A method for analyzing the surrounding rock deformation law based on the property of elastic modulus reduction

Abstract

The present invention belongs to the field of analysis of surrounding rock deformation laws, and discloses a method for analyzing surrounding rock deformation laws based on the property of elastic modulus degradation, including: obtaining data on influencing factors for the post-peak degradation of the elastic modulus of rock samples, and constructing a non-linear degradation model of rock elastic modulus based on the influencing factors; constructing an excavation model for strain-softening surrounding rock, and analyzing the excavation model for strain-softening surrounding rock based on the non-linear degradation model of rock elastic modulus and the finite difference method to obtain stress-strain field data for deep-buried tunnel strain-softening surrounding rock, and obtaining displacement field data based on the stress-strain field data; and performing combined analysis on the stress-strain field data and the displacement field data to obtain surrounding rock deformation law data. The technical solution of the present invention can effectively reflect the degradation process of the elastic modulus under the influence of confining pressure and plastic strain, and obtain surrounding rock deformation laws that conform to the actual situation.

Description

Technical Field

[0001] The present invention belongs to the field of analysis of surrounding rock deformation laws, and particularly relates to a method for analyzing surrounding rock deformation laws based on the property of elastic modulus degradation. Background Art

[0002] Surrounding rock of deep-buried tunnels is often in special occurrence environments such as high in-situ stress, high pore water pressure, and high geothermal temperature. After excavation, large deformations are likely to occur. Excessive surrounding rock deformation will lead to continuous expansion of the loosening zone of the surrounding rock, trigger continuous release of strain energy, cause the load borne by the support structure to gradually increase, and may ultimately exceed the design reserve value of the support strength, resulting in deformation, cracking, and even instability failure of the structure.

[0003] The elastic modulus of the surrounding rock is an important mechanical parameter affecting the deformation degree of the surrounding rock after the excavation of the cavern. It is very necessary to accurately obtain the elastic modulus of the surrounding rock. Common methods for determining the elastic modulus of the surrounding rock include empirical method, test method, numerical simulation method, etc. In general design, the empirical method of engineering analogy is adopted, and the value range of the elastic modulus of each level of surrounding rock is given according to the engineering surrounding rock classification standard, without considering the influence of tunnel excavation disturbance on the elastic modulus of the surrounding rock. At present, in the theoretical analysis and numerical calculation studies of deep-buried tunnels, most are based on the elastoplastic strain-softening model that conforms to the post-peak strength degradation characteristics of the surrounding rock. For example, Bian Kang considered the softening and dilatancy characteristics of the surrounding rock and the corresponding relationship of the principal stresses under different working conditions, and deduced the elastoplastic analytical solution of a circular cavern under the condition of two-way unequal pressure; Lee and Wang stratified the plastic region of the surrounding rock according to the principle of equal radial stress increment, and used the finite difference method to iteratively calculate the numerical solution of the displacement of the circular cavern.

[0004] In the above methods, the elastic modulus of the surrounding rock is regarded as a constant value during the analytical derivation process. However, when analyzing the deterioration effect of the surrounding rock quality through wave velocity tests, it is found that the elastic modulus of the surrounding rock in the excavation disturbance area decreases significantly. Therefore, some scholars have introduced the consideration of the elastic modulus degradation characteristics in the theoretical analysis of deep-buried tunnels. Han et al., Jiang Quan, and Feng Xiating assumed that the elastic modulus of the surrounding rock linearly degrades with the growth of plastic shear strain in the plastic softening region and remains constant in the plastic residual region. Brown believes that the elastic modulus of the surrounding rock can be determined by the confining pressure or the minimum principal stress, and proposed a complex stress-dependent elastic modulus model (PDM). Nawrocki then obtained a simplified depth-dependent elastic modulus model based on the PDM model, and gave the composite function solution of the variation of the elastic modulus in the plastic region of the surrounding rock along the depth direction. These methods give more reasonable calculation results of surrounding rock deformation, but the above elastic modulus degradation process is mainly based on simple linear assumptions, and how this process changes nonlinearly and is affected by which factors remain to be further studied. Summary of the Invention

[0005] The object of the present invention is to provide a method for analyzing the surrounding rock deformation law based on the property of elastic modulus decay to solve the problems existing in the above-mentioned prior art. To achieve the above object, the present invention provides a method for analyzing the surrounding rock deformation law based on the property of elastic modulus decay, including:

[0006] Obtain the influencing factor data of the post-peak decay of the elastic modulus of the rock sample, and construct a non-linear decay model of the rock elastic modulus based on the influencing factors; construct an excavation model of strain-softening surrounding rock, and analyze the excavation model of strain-softening surrounding rock based on the non-linear decay model of the rock elastic modulus and the finite difference method to obtain the stress-strain field data of the strain-softening surrounding rock of the deep-buried tunnel, and obtain the displacement field data based on the stress-strain field data; perform combined analysis on the stress-strain field data and the displacement field data to obtain the surrounding rock deformation law data.

[0007] Optionally, the influencing factor data of the post-peak decay of the elastic modulus of the rock sample include: the plastic strain of the rock sample and the confining pressure applied to the rock sample.

[0008] Optionally, the process of constructing the non-linear decay model of the rock elastic modulus includes: analyzing the variation law of the elastic modulus E of the rock sample with the axial plastic strain under the same confining pressure condition to obtain the non-linear relationship between the elastic modulus E and the axial plastic strain, and separately fitting the non-linear relationship between the elastic modulus E and the axial plastic strain to complete the construction of the non-linear decay model of the rock elastic modulus; The non-linear relationship between the elastic modulus E and the axial plastic strain is analyzed to obtain the non-linear relationship between the elastic modulus E and the axial plastic strain , and the non-linear relationship between the elastic modulus E and the axial plastic strain

[0009] is separately fitted to complete the construction of the non-linear decay model of the rock elastic modulus; The calculation formula for separately fitting the non-linear relationship between the elastic modulus E and the axial plastic strain

[0010]

[0011] b = b1 + b2exp(-b3·σ3)

[0012]

[0013] In the formula: λ, b, and c are all function fitting coefficients, λ i , b i , c i (i = 1, 2, 3) are all fitting coefficients, is the axial plastic strain of the rock sample at the unloading point, σ3 is the confining pressure, the λ3 in refers to the λ3 power of σ3,

[0014] Optionally, the process of constructing the strain-softening surrounding rock excavation model includes: obtaining the mechanical characteristic data of circular tunnel excavation, constructing a circular tunnel excavation model based on the mechanical characteristics of circular tunnel excavation, and constructing a strain-softening surrounding rock excavation model based on the circular tunnel excavation model and in combination with the Hoek-Brown yield criterion;

[0015] Among them, the mechanical characteristic data of circular tunnel excavation include: the uniform stress σ0 acting at infinity in the cross-section, and the support pressure p on the inner wall of the tunnel i , the radius R of the plastic softening region p and the radius R of the plastic residual region f , the radial stress σ at the junction of the elastic-plastic region r2 and the tangential stress σ θ2 , the radial stress σ at the boundary between the plastic softening and residual regions r1 and the tangential stress σ θ1 ;

[0016] The calculation formula for constructing the strain-softening surrounding rock excavation model is:

[0017] Introduce the plastic softening coefficient η characterizing the deterioration degree of the surrounding rock strength parameter:

[0018]

[0019] In the formula, η is the plastic softening coefficient of the deterioration degree of the surrounding rock strength parameter, and respectively represent the axial plastic strain and the radial plastic strain. η actually represents the plastic shear strain of the surrounding rock, and η * represents the critical plastic shear strain of the surrounding rock; m b , s, a are parameters characterizing the surrounding rock strength; σ1 and σ3 are respectively the maximum principal stress and the minimum principal stress of the rock; in the plane strain state, the longitudinal stress is regarded as the intermediate principal stress σ2. In the research section, the tangential stress σ θ of the surrounding rock and the radial stress σ r respectively correspond to the maximum principal stress σ1 and the minimum principal stress σ3; m b , s, a are surrounding rock strength parameters; ω represents the strength parameters m b , s, a; ω p and ω r respectively correspond to the peak strength parameters s p , a p at the elastic-plastic interface under a certain confining pressure σ3 and the residual strength parameters s r , a r in the plastic residual region; in the strain-softening model, the H-B yield criterion is:

[0020] f(σr , σ θ , η) = σ θ -σ r -

[0021] σ ci (m b (η)σ r / σ ci (η) + s(η)) a(η) = 0

[0022] In the formula, the plastic softening coefficient η determines the degree of linear decrease of the strength parameters m b , s, and a with the increase of the plastic shear strain in the plastic softening region, and σ r is the radial stress of the surrounding rock, and σ θ is the tangential stress of the surrounding rock, and σ ci represents the uniaxial compressive strength of the rock, and m b (η), s(η), and a(η) are the strength parameters at a certain plastic softening coefficient η, and σ ci (η) represents the uniaxial compressive strength of the rock at a certain plastic softening coefficient η.

