1. A construction method of a structural plane shear constitutive model based on a disturbance state concept is characterized by comprising the following steps:

based on a disturbance state concept theory, defining a disturbance function DF, and establishing contribution of RI response and FA response relative to observation response; wherein the contribution of the FA response relative to the observed response is represented by DF, the contribution of the RI response relative to the observed response is represented by 1-DF, 0 ≦ DF ≦ 1; the RI response refers to the mechanical response of the material in the RI state, namely the initial response; the FA response refers to the material shear mechanical response in an FA state, namely critical response; the observation response refers to the observed shear mechanical response of the whole rock structure surface material;

combining the shear deformation constitutive relation of the typical structural plane to respectively obtain initial response and critical response;

characterizing a disturbance function DF through a shear test observed quantity, and establishing a structural surface shear deformation constitutive model based on a disturbance state concept;

determining DSC parameters in a structural surface shear deformation constitutive model based on a disturbance state concept;

and substituting the structural surface shearing test data into a structural surface shearing constitutive model based on the disturbance state concept, and verifying that the obtained structural surface shearing constitutive model can accurately simulate the result surface shearing deformation behavior.

2. The method for constructing the structural shear constitutive model based on the disturbance state concept according to claim 1, wherein the step of defining a disturbance function DF based on the disturbance state concept theory further comprises, before establishing contributions of RI response and FA response with respect to the observed response:

definition of the rock structural surface material as a whole consisting of an infinite number of rock units, wherein the total number of rock unitsL, → ∞, the area of the individual rock units being A₀The shear area a may be expressed as a-lA₀The number of the rock units in the RI state at any moment is m, the number of the rock units in the FA state is n, and l is m + n;

obtaining a mechanical equilibrium equation tau_RIA_RI+τ_FAA_FAWhere τ and A represent shear stress and corresponding shear area, τ_RIRefers to the shear stress to which the rock unit is subjected in the RI state, A_RIIs the total area of the rock unit in the RI state, τ_FARepresenting the shear stress to which the rock unit is subjected in the FA regime, A_FAIs the total area of the rock unit in the FA state;

obtaining the shearing area A and the total area A of the rock units in the RI state_RITotal area of rock units in FA regime

Will be provided withInto the mechanical equilibrium equationAnd simultaneously divided by lA₀Then, the shear stress τ is obtained:

obtaining a perturbation function

Will express the formulaAnd substituting the expression l as m + n into the expressionBecomes:

τ＝τ_RI(1-DF)+τ_FADF。

3. the method for constructing the structural surface shear constitutive model based on the disturbance state concept according to claim 1 or 2, wherein the step of obtaining the initial response and the critical response respectively by combining the typical structural surface shear deformation constitutive relation comprises the following specific operation processes:

combining the shear stress tau-shear displacement delta of the constitutive relation curve of the typical structural plane shear deformation to respectively obtain the initial response tau k_sDelta and critical response tau_rWherein k is_sDenoted as shear stiffness, τ_rReferred to as residual shear strength.

4. The method for constructing the structural surface shear constitutive model based on the disturbance state concept according to claim 2, wherein the step represents the disturbance function DF through macroscopic observation, and the method for constructing the structural surface shear deformation constitutive model based on the disturbance state concept comprises the following steps,

as the shear deformation process advances, the number of rock units changing from RI state to FA state also increases, and the number of rock units in FA state n is related to the shear displacement δ as follows:wherein r is a proportional parameter representing the growth rate of the rock unit;

will express the formulaDerived from both sides toThen, combine the equationsAndthe result is dDF/d delta is obtained,

to pairThe expression of the perturbation function DF obtained after integration is:wherein C1 and C2 areIntegration parameters generated during the integration process;

defining parametersWill express the formulaSubstituted into τ ═ k_sδ(1-DF)+τ_rObtaining a structural surface shear deformation constitutive model based on a disturbance state concept after DF (design definition)

Wherein k is_s、τ_rThe parameters are directly obtained by a shear test, and r and eta are DSC parameters.

