Geotechnical material cross-scale constitutive model construction method based on mesomechanics

Abstract

The invention provides a geotechnical material cross-scale constitutive model construction method based on mesomechanics. The geotechnical material cross-scale constitutive model construction method comprises the following steps that S1, a geotechnical material is a heterogeneous composite material with a mesostructure and different microscopic components; s2, establishing a linear elastic constitutive relation of a geotechnical material microcosmic cementing unit based on the geotechnical material microcosmic component; s3, establishing an elastic-plastic constitutive relation of a geotechnical material microcosmic friction unit based on the geotechnical material microcosmic component; s4, introducing the breakage rate of the crushing conversion degree from the mesoscopic cementation unit to the friction unit, and constructing the influence relationship of the mesoscopic cementation unit and the friction unit on the mechanical behavior of the macroscopic geotechnical material; s5, constructing a relationship of conversion from crushing to a friction unit of the mesoscopic elastic cementing unit under a stress condition; and S6, constructing a macro-microstructure cross-scale constitutive model. According to the method, the cross-scale constitutive model capable of reflecting the change of the mesoscopic components of the geotechnical material is constructed, and the macromechanical behavior of the rock sample and the deformation characteristics of the rock sample can be better predicted.

Description

Technical Field

[0001] The present invention relates to the technical field of geotechnical material mechanics, and in particular to a method for constructing and operating a cross-scale constitutive model of geotechnical materials based on microscopic mechanics. Background Art

[0002] Geotechnical materials are composite materials with variable material composition and complex structure. Their complex mechanical properties at the macroscopic level are a reflection of their mesostructure and even microscopic composition. The mesomechanics method can simultaneously consider the macroscopic homogeneity and fine and microscopic heterogeneity of continuous materials, and use "homogenization" as the basic concept to reasonably establish the relationship between macroscopic and fine and microscopic mechanical parameters. This method can not only effectively give the macroscopic properties of composite materials such as geotechnical materials, but also describe the local oscillations of the corresponding physical fields at the fine and microscopic scales. Based on the mesostructure and microscopic material composition of geotechnical materials, this method adopts the homogenization theory to establish a macro-meso-micro cross-scale constitutive model.

[0003] Based on the theoretical framework of rock and soil damage mechanics, Shen Zhujiang and Liu Enlong proposed that rock and soil materials can be regarded as heterogeneous materials containing two phases of microscopic materials. Each microscopic material has its own stress-strain relationship, and the macroscopic mechanical properties of the material are reflected by the mechanical behavior of the two phases and the characteristics of the joint stress and deformation (binary medium model). In this constitutive model, rock and soil materials are assumed to be composed of cementing units with cohesive force and friction units without structure. The two types of materials rely on cementation and friction effects to resist external loads respectively. Under the action of external loads, the cementing unit will break and transform into a friction unit when it reaches its own shear strength. Then, it continues to bear the external load and deform with the mechanical properties of the friction unit, and the macroscopic stress and deformation characteristics of the material are reflected by the joint action of the two. Among them, in order to establish the connection between macroscopic and microscopic parameters, the crushing rate is introduced to characterize the degree of clay mineral destruction and conversion to friction components, and the strain concentration coefficient is introduced to reflect the relationship between local strain and macroscopic strain. This method is based on the mechanical properties of geotechnical materials and better reflects the mechanical properties of the macroscopic body. However, the bonding unit and friction unit are both hypothetical items, and the corresponding mechanical properties are mainly determined by fitting the experimental test results, which fails to truly reflect the mechanical parameters and contributions of the microscopic substances of geotechnical materials. Summary of the invention

[0004] In order to solve the current technical problems, the main purpose of the present invention is to provide a method for constructing a cross-scale constitutive model of geotechnical materials based on mesomechanics. Based on the mesomechanics principle of composite materials and the theory of binary medium model, on the basis of describing geotechnical materials as binary mesostructures, the material composition and action mechanism of microscopic cementing materials and friction materials are further considered, and based on the mesostructural heterogeneity of materials and the similarity of microscopic composition, the MT method and the nonlinear homogenization method are respectively applied to construct a cross-scale constitutive model that can reflect the changes in the mesocomponents of geotechnical materials, so as to better predict the macroscopic mechanical behavior of rock samples, as well as the characteristics of strain hardening-volume shrinkage and post-peak strain softening-volume expansion of rock samples.

[0005] The technical solution adopted by the present invention is: a method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics, characterized in that it includes the following steps: S1. Consider that geomaterials are heterogeneous composite materials with mesostructure and different microcomponents; S2. Establish the linear elastic constitutive relation of the mesoscopic cementation unit of geotechnical materials based on the microscopic components of geotechnical materials; S3. Establish the elastic-plastic constitutive relationship of the meso-friction unit of geotechnical materials based on the micro-components of geotechnical materials; S4. Introduce the damage rate that characterizes the degree of transformation from mesoscopic cementation unit to friction unit, and construct the influence relationship between mesoscopic cementation unit and friction unit on the mechanical behavior of macroscopic geotechnical materials; S5. Construct the relationship between the transformation of the meso-elastic bonding unit into the friction unit under stress conditions; S6. Construct the mechanical relationship between microscopic local terms and microscopic average terms, so as to construct a macroscopic and microscopic cross-scale constitutive model.

