage constitutive model that considers the water absorption softening effect. Summary of the invention

[0006] In view of the above problems, the present invention provides a method for establishing a full-stage constitutive model that reflects the softening effect of rock water absorption, which overcomes the above problems or at least partially solves the above problems.

[0007] In order to solve the above technical problems, the present invention provides a method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption, the method comprising the steps of:

[0008] Establish the pre-yield constitutive relation expression of rock;

[0009] Establishing a post-yield constitutive relation expression of the rock;

[0010] A full-stage constitutive model of rock is established according to the pre-yield constitutive relationship expression and the post-yield constitutive relationship expression.

[0011] Preferably, the step of establishing the pre-yield constitutive relation expression of rock comprises the following steps:

[0012] Establishing the first constitutive relation expression of the rock under isotropic stress condition;

[0013] Establishing a second constitutive relationship expression of the rock under anisotropic stress conditions according to the first constitutive relationship expression;

[0014] Solve the second constitutive relation expression for parameters.

[0015] Preferably, the step of establishing the first constitutive relation expression of the rock under isotropic stress conditions comprises the following steps:

[0016] Obtaining a first basic constitutive relation expression of a soft part in the rock;

[0017] Obtaining a second basic constitutive relation expression of a hard part in the rock;

[0018] The first constitutive relationship expression is established according to the first basic constitutive relationship expression and the second basic constitutive relationship expression.

[0019] Preferably, the first constitutive relation expression is:

[0020]

[0021] Where V and V0 represent the total volume of the material in the current stress state and the stress-free state, respectively, and γ t and γe Respectively represent the proportion of the soft part and the hard part of the rock, K e and K t Respectively represent the bulk modulus of the hard part and the bulk modulus of the soft part, σ h represents the nominal stress of isotropic stress, D represents the damage variable, and the subscripts 0, e, and t represent the stress-free state, the hard part, and the soft part, respectively.

[0022] Preferably, establishing a second constitutive relationship expression of the rock under anisotropic stress conditions according to the first constitutive relationship expression comprises the steps of:

[0023] Obtaining the first constitutive relationship expression;

[0024] Get the principal strain expression in any direction;

[0025] Establishing stress-strain relationship expressions in the directions of the principal stress components according to the first constitutive relationship expression and the arbitrary direction principal strain expression;

[0026] Get boundary condition expressions;

[0027] Establishing a stress-strain boundary relationship expression according to the stress-strain relationship expression and the boundary condition expression;

[0028] Get the damage factor expression;

[0029] A stress-strain characteristic expression is established according to the stress-strain boundary relationship expression and the damage factor expression.

[0030] Preferably, the stress-strain characteristic expression is:

[0031]

[0032] Among them, ε1 represents the first principal strain, E0 and E w Respectively represent the elastic modulus of rock before and after immersion in water, γ t Indicates the proportion of soft parts in rock, E e Indicates Young's modulus of the hard part, E t represents Young's modulus of the soft part, σ1, σ2 and σ3 represent the three principal stresses respectively, and μ represents the Poisson's ratio of rock.

[0033] Preferably, the step of solving the parameters of the second constitutive relationship expression comprises the steps of:

[0034] Obtain stress-strain characteristic expressions;

[0035] Draw a curve graph of the stress-strain characteristic expression;

[0036] Finding the linear elastic deformation stage curve of the curve graph;

[0037] Fitting the linear elastic deformation stage curve using a linear elastic deformation stage straight line;

[0038] Solving the intersection point of the straight line in the linear elastic deformation stage and the horizontal coordinate of the curve graph;

[0039] Solving the proportion of the soft part according to the intersection point;

[0040] Solving the slope of the straight line in the linear elastic deformation stage;

[0041] Calculate the Young's modulus of the hard part according to the slope;

[0042] Obtaining stress-strain data of the compaction section of the linear elastic deformation stage curve;

[0043] The Young's modulus of the soft part is solved according to the stress-strain data of the compaction section.

[0044] Preferably, the step of establishing the post-yield constitutive relation expression of the rock comprises the following steps:

[0045] Establishing a damage constitutive relation expression of the rock;

[0046] Establishing a failure criterion expression for the rock;

[0047] A post-yield constitutive relation expression is established based on the damage constitutive relation expression and the failure criterion expression.

