A calculation method of elastic-plastic model for shield-frozen reinforced rock and soil

Abstract

This invention discloses a calculation method for the elastoplastic model of frozen soil and rock reinforced by shield tunneling. It constructs a sample library of soil and rock masses with water content and soil / rock temperature as inputs and hardening and softening parameters as outputs. A support vector machine (SVM) model is trained to obtain SVM expression models for hardening and softening parameters. The stress-strain constitutive expression of the soil and rock masses based on an intelligent surrogate model is obtained. Finally, an elastoplastic model of the frozen soil layer of the soil and rock masses, including the intelligent surrogate model, is obtained. Combined with the temperature of the soil and rock masses, the surface displacement and settlement values ​​during frozen shield tunneling are obtained, completing the calculation of the elastoplastic model of frozen soil and rock reinforced by shield tunneling. This invention makes good use of soil elastoplastic mechanics, combining the freezing and thawing processes to better reflect the state of frozen soil and rock reinforced by shield tunneling, and describes the characteristics of soil freeze-thaw softening, providing strong guidance for practical engineering.

Description

Technical Field

[0001] This invention relates to the field of tunnel boring machine (TBM) construction technology, and in particular to a method for calculating the elastic-plastic model of frozen and reinforced rock and soil in TBM tunneling. Background Technology

[0002] For shield tunneling projects in complex environments with poor soil conditions, such as water-rich, soft strata, shallow burial, and densely built-up areas, artificial freezing is an effective method for reinforcing unfavorable soil layers. The core principle of this method is to utilize artificial refrigeration technology. Freezing pipes are buried in the soil layer to be treated, and low-temperature refrigerant is introduced into the water-rich strata surrounding the underground space to be excavated. This places the water in the surrounding strata in a temperature field below its freezing point, causing the water in the soil layer to continuously freeze and form ice. This ice then binds the soil particles together, creating a closed, continuous structure. The overall strength and elastic modulus of this soil mass are far greater than the original soil structure before freezing. The freezing method freezes the strata surrounding the excavated soil into a closed, continuous body.

[0003] In reality, apart from frost heave deformation, soil generally conforms to an elastoplastic constitutive relationship. Low-temperature freezing and subsequent thawing alter the mechanical properties of the soil, producing strengthening or deteriorating effects, thus impacting the original constitutive relationship and leading to different mechanical response patterns of soil and rock masses during tunnel boring machine (TBM) construction. Although current freezing methods have been widely applied in engineering, calculations for the freezing and thawing processes typically involve frost heave force calculations and three-dimensional frost heave deformation calculations, failing to effectively integrate the elastoplastic mechanical calculations of soil during the freezing and thawing processes. Summary of the Invention

[0004] This invention discloses a calculation method for the elastic-plastic model of shield tunneling frozen and reinforced rock and soil, in order to overcome the above-mentioned technical problems.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A calculation method for an elastoplastic model of frozen and reinforced rock and soil in tunnel boring machines includes the following steps:

[0007] S1: Establish an elastoplastic model of the frozen soil layer in the shield tunneling frozen and reinforced rock and soil body; the elastoplastic model of the frozen soil layer includes an elastoplastic constitutive model of the frozen soil layer considering the soil hardening parameters during freezing and an elastoplastic constitutive model of the thawing soil layer considering the soil softening parameters during thawing.

[0008] S2: Construct a sample library of soil and rock with water content and soil temperature as inputs and hardening and softening parameters as outputs, in order to train the support vector machine model and obtain the support vector machine expression model of hardening parameters in the elastoplastic constitutive model of the soil layer when frozen and the support vector machine expression model of softening parameters in the elastoplastic constitutive model of the soil layer when thawing.

[0009] S3: Based on the support vector machine expression model of the hardening parameters, obtain the frozen shear modulus and the frozen bulk modulus based on the intelligent surrogate model.

[0010] Based on the support vector machine expression model of the softening parameters, the shear modulus and bulk modulus after melting based on the intelligent surrogate model are obtained.

[0011] S4: Based on the frozen shear modulus and frozen bulk modulus based on the intelligent proxy model, obtain the stress-strain constitutive expression of the soil and rock mass after freezing, considering the hardening factor, based on the intelligent proxy model.

[0012] Based on the shear modulus and bulk modulus after melting based on the intelligent proxy model, the stress-strain constitutive expression of the rock and soil mass after freezing and melting, considering the softening factor, is obtained based on the intelligent proxy model.

[0013] S5: Based on the stress-strain constitutive expression of rock and soil after freezing considering hardening factors and the stress-strain constitutive expression of rock and soil after freezing and thawing considering softening factors, obtain the elastoplastic model of the frozen soil layer of the rock and soil body based on the intelligent agent model, including the elastoplastic constitutive model of the soil layer when frozen and the elastoplastic constitutive model of the soil layer when thawing.