5. The method for constructing the structural surface shear constitutive model based on the disturbance state concept according to claim 4, wherein the method comprises the following steps: the method for determining the DSC parameter in the structural surface shear deformation constitutive model based on the disturbance state concept comprises the following specific operations,

according to peak intensity point (delta)_p，τ_p) The corresponding relation of shear stress-shear displacement satisfies the equationAnd at the peak intensity point (δ)_p，τ_p) At a derivative of the shear stress τ with respect to the shear displacement δ of 0, the following formula is obtained:

after the two formulas are combined, the calculation formulas of DSC parameters eta and r in the structural surface shear deformation constitutive model based on the disturbance state concept are obtained:

6. the method for constructing the structural plane shear constitutive model based on the disturbance state concept according to claim 1 or 2, wherein the method for defining a disturbance function DF and establishing the contribution of RI response and FA response relative to an observed response based on the disturbance state concept theory comprises the following steps:

in the DSC theoretical framework, setting the deformed rock units as the combination of RI state rock units and FA state rock units;

and defining a disturbance function DF, and acquiring the contribution of the response of the RI state rock material unit and the response of the FA state rock material unit relative to the observed shear mechanical response of the whole rock structure surface material.

Background

The structural plane is inserted into the jointed rock mass in a longitudinal and transverse mode, and the bearing capacity, the deformation capacity and the stability of the structural plane are weaker than those of an integral rock mass, so that the deformation and the stability of the rock mass structure are controlled. The jointed rock mass may slip along the structural plane when subjected to external loads or severe changes in environments such as underground engineering excavation, earthquakes and the like. Therefore, the shear mechanical behavior of the structural surface has an important influence on the evaluation of the deformability and safety of rock-soil structures such as rock foundations, mines, tunnels and the like. A great deal of theoretical modeling and prediction research is carried out on the structural surface shear deformation failure mechanism. Goodman firstly establishes a rock structural surface model on the basis of a finite element method, and initiates the application of numerical simulation in structural surface modeling; considering the post-peak softening characteristic of the shear deformation of the structural surface, Simon establishes a CSDS (complete-displacement surface) constitutive model and simulates a full shear stress-shear displacement curve; considering the influence of the initial opening degree on the shearing mechanical property of the structural surface, and establishing a new shearing constitutive model which can be included in numerical software simulation; the PouyaandBommaniYazdi provides a new structural surface complete constitutive-plastic model for the elastoplastic deformation damage process of the rock structural surface; on the other hand, geotechnical engineering experts and engineers use the elastoplasticity theory to widely research the shearing property of the rock structural plane, and greatly improve the understanding of geological engineering workers on the shearing deformation behavior of the structural plane.

Although most of the constitutive models established above can simply describe the phase behavior of structural plane shear deformation, some drawbacks still exist. For example, some shear constitutive models ignore the non-linear deformation characteristic in the structural surface shearing process, and consider the shear deformation as linear deformation, which is greatly different from the actual situation; the parameters of some models have no physical and mechanical significance; some models are too complex and difficult to iterate in numerical calculation, so that the practicability of the constitutive model is reduced, and the popularization and the research of the constitutive model are not facilitated.

Perturbed state concept (DSC) theory was first introduced by FrantziskoninsandDesai^[1]The method is created, and a unique constitutive simulation method is provided for geological materials and interfaces. The method explains the nonlinear behavior of the geological material deformation process from a microscopic angle, and aims to relate the mechanical response of a mesoscopic unit with the macroscopic constitutive relation^2]The research on the failure mechanism and constitutive relation of geological materials from the perspective of Disturbance State Concept (DSC) has become a research hotspot in recent years by combining the erection of a bridge^[3，4]。

[1]Frantziskonis G,Desai CS.Elastoplastic model with damage for strain softening geomaterials.Acta Mechanica.1987；68:151-70.

[2]Sane SM,Desai CS,Jenson JW,Contractor DN,Carlson AE,Clark PU. Disturbed State constitutive modeling of two Pleistocene tills.Quaternary Science Reviews.2008；27:267-83.

[3]Xiao Y,Desai CS.Constitutive Modeling for Overconsolidated Clays Based on Disturbed State Concept.I:Theory.International Journal Of Geomechanics. 2019；19:18.

[4]Fan R-D,Liu M,Du Y-J,Horpibulsuk S.Estimating the compression behaviour of metal-rich clays via a Disturbed State Concept(DSC)model.Applied Clay Science.2016；132-133:50-8.