[0048] Preferably, the step of establishing a full-stage rock constitutive model according to the pre-yield constitutive relationship expression and the post-yield constitutive relationship expression comprises the following steps:

[0049] Obtaining the pre-yield constitutive relation expression and the post-yield constitutive relation expression;

[0050] Get the modified expression;

[0051] Get the peak point boundary condition expression;

[0052] Get the yield point boundary condition expression;

[0053] The full-stage constitutive model of rock is established according to the pre-yield constitutive relationship expression, the post-yield constitutive relationship expression, the correction expression, the peak point boundary condition expression and the yield point boundary condition expression.

[0054] The present application also provides a device for establishing a full-stage rock constitutive model, the device comprising:

[0055] The first building module is used to establish the pre-yield constitutive relation expression of rock;

[0056] The second establishment module is used to establish a post-yield constitutive relation expression of the rock;

[0057] The third establishing module is used to establish a full-stage constitutive model of rock according to the pre-yield constitutive relationship expression and the post-yield constitutive relationship expression.

[0058] The present application provides a method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption, which has at least the following technical effects or advantages:

[0059] (1) By introducing damage variables, an improved THPM model is derived and proposed. This model can effectively reflect the nonlinear deformation characteristics of the compaction stage while fully considering the damage effect caused by water absorption and softening. It is suitable for describing the constitutive relationship of rock in the elastic deformation stage under the combined action of triaxial force and water absorption and softening effect.

[0060] (2) A statistical damage model is used to describe the stress-strain relationship of rock in the post-yield stage. The statistical damage model is modified by introducing a correction coefficient, which solves the technical problem of numerical discontinuity of the double-strain Hooke model and the statistical damage model at the yield point, thereby ensuring the continuity of the full stress-strain curve of the proposed constitutive model.

[0061] (3) The established full-stage constitutive model combines the dual-strain Hooke model (describing the constitutive relationship of rock before yield) and the statistical damage constitutive model (describing the constitutive relationship of rock after yield), effectively giving play to the respective advantages of the two models and solving the problem of the lack of full-stage constitutive models that consider the water absorption softening effect at present. The proposed model is in good agreement with the actual situation and is suitable for describing the constitutive relationship of rock under the combined influence of triaxial loading and water absorption softening damage effect, especially for simulating the obvious nonlinear characteristics of the compaction stage, which can provide technical support for the stability evaluation and optimization design of rock mass engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0063] Figure 1 It is a flow chart of a method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption provided by an embodiment of the present invention;

[0064] Figure 2 It is a structural schematic diagram of a device for establishing a rock full-stage constitutive model provided by an embodiment of the present invention;

[0065] Figure 3 It is a schematic diagram of a typical stress-strain curve of a rock sample under triaxial compression in a method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption provided by an embodiment of the present invention;

[0066] Figure 4 A schematic diagram of comparison between experimental data and model theoretical data under different saturation coefficients and confining pressures in a full-stage constitutive model establishment method reflecting the water absorption softening effect of rock provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0067] The present invention will be described in detail below in conjunction with specific implementations and examples, and the advantages and various effects of the present invention will be more clearly presented. It should be understood by those skilled in the art that these specific implementations and examples are used to illustrate the present invention, rather than to limit the present invention.

[0068] Throughout the specification, unless otherwise specifically stated, the terms used herein should be understood as meanings commonly used in the art. Therefore, unless otherwise defined, all technical and scientific terms used herein have the same meanings as those generally understood by those skilled in the art to which the present invention belongs. In the event of a conflict, the present specification takes precedence.

[0069] Unless otherwise specified, various raw materials, reagents, instruments and equipment used in the present invention can be purchased from the market or prepared by existing methods.

[0070] like Figure 1 In an embodiment of the present application, the present invention provides a method for establishing a full-stage constitutive model that reflects the softening effect of rock water absorption, and the method comprises the steps of:

[0071] S1: Establish the pre-yield constitutive relation expression of rock;

[0072] In the embodiment of the present application, the establishment of the pre-yield constitutive relation expression of the rock comprises the steps of:

[0073] Establishing the first constitutive relation expression of the rock under isotropic stress condition;

[0074] Establishing a second constitutive relationship expression of the rock under anisotropic stress conditions according to the first constitutive relationship expression;

[0075] Solve the second constitutive relation expression for parameters.