[0006] The present invention has the following beneficial effects: 1. The constitutive model of the present invention is based on the principle of micromechanics of composite materials, and expands the original macro-micro binary medium model. On the basis of describing the geotechnical materials as binary microstructures, namely, bonding units and friction units, it further considers the material composition and action mechanism of microscopic bonding materials and friction materials, and based on the heterogeneity of the microstructures and similarity of the microstructures of the materials, the MT (Mori-Tanaka) method and the nonlinear homogenization method are respectively applied to solve the microscopic mechanical parameters of the bonding unit and the friction unit expressed by the microscopic components and mineral physical properties of the geotechnical materials.

[0007] 2. Based on the reasonable connection between the key mechanical characteristics of each component at the micro-meso and meso-macro scales, the present invention constructs a cross-scale constitutive model from micro to meso and then to macro. The newly proposed cross-scale constitutive model reflects the influence of different mineral compositions and porosities in rock samples and external loading conditions, such as confining pressure, on their macroscopic mechanical properties. In addition, compared with the experimental results, the model can well predict the deformation modulus and static strength of rock samples, and better capture the characteristics of strain hardening-volume shrinkage and post-peak strain softening-volume expansion of rock samples.

[0008] 3. The constitutive model of the present invention rationally utilizes the inherent physical parameters of the rock sample, such as the mineral composition, porosity and mechanical properties of mineral crystals. On the premise of effectively obtaining the macroscopic mechanical properties of the rock sample, the number of model parameters is greatly reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In order to more clearly illustrate the specific implementation of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation or the prior art description are briefly introduced below. Obviously, the drawings in the following description are some implementations of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative work: Figure 1 It is the representative characteristics of geotechnical materials at macro, micro and micro levels; Figure 2 It is the microscopic component of the cementing unit; Figure 3 It is the microscopic component of the cementing unit; Figure 4 It is a numerical calculation flow chart of the present invention; Figure 5 Comparison chart of calculated and tested stress-strain of rock samples with different microscopic components. DETAILED DESCRIPTION

[0010] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0011] Embodiment 1: The present invention provides a method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics, comprising the following steps: S1. Consider that geomaterials are heterogeneous composite materials with mesostructure and different microscopic components.

[0012] See also Figure 1In S1, the geotechnical material is regarded as a mesoscopic substance with cementing units and friction units. The cementing unit with cementing properties is elastic, and the friction unit with shear strength provided by friction is elastoplastic. The cementing unit is composed of clay matrix, solid particles and pores, and the friction unit is composed of pores, solid particles and broken clay particles.

[0013] S2. The linear elastic constitutive relationship of the mesoscopic bonding unit of geotechnical materials is established based on the microscopic components of geotechnical materials.

[0014] In S2, the micromechanical properties of each component in the cementing unit are considered, and the constitutive relationship of the cementing unit is expressed by the micromechanical parameters of each component using the homogenization theory.

[0015] First, each intact mesostructured unit is considered as a homogeneous unit with completely elastic properties, and its mechanical properties are described by the generalized Hooke's law. Figure 2 , the schematic diagram of the meso-cemented unit shows the three-phase material composition of the meso-unit at the microscopic scale. Among them, the clay matrix is ​​regarded as the matrix with cementation, and the pores and solid particles (detrital minerals) are two-phase inclusions embedded in the clay matrix.

[0016] Consider that the mesoscopic cementation unit is composed of , and The representative unit volume fraction (RVE) of the three-phase material composition is assumed to be ellipsoidal and randomly distributed, and the mesoscopic elastic mechanical properties can be obtained by the MT (Mori-Tanaka) method. Then, based on the Eshelby equivalent inclusion method and the conservation of energy at two scales, the Hill lemma is introduced to establish the relationship between the elastic stiffness tensors of the microscopic and mesoscopic components, thereby determining the bulk modulus and shear modulus of the mesoscopic cementation unit represented by the moduli and components of microscopic clay minerals, pores and detrital minerals.