[0023] Optionally, the stress-strain field data includes radial stress data at the elastic-plastic interface, stress data in the plastic region, and strain component data in the plastic region.

[0024] Optionally, the process of obtaining the radial stress data σ r2 at the elastic-plastic interface includes:

[0025]

[0026] In the formula, σ ci represents the uniaxial compressive strength of the rock, σ0 represents the uniformly distributed stress acting at infinity in the cross-section, and a p , s p , are the peak strength parameters at the elastic-plastic interface.

[0027] The process of obtaining the stress data in the plastic region and the strain component data in the plastic region includes:

[0028] Obtaining the stress data in the plastic region by the finite difference method:

[0029] Dividing the plastic region in the excavation model of strain-softening surrounding rock into layers:

[0030]

[0031] In the formula: n represents the number of divided rings of the circular ring, and Δσ r is the radial stress increment of each ring, and σ r(n) in the formula represents the support force p at the tunnel walli , σ r(0) represents the radial stress at the junction of the elastic-plastic region, σ r(i-1) and σ r(i) respectively represent the radial stresses on the surrounding rock at the inner and outer boundary hole walls of the i-th ring;

[0032] The strain components within the i-th ring are expressed as:

[0033] ε θ(0) = (1 + μ)(σ0 - σ r2 ) / E0

[0034] ε r(0) = (1 + μ)(σ r2 - σ0) / E0

[0035]

[0036] In the formula, ε r(0) , ε θ(0) respectively represent the radial strain component and the tangential strain component at infinity in the cross-section, μ represents the Poisson's ratio of the surrounding rock, E represents the elastic modulus of the rock mass, E0 is the peak elastic modulus at the elastic-plastic interface, σ0 represents the uniformly distributed stress acting at infinity in the cross-section, σ r2 represents the radial stress at the junction of the elastic-plastic region, ε r(i-1) , ε θ(i-1) are respectively the radial strain component and the tangential strain component at the inner boundary of the i-th ring, ε r(i) , ε θ(i) are respectively the radial strain component and the tangential strain component at the outer boundary of the i-th ring, is the increment of the elastic strain component at the i-th ring, is the increment of the plastic strain component at the i-th ring, Δσ r(i) , Δσ θ(i) respectively represent the radial stress component and the tangential stress component at the i-th ring;

[0037] The increment of the plastic softening coefficient Δη (i) at the i-th ring is:

[0038]

[0039] In the formula, ε r(i) , ε θ(i) are respectively the radial strain component and the tangential strain component at the outer boundary of the i-th ring, ε r(i-1) , ε θ(i-1) are respectively the radial strain component and the tangential strain component at the inner boundary of the i-th ring, is the increment of the elastic strain component at the i-th ring, is the increment of the plastic strain component at the i-th ring;

[0040] The plastic softening coefficient η at the junction of the elastic-plastic region (0) is 0, and the η at the i-th ring is obtained by superimposing the increments of the plastic softening coefficient of the previous i rings (i) ; According to the non-associated flow rule of the surrounding rock:

[0041]

[0042] In the formula, ε r(i) , ε θ(i) are the radial strain component and tangential strain component of the outer boundary of the i-th ring respectively, ε r(i-1) , ε θ(i-1) are the radial strain component and tangential strain component of the inner boundary of the i-th ring respectively, is the increment of the elastic strain component at the i-th ring, is the increment of the plastic strain component at the i-th ring, β is the dilatancy coefficient of the surrounding rock; It can be known from Lee and Pietruszczak that the ratio of the inner and outer boundary radii of the i-th ring is:

[0043]

[0044] In the formula, r (i-1) and r (i) are the surrounding rock radii of the inner and outer boundaries of the i-th ring respectively, η (i-1) is the plastic shear strain of the surrounding rock at the outer boundary of the i-th ring, Δσ r is the radial stress increment of each ring, σ′ r(i) =(σ r(i) +σ′ r(i-1) ) / 2, in the plastic softening region, In the plastic residual region

[0045] Obtain the data of the tangential strain component and radial strain component in the plastic region:

[0046]

[0047] In the formula, ε r(i) , ε θ(i) are the radial strain component and tangential strain component of the outer boundary of the i-th ring respectively, Δu (i) is the increment of the surrounding rock deformation at the inner boundary of the i-th ring, Δr (i) is the surrounding rock radius at the inner boundary of the i-th ring, u (i-1) and u (i) are the surrounding rock deformations of the inner and outer boundaries of the i-th ring respectively, r (i-1) and r (i) are the surrounding rock radii of the inner and outer boundaries of the i-th ring respectively, In the plastic softening region, B (i-1) =σ ci(i-1)(m b(i-1) σ r(i) / σ ci(i-1) +s (i-1) ) a(i-1) , in the plastic residual region, β is the dilatancy coefficient of the surrounding rock. Under stress-strain conditions, β = (1 + sinψ) / (1 - sinψ), where ψ is the dilation angle.

[0048] Optionally, the displacement field data includes: the radius R of the plastic softening region p and the radius R of the plastic residual region f ;

[0049] The process of obtaining the displacement field data includes:

[0050] When entering the k-th ring, plastic residual failure of the surrounding rock begins:

[0051]

[0052] In the formula, R p represents the radius of the plastic softening region, R f represents the radius of the plastic residual region, σ′ r(k) = (σ r(k) + σ′ r(k-1) ) / 2, η (k-1) is the plastic shear strain of the surrounding rock at the outer boundary of the k-th ring, and Δσ r is the radial stress increment of each ring.

[0053] After the surrounding rock enters the plastic residual region, the equilibrium equation in this region is:

[0054]

[0055] In the formula, σ r represents the radial stress of the surrounding rock, r represents the radius of the surrounding rock, s r , a r represent the residual strength parameters of the plastic residual region, and σ ci represents the uniaxial compressive strength of the rock.

[0056] Obtain the boundary conditions: r = R0, σ r = p i ; r = R f , σ r = σ r1 , σ r1 is the radial stress at the junction of the plastic softening and residual regions. Based on the above boundary conditions, the expression for the radius R f of the plastic residual region is obtained:

[0057]

[0058] In the formula, R f represents the radius of the plastic residual area, R0 represents the radius of the intersection area between the elastic-plastic areas, and σ r1 is the radial stress at the junction of plastic softening and the residual area, and σ ci represents the uniaxial compressive strength of the rock, s r and a r represent the residual strength parameters of the plastic residual area, and p i represents the support pressure on the inner wall of the tunnel.

[0059] Optionally, the surrounding rock deformation law data includes: plastic zone surrounding rock deformation law data and elastic zone surrounding rock deformation law data.