[0014] S6: Based on the temperature of the soil and rock mass, the elastoplastic constitutive model of the soil layer when frozen by the intelligent agent model and the elastoplastic constitutive model of the soil layer when thawing by the intelligent agent model, the surface displacement and settlement value of the frozen shield tunneling is obtained to complete the calculation of the elastoplastic model of the frozen reinforced soil and rock mass of the shield tunneling.

[0015] Furthermore, the elastic-plastic constitutive model of the soil layer at the time of freezing in the intelligent agent model is obtained as follows:

[0016]

[0017] The elastic-plastic constitutive model of the soil layer during melting, obtained from the intelligent agent model, is as follows:

[0018]

[0019] Furthermore, the method for establishing the elastoplastic constitutive model of the soil layer considering freezing is as follows:

[0020] First: Obtain the soil hardening parameters at the time of freezing as follows:

[0021]

[0022] In the formula, EH (w,T) is the elastic modulus of the rock and soil at the freezing temperature; E0 is the elastic modulus of the rock and soil before freezing; w is the water content; T is the temperature of the rock and soil; T0 is the freezing-thawing threshold of the rock and soil temperature.

[0023] Secondly, based on the soil hardening parameters at the time of freezing, the stress-strain constitutive expression for the frozen soil and rock mass is established as follows:

[0024]

[0025] In the formula: σ H This represents the stress tensor of the soil layer at the time of freezing. It is the tensor of the elastic strain of the soil layer when it freezes; : is the symbol in tensor operations; D He It is the frozen elastic modulus matrix.

[0026] in,

[0027]

[0028] In the formula: I s G represents a fourth-order symmetric tensor. H K represents the shear modulus after freezing; H Indicates the bulk modulus after freezing; This represents the tensor product obtained by multiplying two vectors.

[0029] Finally: Based on the stress-strain constitutive expression of soil and rock mass considering hardening factors after freezing, the elastic-plastic constitutive model of the soil layer at freezing time is established as follows:

[0030]

[0031] at this time,

[0032] In the formula: F H Let J1 be the plastic yield function of the soil layer at freezing point; I1 be the first invariant of stress; J2(s) be the second invariant of deviatoric stress, where s is an intermediate calculation parameter; I represents the identity matrix, where... i, j represent the row and column indices of the identity matrix, respectively; δ ij For Kroneck symbol; e i This represents a matrix where the elements in the i-th row are 1s and the rest are 0s. denoted as the tensor product of two vectors; c is the cohesion; θ is the Lod angle of stress. It is the internal friction angle.

[0033] Furthermore, the method for establishing the elastoplastic constitutive model of the soil layer during melting is as follows:

[0034] First: Obtain the soil softening parameters during melting as follows:

[0035]

[0036] In the formula, S(w,T) represents the softening parameter; E S (w,T) represents the elastic modulus of the soil when the temperature of the soil recovers from the freezing temperature to room temperature; E0 is the elastic modulus of the soil before freezing.

[0037] Secondly, based on the soil softening parameters during melting, the stress-strain constitutive expression for the rock and soil mass considering softening factors after freezing and thawing is established as follows:

[0038]

[0039] In the formula: σ S This represents the stress tensor of the soil layer during melting; D is the tensor of the elastic strain of the soil layer during melting; Se It is the softened elastic modulus matrix;

[0040] in,

[0041]

[0042] In the formula, I represents a fourth-order symmetric tensor; G S It is the shear modulus after melting; K S is the bulk modulus after melting; G0 is the shear modulus of the soil and rock mass; K0 is the bulk modulus of the soil and rock mass; E0 is the elastic modulus of the soil and rock mass before freezing; μ is the Poisson's ratio of the soil and rock mass before damage; S(w,T) represents the softening parameter; w is the water content, and T is the temperature of the soil and rock mass.

[0043] Finally: Based on the stress-strain constitutive expression considering softening factors after freezing and thawing of soil and rock, the elastic-plastic constitutive model of the soil layer during thawing is established as follows:

[0044]

[0045] at this time,

[0046] Furthermore, the support vector machine representation models for the hardening parameters and softening parameters are as follows:

[0047] SVMH(w,T)=H(w,T)

[0048] SVMS(w,T)=S(w,T)

[0049] In the formula: SVMH(w,T) represents the support vector machine expression of the hardening parameter H(w,T); SVMS(w,T) represents the support vector machine expression of the softening parameter S(w,T).

[0050] Furthermore, the frozen shear modulus and the frozen bulk modulus based on the intelligent agent model are obtained as follows:

[0051]

[0052] Where: SVMG H SVMK represents the frozen shear modulus expressed by a support vector machine. H This represents the frozen bulk modulus expressed by the support vector machine.

[0053] The melted shear modulus and the melted bulk modulus based on the intelligent surrogate model are obtained as follows:

[0054]

[0055] Where: SVMG S SVMK represents the melted shear modulus expressed by the support vector machine. S This represents the bulk modulus after melting, as expressed by the support vector machine.