[0076] In the embodiments of the present application, in order to distinguish the deformation of different components of rock, for pores and cracks, the so-called "soft part", it is assumed that Hooke's law based on natural volume strain applies; for the rock itself, the so-called "hard part", it is assumed that it follows Hooke's law based on engineering volume strain.

[0077] When establishing the pre-yield constitutive relation expression of rock, based on the generalized Hooke's law, by introducing the damage variable, the pre-yield constitutive relation expression of rock under isotropic stress conditions can be established.

[0078] In an embodiment of the present application, the first constitutive relation expression of the rock under isotropic stress conditions is established, comprising the steps of:

[0079] Obtaining a first basic constitutive relation expression of a soft part in the rock;

[0080] Obtaining a second basic constitutive relation expression of a hard part in the rock;

[0081] The first constitutive relationship expression is established according to the first basic constitutive relationship expression and the second basic constitutive relationship expression.

[0082] In the embodiment of the present application, when an isotropic and homogeneous material (such as rock) is subjected to a uniformly distributed load, according to Hooke's law, the material will undergo elastic deformation, and the following expression can be obtained:

[0083] dσ h * =Kdε v,t (1)

[0084] Among them, σ h * is the effective stress for isotropic stress (compression is defined as positive), K is the bulk modulus, ε v,t is the natural volume strain.

[0085] Specifically, the natural volume strain expression is:

[0086]

[0087] where V is the total volume of the material under the current stress state.

[0088] According to the damage theory, the following expression can be obtained:

[0089]

[0090]

[0091] Among them, σ h is the nominal stress of isotropic stress, and D is the damage variable.

[0092] Combining expressions (1), (2) and (4), we can get the following expression:

[0093]

[0094] Taking V as the independent variable and integrating both sides of equation (5), and taking into account the boundary conditions of equation (6), we get equation (7):

[0095]

[0096]

[0097] where V0 is the total volume of the material in the stress-free state.

[0098] In the embodiment of the present application, the concept definition expression of engineering volume strain is as follows:

[0099]

[0100] Similarly, in the above derivation process, when the natural volume strain is replaced by the engineering volume strain, σ h In the integration process, it is used as an independent variable and the following expression is derived:

[0101]

[0102] In order to distinguish the deformation of different components of rocks, for pores and cracks, the so-called "soft part", it is assumed that Hooke's law based on natural volume strain is applicable, and the first basic constitutive relationship expression of the soft part of the rock can be obtained; for the rock itself, the so-called "hard part", it is assumed that it follows Hooke's law based on engineering volume strain, and the second basic constitutive relationship expression of the hard part of the rock can be obtained. Therefore, it can be obtained:

[0103] V0=V 0,e +V 0,t (10)

[0104] dV=dV e +dV t (11)

[0105]

[0106]

[0107] The subscripts 0, e, and t represent the stress-free state, the hardware part, and the software part, respectively. t and γ e They are the proportion of the soft part and the proportion of the hard part in the rock respectively.

[0108] According to the above assumptions, substituting equations (7) and (9) into the above equations, we can obtain:

[0109]

[0110]

[0111] Among them, K e and K t Represent the bulk modulus of the hard body part and the bulk modulus of the soft body part, respectively.

[0112] Combining equations (11), (14) and (15), we can obtain the first constitutive relation expression:

[0113]

[0114] Where V and V0 represent the total volume of the material in the current stress state and the stress-free state, respectively, and γ t and γ e Respectively represent the proportion of the soft part and the hard part of the rock, K e and K t Represent the bulk modulus of the hard part and the soft part, σ h represents the nominal stress of isotropic stress, D represents the damage variable, and the subscripts 0, e, and t represent the stress-free state, the hard part, and the soft part, respectively.