[0017] Specifically, the steps of deriving the homogenization theory and using the micromechanical parameters of each component to express the constitutive relationship of the cementing unit are as follows: Each intact mesoscopic cementation unit is regarded as a homogeneous unit with completely elastic properties, and its mechanical properties are described by the generalized Hooke's law. The clay matrix is ​​regarded as a matrix with cementation, and the pores and solid particles are two-phase inclusions embedded in the clay matrix. It is assumed that the mesoscopic cementation unit is composed of , and The representative unit cell composed of three-phase material with volume fraction is assumed to be ellipsoidal and randomly distributed. The mesoscopic elastic mechanical properties are obtained by the Mori-Tanaka method. The boundary conditions The stress of the matrix and inclusions is obtained according to the volume contribution ratio, so: ; (1) Where: It represents the mechanical properties of the mesoscopic cementation unit; represents the volume fraction of solid particles; represents the stress tensor of the solid particle; represents the volume fraction of clay matrix; represents the stress tensor of the clay matrix; represents the volume fraction of pores; represents the stress tensor of the pore, =0; represents the boundary conditions; The elastic constitutive relations considering different components in the cemented unit are: ; ; (2) Where: , Indicates n The stress tensor of the term (n is the solid particles or clay matrix); , represents the strain tensor of the corresponding term; represents the stiffness matrix of the corresponding term; represents the corresponding flexibility matrix; where each element of the pore stiffness tensor is 0, and its flexibility tensor does not exist; When solid particles are introduced, the concentration factor changes accordingly. , and the pore-phase strain concentration factor After that, the strain relationship between the components is written as: ; (3) ; (4) Based on the Eshelby equivalent inclusion method, the above strain concentration factor is written as: ; (5) ; (6) In the formula, as well as They represent the Eshelby tensors of solid particles and pores, respectively, which are determined by the elastic properties of the matrix, the direction and shape of the inclusions; , represents the flexibility matrix of the clay matrix; , , represent the stiffness matrices of solid particles, clay matrix, and pores, respectively; , , represent the strain tensors of solid particles, clay matrix and pores, respectively; represents the stress tensor of the solid particle; represents the fourth-order unit tensor; For the convenience of calculation, the above stress, strain, stiffness and flexibility tensors are divided into spherical part and deviatoric part, which are described as follows: The isotropic elastic stiffness tensors of each component are: ; (7) Where: Indicates the corresponding phase' n '(n is the stiffness matrix of solid particles or clay matrix); as well as It is the corresponding phase n 'The bulk modulus and shear modulus; is the Kronecker symbol; is the fourth-order identity matrix; Spherical stress tensor Spherical strain tensor The scalar coefficient of ,in as well as , the deviatoric stress tensor Deviatoric strain tensor The scalar coefficient of ,in as well as Based on this, the above formula is written as the spherical part and the partial part, and simplified to: ; (8) In the formula, Indicates the corresponding phase' n '(n is the stiffness matrix of solid particles or clay matrix); as well as It is the corresponding phase n 'The bulk modulus and shear modulus; Similarly, the flexibility matrix is: ; (9) In the formula, Indicates the corresponding phase' n '(n is the flexibility matrix of the solid particles or clay matrix); as well as It is the corresponding phase n 'The bulk modulus and shear modulus; On the basis of the above simplified expressions, considering that the mesoscopic cementation unit is an infinite homogeneous medium composed of ellipsoids, the strain concentration tensor in formula (5) is rewritten in the form of spherical part and deviatoric part as follows: ; (10) Based on the Mori-Tanakat elastic inclusion theory, we have , In the formula n For solid particles gr or clay matrix What ; and are the parameters of pores, clay matrix and solid particles, , ,and Elastic medium, i.e. clay matrix What ; , are the bulk modulus and shear modulus of the clay matrix; Similarly, formula (6) is simplified to: ; (11) In the formula, is the strain concentration tensor of the pore; and is the corresponding parameter of pore; , are the bulk modulus and shear modulus of the clay matrix; Going back to formula (3), consider the hydrostatic pressure ( ) as the boundary condition, and substituting formula (10) into it, the volume strain of the solid particle is: ; (12) Axisymmetric shear stress ( ) boundary conditions, the generalized shear strain of solid particles is: ; (13) The