Disclosure of Invention

Based on the above, the invention aims to provide a construction method of a structural plane shearing constitutive model based on a disturbance state concept, which adopts a disturbance state concept theory to establish a joint shearing constitutive model, simulates the nonlinear characteristics of each shearing deformation stage, and improves the practicability of the model.

In order to solve the technical problems, the invention adopts the following technical scheme:

the invention provides a construction method of a structural plane shear constitutive model based on a disturbance state concept, which comprises the following steps:

based on a disturbance state concept theory, defining a disturbance function DF, and establishing contribution of RI response and FA response relative to observation response; wherein the contribution of the FA response relative to the observed response is represented by DF, the contribution of the RI response relative to the observed response is represented by 1-DF, 0 ≦ DF ≦ 1; the RI response refers to the mechanical response of the material in the RI state, namely the initial response; the FA response refers to the material shear mechanical response in an FA state, namely critical response; the observation response refers to the observed shear mechanical response of the whole rock structure surface material;

combining the shear deformation constitutive relation of the typical structural plane to respectively obtain initial response and critical response;

characterizing a disturbance function DF through a shear test observed quantity, and establishing a structural surface shear deformation constitutive model based on a disturbance state concept;

determining DSC parameters in a structural surface shear deformation constitutive model based on a disturbance state concept;

and substituting the structural surface shearing test data into a structural surface shearing constitutive model based on the disturbance state concept, and verifying that the obtained structural surface shearing constitutive model can accurately simulate the result surface shearing deformation behavior.

In one embodiment, before the step of defining the disturbance function DF based on the concept theory of disturbance state and establishing the contribution of RI response and FA response with respect to the observed response, the step further includes:

definition of rock structural surface material is composed of an infinite number of rock units in its entirety, wherein the total number of rock units is l, l → ∞, and the area of a single rock unit is A₀The shear area a may be expressed as a-lA₀The number of rock units in the RI state at any time is m,the number of rock units in an FA state is n, and l is m + n;

obtaining a mechanical equilibrium equation tau_RIA_RI+τ_FAA_FAWhere τ and A represent shear stress and corresponding shear area, τ_RIRefers to the shear stress to which the rock unit is subjected in the RI state, A_RIIs the total area of the rock unit in the RI state, τ_FARepresenting the shear stress to which the rock unit is subjected in the FA regime, A_FAIs the total area of the rock unit in the FA state;

obtaining the shearing area A and the total area A of the rock units in the RI state_RITotal area A of rock units in FA regime_FA：

Will be provided withSubstituted into the mechanical equilibrium equation τ a ═ τ_RIA_RI+τ_FAA_FAAnd simultaneously divided by lA₀Then, the shear stress τ is obtained:

obtaining a perturbation function

Will express the formulaAnd substituting the expression l as m + n into the expressionIn (d), the expression of shear stress τ becomes:

τ＝τ_RI(1-DF)+τ_FADF。

in one embodiment, the step of obtaining the initial response and the critical response respectively by combining the shear deformation constitutive relation of the typical structural plane includes:

combining the shear stress tau-shear displacement delta of the constitutive relation curve of the typical structural plane shear deformation to respectively obtain the initial response tau k_sDelta and critical response tau_rWherein k is_sDenoted as shear stiffness, τ_rReferred to as residual shear strength.

In one embodiment, the steps characterize the disturbance function DF through macroscopic observation, and the method for establishing the structural surface shear deformation constitutive model based on the disturbance state concept comprises the following steps,

as the shear deformation process advances, such as the shear displacement δ increases, the number of rock units that change from RI state to FA state also increases, and the number of rock units in FA state n is related to the shear displacement δ as follows:wherein r is a proportional parameter representing the growth rate of the rock unit;

will express the formulaDerived from both sides toThen, combine the equationsAndthe result is dDF/d delta is obtained,

to pairThe expression of the perturbation function DF obtained after integration is:wherein C1 and C2 areIntegration parameters generated during the integration process;

defining parametersWill express the formulaSubstituted into τ ═ k_sδ(1-DF)+τ_rObtaining a structural surface shear deformation constitutive model based on a disturbance state concept after DF (design definition)

Wherein k is_s、τ_rThe parameters are directly obtained by a shear test, and r and eta are DSC parameters.

