Tunnel face instability risk assessment method considering the uncertainty of soil strength

Abstract

The present invention provides a method for evaluating the instability risk of a tunnel face considering the uncertainty of soil strength, including determining the basic physical and mechanical parameters, the spatial variability parameters of the soil mass, and the shield machine parameters, establishing a coupled Euler-Lagrange large deformation finite element model of the shield tunnel, conducting an analysis of the stability of the tunnel face in homogeneous soil, extracting the node coordinates of the soil elements in the finite element model, generating a three-dimensional lognormal random field of the soil internal friction angle by the modified linear estimation method according to the spatial variability parameters of the soil mass, and assigning it to the nodes of the soil elements to obtain the strength of the non-uniform soil mass, conducting an analysis of the stability of the tunnel face in non-homogeneous soil, performing multiple Monte Carlo simulations, and obtaining the probability of tunnel face instability. The present invention considers the influence of the spatial variability of soil strength and the opening ratio of the shield machine cutter head on the critical support pressure of the tunnel face, and establishes the relationship between the probability of tunnel face instability and the traditional safety factor.

Description

Technical Field

[0001] The present invention relates to the technical field of tunnel engineering construction safety analysis, and specifically relates to a method for evaluating the instability risk of a tunnel face considering the uncertainty of soil strength. Background Art

[0002] With the increasing shortage of urban space resources, the development of underground space has become one of the main ways of urban development. Shield machines are widely used in the excavation of underground tunnels. During the shield construction process, the support pressure applied in the soil chamber of the shield machine should be sufficient to offset the soil pressure and water pressure outside the tunnel face. Otherwise, the tunnel face will become unstable, resulting in ground subsidence and causing serious damage to nearby infrastructure. Currently, the design method of the face support pressure does not consider the influence of the shield machine cutterhead on the stability of the tunnel face. However, during the actual construction process, a stress arch will form in front of the shield machine cutterhead, and the existence of the stress arch will exert a certain supporting effect on the tunnel face, which will significantly affect the stability of the tunnel face. However, in actual construction, few consider the influence of the shield machine cutterhead on the stability of the tunnel face and the critical support pressure.

[0003] On the other hand, due to the complex geological deposition process of the soil, the strength of the soil has certain spatial variability, and the spatial variability of the soil will significantly affect the stability of the tunnel face, resulting in a large uncertainty in the critical support pressure of the tunnel face. If the uncertainty of soil strength is not considered in the design, the probability of tunnel face instability during shield construction is relatively high. However, in actual construction, few consider the influence of soil strength uncertainty on the stability of the tunnel face.

[0004] In summary, the present invention proposes a method for evaluating the instability risk of a tunnel face considering the uncertainty of soil strength. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method for evaluating the instability risk of a tunnel face considering the uncertainty of soil strength.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for evaluating the instability risk of a tunnel face considering the uncertainty of soil strength, comprising the following steps:

[0008] Step S1: Determine the basic physical and mechanical parameters of the soil at the shield construction site, the spatial variability parameters of the soil, and the shield machine parameters according to in-situ tests and laboratory tests;

[0009] Step S2: Establish a coupled Euler-Lagrange large deformation finite element model of the shield tunnel;

[0010] Step S3: Conduct stability analysis of the tunnel face in homogeneous soil;

[0011] Step S4. Considering the uncertainty of the soil mass, extract the nodal coordinates of the soil elements in the finite element model, and generate a three-dimensional lognormal random field of the soil internal friction angle through the modified linear estimation method according to the spatial variability parameters of the soil mass;

[0012] Step S5. Assign the three-dimensional lognormal random field to the nodes of the soil elements to obtain the non-uniform soil strength, and conduct the stability analysis of the tunnel face in non-homogeneous soil;

[0013] Step S6. Repeat Step S4 and Step S5 to perform multiple Monte Carlo simulations;

[0014] Step S7. When the load factor in non-homogeneous soil is greater than that in homogeneous soil, the tunnel face becomes unstable, and obtain the instability probability of the tunnel face.