generalized shear stress is , the generalized shear strain is ; , For the corresponding phase n '(n is the bulk modulus and shear modulus of the solid particles or clay matrix); and is the parameter of solid particle item; Similarly, based on formulas (4) and (11), the volume strain and generalized shear strain of the pore are: ; (14) ; (15) The generalized shear stress is , the generalized shear strain is ; , For the corresponding phase n '(n is the bulk modulus and shear modulus of the solid particles or clay matrix); and is the corresponding parameter of pore; Here, considering the conservation of energy on two scales and introducing the Hill lemma, we get the following results: ; (16) in, Indicates the corresponding phase' n '( n For solid particles gr or clay matrix What )’s flexibility matrix; as well as It is the corresponding phase n '( n For solid particles gr or clay matrix What )’s bulk modulus and shear modulus; Indicates the corresponding phase' n '( n For solid particles gr or clay matrix What )’s stiffness matrix; , is the boundary stress tensor; represents the fourth-order unit tensor; Therefore, the relationship between the elastic stiffness tensors of the micro and meso components is established as follows: ; (17) ; (18) in as well as It is the corresponding phase n '( n For solid particles gr or clay matrix What )’s bulk modulus and shear modulus; Corresponding phase' n '( n For solid particles gr、 Clay matrix What or pores you ) volume fraction; , Respectively represent the corresponding phase' n '( n For solid particles gr or clay matrix What )’s shear stress and spherical stress; , denote the shear stress and spherical stress tensor of the mesoscopic cementation unit, respectively; and are the bulk modulus and shear modulus of the mesoscopic cementation unit; Considering the local stress-strain relationship of solid particles , and substituting equation (3) into equation (1), the relationship between the clay matrix and the representative unit body stress is: ; (19) In the formula represents the stress tensor of the solid particle; , are the volume fractions of solid particles and clay matrix, respectively; represents the flexibility matrix of the clay matrix; represents the stiffness matrix of the solid particles; It represents the strain concentration factor of solid particles; , , represent the strain tensors of solid particles, clay matrix and pores, respectively; represents the fourth-order unit tensor; represents the stress tensor of the mesoscopic cementation unit; Using formulas (8), (9) and (10), the above tensor It can be written as: ; (20) In the formula 、 are the bulk moduli of the solid particles and the clay matrix, respectively; 、 are the shear moduli of solid particles and clay matrix, respectively; and are the corresponding parameters for clay matrix; 、 、 are the volume fractions of solid particles, clay matrix and pores in the mesoscopic cementation unit, respectively; Based on this, using equations (19) and (20), the strain of the solid particles in equations (12) and (13) is directly related to the boundary conditions of the representative unit cell and the mechanical properties of its internal microscopic components: ;(twenty one) (twenty two) In the formula 、 are the bulk moduli of the solid particles and the clay matrix, respectively; 、 are the shear moduli of solid particles and clay matrix, respectively; and are the corresponding parameters for clay matrix; 、 、 are the volume fractions of solid particles, clay matrix and pores in the mesoscopic cementation unit, respectively; , is the boundary shear stress and spherical stress of the mesoscopic cementation unit; , are the solid particle shear strain and spherical strain, respectively; Similarly, based on equations (19), (20), (14) and (15), the volume strain and generalized shear strain of the pore are: ;(twenty three) ;(twenty four) In the formula , is the corresponding parameter of pore; , are pore shear strain and spherical strain, respectively; Substituting the spherical component relations in equations (21) and (23) into equation (17), the bulk modulus of the mesoscopic cemented unit is simplified to It can be expressed as: ; (25) Similarly, substituting equations (22) and (24) into equation (18), the shear modulus of the bonded element is have: ; (26) In the formula 、 are the bulk moduli of the solid particles and the clay matrix, respectively; 、 are the shear moduli of solid particles and clay matrix, respectively; and are the corresponding parameters for clay matrix; , is the corresponding parameter of pore; 、 、 are the volume fractions of solid particles, clay matrix and pores in the mesoscopic cementation unit, respectively; , is the boundary shear stress and spherical stress of the mesoscopic cementation unit; , are the solid particle shear strain and spherical strain, respectively; , are pore shear strain and spherical strain, respectively; when or When is equal to 0, equations (25) and (26) degenerate into the two-phase solution of the Mori-Tanaka method.