[0060] Optionally, the process of obtaining the plastic zone surrounding rock deformation law data includes:

[0061]

[0062] In the formula, u (i-1) and u (i) are the surrounding rock deformations at the inner and outer boundaries of the i-th ring respectively, r (i-1) and r (i) are the surrounding rock radii at the inner and outer boundaries of the i-th ring respectively, In the plastic softening area, B (i-1) = σ ci(i-1) (m b(i-1) σ r(i) / σ ci(i-1) + s (i-1) ) a(i-1) , in the plastic residual area, β is the dilatancy coefficient of the surrounding rock. Under stress-strain conditions, β = (1 + sinψ) / (1 - sinψ), and ψ is the dilation angle;

[0063] The process of obtaining the elastic zone surrounding rock deformation law data includes:

[0064]

[0065] In the formula, and u e are the elastic radial stress, elastic tangential stress and surrounding rock deformation respectively, E0 is the peak elastic modulus at the elastic-plastic interface, r is the surrounding rock radius, μ is the Poisson's ratio of the surrounding rock, σ0 is the uniformly distributed stress acting at infinity in the cross-section, and σ r2 is the radial stress at the junction of the elastic-plastic areas, and R p is the radius of the plastic softening area.

[0066] The technical effects of the present invention are as follows: The present invention provides a method for analyzing the surrounding rock deformation law based on the elastic modulus degradation property, including: obtaining the influence factor data of the post-peak degradation of the rock sample elastic modulus, and constructing a non-linear degradation model of the rock elastic modulus based on the influence factors; constructing a strain-softening surrounding rock excavation model, and analyzing the strain-softening surrounding rock excavation model based on the non-linear degradation model of the rock elastic modulus and the finite difference method to obtain the stress-strain field data of the deep-buried tunnel strain-softening surrounding rock, and obtaining the displacement field data based on the stress-strain field data; combining and analyzing the stress-strain field data and the displacement field data to obtain the surrounding rock deformation law data.

[0067] The present invention provides a method for analyzing the surrounding rock deformation law based on the elastic modulus degradation property, which reasonably considers the degradation characteristics of the surrounding rock elastic modulus in tunnel design. In the past, the research method assuming a constant peak elastic modulus underestimated the solution of the surrounding rock deformation at the tunnel wall, and the safety of the cavern design was often underestimated. When evaluating the surrounding rock stability, it may be considered that the surrounding rock that has already been damaged has not been damaged. Therefore, the corresponding calculation results and designs are all on the unsafe side. The design of this application uses a non-linear fitting method to construct a non-linear degradation model of the rock elastic modulus, which can effectively reflect the degradation process of the elastic modulus under the influence of confining pressure and plastic strain; at the same time, it fully analyzes the stress-strain field data and displacement field data of each region of the deep-buried tunnel strain-softening surrounding rock to obtain the actual surrounding rock deformation law, and the support design is safer. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0069] Figure 1 is the calculation flow chart in the embodiment of the present invention;

[0070] Figure 2 is the scatter distribution diagram of the elastic modulus changing with the axial plastic strain of two rocks in the post-peak stage under different confining pressure conditions in the embodiment of the present invention, where Figure 2 (a) is the scatter distribution diagram of the elastic modulus changing with the axial plastic strain of the intact core Blanco Mera granite under different confining pressures in the post-peak stage in the embodiment of the present invention, Figure 2 (b) is the scatter distribution diagram of the elastic modulus changing with the axial plastic strain of 146mm Moura coal rock under different confining pressures in the post-peak stage in the embodiment of the present invention;

[0071] Figure 3 is the curve of the elastic modulus changing with the axial plastic strain of two rocks under different confining pressures fitted separately in the embodiment of the present invention, whereFigure 3 (a) is the curve of the elastic modulus of intact core Blanco Mera granite varying with axial plastic strain under different confining pressures in the embodiment of the present invention, Figure 3 (b) is the curve of the elastic modulus of 146mm Moura coal rock varying with axial plastic strain under different confining pressures in the embodiment of the present invention;

[0072] Figure 4 are the overall fitting and individual fitting curves of the two rocks in the embodiment of the present invention based on the non-linear degradation model of elastic modulus under different confining pressures. Among them, Figure 4 (a) are the overall fitting and individual fitting curves of Blanco Mera granite based on the non-linear degradation model of elastic modulus under different confining pressures in the embodiment of the present invention, Figure 4 (b) are the overall fitting and individual fitting curves of 146mm diameter Moura coal rock based on the non-linear degradation model of elastic modulus under different confining pressures in the embodiment of the present invention;

[0073] Figure 5 is the circular tunnel excavation model in the embodiment of the present invention;

[0074] Figure 6 are the curves of strength parameters varying with the plastic softening coefficient in the embodiment of the present invention. Among them, Figure 6 (a) is the curve of the maximum principal stress of the surrounding rock in the embodiment of the present invention, Figure 6 (b) are the curves of each strength parameter varying with the plastic softening coefficient in the embodiment of the present invention;

[0075] Figure 7 are the peak and residual strength fitting curves of two rock samples under the H-B yield criterion in the embodiment of the present invention. Among them, Figure 7 (a) are the peak and residual strength fitting curves of Blanco Mera granite under the H-B yield criterion in the embodiment of the present invention, Figure 7 (b) are the peak and residual strength fitting curves of 146mm Moura coal rock under the H-B yield criterion in the embodiment of the present invention;

[0076] Figure 8 is the schematic diagram of the concentric rings for dividing the plastic softening area and the residual area in the embodiment of the present invention;

[0077] Figure 9 is the stress-strain curve of the cyclic loading triaxial test in the embodiment of the present invention;

[0078] Figure 10 are the distribution of the surrounding rock deformation and stress components in the embodiment of the present invention. Among them, Figure 10 (a) is the schematic diagram of the surrounding rock deformation distribution in the embodiment of the present invention, Figure 10(b) Schematic diagram of stress component distribution in the embodiment of the present invention;

[0079] Figure 11 It is the curve of the elastic modulus of surrounding rock varying with the radius under different critical softening coefficients in the embodiment of the present invention, where Figure 11 (a) It is the curve of the elastic modulus of the Blanco Mera granite cavern varying with the radius in the embodiment of the present invention, Figure 11 (b) It is the curve of the elastic modulus of the Moura coal mine cavern varying with the radius in the embodiment of the present invention;

[0080] Figure 12 It is the curve of the elastic modulus of surrounding rock varying with the axial plastic strain under different critical softening coefficients in the embodiment of the present invention, where Figure 12 (a) It is the curve of the elastic modulus of the Blanco Mera granite cavern varying with the axial plastic strain in the embodiment of the present invention, Figure 12 (b) It is the curve of the elastic modulus of the Moura coal mine cavern varying with the axial plastic strain in the embodiment of the present invention;

[0081] Figure 13 It is the curve of the confining pressure of the plastic region varying with the axial plastic strain in the embodiment of the present invention, where Figure 13 (a) It is the curve of the confining pressure of the Blanco Mera granite cavern varying with the axial plastic strain in the embodiment of the present invention, Figure 13 (b) It is the curve of the confining pressure of the Moura coal mine cavern varying with the axial plastic strain in the embodiment of the present invention. Detailed implementation manners

[0082] Now, various exemplary implementation manners of the present invention will be described in detail. This detailed description should not be regarded as a limitation of the present invention, but should be understood as a more detailed description of certain aspects, characteristics, and implementation schemes of the present invention. It should be noted that, without conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the drawings and in combination with the embodiments.

[0083] As Figures 1 - 13 shown, in this embodiment, a method for analyzing the deformation law of surrounding rock based on the property of elastic modulus reduction is provided, including:

[0084] Obtain data on the influencing factors of the post-peak decay of the elastic modulus of rock samples, and construct a non-linear decay model of rock elastic modulus based on the influencing factors; construct an excavation model of strain-softening surrounding rock, and analyze the excavation model of strain-softening surrounding rock based on the non-linear decay model of rock elastic modulus and the finite difference method to obtain the stress-strain field data of deep-buried tunnel strain-softening surrounding rock, and obtain displacement field data based on the stress-strain field data; conduct a combined analysis of the stress-strain field data and the displacement field data to obtain the surrounding rock deformation law data.