[0056] Furthermore, the stress-strain constitutive expression for the frozen soil and rock mass based on the intelligent agent model, considering hardening factors, is obtained as follows:

[0057]

[0058] in,

[0059]

[0060] Where: SVMσ H SVMD represents the stress tensor of the soil layer at freezing time, expressed using a support vector machine. He This represents the frozen elastic modulus matrix expressed using a support vector machine.

[0061] The stress-strain constitutive expression for the rock and soil mass after freezing and thawing, taking into account softening factors, based on the intelligent agent model, is obtained as follows:

[0062]

[0063] in,

[0064]

[0065] Where: SVMσ SThis represents the stress tensor of the soil layer during melting, expressed using a support vector machine (SVMD). Se This represents the softened elastic modulus matrix expressed based on a support vector machine.

[0066] Beneficial Effects: This invention provides a method for calculating the elastoplastic model of frozen soil and rock for shield tunneling. By constructing a sample library of soil and rock with water content and soil temperature as inputs and hardening and softening parameters as outputs, a support vector machine (SVM) model is trained. This allows for the acquisition of SVM expressions for hardening parameters in the elastoplastic constitutive model of the soil layer during freezing and for softening parameters in the elastoplastic constitutive model of the soil layer during thawing. Furthermore, it obtains the shear modulus, bulk modulus, and shear modulus after freezing and thawing based on an intelligent surrogate model. Further, it acquires stress-strain constitutive expressions for soil and rock considering hardening factors after freezing and for softening factors after freezing and thawing, based on the intelligent surrogate model. Finally, it yields an elastoplastic model of the frozen soil layer including the intelligent surrogate model. Combined with the soil and rock temperature, it obtains the surface displacement and settlement values ​​during frozen shield tunneling, thus completing the calculation of the elastoplastic model of frozen soil and rock for shield tunneling. This invention makes good use of soil elastoplastic mechanics, combining the freezing and thawing processes, which can better reflect the state of the frozen and reinforced rock and soil in shield tunneling, describe the characteristics of soil freeze-thaw softening, and has a strong guiding role for engineering practice. Attached Figure Description

[0067] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0068] Figure 1 This is a flowchart of the calculation method for the elastic-plastic model of shield tunneling frozen and reinforced rock and soil according to the present invention;

[0069] Figure 2 This is a flowchart of the calculation method for the strengthening-softening elastoplastic model of frozen rock and soil in shield tunneling according to an embodiment of the present invention;

[0070] Figure 3 This is a flowchart of the Abaqus secondary development process in an embodiment of the present invention;

[0071] Figure 4 This is a schematic diagram of the formation of the frozen soil wall in an embodiment of the present invention;

[0072] Figure 5 This is a model diagram of a tunnel boring machine excavation in an embodiment of the present invention;

[0073] Figure 6a This is a vertical displacement cloud map of the shield tunnel section without freezing in an embodiment of the present invention.

[0074] Figure 6b This is a vertical displacement cloud map of the shield tunnel section with a freezing temperature of -5℃ in an embodiment of the present invention.

[0075] Figure 6c This is a vertical displacement cloud map of the shield tunnel section with a freezing temperature of -10℃ in an embodiment of the present invention. Figure 7 This is the surface settlement curve during single-tunnel excavation in an embodiment of the present invention;

[0076] Figure 8a This is a distribution diagram of the softened zone after melting at a freezing temperature of -5℃ in an embodiment of the present invention;

[0077] Figure 8b This is a distribution diagram of the softened zone after melting at a freezing temperature of -10℃ in an embodiment of the present invention. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] This embodiment introduces a calculation method for an elastic-plastic model of frozen and reinforced rock and soil in shield tunneling, such as... Figure 1 and Figure 2 As shown, it includes the following steps:

[0080] S1: Establish an elastoplastic model of the frozen soil layer for the shield-frozen reinforcement of rock and soil during the shield freezing method construction process; the elastoplastic model of the frozen soil layer includes an elastoplastic constitutive model of the frozen soil layer considering the soil hardening parameters during freezing and an elastoplastic constitutive model of the thawing soil layer considering the soil softening parameters during thawing.

[0081] Preferably, the method for establishing the elastoplastic constitutive model of the soil layer considering freezing is as follows:

[0082] Specifically, in this embodiment, the soil and rock mass during the shield tunneling freezing method is considered as a continuous porous medium. Since the soil layer hardens during freezing, and the degree of hardening is affected by water content and low temperature, the hardening parameter is chosen as a function of water content and freezing temperature, expressed as H(w,T). Freezing increases the elastic modulus and also has a certain impact on the plastic internal variables. When the temperature is lower than the room temperature freezing temperature,

[0083] First: Obtain the soil hardening parameters at the time of freezing as follows:

[0084]

[0085] In the formula, E H (w,T) is the elastic modulus of the rock and soil at the freezing temperature; E0 is the elastic modulus of the rock and soil before freezing; w is the water content; T is the temperature of the rock and soil; T0 is the freezing-thawing threshold of the rock and soil temperature.