[0018] Therefore, the linear elastic constitutive relation of the mesoscopic bonding unit of geotechnical materials based on the mechanical properties of the microscopic components of geotechnical materials is constructed.

[0019] S3. The elastic-plastic constitutive relationship of the micro-friction unit of geotechnical materials is established based on the micro-components of geotechnical materials.

[0020] When the bonding unit reaches its strength, it is transformed into a friction unit, which provides shear strength through friction and has elastic-plastic mechanical behavior.

[0021] See also Figure 3 , which gives the microscopic components of the friction unit, which consists of volume fractions The volume fraction of the broken clay particles is The solid particles (detrital minerals) and volume fraction are The total volume of the microscopic friction unit is .

[0022] The meso-friction unit is composed of a solid phase and pores. The solid phase includes broken clay particles and detrital minerals, and the pores are inclusions. A nonlinear homogenization method based on the modified secant modulus method is used here to obtain the elastic-plastic mechanical behavior of the friction unit. For the solid matrix, due to the significant difference in stiffness between clay particles and detrital minerals, the elastic properties of the solid phase are obtained using the MT method (with broken clay particles as the matrix). The yield function of the friction unit is determined using the strength criterion of porous friction geomaterials derived by Maghous. Considering the use of non-associated flow laws that reflect the mechanical properties of friction materials and the complementary consistency conditions of ideal elastic-plasticity, the elastic-plastic constitutive relationship of the meso-friction unit represented by the moduli and components of microscopic broken clay particles, pores and detrital minerals is established.

[0023] Specifically, the steps to establish the elastoplastic constitutive relation of the mesoscopic friction unit represented by the modulus and components of microscopic damaged clay particles, pores and debris minerals are as follows: Bulk modulus of the solid phase: ; Shear modulus: ,as well as: Relative volume fraction: ; In the formula , are the volume fractions of solid particles and broken clay particles in the mesoscopic friction unit, respectively; 、 are the bulk moduli of solid particles and microscopic broken clay particles, respectively; 、 are the shear moduli of solid particles and microscopic broken clay particles, respectively; , is the corresponding parameter of broken clay particles; The solid phase in the friction unit obeys the Drucker-Prager criterion: ; (27) Where: is the friction coefficient, is tensile stress; is the local stress field in the solid phase; the hydrostatic pressure is ; The generalized shear stress is ,and ; Compressive stress and compressive strain are positive; According to the strength criterion of porous friction geomaterials derived by Maghous, the yield criterion of the micro-friction unit is: ; (28) In the formula: superscript ' F ' represents the friction unit; the friction unit body stress , friction unit shear stress ,and ; Based on the linear description of the elastic behavior of the friction unit, the adopted tangent modulus is applicable to the above strength criterion. Based on this, the elastic incremental constitutive relation of the mesoscopic friction unit is: ; (29) ; (30) In the formula, as well as represent the tangent bulk modulus and tangent shear modulus of the friction element respectively; , are the elastic shear strain increment and elastic body strain increment of the micro-friction unit, respectively; , are the elastic shear stress increment and elastic body stress increment of the micro-friction unit, respectively; The Hashin-Shtrikman model is used to determine the elastic constants of isotropic mesoporous media. The elastic parameters of the meso friction unit are: ; (31) ; (32) In the formula is the volume fraction of pores in the mesoscopic friction unit; and are the bulk modulus and shear modulus of the solid equivalent; Back to the yield function in formula (28), in order to better reflect the deformation characteristics of the friction material, the non-associated flow law is adopted and the shear dilatancy coefficient is introduced After that, the plastic potential is expressed as: ; (33) in is the friction coefficient, is tensile stress; is the shear stress of the friction unit; is the body stress of the friction unit; if , the law of flow is related; List the elastic and plastic parts of the strain increment for a mesoscopic friction element separately: ; (34) ; (35) Where: and are the volume strain and generalized shear strain of the micro-friction unit, respectively; superscript ' F e 'as well as' F p 'represent the mechanical parameters of the elastic and plastic parts of the friction unit respectively; Based on the orthogonal law given by plastic flow, the plastic strain increment is: ; (36) ; (37) Where: is the plastic multiplier; is the yield function; is the plasticity function; is the shear stress of the friction unit; is the volume stress of the friction unit; Substituting the above two equations into equation (29) and equation (30), the elastic increment relationship is: ; (38) ; (39) In the formula, as well as represent the tangent bulk modulus and tangent shear modulus of the friction element respectively; , are the shear strain increment and elastic body strain increment of the micro-friction unit, respectively; , are the elastic shear stress increment and elastic body stress increment of the micro-friction unit, respectively; Supplementary consistency conditions considering perfect elastic-plasticity: , and substitute formulas (38) and (39) to obtain the plastic multiplier : ; (40) Where: ; (41) Therefore, the incremental stress-strain relationship in the friction element can be simplified as: ; (42) ; (43) Where: ; ; ; ; as well as: ; ; ; ; Where: represents the average stress increment of the friction element; are the modulus parameters of the friction unit body strain increment and shear strain increment contributing to the friction unit body stress increment; and are the modulus parameters of the friction unit volume strain increment and shear strain increment's contribution to the friction unit shear stress increment; represents the shear stress increment of the friction unit; as well as represent the tangent bulk modulus and tangent shear modulus of the friction element respectively; , are the shear strain increment and elastic body strain increment of the micro-friction unit, respectively; , are the elastic shear stress increment and elastic body stress of the mesoscopic friction unit, respectively; is the plastic multiplier; is the yield function; is the plasticity function; is the volume fraction of pores in the mesoscopic friction unit; is the friction coefficient, is tensile stress; Therefore, the linear elastic constitutive relation of the mesoscopic friction unit of geotechnical materials based on the mechanical properties of the microscopic components of geotechnical materials is constructed.