[0115] In an embodiment of the present application, establishing a second constitutive relationship expression of the rock under anisotropic stress conditions according to the first constitutive relationship expression comprises the following steps:

[0116] Obtaining the first constitutive relationship expression;

[0117] Get the principal strain expression in any direction;

[0118] Establishing stress-strain relationship expressions in the directions of the principal stress components according to the first constitutive relationship expression and the arbitrary direction principal strain expression;

[0119] Get boundary condition expressions;

[0120] Establishing a stress-strain boundary relationship expression according to the stress-strain relationship expression and the boundary condition expression;

[0121] Get the damage factor expression;

[0122] A stress-strain characteristic expression is established according to the stress-strain boundary relationship expression and the damage factor expression.

[0123] In the embodiment of the present application, according to the generalized Hooke's law, the expression of the principal strain in any direction is:

[0124]

[0125] Among them, σ1, σ2 and σ3 are the three principal stresses, E and μ are the elastic modulus and Poisson's ratio of the rock.

[0126] By transforming formula (17), we can get:

[0127]

[0128] Assuming that the conclusion of formula (16) is applicable to anisotropic stress conditions, similarly, in each principal stress direction, the rock can also be divided into two parts: the soft part and the hard part. Therefore, the stress-strain relationship expression of each principal stress component direction of formula (19) can be derived based on the first constitutive relationship expression of formula (16) and the principal strain expression of any direction of formula (18):

[0129]

[0130] The relevant parameters in formula (19) are defined as follows:

[0131]

[0132]

[0133]

[0134]

[0135] γ' e =1-γ' t (i=1,2,3) (24)

[0136] Among them, ε1, ε2, ε3 represent the three principal strains respectively; γ' t and γ' e are the proportion of the soft part and the proportion of the hard part of the whole rock in a certain main direction under stress-free environment; E t and E e are Young's modulus of the soft part and Young's modulus of the hard part respectively; l i is the length of the rock in the i principal direction.

[0137] According to the definitions of equations (22)-(24), the following expressions can be obtained:

[0138]

[0139] Considering the small volume proportion of pores and cracks in rocks, γ' t It is usually much smaller than 1, so it can be ignored in formula (25), and the following expression can be obtained:

[0140]

[0141] Combining equations (11), (12), (13) and (26), we can obtain the following expression:

[0142]

[0143] According to the theory of elasticity, volume strain is the sum of three principal strains, and the following expression can be obtained:

[0144] dε v =dε1+dε2+dε3 (28)

[0145] Combining equations (19), (27) and (28), we can obtain the following expression:

[0146]

[0147] Under isotropic stress conditions, equations (16) and (29) are consistent, so we can get:

[0148]

[0149] K t =E t (31)

[0150] As mentioned above, γ t and γ' t Usually much smaller than 1, it can be ignored. Therefore, we can get:

[0151]

[0152] Integrating both sides of equation (19) and considering the boundary condition expression (equation (33)), the stress-strain boundary relationship expression of equation (34) can be obtained:

[0153]

[0154]

[0155] According to the damage mechanics theory, the damage factor D caused by the water absorption softening effect in formula (34) is expressed as:

[0156]

[0157] Among them, D wis the damage variable considering the immersion time w (days), E0 and E w are the elastic modulus of rock before and after immersion in water, respectively.

[0158] Under the conditions of triaxial compression test in the laboratory, σ2 is equal to σ3. Combining equation (34) and equation (35), the stress-strain characteristic expression can be obtained:

[0159]

[0160] Among them, ε1 represents the first principal strain, E0 and E w Respectively represent the elastic modulus of rock before and after immersion in water, γ t Indicates the proportion of soft parts in rock, E e Indicates Young's modulus of the hard part, E t represents Young's modulus of the soft part, σ1, σ2 and σ3 represent the three principal stresses respectively, and μ represents the Poisson's ratio of rock.

[0161] Formula (36) is an expression that describes the stress-strain characteristics of rock in the compaction stage and the linear elastic deformation stage when it is subjected to triaxial loading and water softening.

[0162] In an embodiment of the present application, the step of solving the parameters of the second constitutive relationship expression includes the following steps:

[0163] Obtain stress-strain characteristic expressions;

[0164] Draw a curve graph of the stress-strain characteristic expression;

[0165] Finding the linear elastic deformation stage curve of the curve graph;

[0166] Fitting the linear elastic deformation stage curve using a linear elastic deformation stage straight line;

[0167] Solving the intersection point of the straight line in the linear elastic deformation stage and the horizontal coordinate of the curve graph;

[0168] Solving the proportion of the soft part according to the intersection point;

[0169] Solving the slope of the straight line in the linear elastic deformation stage;

[0170] Calculate the Young's modulus of the hard part according to the slope;

[0171] Obtaining stress-strain data of the compaction section of the linear elastic deformation stage curve;

[0172] The Young's modulus of the soft part is solved according to the stress-strain data of the compaction section.