[0085] In this embodiment, through the mechanical response of the surrounding rock in the triaxial cyclic loading and unloading test in existing research, a non-linear fitting method is used to construct a non-linear decay model of rock elastic modulus, which can effectively reflect the decay process of the elastic modulus under the influence of confining pressure and plastic strain; based on the rock modulus decay model, the numerical solutions of the stress-strain field and displacement field of deep-buried tunnel strain-softening surrounding rock are derived by the finite difference method, combined with the numerical solutions and according to whether the confining pressure and plastic strain affect the elastic modulus of the surrounding rock;

[0086] Figure 9 is a schematic diagram of the stress-strain curve of the cyclic loading triaxial test, where E is the elastic modulus of the rock sample, and are the axial plastic strain and axial elastic strain of the rock sample at the unloading point respectively. Due to the different stress paths in the process of cyclic loading and unloading of the load, multiple plastic hysteresis loops are formed on the stress-strain curve, and the slope between the unloading point and the reloading point on the plastic hysteresis loop is the elastic modulus at the unloading point.

[0087] To explore the decay mechanism of the post-peak elastic modulus of the surrounding rock, in this embodiment, based on the cyclic loading triaxial test, some rock sample data in the test (intact core Blanco Mera granite rock sample, 146 mm diameter Moura coal rock sample) are processed, the change law of the elastic modulus of the rock sample is analyzed, and the influencing factors that control the post-peak decay process of the rock elastic modulus are summarized. According to the above method, the scatter distribution of the relationship between the elastic modulus and axial plastic strain under different confining pressure conditions in the post-peak stage of the two rocks is obtained, as shown in Figure 2 . From Figure 2 it can be seen that the elastic modulus of the rock sample under different confining pressure conditions rapidly decays in the plastic softening stage after the peak, while the decay of the elastic modulus is gentle and tends to be stable in the plastic residual stage, and the relationship with the axial plastic strain shows obvious non-linearity. At the same time, the influence of the change of confining pressure on the elastic modulus of the rock sample is also significant. The higher the confining pressure, the larger the overall elastic modulus of the rock sample. The results show that the post-peak decay process of the elastic modulus of the above two rock samples is closely related to the plastic strain and the confining pressure. Therefore, this embodiment proposes to construct a non-linear decay model of elastic modulus that comprehensively considers the influence of confining pressure and axial plastic strain. The model construction process is divided into the following two steps:

[0088] Without considering the influence of confining pressure, analyze the variation law of the elastic modulus E of rock samples with axial plastic strain under the same confining pressure condition, and separately fit the non-linear relationship between the elastic modulus and axial plastic strain. The fitting function is as follows: In the formula: a, b, and c are all function fitting coefficients. (2) Among the three fitting coefficients a, b, and c, both coefficients a and c show a trend of gradually increasing with the increase of confining pressure until approaching a certain asymptotic value, while coefficient b shows a trend of gradually decreasing with the increase of confining pressure and finally reaching a certain residual value. Therefore, the non-linear fitting method can also be used to separately determine the relationship between the fitting coefficients a, b, and c and the confining pressure σ3, and then obtain the overall fitting result of the elastic modulus affected by both confining pressure and axial plastic strain. The variation of the fitting coefficients a, b, and c with the confining pressure σ3 can be expressed as follows:

[0089]

[0090] In the formula: a, b, and c are all function fitting coefficients. (2) Among the three fitting coefficients a, b, and c, both coefficients a and c show a trend of gradually increasing with the increase of confining pressure until approaching a certain asymptotic value, while coefficient b shows a trend of gradually decreasing with the increase of confining pressure and finally reaching a certain residual value. Therefore, the non-linear fitting method can also be used to separately determine the relationship between the fitting coefficients a, b, and c and the confining pressure σ3, and then obtain the overall fitting result of the elastic modulus affected by both confining pressure and axial plastic strain. The variation of the fitting coefficients a, b, and c with the confining pressure σ3 can be expressed as follows:

[0091]

[0092] b = b1 + b2exp(-b3·σ3)(2b)

[0093]

[0094] In the formula: λ, b, and c are all function fitting coefficients, λ i , b i , c i (i = 1, 2, 3) are all fitting coefficients, is the axial plastic strain of the rock sample at the unloading point, σ3 is the confining pressure, the λ3 in refers to the λ3 power of σ3, the c3 in refers to the c3 power of σ3.

[0095] The model coefficients of the two rocks are shown in Table 1. The comprehensive formulas (1) - (2) are the non-linear degradation model of the elastic modulus. The separate fitting results of Blanco Mera granite and intact rock of Moura coal rock with a diameter of 146 mm according to formula (1) are as Figure 3 shown. The linear regression coefficient R 2 values of the fitting curves under different confining pressures are all greater than 0.85, indicating that the goodness of fit of the non-linear separate fitting of the model is high

[0096] Table 1 Model coefficients of the non-linear degradation of the elastic modulus for the two rocks

[0097]

[0098] Figure 4The overall fitting of two kinds of rocks under different confining pressures based on the nonlinear degradation model of elastic modulus and the separate fitting curves without considering the influence of confining pressure are given. It can be seen from Figure 4 that the overall fitting obtained from the nonlinear degradation model of elastic modulus is in good agreement with the separate fitting results. It shows that the model can better reflect the post-peak degradation characteristics of the elastic modulus of the above two kinds of rocks, fully verifying the rationality of the model.

[0099] Mechanical characteristics of circular chamber excavation: Assume that the chamber under study is a deep-buried circular tunnel (H≥20R0, where R0 is the radius of the circular chamber) and infinitely long longitudinally. During the calculation process, the surrounding rock is always in a plane strain state and the surrounding rock is a homogeneous, isotropic elastoplastic material. The strain-softening surrounding rock mechanics

[0100] model is as shown in Figure 5 . A uniform ground stress σ0 acts at an infinite distance from the cross-section, and the support pressure on the inner wall of the chamber is p i . When the support pressure p i is small, a plastic residual region may appear in the surrounding rock. The radii of the plastic softening region and the plastic residual region are R p and R f respectively. The radial stress and tangential stress at the junction of the elastic-plastic region are σ r2 and σ θ2 respectively. The radial stress and tangential stress at the boundary between the plastic softening and residual regions are σ r1 and σ θ1 .

[0101] The Hoek-Brown (H-B) yield criterion is as follows: σ1 = σ3 + σ ci (m b σ3 / σ ci +s) a (3)

[0102] In the formula: σ ci represents the uniaxial compressive strength of the rock; m b , s, and a are parameters characterizing the strength of the surrounding rock; σ1 and σ3 are the maximum principal stress and minimum principal stress of the rock respectively. Under the plane strain state, the longitudinal stress can be regarded as the intermediate principal stress σ2. In the research section, the tangential stress σ θ and the radial stress σ r of the surrounding rock correspond to the maximum principal stress σ1 and the minimum principal stress σ3 (confining pressure in the triaxial test) respectively.

[0103] Strain-softening model: In the strain-softening model, the plastic softening coefficient η characterizing the degradation degree of the surrounding rock strength parameter is introduced, generally expressed as

[0104]

[0105] In the formula: and respectively represent the axial plastic strain and the radial plastic strain, and η actually represents the plastic shear strain of the surrounding rock.

[0106] In the strain-softening model, η * represents the critical plastic softening coefficient (i.e., the critical plastic shear strain), which is the key parameter controlling the transition of the surrounding rock from the plastic softening region to the plastic residual region, and represents the plastic shear strain at the junction of the plastic softening region and the plastic residual region. When η = 0, the surrounding rock is in the elastic stage; when 0 ≤ η < η * , the surrounding rock is in the plastic softening stage; when η ≥ η * , the surrounding rock is in the plastic residual stage. Under the given confining pressure condition, the curves of the maximum principal stress of the surrounding rock and the strain-softening characteristics of each strength parameter are as Figure 5 shown.

[0107] Figure 6 (a), represents the peak strength of the surrounding rock, represents the residual strength of the surrounding rock. Figure 6 (b), for the surrounding rock strength parameters m b , s, a are linear piecewise functions of η:

[0108]

[0109] In the formula: ω represents the strength parameters m b , s, a; ω p and ω r respectively correspond to the peak strength parameters s p , a p at the elastic-plastic interface under a certain confining pressure σ3 and the residual strength parameters s r , a r .