[0086] Secondly, based on the soil hardening parameters at the time of freezing, the stress-strain constitutive expression for the soil and rock mass considering hardening factors after freezing is established as follows:

[0087]

[0088] In the formula: σ H This represents the stress tensor of the soil layer at the time of freezing. It is the tensor of the elastic strain of the soil layer when it freezes; : is the symbol in tensor operations, indicating double dot product, representing the components being multiplied in a certain order; D He It is the frozen elastic modulus matrix.

[0089] in,

[0090]

[0091] Among them, G H K H The relationship with G0 and K0 is expressed as follows:

[0092]

[0093] In the formula: I s G represents a fourth-order symmetric tensor. H K represents the shear modulus after freezing; H Indicates the bulk modulus after freezing; This represents the tensor product obtained by multiplying two vectors.

[0094] Finally: Based on the stress-strain constitutive expression of soil and rock mass considering hardening factors after freezing, the elastic-plastic constitutive model of the soil layer at freezing time is established as follows:

[0095] Specifically, since the internal friction angle is not sensitive to changes in freezing hardening and thawing softening, its impact is relatively small; therefore, only the effect of damage on cohesion is considered. During freezing, the soil layer hardens, and its elastoplastic constitutive model is as follows:

[0096]

[0097] in,

[0098] J2(s)=(1 / 2)s:s

[0099] at this time,

[0100] In the formula: F H Let be the plastic yield function of the soil layer at freezing point; I1 is the first invariant of stress; J2(s) is the second invariant of deviatoric stress, and s is an intermediate calculation parameter; I represents the identity matrix, i.e., all elements on the main diagonal are 1, where i and j represent the row and column indices of the identity matrix, respectively, where i, j = 1, 2, 3, δ ij For Kroneck symbol; e i This represents a matrix where the elements in the i-th row are 1s and the rest are 0s. denoted as the tensor product of two vectors; c is the cohesion; θ is the Lode angle of stress. It is the internal friction angle;

[0101] Preferably, the method for establishing the elastoplastic constitutive model of the soil layer during melting is as follows:

[0102] Specifically, when the frozen soil layer recovers from its freezing temperature to its original temperature (i.e., thaws), soil damage and softening occur, manifested as a decrease in the elastic modulus. The softening parameter is chosen as a function of water content *w* and freezing temperature *T*, denoted as S(w,T). When the temperature *T* recovers from the freezing temperature to the original room temperature, firstly, the soil softening parameters at thawing are obtained as follows:

[0103]

[0104] In the formula, S(w,T) represents the softening parameter; E S (w,T) represents the elastic modulus of the soil when the temperature of the soil recovers from the freezing temperature to the original room temperature (0 degrees); E0 is the elastic modulus of the soil before freezing.

[0105] Secondly, based on the soil softening parameters during melting, the stress-strain constitutive expression for the rock and soil mass considering softening factors after freezing and thawing is established as follows:

[0106]

[0107] In the formula: σ S This represents the stress tensor of the soil layer during melting; D is the tensor of the elastic strain of the soil layer during melting; Se It is the softened elastic modulus matrix;

[0108] in,

[0109]

[0110] GS K S The relationship with G0 and K0 is expressed as follows:

[0111]

[0112] In the formula, I S G represents a fourth-order symmetric tensor; S It is the shear modulus after melting; K S is the bulk modulus after melting; G0 is the shear modulus of the soil and rock mass; K0 is the bulk modulus of the soil and rock mass; E0 is the elastic modulus of the soil and rock mass before freezing; μ is the Poisson's ratio of the soil and rock mass before damage; S(w,T) represents the softening parameter; w is the water content, and T is the temperature of the soil and rock mass.

[0113] Finally: Based on the stress-strain constitutive expression considering softening factors after freezing and thawing of soil and rock, the elastoplastic constitutive model of the soil layer during thawing is established as follows: At this time, the soil layer undergoes damage and softening during thawing:

[0114]

[0115] at this time,

[0116] Specifically, the elastoplastic model of the frozen soil layer in this embodiment is solved using the Newton-Raphson method of the incremental finite element method.