In one embodiment, the method for determining the DSC parameter in the structural plane shear deformation constitutive model based on the disturbance state concept comprises the following specific operations,

according to peak intensity point (delta)_p，τ_p) The corresponding relation of shear stress-shear displacement satisfies the equationAnd at the peak intensity point (δ)_p，τ_p) At a derivative of the shear stress τ with respect to the shear displacement δ of 0, the following formula is obtained:

after the two formulas are combined, the calculation formulas of DSC parameters eta and r in the structural surface shear deformation constitutive model based on the disturbance state concept are obtained:

in one embodiment, the method for defining a disturbance function DF and establishing the contribution of RI response and FA response with respect to an observed response based on the disturbance state concept theory includes the following steps:

in the DSC theoretical framework, setting the deformed rock units as the combination of RI state rock units and FA state rock units;

and defining a disturbance function DF, and acquiring the contribution of the response of the RI state rock material unit and the response of the FA state rock material unit relative to the observed shear mechanical response of the whole rock structure surface material.

In summary, the construction method of the structural surface shearing constitutive model based on the disturbance state concept provided by the invention adopts the disturbance state concept theory to establish the joint shearing constitutive model, so that the nonlinear characteristics of each shearing deformation stage are simulated, and the practicability of the model is improved.

Drawings

Fig. 1 is a schematic flow chart of a method for constructing a structural plane shear constitutive model based on a disturbance state concept according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a rock structural plane shearing process under the concept of a disturbance state provided by an embodiment of the invention;

FIG. 3 is a schematic diagram of a structural plane shear mechanical response curve provided by an embodiment of the present invention;

FIG. 4 is a graph comparing a constitutive model curve provided by an embodiment of the invention with shear test data based on a quartzite structural plane;

FIG. 5 is a graph comparing the constitutive model curve provided by the embodiment of the present invention with shear test data of four structural planes;

FIG. 6 is a graph comparing the constitutive model curve provided by the embodiment of the present invention with shear test data of four other structural planes.

Detailed Description

For further understanding of the features and technical means of the present invention, as well as the specific objects and functions attained by the present invention, the present invention will be described in further detail with reference to the accompanying drawings and detailed description.

Fig. 1 is a schematic flow chart of a first method for constructing a structural plane shear constitutive model based on a disturbance state concept, which is provided in an embodiment of the present invention, and as shown in fig. 1, the method for constructing a structural plane shear constitutive model based on a disturbance state concept specifically includes the following steps:

step S1, defining a disturbance function DF based on the disturbance state concept theory, and establishing the contribution of RI response and FA response relative to the observation response; wherein the contribution of the FA response relative to the observed response is represented by DF, the contribution of the RI response relative to the observed response is represented by 1-DF, 0 ≦ DF ≦ 1; RI response refers to a material shear mechanical response in the RI state (relatively intact state), i.e. an initial response; the FA response is designated as a material shear mechanical response in an FA state (a fully adjusted state), namely a critical response; the observed response refers to the observed shear mechanical response of the whole rock structural surface material.

The step S1, based on the disturbance state concept theory, is a method for defining a disturbance function DF and establishing contributions of RI response and FA response with respect to an observed response, and includes the following steps:

step S11, in the DSC theoretical framework, setting the deformed rock units as the combination of RI state rock units and FA state rock units;

step S12, defining a disturbance function DF, and acquiring the contribution of the response of the RI state rock material unit and the response of the FA state rock material unit relative to the observed shear mechanical response of the whole rock structure surface material; after the tangential load of the structural surface is applied, the observed shear mechanical response of the whole rock structural surface material comprises the response of RI state rock material units and/or the response of FA state rock material units, the contribution of the response of the FA state rock material units relative to the observed shear mechanical response of the whole rock structural surface material is DF, and the contribution of the response of the RI state rock material units relative to the observed shear mechanical response of the whole rock structural surface material is 1-DF.