[0110] Therefore, in the strain-softening model, the H-B yield criterion (Equation (3)) can be expressed as

[0111]

[0112] In the formula, η is the plastic softening coefficient of the deterioration degree of the surrounding rock strength parameter, and respectively represent the axial plastic strain and the radial plastic strain, η actually represents the plastic shear strain of the surrounding rock, η * represents the critical plastic shear strain of the surrounding rock; m b, s, and a are parameters characterizing the surrounding rock strength; σ1 and σ3 are the maximum and minimum principal stresses of the rock, respectively; in the plane strain state, the longitudinal stress is regarded as the intermediate principal stress σ2, and within the research section, the tangential stress σ θ and the radial stress σ r correspond to the maximum principal stress σ1 and the minimum principal stress σ3, respectively; m b , s, and a are the surrounding rock strength parameters; ω represents the strength parameters m b , s, and a; ω p and ω r correspond to the peak strength parameters sp and ap at the elastic-plastic interface under a certain confining pressure σ3, and the residual strength parameters s r and a r in the plastic residual region, respectively. Surrounding rock strength parameters:

[0113] Based on the triaxial compression tests of two types of surrounding rocks under 5 σ3 (i.e., confining pressures), the peak strengths and residual strengths of the surrounding rocks under different σ3 are obtained as shown in Tables 2 and 3. Referring to the research of Arzúa et al., the corresponding relationships between the peak strengths and residual strengths of the two types of surrounding rocks and the applied confining pressures are respectively fitted using Equation (3) to determine the H-B strength parameters m b , s, and a of the surrounding rocks in the elastic stage and plastic residual stage. The fitting curves of the peak and residual strengths of the two rock samples are as Figure 7 shown.

[0114] Table 2 Strength test values of the intact core Blanco Mera granite

[0115]

[0116] Table 3 Strength test values of the Moura coal rock with a diameter of 146 mm

[0117]

[0118]

[0119] According to the improved H-B yield criterion, the H-B strength parameters can be expressed as:

[0120]

[0121] where GSI (geotechnical strength index) represents the geological strength index, which is generally used for the surrounding rock quality classification; m iis a constant, representing the frictional characteristics of the surrounding rock; D is the disturbance coefficient of the surrounding rock, mainly reflecting the deterioration effect of construction disturbance on the parameters of the surrounding rock. In the study of the two types of test surrounding rocks, the influence of construction disturbance is not considered, and the disturbance coefficient D is assumed to be 0.

[0122] Since the rock cores of the rock samples used for indoor tests are intact, without obvious cracks and failure surfaces, the corresponding Geological Strength Index (GSI) value of the surrounding rock is taken as 100. It is considered that the peak strength GSI of the elastic stage of the surrounding rock p is 100, and the corresponding peak Hoek-Brown strength parameters s p 、a p can be obtained by using Equations (7) - (9), as shown in Table 4. For the surrounding rock in the post-peak stage, with the deterioration of the quality of the surrounding rock, the strength index of the surrounding rock gradually decreases. Therefore, on the basis of determining the peak Hoek-Brown strength parameters, the residual Hoek-Brown strength parameters s r 、a r can be obtained from the residual strength index GSI of the surrounding rock in the plastic residual area. Cai et al. have given the empirical formula for solving GSI r according to GSI p . For Blanco Mera granite, GSI r is selected as 30, 25, 20, 15 respectively. For Moura coal rock, GSI p is selected as 80, 75, 70, 65, 60, 55 respectively. According to the above calculation method, the peak and residual mechanical parameters of the two types of surrounding rocks are obtained by fitting, as shown in Table 5 and Table 6. p respectively.

[0123] Elastic modulus of the surrounding rock: The influence of the quality of the surrounding rock on the elastic modulus of the surrounding rock is also significant. The elastic modulus decreases with the deterioration of the quality of the surrounding rock. Based on a large number of on-site test data, the relationship equation between the elastic modulus of the surrounding rock and the elastic modulus of the rock:

[0124]

[0125] In the formula, E rm represents the elastic modulus of the surrounding rock; E i represents the elastic modulus in the state of intact rock. Without considering the influence of the disturbance coefficient D, it is taken as 0. It can be seen from Equation (11) that the elastic modulus of the corresponding surrounding rock under different strength indexes can be calculated according to the elastic modulus in the state of intact rock.

[0126] Table 4 Mechanical parameters of two intact rock samples based on indoor triaxial tests

[0127]

[0128] Table 5 Mechanical parameters of Blanco Mera granite surrounding rock

[0129]

[0130] Table 6 Mechanical Parameters of Surrounding Rock of Moura Coal Seam

[0131]

[0132] According to the foregoing conditions, the equilibrium differential equation and displacement compatibility equation satisfied by the mechanical excavation model are as follows:

[0133]

[0134] Stress-strain field in the elastic region: According to the elastic theory, the closed-form solutions of the stress components and radial displacement in the elastic region are as follows:

[0135]

[0136] In the formula, and u e are the elastic radial stress, elastic tangential stress and surrounding rock deformation respectively. E0 is the peak elastic modulus at the elastic-plastic interface, r is the radius of the surrounding rock, μ is the Poisson's ratio of the surrounding rock, σ0 is the uniformly distributed stress acting at infinity in the cross-section, σ r2 is the radial stress at the junction of the elastic-plastic region, R p is the radius of the plastic softening region.

[0137] From equations (3), (13a) and (13b), the radial stress at the junction of the elastic-plastic region can be obtained by the Newton-Raphson method

[0138]

[0139] In the formula, σ ci represents the uniaxial compressive strength of the rock, σ0 represents the uniformly distributed stress acting at infinity in the cross-section, a p , s p , are the peak strength parameters at the elastic-plastic interface. Stress-strain field in the plastic region:

[0140] The stress-strain field in the strain softening region cannot be obtained by a closed-form solution. In this embodiment, the finite difference method is used to solve the stress-strain field in the plastic region. Figure 8 Briefly describes the layering of the plastic region of the surrounding rock. The plastic region consists of a softening region and a residual region; the plastic region is divided into n concentric rings, and the junction of the elastic-plastic region is defined as the 0th ring. Then σ θ(0) and σ r(0) represent the tangential stress and radial stress at the junction of the elastic-plastic region respectively; σ θ(n) and σ r(n)respectively represent the tangential stress and radial stress exerted on the surrounding rock at the hole wall; the inner and outer boundaries of the i-th ring correspond to the radii r i-1 and r i , at this time, the stress components corresponding to the inner and outer boundaries are σ θ(i-1) , σ r(i-1) and σ θ(i) , σ r(i) . The basis for dividing the circular rings in the plastic region is to make the radial stress increments of adjacent circular rings equal. The specific division criterion is as follows:

[0141]

[0142] where: n represents the number of circular ring divisions, Δσ r is the radial stress increment of each ring, and σ r(n) in the formula represents the support force p i at the hole wall, σ r(0) represents the radial stress at the junction of the elastic-plastic region, and σ r(i-1) and σ r(i) respectively represent the radial stresses exerted on the surrounding rock at the inner and outer boundaries of the i-th ring. Considering the unloading path of the surrounding rock, there should be elastic strain increments in the plastic region. Therefore, the strain components in the i-th ring are expressed as follows:

[0143]

[0144] where: ε r(i-1) , ε θ(i-1) are the radial strain component and tangential strain component at the inner boundary of the i-th ring respectively, ε r(i) , ε θ(i) are the radial strain component and tangential strain component at the outer boundary of the i-th ring respectively, is the increment of the elastic strain component at the i-th ring, is the increment of the plastic strain component at the i-th ring.