[0117] Specifically, in the calculation of the elastoplastic model of frozen soil layers, it is difficult to give explicit formulas for the hardening parameter H(w,T) and softening parameter S(w,T). These formulas are crucial for calculating the elastoplastic model of frozen soil layers. This embodiment uses the SVMH(w,T) and SVMS(w,T) intelligent surrogate models to replace the original formulas. The steps for establishing the SVMH(w,T) intelligent surrogate model are as follows:

[0118] For different combinations of moisture content (w) and temperature (T), the elastic modulus of the corresponding specimens was obtained through uniaxial tests using freezing and melting experiments. The hardening and softening parameters were calculated using the following formulas:

[0119] S2: Construct a sample library of soil and rock masses with different water contents w and soil and rock temperatures T as inputs, and hardening parameters H(w,T) and softening parameters S(w,T) as outputs, to train the support vector machine model, and then obtain the support vector machine SVM expression model of hardening parameter H(w,T) in the elastoplastic constitutive model of the soil layer when frozen and the support vector machine SVM expression model of softening parameter S(w,T) in the elastoplastic constitutive model of the soil layer when thawing;

[0120] Specifically, the soil and rock sample library established in this embodiment is as follows:

[0121] {w1,T1;H1(w1,T1),S1(w1,T1)}, {w2,T2;H2(w2,T2),S2(w2,T2)},

[0122] {w3,T3;H3(w3,T3),S3(w3,T3)},…,{w m ,T m H m (w m ,T m ),S m (w m ,T m )}、

[0123] {w m+1 ,T m+1 H m+1 (w m+1 ,T m+1 ),S m+1 (w m+1 ,T m+1 )}、…、{w n ,T n H n (w n ,T n ),S n (w n ,T n )}(11)

[0124] Among them, w n T represents the water content of the nth sample; n H represents the temperature of the nth sample. n S represents the hardening parameter of the nth sample; n This represents the softening parameter of the nth sample; n is the total number of soil and rock samples, and m is the number of training samples, where n>m>1.

[0125] Specifically, in this embodiment, the support vector machine model is trained using the sample library of the aforementioned soil and rock mass. Wherein, {w1,T1;H1(w1,T1),S1(w1,T1)}, {w2,T2;H2(w2,T2),S2(w2,T2)}, {w3,T3;H3(w3,T3),S3(w3,T3)}, ..., {w m ,T m H m (w m ,T m ),S m (w m ,T m{w} is the learning sample; m+1 ,T m+1 H m+1 (w m+1 ,T m+1 ),S m+1 (w m+1 ,T m+1 )}、…、{w n ,T n H n (w n ,T n ),S n (w n ,T n )} represents the sample for the prediction test.

[0126] Specifically, this embodiment uses cross-validation to select the hyperparameters of the SVM, including the kernel parameter σ and the penalty factor C. The goal of cross-validation is to minimize the absolute error between the predicted and actual values.

[0127] Preferably, the support vector machine (SVM) expression models for hardening parameters H(w,T) and softening parameters S(w,T) are obtained as follows:

[0128] SVMH(w,T)=H(w,T) (T-11)

[0129] SVMS(w,T)=S(w,T) (T-12)

[0130] In the formula: SVMH(w,T) represents the support vector machine expression of the hardening parameter H(w,T); SVMS(w,T) represents the support vector machine expression of the softening parameter S(w,T);

[0131] S3: Based on the support vector machine (SVM) expression model of hardening parameter H(w,T), obtain the frozen shear modulus and the frozen bulk modulus based on the intelligent surrogate model.

[0132] Based on the support vector machine (SVM) expression model of the softening parameter S(w,T), the melted shear modulus and the melted bulk modulus based on the intelligent surrogate model are obtained.

[0133] Preferably, the frozen shear modulus and the frozen bulk modulus based on the intelligent agent model are obtained as follows:

[0134]

[0135] Where: SVMG H SVMK represents the frozen shear modulus expressed by a support vector machine. HThis represents the frozen bulk modulus expressed by the support vector machine.

[0136] The melted shear modulus and the melted bulk modulus based on the intelligent surrogate model are obtained as follows:

[0137]

[0138] Where: SVMG S SVMK represents the melted shear modulus expressed by the support vector machine. S This represents the melted bulk modulus expressed by the support vector machine.

[0139] S4: Based on the frozen shear modulus and frozen bulk modulus based on the intelligent proxy model, obtain the stress-strain constitutive expression of the soil and rock mass after freezing, considering the hardening factor, based on the intelligent proxy model.

[0140] Based on the shear modulus and bulk modulus after melting based on the intelligent proxy model, the stress-strain constitutive expression of the rock and soil mass after freezing and melting, considering the softening factor, is obtained based on the intelligent proxy model.