[0173] In the embodiment of the present application, as shown in formula (36), the parameters to be solved in the model are the Young's modulus E of the soft part,t , Young's modulus E of the hard part e Ratio of software part γ t The above three parameters can be obtained by the following method: First, draw a curve graph of the stress-strain characteristic expression, and you can get the following: Figure 3 The curve shown in the figure shows that the stress-strain relationship of the linear elastic deformation stage curve (AB) can be well fitted into a straight line (linear elastic deformation stage straight line). The strain corresponding to the intersection of the linear elastic deformation stage straight line and the horizontal axis can be regarded as the proportion of the soft part in a main direction γ' t , so γ t It can be obtained according to formula (27). The slope of the straight line in the linear elastic deformation stage is like Figure 3 As shown in Figure 3, since the exponential term on the right side of Eq. (36) can be ignored under relatively high stress conditions and the stress-strain relationship is very close to linear, E can be obtained based on this. e Finally, on the basis of obtaining other parameters of formula (36), a set of stress-strain data of the compaction section is substituted into formula (36) to obtain E t .

[0174] S2: Establishing the post-yield constitutive relation expression of the rock;

[0175] In an embodiment of the present application, the establishment of the post-yield constitutive relation expression of the rock comprises the steps of:

[0176] Establishing a damage constitutive relation expression of the rock;

[0177] Establishing a failure criterion expression for the rock;

[0178] A post-yield constitutive relation expression is established based on the damage constitutive relation expression and the failure criterion expression.

[0179] In the embodiment of the present application, the specific steps of establishing the damage constitutive relation expression of rock are:

[0180] According to the generalized Hooke's law and the damage definition in damage theory, when the rock specimen is subjected to triaxial load, the constitutive relation of the rock can be described as:

[0181] σ i =Eε i (1-D)+μ(σ j +σ k ) (37)

[0182] Since the damage evolution process of rock materials can be regarded as the heterogeneous destruction process of local rock particles, according to the theory of statistical damage mechanics, the damage variable expression of rock under triaxial load can be defined from a microscopic perspective:

[0183]

[0184] Among them, D l is the damage variable of rock under triaxial load; η0 is the strength of rock particles; β and η are the shape parameter and scale parameter of the distribution function respectively.

[0185] According to the equivalent strain principle, when the rock is subjected to the water absorption softening effect and triaxial loading in sequence, the constitutive relationship of the rock can be described as follows:

[0186] σ i =E w ε i (1-D l )+μ(σ j +σ k ) (39)

[0187] σ i =E0ε i (1-D m )+μ(σ j +σ k ) (40)

[0188] Among them, D m is the total damage variable caused by the water absorption softening effect and triaxial loading, as shown in formula (41):

[0189] D m =D l +D w -D l D w (41)

[0190] In the embodiment of the present application, the specific steps of establishing the rock failure criterion expression are:

[0191] According to the theory of statistical mechanics, the failure criterion of rock particles can be expressed as follows:

[0192] η(σ * )-k0=0 (42)

[0193] Among them, η(σ * ) is the rock stress level, k0 is the inherent strength of the rock.

[0194] In the embodiment of the present application, the Mohr-Coulomb criterion is used as the failure criterion. Accordingly, the expression of k0 is shown in formula (43). When η(σ * )≥k0, rock particles are destroyed:

[0195] k0=2c t cosφt / (1-sinφ t ) (43)

[0196] η=σ1 * -ασ3 * (44)

[0197] Where α=(1+sinφ t ) / (1-sinφ t )(45), c t and φ t are the cohesion and internal friction angle of the rock after immersion time t (days).