[0145] The initial values of the strain components in the plastic region are the strain components ε r(0) , ε θ(0) at the junction of the elastic-plastic region, which can be obtained from equations (12) and (13)

[0146]

[0147] where, ε r(0) , ε θ(0) respectively represent the radial strain component and tangential strain component at infinity in the cross-section, μ represents the Poisson's ratio of the surrounding rock, E0 is the peak elastic modulus at the elastic-plastic interface, σ0 represents the uniform stress acting at infinity in the cross-section, and σ r2 represents the radial stress at the junction of the elastic-plastic region.

[0148] and can be obtained from Hooke's law, and the formula is as follows:

[0149]

[0150] In the formula, is the increment of the elastic strain component at the i-th ring, μ represents the Poisson's ratio of the surrounding rock, E represents the elastic modulus of the rock mass, and Δσ r(i) , Δσ θ(i) represent the radial stress component and the tangential stress component at the i-th ring respectively.

[0151] According to Equation (4), the increment of the plastic softening coefficient Δη (i) at the i-th ring can be obtained from the following formula

[0152]

[0153] In the formula, is the increment of the plastic strain component at the i-th ring. Since it is difficult to directly obtain and , the calculation process can be simplified by combining Equation (16), that is, by subtracting the corresponding elastic strain component increment from the tangential and radial strain component increments to obtain and After simplification, the calculation method of Δη (i) is as follows:

[0154]

[0155] In the formula, Δη (i) represents the increment of the plastic softening coefficient at the i-th ring, ε r(i-1) , ε θ(i-1) are the radial strain component and the tangential strain component of the inner boundary of the i-th ring respectively, and ε r(i) , ε θ(i) are the radial strain component and the tangential strain component of the outer boundary of the i-th ring respectively, is the increment of the elastic strain component at the i-th ring.

[0156] The plastic softening coefficient η (0) at the junction of the elastic-plastic region is 0. According to Equation (21), the plastic softening coefficient increment of the first i rings is superimposed to obtain η (i) at the i-th ring.

[0157] According to the non-associated flow rule of the surrounding rock, it can be obtained that

[0158]

[0159] In the formula, β is the dilatancy coefficient of the surrounding rock. Under stress-strain conditions, β = (1 + sinψ) / (1 - sinψ), where ψ is the dilation angle. is the increment of the plastic strain component at the i-th ring.

[0160] Next, combining equations (16) and (21) gives

[0161]

[0162] In the formula, ε r(i-1) and ε θ(i-1) are the radial strain component and tangential strain component of the inner boundary of the i-th ring respectively, ε r(i) and ε θ(i) are the radial strain component and tangential strain component of the outer boundary of the i-th ring respectively. is the increment of the elastic strain component at the i-th ring, β is the dilatancy coefficient of the surrounding rock. Under stress-strain conditions, β = (1 + sinψ) / (1 - sinψ), where ψ is the dilation angle.

[0163] According to Lee and Pietruszczak, the ratio of the inner and outer boundary radii of the i-th ring should conform to the following formula:

[0164]

[0165] In the formula: r (i-1) and r (i) are the radii of the surrounding rock of the inner and outer boundaries of the i-th ring respectively, η (i-1) is the plastic shear strain of the surrounding rock at the outer boundary of the i-th ring, Δσ r is the increment of the radial stress of each ring, σ′ r(i) = (σ r(i) + σ′ r(i-1) ) / 2. In the plastic softening region, In the plastic residual region,

[0166]

[0167] To solve the strain components in the plastic region, equation (12) can be approximated as

[0168]

[0169] In the formula, ε r(i) and ε θ(i) are the radial strain component and tangential strain component of the outer boundary of the i-th ring respectively, Δu (i) is the increment of the surrounding rock deformation at the inner boundary of the i-th ring, Δr (i) is the radius of the surrounding rock at the inner boundary of the i-th ring, u (i-1) and u (i) are the surrounding rock deformations of the inner and outer boundaries of the i-th ring respectively, r(i-1) and r (i) are the surrounding rock radii of the inner and outer boundaries of the i-th ring respectively.

[0170] Combining Eqs. (24), (22) and (18), the approximate expressions of the displacement and strain components of the surrounding rock in the plastic region are obtained as follows:

[0171]

[0172] where u (i-1) and u (i) are the deformations of the surrounding rock at the inner and outer boundaries of the i-th ring respectively, r (i-1) , r (i) are the surrounding rock radii at the inner and outer boundaries of the i-th ring respectively, Δu (i) is the increment of the deformation of the surrounding rock at the inner boundary of the i-th ring, Δr (i) is the surrounding rock radius at the inner boundary of the i-th ring, ε r(i) , ε θ(i) are the radial strain component and tangential strain component at the outer boundary of the i-th ring respectively, β is the dilatancy coefficient of the surrounding rock, under the stress-strain condition, β = (1 + sinψ) / (1 - sinψ), ψ is the dilation angle, where,

[0173] In the plastic softening region, B (i-1) = σ ci(i-1) (m b(i-1) σ r(i) / σ ci(i-1) + s (i-1) ) a(i-1) ,

[0174] In the plastic residual region,

[0175] Assume that when entering the k-th ring, the surrounding rock begins to undergo plastic residual failure. At this time, Eq. (23) can be expressed by successive multiplication as

[0176]

[0177] where R p represents the radius of the plastic softening region, R f represents the radius of the plastic residual region, σ′ r(k) = (σ r(k) + σ′ r(k-1) ) / 2, η (k-1) is the plastic shear strain of the surrounding rock at the outer boundary of the k-th ring, Δσ r is the radial stress increment of each ring.

[0178] According to Eqs. (23), (26) - (28), it can be seen that under certain working conditions, R pis a fixed value. The calculation results of the strain components in each ring within the plastic region are independent of the magnitude of R p Therefore, the multiplicative term on the right side of Equation (28) is constant. Combining with Equation (15), it can be seen that when σ r2 is constant, the radial stress σ r1 at the junction of the plastic softening and residual regions is only determined by the number of rings k entering the plastic residual region.

[0179] After the surrounding rock enters the plastic residual region, the equilibrium equations within this region can be obtained from Equations (4) and (11):

[0180]

[0181] In the formula, σ r represents the radial stress of the surrounding rock, r represents the radius of the surrounding rock, s r and a r represent the residual strength parameters of the plastic residual region, and σ ci represents the uniaxial compressive strength of the rock.

[0182] Substituting the boundary conditions r = R0, σ r = p i ; r = R f , σ r = σ r1 , where σ r1 is the radial stress at the junction of the plastic softening and residual regions, into Equation (29), the expression for the radius R f of the plastic residual region is obtained:

[0183]

[0184] In the formula, R f represents the radius of the plastic residual region, R0 represents the radius of the elastic-plastic region junction, σ r1 is the radial stress at the junction of the plastic softening and residual regions, σ ci represents the uniaxial compressive strength of the rock, s r and a r represent the residual strength parameters of the plastic residual region, and p i represents the support pressure on the inner wall of the tunnel.

[0185] The calculation process of this embodiment can be divided into two parts. The first part (before obtaining R p ), the stress and strain components in the plastic softening region and the residual region can be obtained from Equations (15) to (24), (26), and (27). The second part, based on the first part, R f and R p can be obtained successively according to Equations (30) and (28)., at this time, according to the strain components in the plastic zone obtained and Equation (25), the deformation of the surrounding rock at any radius in the plastic zone can be calculated. After that, the stress components and the deformation of the surrounding rock in the elastic region can also be obtained from Equation (13). For the sake of intuition, the calculation process under the strain-softening model considering the post-peak reduction of the elastic modulus of the surrounding rock is listed in Figure 1 in.