[0141] Preferably, the stress-strain constitutive expression for the frozen soil mass based on the intelligent agent model, considering hardening factors, is obtained as follows:

[0142]

[0143] in,

[0144]

[0145] Where: SVMσ H SVMD represents the stress tensor of the soil layer at freezing time, expressed using a support vector machine. H "e" represents the frozen elastic modulus matrix expressed based on support vector machine;

[0146] The stress-strain constitutive expression for the rock and soil mass after freezing and thawing, taking into account softening factors, based on the intelligent agent model, is obtained as follows:

[0147]

[0148] in,

[0149]

[0150] Where: SVMσ S This represents the stress tensor of the soil layer during melting, expressed using a support vector machine (SVMD). S"e" represents the softened elastic modulus matrix expressed based on support vector machine;

[0151] S5: Based on the stress-strain constitutive expression of the rock and soil mass considering hardening factors after freezing and the stress-strain constitutive expression of the rock and soil mass considering softening factors after freezing and thawing, the elastic-plastic model of the frozen soil layer of the rock and soil mass of the intelligent agent model is obtained, that is, the strengthening-softening elastic-plastic model of the rock and soil mass of the intelligent agent model for shield tunneling, including the elastic-plastic constitutive model of the soil layer when frozen and the elastic-plastic constitutive model of the soil layer when thawing.

[0152] Specifically, substitute formulas (T-11) and (T-12) into formulas (T-3), (T-4), (T-8), (T-9), (T-10), and (T-5). This yields the intelligent agent model for calculating the strengthening-softening elasto-plastic model of the soil and rock mass during shield tunneling. The corresponding calculations for hardening after freezing are shown in formulas (T-13), (T-14), and (T-17). The corresponding calculations for hardening after freezing are shown in formulas (T-15), (T-16), and (T-18).

[0153] Preferably, the elastic-plastic constitutive model of the soil layer at the time of freezing in the intelligent agent model is obtained as follows:

[0154]

[0155] The elastic-plastic constitutive model of the soil layer during melting, obtained from the intelligent agent model, is as follows:

[0156]

[0157] S6: Based on the temperature of the soil and rock mass, the elastoplastic constitutive models of the soil layer when frozen and the soil layer when thawing in the intelligent agent model are used to obtain the surface displacement and settlement values ​​of the frozen shield tunneling construction based on the Newton-Raphson method, so as to complete the calculation of the elastoplastic model of the frozen reinforced soil and rock mass of the shield tunneling.

[0158] Specifically, the elastoplastic model of the frozen soil layer in the intelligent agent model, i.e., the reinforced-softened elastoplastic model of the shield tunneling soil in the intelligent agent model, is embedded into the finite element calculation method; among which, the reinforced-softened elastoplastic model of the soil also needs to be programmed using the finite element stress reflection algorithm. For example... Figure 3Using the secondary development platform provided by ABAQUS, the corresponding UMAT subroutine is written in FORTRAN. When ABAQUS calls the user subroutine, it uses two actual parameters, KSTEP and KINC, to transfer the current STEP and INCREMENT values ​​to the user subroutine, thus achieving the interconnection between the main program and the UMAT subroutine. Employing the Newton-Raphson iteration process, knowing the result of the m-th iteration step, the calculation process for the (m+1)-th increment step is as follows: where m represents the iteration step number.

[0159] 1. Initialize the external force vector for step m+1 to F. m+1 =F m +△F, and simultaneously initialize the nodal displacement vector U m+1 =U m ;

[0160] Among them, F m U represents the external force vector at the end of the m-th iteration step; m ΔF represents the nodal displacement vector at the end of the m-th iteration step; ΔF represents the external force increment at the (m+1)-th iteration step.

[0161] 2. Begin the overall equilibrium iteration of the structure, first calculating the residual stress of the structure. Among them F int These are the internal forces of the structure; This represents the residual stress in the structure;

[0162] 3. Then, the global stiffness matrix K is formed from the uniform stiffness matrix to solve for the updated nodal displacement increments. Therefore, the strain increment Δε is calculated. m+1 Then, the convergence of the overall equilibrium iteration is checked. The calculation of the elastic stiffness matrix is ​​achieved through formulas (2) and (6). The elastic-plastic stiffness matrix needs to be calculated by combining formulas (9) and (10) through the plastic stress reflection algorithm.

[0163] if It fails to converge and the iterative calculation is repeated. Here, TOL represents the set convergence error; ΔU m+1 This represents the node displacement increment after the (m+1)th iteration step;

[0164] 4. Start stress update. This step is implemented through the UMAT subroutine. The strain increment calculated in the previous step is transferred to the subroutine. Based on the stress regression mapping algorithm in the previous section, the updated stress and uniform stiffness matrix are calculated, and then a new round of iteration begins.

[0165] 5. At the end of the increment step, update the displacement of step m+1, U. m+1 =U m+ΔU m+1 U m Let represent the surface displacement and settlement value after the m-th iteration step.

[0166] Specifically, the steps for numerical simulation of shield tunneling construction in frozen ground in this embodiment are as follows:

[0167] (a) Establish a finite element model for shield tunneling in frozen strata;

[0168] (b) Set the boundary conditions for shield tunneling;

[0169] (c) Assigning geological parameters for shield tunneling;

[0170] (d) Conduct numerical simulation of shield tunneling construction;

[0171] (e) Solve using the elastoplastic finite element method; that is, call the algorithm of the above frozen soil layer freezing hardening and thawing softening model.