[0024] S4. The damage rate, which characterizes the degree of transformation from mesoscopic cementation unit to friction unit, is introduced to construct the influence relationship between mesoscopic cementation unit and friction unit on the mechanical behavior of macroscopic geotechnical materials.

[0025] In S4, since the breakage rate is an internal variable that characterizes the degree of fracture of the cementation unit, its evolution form is assumed to be related to the strength distribution of the meso-cementation unit; for the macro-representative unit body, the micro-minerals and pores in the meso-unit are distributed as a certain function, and the strength of the cementation unit also changes with the change of the spatial coordinates of the unit body. The strength distribution of the meso-homogeneous cementation unit is set to obey the Weibull distribution, and the influence relationship between the meso-cementation unit and the friction unit on the mechanical behavior of the macro-geotechnical material is constructed.

[0026] The steps of constructing the relationship between the influence of microscopic bonding unit and friction unit on the mechanical behavior of macroscopic geotechnical materials include: According to the binary medium concept, the macroscopic rock sample is composed of homogeneous cementation units and homogeneous friction units. The stress and strain of the macroscopic representative unit are expressed by the volume average of each microscopic component: ; (44) ; (45) Where: and denote the macroscopic stress and strain tensors, respectively, and is the stress-strain tensor of the homogeneous cemented unit; superscript ' F ' represents the parameters of the homogeneous friction unit; is the breakage rate; The damage rate characterizes the damage degree of the cemented unit in the macroscopic representative unit body, and it increases monotonically from 0 to 1 with the application of external load; Based on the above total stress-strain relationship from macroscopic to microscopic scale, the corresponding incremental expression is: ; (46) ; (47) Where: is the damage rate increment; the superscript '0' indicates the current state value of stress, strain and damage rate; Since the above composite materials are homogeneous in macroscopic terms, The term can be assumed to be The macroscopic stress increment disturbance caused by converting the volume fraction of cementing unit into friction unit can be similarly It is regarded as the strain increment disturbance value at the macro scale; Therefore, separating the microscopic and macroscopic terms in equations (46) and (47) yields: ; (48) ; (49) Where: and They represent the stress and strain tensors of the homogeneous mesoscopic friction unit in the current state respectively; and are the stress and strain tensors of the homogeneous cemented unit; and are the stress and strain increments of the homogeneous cemented unit; and are the stress and strain increments of the homogeneous friction element; and denote the macroscopic stress and strain increments, respectively; is the damage rate value in the current state, is the breakage rate increment; The macroscopic representative unit body without considering the stress and strain disturbance caused by the change of the breakage rate is defined as the macroscopic free body, and the stress and strain increments of the macroscopic free body are written as , , so the stress and strain increments of the macroscopic free body are: ; (50) ; (51) Based on this, the macro-micro stress-strain increment relationship is: ; (52) ; (53) In the formula and are the stress and strain increments of the homogeneous cemented unit; and are the stress and strain increments of the homogeneous friction element; is the damage rate value in the current state; is the breakage rate increment; In order to study the stress-strain relationship between cross-scale components under the condition of continuous transformation of mesoscopic components, a self-consistent method is used to solve it. Therefore, it is assumed that the mesoscopic components are sufficiently small ellipsoidal inclusions embedded in the equivalent medium, and the macroscopic equivalent medium is regarded as a matrix determined by the mechanical properties of the mesoscopic components and their mutual mechanical interaction relationship. Based on the extended SCS model suitable for elastic-plastic problems, under the approximate assumption that the tangent elastic-plastic modulus is isotropic, the incremental relationship is: ; (54) In the formula k represents the mesoscopic bonding unit or the mesoscopic friction unit, and Respectively represent units k The incremental values ​​of strain and stress tensors; and are the incremental values ​​of strain and stress of the macroscopic representative unit volume respectively; Characterize the tangent stiffness tensor of the macroscopic representative unit cell; is the constraint stiffness matrix, and its value is ; is the Eshelby tensor, which is determined by the tangent mechanical parameters of the macroscopic representative unit body. is a fourth-order unit tensor; Considering that the mesoscopic cementation unit and friction unit are small enough for the macroscopic representative unit (RVE), and they have similar ellipsoidal shapes and random orientations, the macroscopic representative unit (RVE) is divided into two phases: homogeneous cementation unit and homogeneous friction unit. Based on the mean field method, formula (54) can be simplified as follows: ; (55) ; (56) in: is the tangent stiffness tensor of the macroscopic free body, ; The constraint tensor has ; Above The Eshelby solution of the macroscopic representative unit cell is: ; (57) in: is the Kronecker symbol; and are the tangent bulk modulus and tangent shear modulus of the macroscopic free body, respectively; Introducing the strain concentration tensor of homogeneous bonding elements and friction elements and To express the incremental strain relationship between the two homogeneous phases and the macroscopic free body respectively: ; (58) ; (59) The local incremental constitutive relations of the homogeneous bonding unit and the friction unit are: ,as well as ; in as well as They represent the tangent stiffness tensors of the two homogeneous phases respectively; Substituting formulas (58) and (59) into formulas (55) and (56), respectively, the strain concentration tensor represented by the tangent stiffness tensor of each component is: ; (60) ; (61) In the formula , and denote the tangent stiffness tensors of the bonding unit, friction unit and macroscopic free body, respectively; is the constraint stiffness matrix of the macro free body; Substituting formulas (58), (59), (60) and (61) into formula (53), we can use and Eliminate the constraint tensor , we get the relationship between the macroscopic phase and the microscopic homogeneous phase tangent stiffness tensor: ; (62) Based on this, by solving formula (62) and formula (57) together, the elastic-plastic tangent stiffness tensor of the macroscopic free body can be obtained. Therefore, the stress-strain increment relationship of the macroscopic representative unit body considering the change of the damage rate is: ; (63) Therefore, the stress-strain increment relationship of the macroscopic representative unit body represented by the strain concentration tensor is as follows: ; (64) in , denote the tangent stiffness tensors of the bonding unit and the friction unit, respectively; is the Eshelby tensor; and denote the strain concentration tensors of the bonding element and the friction element respectively; and They represent the stress and strain tensors of the homogeneous mesoscopic friction unit in the current state respectively; and are the stress and strain tensors of the homogeneous cemented unit; and are the stress and strain increments of the homogeneous cemented unit; and are the stress and strain increments of the homogeneous friction element; and denote the macroscopic stress and strain increments, respectively; is the damage rate value in the current state, is the breakage rate increment; Therefore, the influence relationship between the microscopic bonding unit and the friction unit on the macroscopic mechanical behavior of geotechnical materials is constructed.

[0027] S5. Construct the relationship of transformation of micro-elastic bonding unit into friction unit under stress condition.

[0028] The evolution of the damage rate affects the incremental constitutive relation of the macroscopic representative unit (RVE). Since the damage rate is an internal variable that characterizes the degree of fracture of the cementation unit, its evolution is assumed to be related to the strength distribution of the mesoscopic cementation unit. For the macroscopic representative unit (RVE), the microscopic minerals and pores in the mesoscopic unit are distributed as a certain function, so the strength of the cementation unit also changes with the change of the spatial coordinates of the unit. In order to avoid repeated iterative calculations of the strength of the local mesoscopic cementation unit, we consider that the strength distribution of the mesoscopic homogeneous cementation unit follows the Weibull distribution.

[0029] Specifically, the probability density function of the breakage rate is: ; (65) Where: F is the distribution variable of mesoscopic strength; M and are the parameters of the Weibull distribution determined by the fitting method; Macroscopic irreversible plastic strain As an indicator for judging the degree of damage of cementing units, its state range is [ ], the increment of the breakage rate is: ; (66) Therefore, the total amount of breakage rate is in the form of: ; (67) Where: represents the total amount of breakage rate; F is the distribution variable of micro strength; M and are the parameters of the Weibull distribution determined by the fitting method; represents the macroscopic irreversible plastic strain; Thus, the relationship between the transformation of the micro-elastic bonding unit into the friction unit under stress conditions is constructed.

[0030] S6. Construct the mechanical relationship between the microscopic local terms and the microscopic average terms, thereby constructing a macroscopic and microscopic cross-scale constitutive model.

[0031] The mechanical relationship between the homogeneous bonding unit (composed of p mesoscopic bonding units) and the homogeneous friction unit (composed of q mesoscopic friction units) and the local mesoscopic bonding unit and the local mesoscopic friction unit is constructed.