[0015] Further, in the said Step S1, the basic physical and mechanical parameters include the elastic modulus E, Poisson's ratio ν, and unit weight γ of the soil mass.

[0016] Further, in the said Step S1, the spatial variability parameters of the soil mass include the average internal friction angle of the soil mass, horizontal correlation length ΘH, vertical correlation length ΘV, and coefficient of variation COV;

[0017] The parameters of the shield machine include the diameter D of the cutterhead of the shield machine and the opening ratio ξ.

[0018] Further, the said Step S2 specifically includes:

[0019] Step S21. According to the buried depth C of the tunnel, diameter D, and the opening ratio ξ of the cutterhead of the shield machine, establish a geometric model of the shield tunnel, where the soil mass is simulated by the Eulerian body, and the cutterhead and shield body of the shield machine are simulated by the Lagrangian body;

[0020] Step S22. Assign the material parameters of the soil mass, cutterhead, and shield body in the model, use the Mohr-Coulomb model to simulate the soil mass, input the elastic modulus E, Poisson's ratio ν, and unit weight γ of the soil mass, and use rigid bodies to simulate the cutterhead and shield body;

[0021] Step S23. Set the model boundary conditions, apply full constraint boundary conditions in three directions to the bottom of the model, apply normal constraint conditions to the sides of the model, and apply fixed constraints to the shield body and cutterhead of the shield machine;

[0022] Step S24. Set the model load conditions, apply the gravitational acceleration g to the entire model, and at the same time apply the support pressure to the tunnel face, and its initial value P0 is equal to the initial ground stress at the tunnel axis;

[0023] Step S25: Set the element type and divide the mesh. The soil mass is simulated using three-dimensional eight-node Euler elements, and the shield machine and cutter head are simulated using three-dimensional eight-node solid elements. Set the minimum element size of the soil mass, shield machine, and cutter head to D / 30, and divide the mesh.

[0024] Furthermore, in the said step S3, input the average internal friction angle of the soil mass By gradually reducing the support pressure P at the face of the opening of the cutter head until the face fails, extract the relationship curve between the velocity v of the soil mass on the face and the normalized support pressure P / P0, and use the pressure corresponding to the inflection point of the curve as the critical support pressure P of the face in homogeneous soil c , which can be expressed by the load coefficient Nγ:

[0025] N γ = P c / γD (1)

[0026] where γ is the unit weight.

[0027] Furthermore, the said step S4 specifically includes:

[0028] Step S41: Assign a value to each node using an independent standard normal random vector r;

[0029] Step S42: Perform Cholesky decomposition on the cross-correlation matrix, and replace the random vector r in each node with Q, and we can get:

[0030] C = L·L T (2)

[0031] Q = L·r (3)

[0032] where L is a lower triangular matrix. Through the transformation of equation (3), the uncorrelated random vector r can be transformed into a correlated random vector with the correlation matrix C. The random vectors Q defined at the unit nodes in three-dimensional space form a leading random field;

[0033] Step S43: Translate and rotate the leading random field to generate an attribute field. The position vector is y, and the mapping relationship between the two is as follows:

[0034] s = J·y + ε (4)

[0035] J = J3J2J1 (5)

[0036]

[0037]

[0038]

[0039] Among them, J is the Jacobian matrix, and J1, J2, and J3 are the components of the Jacobian matrix; ψ1, ψ2, and ψ3 are the rotation angles in three directions, and according to symmetry, their values are uniformly distributed in the interval [0, π / 2]; ε is the translation vector with three direction components, and the property field can be obtained through the rotation and translation in Equation (4).

[0040] Step S44: Interpolate any point of the property field by using the 8 nodes of the elements of the leading random field as follows:

[0041]

[0042] Among them, Q j (y) is the value of the j-th component of the random vector Q at point y; is the value of the j-th component of the random vector Q at the i-th node of element k; Ni(y) is the shape function value of the eight-node element;

[0043] Step S45: Convert the above-generated normal random field into a lognormal random field through an exponential transformation as follows:

[0044]

[0045]

[0046]

[0047] In the formula, is the internal friction angle of the soil; obeys a lognormal distribution with the mean and standard deviation; are respectively the mean and variance of the mean.