[0172] (f) Output the calculation results of surface displacement and settlement during the construction of the frozen shield tunnel.

[0173] This embodiment considers the calculation model for strengthening frozen soil at low temperatures and softening frozen-thawed soil, and presents an intelligent method for determining support vector machine parameters, a secondary development method for the Abaqus finite element model, and a finite element numerical calculation method for shield tunneling in frozen soil layers. In a specific embodiment of the invention, the soil freezing process is as follows: Figure 4 As shown, the refrigerant liquid vaporizes directly inside the freezing pipe, absorbing a large amount of heat from the ground, allowing the frozen soil wall to form in a very short time. Excavation of the tunnel boring machine (TBM) within the frozen soil wall area is characterized by high speed and high load-bearing capacity of the frozen soil wall. Figure 5 This is a model of the excavation of a shield tunnel after freezing. Based on this established model, element meshes are generated, and the finite element method of this embodiment is used for calculation. Figure 6a , Figure 6b , Figure 6c The figure shows the vertical displacement contour maps of the shield tunnel section at different freezing temperatures. As can be seen from the figure, as the freezing temperature changes from unfrozen to -5℃ to -10℃, the displacement of the surrounding rock arch increases from 30.2mm, 15.9mm to 7.7mm. This indicates that the displacement of the surrounding rock of the shield tunnel decreases as the freezing temperature increases. Figure 7 Working conditions one, two, and three represent three scenarios: freezing temperature never frozen, freezing temperature -5℃ to freezing temperature -10℃, respectively. It can be seen that as the freezing temperature decreases, the surface settlement curve during single-tunnel excavation also continuously decreases. Figure 8a and 8bThe diagram shows the distribution of softened areas during shield tunneling after thawing at -5℃ and -10℃. The greater the degree of freezing, the greater the softening after thawing. As can be seen from the diagram, the model established in this embodiment can describe the characteristics of soil freeze-thaw softening.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A calculation method for an elastic-plastic model of frozen and reinforced rock and soil for shield tunneling, characterized in that, Includes the following steps: S1: Establish an elastoplastic model of the frozen soil layer in the shield tunneling frozen and reinforced rock and soil body; the elastoplastic model of the frozen soil layer includes an elastoplastic constitutive model of the frozen soil layer considering the soil hardening parameters during freezing and an elastoplastic constitutive model of the thawing soil layer considering the soil softening parameters during thawing. S2: Construct a sample library of soil and rock with water content and soil temperature as inputs and hardening and softening parameters as outputs, in order to train the support vector machine model and obtain the support vector machine expression model of hardening parameters in the elastoplastic constitutive model of the soil layer when frozen and the support vector machine expression model of softening parameters in the elastoplastic constitutive model of the soil layer when thawing. S3: Based on the support vector machine expression model of the hardening parameters, obtain the frozen shear modulus and the frozen bulk modulus based on the intelligent surrogate model. Based on the support vector machine expression model of the softening parameters, the shear modulus and bulk modulus after melting based on the intelligent surrogate model are obtained. S4: Based on the frozen shear modulus and frozen bulk modulus based on the intelligent proxy model, obtain the stress-strain constitutive expression of the soil and rock mass after freezing, considering the hardening factor, based on the intelligent proxy model. Based on the shear modulus and bulk modulus after melting based on the intelligent proxy model, the stress-strain constitutive expression of the rock and soil mass after freezing and melting, considering the softening factor, is obtained based on the intelligent proxy model. S5: Based on the stress-strain constitutive expression of rock and soil after freezing considering hardening factors and the stress-strain constitutive expression of rock and soil after freezing and thawing considering softening factors, obtain the elastoplastic model of the frozen soil layer of the rock and soil body based on the intelligent agent model, including the elastoplastic constitutive model of the soil layer when frozen and the elastoplastic constitutive model of the soil layer when thawing. S6: Based on the temperature of the soil and rock mass, the elastoplastic constitutive model of the soil layer when frozen by the intelligent agent model and the elastoplastic constitutive model of the soil layer when thawing by the intelligent agent model, the surface displacement and settlement value of the frozen shield tunneling is obtained to complete the calculation of the elastoplastic model of the frozen reinforced soil and rock mass of the shield tunneling.