[0032] The main idea of ​​the mesomechanics method to solve cross-scale problems is to grasp the key mechanical properties of different scales and establish reasonable connections between the mechanical properties. It does not focus on countless specific local coordinates, but starts from the perspective of "phase", studies the mechanical relationship between phases, and determines the macroscopic homogeneous mechanical properties of materials composed of different phases. This is also an important reason why this method can be applied to constitutive model research. The characteristics of the "phase" mainly consider that the material in the phase has uniform mechanical properties, or the homogeneous mechanical properties of the "phase" are obtained by the volume average of the mechanical properties of the local components.

[0033] Specifically, in S6, the steps of constructing the mechanical relationship between the mesoscopic local term and the mesoscopic average term include: The mechanical relationship between the average phase and the local phase is shown below: ; (68) ; (69) and are the stress and strain of the homogeneous cemented unit; and represents the stress and strain of the rth mesoscopic local cementation unit; and are the stress and strain increments of the homogeneous friction element; and represents the stress and strain of the i-th microscopic local bonding unit; p and q represent the number of local bonding units and friction units, respectively.

[0034] By using the mineral composition and pore distribution function obtained by micromechanical testing methods, the stress relationship of the microscopic local unit is: ; ; (70) ; ; (71) In the formula For the The volume fractions of solid particles, broken clay particles and pores in each friction unit; For the The volume fractions of solid particles, clay matrix and pores in a cementing unit, , is the phase in the micro-unit ”( For solid particles gr、 Broken clay particles What or pores you ), which is determined by the spatial coordinates of the mesoscopic unit.

[0035] It can be seen that the smaller the micro-component division (the larger p and q), the more specific the consideration of local mechanical properties, which also makes the calculation more complicated. Therefore, the patent of this invention adopts the most simplified method, that is, assuming p=q=1, to verify the model. In this way, the mechanical behavior of the rock sample can be verified based on the appropriate constitutive parameter value conditions by simply testing the mineral composition and average porosity of the entire macro-representative unit.

[0036] Using the rock samples with different micromechanical parameters in Table 1 and Table 2, set reasonable constitutive model parameters Table 3, using the above cross-scale constitutive model, according to the following numerical combination Figure 4 The method flow chart predicts the macroscopic mechanical properties of the rock samples and compares them with the test results.

[0037]

[0038]

[0039]

[0040] The macroscopic mechanical properties of rock samples with different micromechanical compositions were compared with the experimental results. Figure 5 . It can be found that the macroscopic mechanical performance of the rock samples is consistent with their microscopic mineral composition: the more high-hardness clastic minerals there are in the whole rock and the smaller the porosity, the greater the macroscopic deformation modulus and static strength of the rock sample; rock sample No. 3 has the highest content of clastic minerals, and its hardness and strength are also the greatest. In addition, by comparing the experimental data with the calculated curve, the model results can better describe the stress-deformation development trend of rock samples at different depths, and its stress-axial strain relationship and stress-lateral strain relationship have good correspondence, and the strength prediction of the model is also relatively accurate. At the same time, when the model parameters are relatively few, the model can still better reflect the characteristics of strain softening accompanied by rapid growth of lateral strain in the corresponding stage.

Claims

1. A method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics, characterized in that: The following steps are involved: S1. Consider that geomaterials are heterogeneous composite materials with mesostructure and different microcomponents; S2. Establish the linear elastic constitutive relation of the mesoscopic cementation unit of geotechnical materials based on the microscopic components of geotechnical materials; S3. Establish the elastic-plastic constitutive relationship of the meso-friction unit of geotechnical materials based on the micro-components of geotechnical materials; S4. Introduce the damage rate that characterizes the degree of transformation from mesoscopic cementation unit to friction unit, and construct the influence relationship between mesoscopic cementation unit and friction unit on the mechanical behavior of macroscopic geotechnical materials; S5. Construct the relationship between the transformation of the meso-elastic bonding unit from the crushing to the friction unit under stress conditions; S6. Construct the mechanical relationship between microscopic local terms and microscopic average terms, so as to construct a macroscopic and microscopic cross-scale constitutive model.

2. The method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics according to claim 1 is characterized in that: In S1, geotechnical materials are regarded as mesoscopic materials with cementing units and friction units. The cementing units with cementing properties are elastic, and the friction units with shear strength provided by friction are elastoplastic. The cementing units are composed of clay matrix, solid particles and pores, and the friction units are composed of pores, solid particles and broken clay particles.

3. The method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics according to claim 2 is characterized in that: In S2, the micromechanical properties of each component in the cementing unit are considered, and the constitutive relationship of the cementing unit is expressed by the micromechanical parameters of each component using the homogenization theory.