Referring to fig. 2, in one embodiment, before the step S1 of defining the disturbance function DF based on the concept theory of disturbance state and establishing the contribution of RI response and FA response relative to the observed response, the method further includes

Step S1-1, defining that the rock structural surface material is entirely composed of an infinite number of rock units, wherein the total number of the rock units is l, l → ∞, and the area of a single rock unit is A₀The shear area a may be expressed as a-lA₀The number of rock units in the RI state at any time is m, the number of rock units in the FA state is n, and l is m + n.

Step S1-2, obtaining the mechanical equilibrium equation τ a ═ τ_RIA_RI+τ_FAA_FAWhere τ and A represent shear stress and corresponding shear area, τ_RIRefers to the shear stress to which the rock unit is subjected in the RI state, A_RIIs the total area of the rock unit in the RI state, τ_FARepresenting the shear stress to which the rock unit is subjected in the FA regime, A_FAIs the total area of the rock unit in the FA state; the application of external forces (both normal and shear directions) at various stages of the overall process of rock structural face shear failure is a quasi-static process. Therefore, the shear direction along the rock structural surface should be in a quasi-equilibrium force state, and the mechanical equilibrium of the shear stress loading direction is considered, so that the mechanical equilibrium equation tau A is obtained_RIA_RI+τ_FAA_FA。

Before the shearing process occurs, all rock units are in an RI state; in the whole shearing process of the whole rock structural surface material, under the shearing action, the rock units turning from the RI state to the FA state are gradually increased, and the process is quick and irreversible; when the shearing process enters the residual stage, all rock units enter the FA state.

Step S1-3, obtaining the shearing area A and the total area A of the rock units in the RI state_RITotal area A of rock units in FA regime_FA：

Step S1-4, step S1-3The mechanical balance equation τ a ═ τ r substituted into step S1-2_RIA_RI+τ_FAA_FAAnd simultaneously divided by lA₀Then, an expression of the shear stress τ is obtained:

step S1-5, obtaining a disturbance functionThe number of rock units in the FA state and the rate of increase thereof characterize the degree of destruction of the rock material from another point of view, which is known in the art and need not be described in detail herein, and therefore the disturbance function DF is represented by the ratio of the number n of rock units in the FA state to the total number l of rock units.

Step S1-6, expression of step S1-5And substituting the expression l ═ m + n of step S1-1 into the expression of step S1-4In step S1-4, the expression of the shear stress τ becomes:

τ＝τ_RI(1-DF)+τ_FADF。

and step S2, combining the shear deformation constitutive relation of the typical structural plane to respectively obtain an initial response and a critical response.

Referring to fig. 3, the step S2, the method for obtaining the initial response and the critical response respectively by combining the shear deformation constitutive relation of the typical structural plane, includes the following specific operations:

combining the shear stress tau-shear displacement delta of the constitutive relation curve of the typical structural plane shear deformation to respectively obtain the initial response tau k_sDelta and critical response tau_rWherein k is_sDenoted as shear stiffness, τ_rReferred to as residual shear strength.

The constitutive curve tau-delta and the mechanical response of rock structural surface materials in the whole shearing process of a typical structural surface can be divided into 4 stages, specifically a quasi-elastic stage (oa region), a pre-peak nonlinear stage (ab region), a post-peak softening stage (bc region) and a residual strength stage (cd region); the RI response represents a quasi-elastic stage, and at the moment, the shear stress tau and the shear displacement delta are approximately in a linear elastic relationship; the FA response represents the residual intensity phase, and the shear stress tau has reached a stable value called the residual shear intensity tau_r(ii) a The shear mechanical response observed in the structural plane shear test is the reaction of RI response and FA response, in the quasi-elastic stage, the disturbance is small and is approximately no disturbance, the rock units can be approximately considered to be in RI state, namely n is 0, in steps 1-5And τ ═ τ in steps 1 to 6_RI(1-DF)+τ_FAThe disturbance function DF of DF is 0, when the deformation characteristics of RI-state rock units are approximately in the quasi-elastic phase, and therefore, from the equation τ_RI(1-DF)+τ_FADF may be derived as the expression τ ═ τ_RI＝k_sδ, where k_sThe index is shear stiffness, and is expressed by the slope of a constitutive model curve tau-delta in the shearing overall process of a typical structural plane in a quasi-elastic stage; when the disturbance reaches the complete disturbance stage, the equation τ is τ_RI(1-DF)+τ_FADF is equal to 1, and all shear mechanical responses in fig. 3 are FA responses, i.e. shear stress enters the residual intensity stage, so from the equation τ_RI(1-DF)+τ_FADF may be derived as the expression τ ═ τ_FA＝τ_r。