[0198] According to formula (39), we can get:

[0199] σ1=E w ε1(1-D l )+μ(σ2+σ3) (46)

[0200] Therefore, the transformation results in the following expression:

[0201]

[0202] According to formula (3), we can get:

[0203] σ1 * =σ1 / (1-D l ) (48)

[0204] σ3 * =σ3 / (1-D l ) (49)

[0205] Combining equations (47), (48) and (49), we can obtain:

[0206]

[0207]

[0208] Substituting equations (50) and (51) into equation (44), the failure criterion can be expressed as follows:

[0209]

[0210] In the embodiment of the present application, the specific steps of establishing the post-yield constitutive relation expression according to the damage constitutive relation expression and the failure criterion expression are as follows:

[0211] Combining equations (37), (38), (41), (46) and (52), the constitutive relation expression and total damage variable expression of rock under the combined action of water absorption softening effect and triaxial loading are:

[0212]

[0213]

[0214] In the embodiment of the present application, the statistical damage model based on the Mohr-Coulomb criterion is suitable for representing the stress-strain relationship after rock yielding; on the other hand, as mentioned above, TPHM has unique advantages in describing the nonlinear deformation characteristics of the elastic stage. Therefore, the above two models can respectively describe the stress-strain relationship of rock before yielding and after yielding.

[0215] S3: Establishing a full-stage constitutive model of rock according to the pre-yield constitutive relationship expression and the post-yield constitutive relationship expression.

[0216] In an embodiment of the present application, the step of establishing a full-stage rock constitutive model according to the pre-yield constitutive relationship expression and the post-yield constitutive relationship expression comprises the following steps:

[0217] Obtaining the pre-yield constitutive relation expression and the post-yield constitutive relation expression;

[0218] Get the modified expression;

[0219] Get the peak point boundary condition expression;

[0220] Get the yield point boundary condition expression;

[0221] The full-stage constitutive model of rock is established according to the pre-yield constitutive relationship expression, the post-yield constitutive relationship expression, the correction expression, the peak point boundary condition expression and the yield point boundary condition expression.

[0222] In the embodiment of the present application, however, since the stress values ​​calculated by the above two models are not equal at the yield point, a breakpoint will appear at the yield point in the entire stress-strain curve; in this case, the above two models cannot be combined to form a coherent curve, resulting in obvious defects in the constitutive model.

[0223] In order to maintain the numerical continuity of the statistical damage model and the TPHM model at the yield point, the present application further proposes an improved method, that is, introducing a correction coefficient into the constitutive relationship expression and correcting the statistical damage model, as shown in equations (55)-(57):

[0224]

[0225]

[0226]

[0227] Define σ 1p ,σ 2p ,σ 3p and ε 1p are the first principal stress, second principal stress, third principal stress and first principal strain at the peak point. Equation (55) satisfies the boundary condition expression of the peak point, which is:

[0228]

[0229]

[0230] Similarly, define σ 1y ,σ 2y ,σ 3y and ε 1y are the first principal stress, second principal stress, third principal stress and first principal strain at the yield point respectively. Equation (55) satisfies the boundary condition expression of the yield point, which is:

[0231]

[0232]

[0233] According to formula (56), the failure criterion of the peak point can be expressed as follows:

[0234]

[0235] Combining equations (52), (55), (58) and (59), we can obtain the following expression:

[0236]

[0237]

[0238] Reorganizing equation (64) yields:

[0239]

[0240] According to formula (56), we can get the following formula:

[0241]

[0242] Substituting formula (66) into formula (65), we can obtain:

[0243]

[0244] Combining equations (63) and (67), we can obtain:

[0245]

[0246]

[0247] Substituting equations (68) and (69) into equation (55) and combining them with equations (60) and (61), C1 and C2 can be solved by the iterative method in Matlab.

[0248] like Figure 2 The present application also provides a device for establishing a full-stage rock constitutive model, the device comprising:

[0249] The first building module 10 is used to build a pre-yield constitutive relation expression of rock;

[0250] The second establishing module 20 is used to establish a post-yield constitutive relation expression of the rock;

[0251] The third establishing module 30 is used to establish a full-stage constitutive model of rock according to the pre-yield constitutive relationship expression and the post-yield constitutive relationship expression.

[0252] The present application provides a device for establishing a full-stage constitutive model of rock, which can execute the aforementioned method for establishing a full-stage constitutive model that reflects the softening effect of rock water absorption.