4. The method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics according to claim 3 is characterized in that: The steps to derive the constitutive relationship of the cemented unit using the micromechanical parameters of each component using the homogenization theory are as follows: Each intact mesoscopic cementation unit is regarded as a homogeneous unit with completely elastic properties, and its mechanical properties are described by the generalized Hooke's law. The clay matrix is ​​regarded as a matrix with cementation, and the pores and solid particles are two-phase inclusions embedded in the clay matrix. It is assumed that the mesoscopic cementation unit is composed of , and The representative unit body of the three-phase material composition with different volume fractions is assumed. The microscopic particles in the mesoscopic cementation unit are assumed to be ellipsoidal and randomly distributed. The mesoscopic elastic properties are obtained using the Mori-Tanaka method. Among them, the bulk modulus of the mesoscopic cementation unit is It is expressed as: ；（25） Shear modulus of the bonded element have: ;（26） Where: 、 are the bulk moduli of the solid particles and the clay matrix, respectively; 、 are the shear moduli of solid particles and clay matrix, respectively; and are the corresponding parameters for clay matrix; , is the corresponding parameter of pore; 、 、 are the volume fractions of solid particles, clay matrix and pores in the mesoscopic cementation unit, respectively; , is the boundary shear stress and spherical stress of the mesoscopic cementation unit; , are the solid particle shear strain and spherical strain respectively; , are pore shear strain and spherical strain, respectively; when or When is equal to 0, equations (25) and (26) degenerate into the two-phase solution of the Mori-Tanaka method; Therefore, the linear elastic constitutive relation of the mesoscopic bonding unit of geotechnical materials based on the mechanical properties of the microscopic components of geotechnical materials is constructed.

5. The method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics according to claim 1, characterized in that: In S3, the mesoscopic friction unit is composed of a solid phase and pores. The solid phase includes broken clay particles and debris minerals. The nonlinear homogenization method based on the modified secant modulus method is used to obtain the elastoplastic mechanical behavior of the friction unit. The elastic properties of the solid phase are obtained using the MT method. The yield function of the friction unit is determined using the strength criterion of Maghous' porous friction geomaterials. The non-associated flow law and the supplementary consistency condition of ideal elastic-plasticity are used to establish the elastoplastic constitutive relationship of the mesoscopic friction unit of geotechnical materials.

6. The method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics according to claim 5, characterized in that: The stress-strain relationship of the micro-friction unit of geotechnical materials is: ；(42) ； (43) Where: ； ； ； ； as well as: ； ； ； ； Where: represents the average stress increment of the friction element; are the modulus parameters of the friction unit body strain increment and shear strain increment contributing to the friction unit body stress increment; and are the modulus parameters of the friction unit volume strain increment and shear strain increment's contribution to the friction unit shear stress increment; represents the shear stress increment of the friction unit; as well as represent the tangent bulk modulus and tangent shear modulus of the friction element respectively; , are the shear strain increment and elastic body strain increment of the micro-friction unit, respectively; , are the elastic shear stress increment and elastic body stress of the micro-friction unit, respectively; is the plastic multiplier; is the yield function; is the plasticity function; is the volume fraction of pores in the mesoscopic friction unit; is the friction coefficient, is tensile stress; Therefore, the linear elastic constitutive relation of the mesoscopic friction unit of geotechnical materials based on the mechanical properties of the microscopic components of geotechnical materials is constructed.

7. The method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics according to claim 1, characterized in that: In S4, since the breakage rate is an internal variable that characterizes the degree of fracture of the cementation unit, its evolution form is assumed to be related to the strength distribution of the meso-cementation unit; for the macro-representative unit body, the micro-minerals and pores in the meso-unit are distributed as a certain function, and the strength of the cementation unit also changes with the change of the spatial coordinates of the unit body. The strength distribution of the meso-homogeneous cementation unit is set to obey the Weibull distribution, and the influence relationship between the meso-cementation unit and the friction unit on the mechanical behavior of the macro-geotechnical material is constructed.

8. The method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics according to claim 7, characterized in that: The stress-strain increment relationship of the macroscopic representative unit body is: ； (64) Where: and denote the macroscopic stress and strain increments, respectively; is the damage rate value in the current state; , denote the tangent stiffness tensors of the bonding unit and the friction unit, respectively; and denote the strain concentration tensors of the bonding element and the friction element respectively; is the breakage rate increment; and They represent the stress and strain tensors of the homogeneous mesoscopic friction unit in the current state respectively; and are the stress and strain tensors of the homogeneous cemented unit; Therefore, the influence relationship between the microscopic bonding unit and the friction unit on the macroscopic mechanical behavior of geotechnical materials is constructed.

9. The method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics according to claim 1, characterized in that: In S5, the relationship between the transformation of the meso-elastic cementation unit from the crushing to the friction unit under stress conditions is constructed, which includes the following steps: In order to avoid repeated iterative calculation of the strength of local mesoscopic cemented units, the strength distribution of mesoscopic homogeneous cemented units is considered to follow the Weibull distribution; Therefore, the probability density function of the breakage rate is: ；（65） Macroscopic irreversible plastic strain As an indicator for judging the degree of damage of cementing units, its state range is [ ], the increment of the breakage rate is: ；（66） Therefore, the total amount of breakage rate is in the form of: ；（67） Where: represents the total amount of breakage rate; F is the distribution variable of micro strength; M and are the parameters of the Weibull distribution determined by the fitting method; represents the macroscopic irreversible plastic strain; Thus, the relationship between the transformation of the micro-elastic bonding unit into the friction unit under stress conditions is constructed.

10. The method for constructing a cross-scale constitutive model of geotechnical materials based on micromechanics according to claim 1, characterized in that: In S6, the mechanical relationship between the mesoscopic local term and the mesoscopic average term is: ；（68） ；（69） and are the stress and strain of the homogeneous cemented unit; and represents the stress and strain of the rth mesoscopic local cementation unit; and are the stress and strain increments of the homogeneous friction element; and represents the stress and strain of the i-th microscopic local bonding unit; p and q represent the number of local bonding units and friction units, respectively.

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