Specifically, the shear constitutive relation of the typical structural plane is further described in four stages:

(1) quasi-elastic phase (oa region shown in fig. 3); when the shearing just occurs (starting point o), the deformation of the structural surface microprotrusions is insignificant within a small shearing displacement range. At this stage, the shear constitutive curve τ - δ is approximately linear in shape, where the slope of the τ - δ curve is the shear stiffness k_s. In this process, the number of rock units transitioning from the RI state to the FA state is small, and therefore all rock units are considered to be in a "relatively intact" state (RI);

(2) the pre-peak non-linear phase (ab region shown in fig. 3), where the non-linear nature of the structural plane shear deformation begins to be significant. As the shear displacement δ increases, the shear stress exhibits a non-linear increase compared to the previous stage (oa region), and the rate of increase is significantly slower than in the previous stage (oa region). At this time, the number of rock units converted into the "fully adjusted" state (FA) is greatly increased;

(3) post-peak softening phase (bc region shown in fig. 3). At this stage, the shear stress τ decreases sharply with an increase in the shear displacement δ, and the asperities of the structured surface are largely destroyed. The number of rock units in the "fully adjusted" state (FA) is greatly increased;

(4) residual intensity phase (cd region shown in fig. 3). At this stage, the shear stress hardly changes as the shear displacement δ increases. The rock face loses its bonding force completely. All rough surfaces are worn and only a stable residual friction remains, i.e. the residual shear strength τ_r. The rock units are almost in the "fully adjusted" state (FA).

And S3, representing the disturbance function DF through the observed quantity of the shear test, and establishing a structural surface shear deformation constitutive model based on the disturbance state concept.

Specifically, the step S3 is a method for establishing a structural surface shear deformation constitutive model based on a disturbance state concept by characterizing a disturbance function DF through a shear test observed quantity, and includes the following steps:

step S3-1, as the shear deformation process advances, such as the shear displacement δ increases, the number of rock units in the RI state to the FA state also increases, and the relationship between the number of rock units in the FA state n and the shear displacement δ at a certain shear displacement δ is as follows:

where r is a proportional parameter representing the rate of growth of the rock unit.

Step S3-2, expression in step S3-1Derived from both sides toThen, combine the equationsAndthe result is dDF/d delta is obtained,

the method is a known technology, and is applied to rock mechanics to obtain a proper disturbance function DF to describe the relation dDF/d delta between disturbance and the shearing characteristic of a rock structural surface.

Step S3-3, pairThe expression of the perturbation function DF obtained after integration is:

wherein C1 and C2 areThe integration parameters generated during the integration process.

Step S3-4, defining parametersExpression in step S3-3Substituted into τ ═ k_sδ(1-DF)+τ_rObtaining a structural surface shear deformation constitutive model based on a disturbance state concept after DF (design definition)

Wherein k is_s、τ_rThe parameters are shear mechanical parameters which can be directly obtained through a shear test; r and eta are DSC parameters.

As shown in table 1, comparing the structural surface shear deformation constitutive model based on the disturbance state concept with the rest models, empirical models and the like established based on the elasto-plastic theory, the structural surface shear deformation constitutive model based on the disturbance state concept has the advantages of simple form, less model parameters, easy solution and physical significance.

TABLE 1 common shear constitutive model and its characteristics

Step S4, determining DSC parameters r and eta in the structural surface shear deformation constitutive model based on the disturbance state concept; wherein the peak intensity point (delta) of shear deformation is determined according to the structural plane_p，τ_p) And acquiring DSC parameters r and eta of the structural surface shear deformation constitutive model based on the disturbance state concept.