[0253] In order to verify the rationality of the method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption provided by this application, it is necessary to carry out triaxial compression tests of rocks under different saturation coefficients and confining pressures. The rock samples used for the test were selected from the rock blocks of the middle-weathered shale layer in northwestern Hubei. The samples were first processed into Φ50mm×100mm standard cylindrical samples; in order to ensure the uniformity and integrity of the samples as much as possible, the cracked samples were first removed after processing, and then the remaining samples were tested for acoustic wave velocity, and the samples with large wave velocity deviations were removed.

[0254] In order to obtain the specimens for the triaxial compression test, the specimens were first dried in an oven and then prepared in the following manner: first, the specimens were placed in a water tank and filled with water to 1 / 4 of the specimen height; then, an equal amount of water was added every 2 hours for a total of 4 times, and all the specimens were immersed in water. The water absorption time of the three groups of specimens was approximately 7 days, 21 days, and 42 days, respectively.

[0255] In order to quantitatively characterize the water absorption degree of each rock sample, the saturation of each rock sample is defined based on the rock sample after 42 days of water absorption. Therefore, the concept of saturation coefficient is introduced as follows:

[0256] w s =ω t / ω s (70)

[0257] Among them, ω t =m t / md ×100% (71)

[0258] In the formula, w s is the saturation coefficient, ω t is the moisture content after t days of water absorption, ω s is the saturated water content, m t is the weight of the rock sample after absorbing water for t days, m d is the weight of the rock sample after drying. The above parameters can be obtained by weighing the corresponding specimens with a balance. After water absorption treatment, the saturation coefficients of the four groups of specimens were 0, 0.2, 0.5, and 1.0, respectively. Triaxial compression tests were carried out under four groups of confining pressures (10MPa, 20MPa, 30MPa, and 40MPa). The test process is: first apply the confining pressure and increase it to a predetermined value, then keep the confining pressure unchanged, and increase the axial pressure until the specimen breaks. Four groups of initial confining pressures were designed for the triaxial compression test, which were 10, 20, 30, and 40MPa, respectively. The loading process adopts displacement control, and the axial pressure loading rate is 0.002mm / s.

[0259] Figure 3 Comparison of stress-strain curves between test results and model-based results. The results show that the full-stage constitutive model obtained by the full-stage constitutive model establishment method reflecting the water absorption softening effect of rock provided in this application is in good agreement with the test data under different saturation coefficients and confining pressures. In addition, it is also proved that the segmented description of the stress-strain curve under the combined action of water absorption softening effect and triaxial loading is reasonable, and it is feasible to use TPHM to simulate the pre-yield stage of the stress-strain curve and the post-yield stage using the statistical damage model.

[0260] The present application provides a method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption, which has at least the following technical effects or advantages:

[0261] (1) By introducing damage variables, an improved THPM model is derived and proposed. This model can effectively reflect the nonlinear deformation characteristics of the compaction stage while fully considering the damage effect caused by water absorption and softening. It is suitable for describing the constitutive relationship of rock in the elastic deformation stage under the combined action of triaxial force and water absorption and softening effect.

[0262] (2) A statistical damage model is used to describe the stress-strain relationship of rock in the post-yield stage. The statistical damage model is modified by introducing a correction coefficient, which solves the technical problem of numerical discontinuity of the double-strain Hooke model and the statistical damage model at the yield point, thereby ensuring the continuity of the full stress-strain curve of the proposed constitutive model.

[0263] (3) The established full-stage constitutive model combines the dual-strain Hooke model (describing the constitutive relationship of rock before yield) and the statistical damage constitutive model (describing the constitutive relationship of rock after yield), effectively giving play to the respective advantages of the two models and solving the problem of the lack of full-stage constitutive models that consider the water absorption softening effect at present. The proposed model is in good agreement with the actual situation and is suitable for describing the constitutive relationship of rock under the combined influence of triaxial loading and water absorption softening damage effect, especially for simulating the obvious nonlinear characteristics of the compaction stage, which can provide technical support for the stability evaluation and optimization design of rock mass engineering.

[0264] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that the process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of more restrictions, the elements defined by the sentence "including one..." do not exclude the existence of other identical elements in the process, method, article or device including the elements. The above is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. The various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features applied for herein.