2. The method for calculating the elastic-plastic model of shield tunnel frozen and reinforced soil and rock as described in claim 1, characterized in that, The elastic-plastic constitutive model of the soil layer at the time of freezing, obtained by the intelligent agent model, is as follows: The elastic-plastic constitutive model of the soil layer during melting, obtained from the intelligent agent model, is as follows:

3. The method for calculating the elastic-plastic model of shield tunnel frozen and reinforced soil and rock as described in claim 1, characterized in that, The method for establishing the elastoplastic constitutive model of the soil layer considering freezing is as follows: First: Obtain the soil hardening parameters at the time of freezing as follows: In the formula, E H (w,T) represents the elastic modulus of the rock and soil at the freezing temperature; E0 represents the elastic modulus of the rock and soil before freezing; w represents the water content; T represents the temperature of the rock and soil; and T0 represents the freezing-thawing threshold of the rock and soil temperature. Secondly, based on the soil hardening parameters at the time of freezing, the stress-strain constitutive expression for the frozen soil and rock mass is established as follows: Where: σ H This represents the stress tensor of the soil layer at the time of freezing. It is the tensor of the elastic strain of the soil layer when it freezes; : is the symbol in tensor operations; D He It is the frozen elastic modulus matrix. in, In the formula: I s G represents a fourth-order symmetric tensor. H K represents the shear modulus after freezing; H Indicates the bulk modulus after freezing; This represents the tensor product obtained by multiplying two vectors. Finally: Based on the stress-strain constitutive expression of soil and rock mass considering hardening factors after freezing, the elastic-plastic constitutive model of the soil layer at freezing time is established as follows: at this time, In the formula: F H Let J1 be the plastic yield function of the soil layer at freezing point; I1 be the first invariant of stress; J2(s) be the second invariant of deviatoric stress, where s is an intermediate calculation parameter; I represents the identity matrix, where... i, j represent the row and column indices of the identity matrix, respectively; δ ij For Kronecker symbol; e i This represents a matrix where the elements in the i-th row are 1s and the rest are 0s. denoted as the tensor product of two vectors; c is the cohesion; θ is the Lod angle of stress. It is the internal friction angle.

4. The method for calculating the elastic-plastic model of shield tunnel frozen and reinforced soil and rock as described in claim 1, characterized in that, The method for establishing the elastoplastic constitutive model of the soil layer during melting is as follows: First: Obtain the soil softening parameters during melting as follows: In the formula, S(w,T) represents the softening parameter; E S (w,T) represents the elastic modulus of the soil mass when the temperature of the soil mass recovers from the freezing temperature to room temperature; E0 is the elastic modulus of the soil mass before freezing. Secondly, based on the soil softening parameters during melting, the stress-strain constitutive expression for the rock and soil mass considering softening factors after freezing and thawing is established as follows: Where: σ S This represents the stress tensor of the soil layer during melting; D is the tensor of the elastic strain of the soil layer during melting; Se It is the softened elastic modulus matrix; in, In the formula, I represents a fourth-order symmetric tensor; G S It is the shear modulus after melting; K S is the bulk modulus after melting; G0 is the shear modulus of the soil and rock mass; K0 is the bulk modulus of the soil and rock mass; E0 is the elastic modulus of the soil and rock mass before freezing; μ is the Poisson's ratio of the soil and rock mass before damage; S(w,T) represents the softening parameter; w is the water content, and T is the temperature of the soil and rock mass. Finally: Based on the stress-strain constitutive expression considering softening factors after freezing and thawing of soil and rock, the elastic-plastic constitutive model of the soil layer during thawing is established as follows: at this time, 5. The method for calculating the elastic-plastic model of shield tunnel frozen and reinforced soil and rock as described in claim 1, characterized in that, The support vector machine (SVM) representation models for hardening parameters and softening parameters are as follows: SVMH(w,T)=H(w,T) SVMS(w,T)=S(w,T) In the formula: SVMH(w,T) represents the support vector machine expression of the hardening parameter H(w,T); SVMS(w,T) represents the support vector machine expression of the softening parameter S(w,T).

6. The method for calculating the elastic-plastic model of shield tunnel frozen and reinforced soil and rock as described in claim 1, characterized in that, The frozen shear modulus and frozen bulk modulus based on the intelligent surrogate model are obtained as follows: Where: SVMG H SVMK represents the frozen shear modulus expressed by a support vector machine. H This represents the frozen bulk modulus expressed by the support vector machine. The melted shear modulus and the melted bulk modulus based on the intelligent surrogate model are obtained as follows: Where: SVMG S SVMK represents the melted shear modulus expressed by the support vector machine. S This represents the bulk modulus after melting, as expressed by the support vector machine.

7. The method for calculating the elastic-plastic model of shield tunnel frozen and reinforced soil and rock as described in claim 1, characterized in that, The stress-strain constitutive expression for the frozen soil and rock mass based on the intelligent agent model, considering hardening factors, is obtained as follows: in, Where: SVMσ H SVMD represents the stress tensor of the soil layer at freezing time, expressed using a support vector machine. He This represents the frozen elastic modulus matrix expressed using a support vector machine. The stress-strain constitutive expression for the rock and soil mass after freezing and thawing, taking into account softening factors, based on the intelligent agent model, is obtained as follows: in, Where: SVMσ S This represents the stress tensor of the soil layer during melting, expressed using a support vector machine (SVMD). Se This represents the softened elastic modulus matrix expressed based on a support vector machine.

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