[0186] To verify the reliability of the method in this embodiment, the distribution curves of the deformation of the surrounding rock and the distribution curves of the stress components of the surrounding rock are calculated by using the Wang method, the Lee and Pietruszczak method and the method in this embodiment, as shown in Figure 10 . The specific parameters are taken from the research of Lee et al.: the radius of the circular tunnel is taken as 2 m, the Poisson's ratio is taken as 0.3, the initial in-situ stress σ0 = 15 MPa, the support pressure p i = 2.5 MPa, the elastic modulus of the surrounding rock is 5700 MPa, the peak uniaxial compressive strength and the residual uniaxial compressive strength are 30 MPa and 25 MPa respectively, the peak strength parameters m p , s p , a p and the residual strength parameters m r , s r , a r are 1.7, 0.0039, 0.55 and 0.85, 0.0019, 0.6 respectively. Without considering the dilatancy effect of the surrounding rock, the dilatancy angle of the whole plastic region is taken as 0°, and the critical plastic softening coefficient η * is taken as 0.004; when the number of concentric rings n taken for calculation is 500, the calculation accuracy can be fully guaranteed, Figure 10 (a) The abscissa uses dimensionless units, representing the size of the surrounding rock radius, and the ordinate represents the deformation of the surrounding rock; Figure 10 (b) The ordinate represents the stress component.

[0187] From Figure 10 it can be seen that for, comparing the deformation of the surrounding rock at different radii and the distribution of the tangential stress and radial stress calculated by the Wang method and the Lee method, the calculation results of the algorithm in this embodiment are basically the same, which verifies the correctness of the algorithm in this embodiment to a certain extent.

[0188] Effect of the critical softening coefficient on the elastic modulus: Set p i to 0 MPa, and use the nonlinear reduction model of the elastic modulus to calculate the distribution of the elastic modulus of the surrounding rock in the plastic region under different η * . For Blanco Mera granite, assume that the rock mass GSI p in the elastic stage = 30, set η * to be 0.025, 0.035, 0.045, 0.055, 0.065 respectively. For Moura coal rock, assume that the rock mass GSI in the elastic stagep = 65, set η * to 0.016, 0.02, 0.024, 0.028, 0.032. The actual η of the two kinds of rocks calculated based on the triaxial test results * are 0.035 and 0.032 respectively. Figure 11 The curves of the elastic modulus of the two kinds of surrounding rocks varying with the radius of the plastic zone surrounding rock under different critical plastic softening coefficients are given.

[0189] From Figure 11 it can be seen that the distribution laws of the elastic modulus of the surrounding rock along the radial depth direction of the surrounding rock under different η * are roughly similar. The elastic modulus shows a non-linear decrease in the plastic zone, and the decreasing rate gradually decreases with the decrease of the surrounding rock radius r, and finally tends to be gentle at the tunnel wall, and the elastic modulus drops to the lowest value. At the same time, it can be found that the decreasing rates of the elastic modulus corresponding to different η * in the plastic softening region are basically the same, and are significantly faster than that in the residual region, and the decreasing rate undergoes a significant turning at the junction of the plastic softening region and the residual region. Therefore, the influence of η * on the elastic modulus of the surrounding rock is mainly: the larger η * is, the larger the elastic modulus at the same surrounding rock radius in the plastic softening region; while in the plastic residual region, the influence of η * is negligible, and the distributions of the elastic modulus of the surrounding rock along the radial depth direction under different η * are basically the same.

[0190] To deeply explore the influence effects of the confining pressure and plastic strain on the elastic modulus of the surrounding rock, the curves of the elastic modulus of the two kinds of surrounding rocks varying with the axial plastic strain are given, as Figure 12 . The elastic modulus does not linearly decrease with the increase of the axial plastic strain, but undergoes an obvious turning at the junction of the plastic softening region and the residual region. Figure 13 As shown in the curves of the confining pressure σ3 and the axial plastic strain relationship under different η * , by comparing Figure 12 , Figure 13 , it can be seen that the variation laws of σ3 and the elastic modulus with the axial plastic strain show a high degree of similarity, indicating that the difference in the elastic modulus of the surrounding rock is caused by the change of σ3. By comparing the two types of tunnel surrounding rocks represented by Blanco Mera granite and Moura coal rock, the degrees of influence of σ3 on their elastic moduli are also different. The difference in the elastic modulus caused by the change of σ3 at the same axial plastic strain of Blanco Mera granite is smaller than that of Moura coal rock.

[0191] As described above, it is only the preferred specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for analyzing the surrounding rock deformation law based on the property of elastic modulus reduction, characterized in that, Including: Obtaining data on the influencing factors for the post-peak decay of the elastic modulus of rock samples, and constructing a non-linear decay model for the rock elastic modulus based on the influencing factors; The process of constructing the non-linear decay model for the rock elastic modulus includes: Analyze the variation law of the elastic modulus E of rock samples under the same confining pressure condition with the axial plastic strain to obtain the non-linear relationship between the elastic modulus E and the axial plastic strain . Fit the non-linear relationship between the elastic modulus E and the axial plastic strain individually to complete the construction of the non-linear decay model of the rock elastic modulus; Among them, the calculation formula for separately fitting the nonlinear relationship between the elastic modulus E and the axial plastic strain ε1 p is as follows: b = b1 + b2exp(-b3·σ3) where: λ, b, and c are all function fitting coefficients, and λ i , b i , c i (i = 1, 2, 3) are all fitting coefficients, is the axial plastic strain of the rock sample at the unloading point, σ3 is the confining pressure, the λ3 in refers to the λ3 power of σ3, and the c3 in Constructing an excavation model for strain-softening surrounding rock, analyzing the excavation model for strain-softening surrounding rock based on the non-linear decay model of the rock elastic modulus and the finite difference method to obtain stress-strain field data for the deep-buried tunnel strain-softening surrounding rock, and obtaining displacement field data based on the stress-strain field data; Performing combined analysis on the stress-strain field data and the displacement field data to obtain data on the deformation law of the surrounding rock.

2. The method for analyzing the deformation law of the surrounding rock according to claim 1, wherein The data on the influencing factors for the post-peak decay of the elastic modulus of the rock samples includes: the plastic strain of the rock samples and the confining pressure on the rock samples.

3. The method for analyzing the deformation law of the surrounding rock according to claim 1, wherein The process of constructing the excavation model for strain-softening surrounding rock includes: Obtaining data on the mechanical characteristics of circular chamber excavation, constructing a circular chamber excavation model based on the mechanical characteristics of circular chamber excavation, and constructing an excavation model for strain-softening surrounding rock based on the circular chamber excavation model and in combination with the Hoek-Brown yield criterion; Among them, the data on the mechanical characteristics of circular chamber excavation includes: At an infinite distance from the cross-section, a uniform stress σ0 acts, and the support pressure on the inner wall of the cavity is p i , the radius R of the plastic softening region p and the radius R of the plastic residual region f , the radial stress σ at the junction of the elastic-plastic region r2 and the tangential stress σ θ2 , the radial stress σ at the boundary between the plastic softening and residual regions r1 and the tangential stress σ θ1 ; The calculation formula for constructing the excavation model for strain-softening surrounding rock is: Introducing the plastic softening coefficient η characterizing the deterioration degree of the surrounding rock strength parameter: In the formula, η is the plastic softening coefficient of the deterioration degree of the surrounding rock strength parameter. and respectively represent the axial plastic strain and the radial plastic strain. η actually represents the plastic shear strain of the surrounding rock, and η * represents the critical plastic shear strain of the surrounding rock; m b , s, and a are parameters characterizing the surrounding rock strength; σ1 and σ3 are respectively the maximum principal stress and the minimum principal stress of the rock. Under the plane strain state, the longitudinal stress is regarded as the intermediate principal stress σ2. In the research section, the tangential stress σ θ of the surrounding rock and the radial stress σ r respectively correspond to the maximum principal stress σ1 and the minimum principal stress σ3; m b , s, and a are the surrounding rock strength parameters; ω represents the strength parameters m b , s, and a; ω p and ω r respectively correspond to the peak strength parameters s p , a p at the elastic-plastic interface under a certain confining pressure σ3 and the residual strength parameters s r , a r in the plastic residual area; In the strain-softening model, the H-B yield criterion is: f(σ r ,σ θ ,η) = σ θ -σ r - σ ci (m b (η)σ r / σ ci (η)+s(η)) a(η) =0 In the formula, the plastic softening coefficient η determines the strength parameters m b , s, and a represent the degree of linear decrease with the increase of plastic shear strain in the plastic softening region, and σ r is the radial stress of the surrounding rock, and σ θ is the tangential stress of the surrounding rock, and σ ci represents the uniaxial compressive strength of the rock, and m b (η), s(η), and a(η) are the strength parameters at a certain plastic softening coefficient η, and σ ci (η) represents the uniaxial compressive strength of the rock at a certain plastic softening coefficient η.