Referring to fig. 3, in detail, the step S4 of determining the DSC parameters r and η in the structural shear deformation constitutive model based on the perturbation state concept includes the following specific operations:

according to peak intensity point (delta)_p，τ_p) The corresponding relation of shear stress-shear displacement satisfies the equationAnd at the peak intensity point (δ)_p，τ_p) At a derivative of the shear stress τ with respect to the shear displacement δ of 0, the following formula is obtained:

after the two formulas are combined, the calculation formulas of DSC parameters eta and r in the structural surface shear deformation constitutive model based on the disturbance state concept are obtained:

and step S5, substituting the structural surface shearing test data into a structural surface shearing constitutive model based on the disturbance state concept, verifying that the obtained structural surface shearing constitutive model can accurately simulate the shearing deformation behavior of the result surface, and can fully reflect the shearing deformation characteristics of each stage in the shearing process.

Specifically, step S5 is to substitute the structural plane shear test data into the structural plane shear constitutive model based on the disturbance state concept, and verify that the obtained structural plane shear constitutive model can accurately simulate the result plane shear deformation behavior and can sufficiently reflect the shear deformation characteristics of each phase of the shearing process, and the specific steps include:

shear test data verification based on quartzite structural plane

In order to compare the shearing characteristic difference between the real natural rock structural surface and the replica thereof, the SinghandBasu carries out a shearing test with the normal stress of 0.22-0.71 MPa on the quartzite structural surface for many times.

This verification uses the positive stress sigma_n0.23MPa and σ_nFor example, a structural plane shear deformation constitutive model based on the perturbation state concept was verified in detail in test data of 0.44 MPa. Sigma_n0.23MPa and σ_nThe test data of 0.44MPa is shown in table 2.

TABLE 2 SinghandBasu shear test results

σn(MPa)	ks(MPa/mm)	τp(MPa)	δp(mm)	τr(MPa)
					0.23	0.237	0.34	1.50	0.208
0.44	0.279	0.55	2.00	0.418

All test parameters in Table 2, such as the peak shear stress τ, are set_pPeak shear displacement delta_pEqual substitution into equationThe parameters r and η obtained are as follows:

the shear test results in Table 2 and the calculated model parameters r and η are respectively substituted into the equationThe final structural surface shear deformation constitutive model expression based on the disturbance state concept is obtained as follows:

referring to fig. 4, fig. 4 is a schematic diagram illustrating a shear deformation curve calculated by a structural plane shear constitutive model based on a disturbance state concept and an actual shear deformation result. The actual shearing constitutive relation is well matched with a structural plane shearing constitutive model prediction curve based on a disturbance state concept. From the results, the two have considerable agreement, wherein the correlation coefficient R²0.901 and 0.959 respectively, the structural plane shear constitutive model based on the disturbance state concept can fully simulate the linear and nonlinear behaviors in the structural plane shear deformation.

Direct shear test data verification of four natural structural surfaces and artificial structural surfaces

In order to visually and conveniently verify the adaptability and the rationality of the proposed structural surface shear constitutive model based on the disturbance state concept, shear tests of 8 different types of natural structural surfaces and artificial structural surfaces are taken as an example for verification. The experimental data for these selected natural and artificial structural surfaces are shown in table 3.

Table 3 four natural structural surface and artificial structural surface test data and structural surface shear constitutive model based on disturbance state concept

Such as equationShown in the table 3, structural plane shearing constitutive model parameters, constitutive model expressions and correlation coefficients R based on disturbance state concepts corresponding to the test data are calculated respectively²And the like. The constitutive relation (tau-delta) curves of the model curves and the test results are compared as shown in FIGS. 5-6. From the comparison results of fig. 5-6, it can be seen that although there are some slight differences between the model curve and the test data, the model curve can sufficiently reflect the shear deformation characteristics of each stage presented by the test data. Correlation coefficient R of FIGS. 5 to 6²Are all larger than 0.88, and the model is proved to have good description.

In conclusion, compared with the existing shearing constitutive model, the structural surface shearing deformation constitutive model based on the disturbance state concept has the advantages that the model formula is simple, the parameters are easy to solve, the clear physical significance is realized, the model curve expression is well matched with the structural surface test data, the established model is reasonable, and the practicability of the model is improved.

The above examples are merely illustrative of several embodiments of the present invention, and the description thereof is more specific and detailed, but not to be construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.