[0265] In short, the above is only a preferred embodiment of the technical solution of the present invention, and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption, characterized in that: The method comprises the steps of: Establish the pre-yield constitutive relation expression of rock; Establishing a post-yield constitutive relation expression of the rock; Establishing a full-stage constitutive model of rock according to the pre-yield constitutive relationship expression and the post-yield constitutive relationship expression; The establishment of the pre-yield constitutive relation expression of rock comprises the steps of: Establishing the first constitutive relation expression of the rock under isotropic stress condition; Establishing a second constitutive relationship expression of the rock under anisotropic stress conditions according to the first constitutive relationship expression; Solving the parameters of the second constitutive relation expression; The step of establishing the first constitutive relation expression of the rock under isotropic stress conditions comprises the following steps: Obtaining a first basic constitutive relation expression of a soft part in the rock; Obtaining a second basic constitutive relation expression of a hard part in the rock; Establishing the first constitutive relationship expression according to the first basic constitutive relationship expression and the second basic constitutive relationship expression; The first constitutive relation expression is: ， Among them, V and Represent the total volume of the material in the current stress state and the stress-free state, respectively. and Respectively represent the proportion of the soft part and the hard part of the rock. and represent the bulk modulus of the hard part and the bulk modulus of the soft part, respectively. represents the nominal stress of isotropic stress, D represents the damage variable, and the subscripts 0, e, and t represent the stress-free state, the hard part, and the soft part, respectively; The method of establishing a second constitutive relationship expression of the rock under anisotropic stress conditions according to the first constitutive relationship expression comprises the following steps: Obtaining the first constitutive relationship expression; Get the principal strain expression in any direction; Establishing stress-strain relationship expressions in the directions of the principal stress components according to the first constitutive relationship expression and the arbitrary direction principal strain expression; Get boundary condition expressions; Establishing a stress-strain boundary relationship expression according to the stress-strain relationship expression and the boundary condition expression; Get the damage factor expression; Establishing a stress-strain characteristic expression according to the stress-strain boundary relationship expression and the damage factor expression; The stress-strain characteristic expression is: ， in, represents the first principal strain, and Respectively represent the elastic modulus of rock before and after immersion in water, Indicates the proportion of soft parts in rock. represents the Young's modulus of the hard part, represents the Young's modulus of the soft part, , and They represent the three principal stresses respectively, and μ represents the Poisson's ratio of rock.

2. The method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption according to claim 1 is characterized in that: The step of solving the parameters of the second constitutive relation expression comprises the steps of: Obtain stress-strain characteristic expressions; Draw a curve graph of the stress-strain characteristic expression; Finding the linear elastic deformation stage curve of the curve graph; Fitting the linear elastic deformation stage curve using a linear elastic deformation stage straight line; Solving the intersection point of the straight line in the linear elastic deformation stage and the horizontal coordinate of the curve graph; Solving the proportion of the soft part according to the intersection point; Solving the slope of the straight line in the linear elastic deformation stage; Calculate the Young's modulus of the hard part according to the slope; Obtaining stress-strain data of the compaction section of the linear elastic deformation stage curve; The Young's modulus of the soft part is solved according to the stress-strain data of the compaction section.

3. The method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption according to claim 1 is characterized in that: The step of establishing the post-yield constitutive relation expression of the rock comprises the following steps: Establishing a damage constitutive relation expression of the rock; Establishing a failure criterion expression for the rock; A post-yield constitutive relation expression is established based on the damage constitutive relation expression and the failure criterion expression.

4. The method for establishing a full-stage constitutive model reflecting the softening effect of rock water absorption according to claim 1 is characterized in that: The step of establishing a full-stage rock constitutive model according to the pre-yield constitutive relationship expression and the post-yield constitutive relationship expression comprises the following steps: Obtaining the pre-yield constitutive relation expression and the post-yield constitutive relation expression; Get the modified expression; Get the peak point boundary condition expression; Get the yield point boundary condition expression; The full-stage constitutive model of rock is established according to the pre-yield constitutive relationship expression, the post-yield constitutive relationship expression, the correction expression, the peak point boundary condition expression and the yield point boundary condition expression.

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