4. The method for analyzing the deformation law of the surrounding rock according to claim 1, wherein The stress-strain field data includes radial stress data at the elastic-plastic interface, stress data in the plastic region, and strain component data in the plastic region.

5. The method for analyzing the deformation law of the surrounding rock according to claim 4, wherein The process of obtaining the radial stress data σ at the elastoplastic interface r2 includes: where σ ci represents the uniaxial compressive strength of the rock, σ0 represents the uniformly distributed stress acting at an infinite distance from the cross-section, a p , s p , are the peak strength parameters at the elastic-plastic interface.

6. The method for analyzing the deformation law of the surrounding rock according to claim 4, wherein The process of obtaining the stress data in the plastic region and the strain component data in the plastic region includes: Obtaining the stress data in the plastic region by the finite difference method: Layering the plastic region in the excavation model for strain-softening surrounding rock: where: n represents the number of divided circles of the ring, Δσ r is the radial stress increment of each ring, and σ in the formula r(n) represents the support force p at the tunnel wall i , σ r(0) represents the radial stress at the junction of the elastic-plastic region, σ r(i-1) and σ r(i) respectively represent the radial stresses on the surrounding rock at the inner and outer boundary tunnel walls of the i-th ring; The strain components in the i-th ring are expressed as: ε θ(0) =(1 + μ)(σ0 - σ r2 ) / E0 ε r(0) =(1 + μ)(σ r2 - σ0) / E0 In the formula, ε r(0) , ε θ(0) respectively represent the radial strain component and the tangential strain component at infinity in the cross-section. μ represents the Poisson's ratio of the surrounding rock, E represents the elastic modulus of the rock mass, E0 is the peak elastic modulus at the elastic-plastic interface, σ0 represents the uniform stress acting at infinity in the cross-section, σ r2 represents the radial stress at the junction of the elastic-plastic region, ε r(i-1) , ε θ(i-1) are respectively the radial strain component and the tangential strain component of the inner boundary of the i-th ring, ε r(i) , ε θ(i) are respectively the radial strain component and the tangential strain component of the outer boundary of the i-th ring, is the increment of the elastic strain component at the i-th ring, is the increment of the plastic strain component at the i-th ring, Δσ r(i) , Δσ θ(i) respectively represent the radial stress component and the tangential stress component at the i-th ring; The increment of the plastic softening coefficient Δη at the ith ring (i) is as follows: where ε r(i) , ε θ(i) are the radial strain component and the tangential strain component of the outer boundary of the i-th ring respectively, and ε r(i-1) , ε θ(i-1) are the radial strain component and the tangential strain component of the inner boundary of the i-th ring respectively, is the increment of the elastic strain component at the i-th ring, is the increment of the plastic strain component at the i-th ring; Plastic softening coefficient η at the junction of the elastic-plastic region (0) is 0, and η at the i-th ring is obtained by superimposing the increment of the plastic softening coefficient of the previous i rings (i) ; According to the non-associated flow rule of the surrounding rock: where ε r(i) , ε θ(i) are respectively the radial strain component and the tangential strain component of the outer boundary of the i-th ring, and ε r(i-1) , ε θ(i-1) are respectively the radial strain component and the tangential strain component of the inner boundary of the i-th ring, is the increment of the elastic strain component at the i-th ring, is the increment of the plastic strain component at the i-th ring, and β is the dilatancy coefficient of the surrounding rock; The ratio of the inner and outer boundary radii of the i-th ring is: where r (i-1) and r (i) are the surrounding rock radii of the inner and outer boundaries of the i-th ring respectively, η (i-1) is the plastic shear strain of the surrounding rock at the outer boundary of the i-th ring, Δσ r is the radial stress increment of each ring, σ′ r(i) =(σ r(i) +σ′ r(i-1) ) / 2, within the plastic softening region, within the plastic residual region Obtaining the tangential strain component data and the radial strain component data in the plastic region: where ε r(i) and ε θ(i) are the radial strain component and tangential strain component of the outer boundary of the i-th ring respectively, Δu (i) is the increment of surrounding rock deformation at the inner boundary of the i-th ring, Δr (i) is the radius of the surrounding rock at the inner boundary of the i-th ring, u (i-1) and u (i) are the surrounding rock deformations at the inner and outer boundaries of the i-th ring respectively, r (i-1) and r (i) are the radii of the surrounding rock at the inner and outer boundaries of the i-th ring respectively, In the plastic softening region, B (i-1) = σ ci(i-1) (m b(i-1) σ r(i) / σ ci(i-1) + s (i-1) ) a(i-1) , in the plastic residual region, β is the dilatancy coefficient of the surrounding rock. Under stress-strain conditions, β = (1 + sinψ) / (1 - sinψ), where ψ is the dilation angle.

7. The method for analyzing the deformation law of the surrounding rock according to claim 6, wherein The displacement field data includes: the radius R of the plastic softening region p and the radius R of the plastic residual region f ; The process of obtaining the displacement field data includes: When entering the k-th ring, plastic residual failure of the surrounding rock begins: wherein, R p represents the radius of the plastic softening zone, R f represents the radius of the plastic residual zone, σ′ r(k) =(σ r(k) +σ′ r(k-1) ) / 2, η (k-1) is the plastic shear strain of the surrounding rock at the outer boundary of the k-th ring, Δσ r is the radial stress increment of each ring. After the surrounding rock enters the plastic residual region, the equilibrium equation in this region is: In the formula, σ r represents the radial stress of the surrounding rock, r represents the radius of the surrounding rock, m b r , s r , a r represent the residual strength parameters of the plastic residual area, and σ ci represents the uniaxial compressive strength of the rock. Obtain the boundary conditions: r = R0, σ r = p i ; r = R f , σ r = σ r1 , σ r1 is the radial stress at the junction of the plastic softening and residual regions, and the radius R f of the plastic residual region is obtained based on the above boundary conditions, and the expression is: wherein, R f represents the radius of the plastic residual region, R0 represents the radius of the boundary region between the elastic-plastic regions, σ r1 is the radial stress at the junction of the plastic softening and the residual region, σ ci represents the uniaxial compressive strength of the rock, s r , a r represent the residual strength parameters of the plastic residual region, p i represents the support pressure on the inner wall of the tunnel.

8. The method for analyzing the deformation law of the surrounding rock according to claim 1, wherein The data on the deformation law of the surrounding rock includes: data on the deformation law of the plastic zone surrounding rock and data on the deformation law of the elastic zone surrounding rock.

9. The method for analyzing the deformation law of the surrounding rock according to claim 8, wherein The process of obtaining the data on the deformation law of the plastic zone surrounding rock includes: where u (i-1) and u (i) are the surrounding rock deformations at the inner and outer boundaries of the i-th ring respectively, r (i-1) and r (i) are the surrounding rock radii at the inner and outer boundaries of the i-th ring respectively, In the plastic softening region, B (i-1) = σ ci(i-1) (m b(i-1) σ r(i) / σ ci(i-1) + s (i-1) ) a(i-1) , in the plastic residual region, β is the dilatancy coefficient of the surrounding rock. Under stress-strain conditions, β = (1 + sinψ) / (1 - sinψ), where ψ is the dilation angle; The process of obtaining the data on the deformation law of the elastic zone surrounding rock includes: In the formula, and u e are the elastic radial stress, elastic tangential stress and surrounding rock deformation respectively. E0 is the peak elastic modulus at the elastoplastic interface, r is the radius of the surrounding rock, μ is the Poisson's ratio of the surrounding rock, σ0 is the uniformly distributed stress acting at infinity in the cross-section, σ r2 is the radial stress at the junction of the elastoplastic region, R p is the radius of the plastic softening region.

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