[0048] Furthermore, in step S5, in the analysis of the stability of the tunnel face in inhomogeneous soil, gradually reduce the support pressure P ran at the tunnel face where the cutter head is opened until the tunnel face fails, and extract the relationship curve between the velocity of the soil on the tunnel face and the normalized support pressure P ran / P0. The pressure corresponding to the inflection point of the curve is the critical support pressure P c，ran of the tunnel face in this random soil sample, which can be represented by the load factor N γ，ran as follows:

[0049] N γ，ran = P c，ran / γD (13)

[0050] Furthermore, in step S6, perform at least 100 Monte Carlo simulations.

[0051] Further, in the step S7, the calculation formula for the instability probability of the tunnel face is as follows:

[0052]

[0053] In the formula, k is the safety factor; N γ is the load factor in the homogeneous soil calculated in the third step; and are the mean and standard deviation of the load factor N γ，ran in 100 inhomogeneous soil samples in the step S6; Φ is the cumulative normal function, and its mean and standard deviation are respectively and

[0054] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0055] The tunnel face instability risk assessment method considering the uncertainty of soil strength provided by the present invention takes into account the spatial variability of soil strength and the influence of the opening ratio of the shield cutter head on the critical support pressure of the tunnel face, and establishes the relationship between the tunnel face instability probability and the traditional safety factor. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is the flow chart of the tunnel face instability risk assessment method considering the uncertainty of soil strength of the present invention.

[0057] Figure 2 is the specific implementation process diagram of the present invention.

[0058] Figure 3(a) is the full model diagram in the coupled Euler-Lagrange large deformation finite element model of the shield tunnel.

[0059] Figure 3(b) is the half model diagram in the coupled Euler-Lagrange large deformation finite element model of the shield tunnel.

[0060] Figure 4 is the relationship curve between the velocity of the tunnel face in homogeneous soil and the normalized support pressure.

[0061] Figure 5(a) is the full model of the internal friction angle nephogram of a typical inhomogeneous soil sample.

[0062] Figure 5(b) is the half model of the internal friction angle nephogram of a typical inhomogeneous soil sample.

[0063] Figure 6 is the relationship curve between the velocity of the tunnel face in a typical inhomogeneous soil sample and the normalized support pressure.

[0064] Figure 7 is the frequency distribution diagram of the stability coefficient in 100 inhomogeneous soil samples. Detailed implementation mode

[0065] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention.

[0066] In the related art, a stress arch will be formed in front of the cutter head of the shield machine. The existence of the stress arch will form a certain supporting effect on the heading face and will significantly affect the stability of the heading face. However, in actual construction, little consideration is given to the influence of the shield machine cutter head on the stability of the heading face and the critical support pressure; and due to the complex geological deposition process of the soil mass, the strength of the soil mass has a certain variability in space, and the spatial variability of the soil mass will significantly affect the stability of the tunnel heading face, making the critical support pressure of the heading face have a large uncertainty. However, in actual construction, little consideration is given to the influence of the uncertainty of soil strength on the stability of the heading face.

[0067] To solve the above problems, the present invention provides a method for risk assessment of tunnel heading face instability considering the uncertainty of soil strength, as Figure 1 and Figure 2 shown, including the following steps:

[0068] Step S1: To establish a coupled Euler-Lagrange large deformation finite element model for heading face instability analysis, determine the basic physical and mechanical parameters of the soil mass at the shield construction site, the spatial variability parameters of the soil mass, and the shield machine parameters according to on-site tests and laboratory tests;

[0069] Step S2: Establish a coupled Euler-Lagrange large deformation finite element model of the shield tunnel;

[0070] Step S3: Conduct stability analysis of the tunnel heading face in homogeneous soil;

[0071] Step S4: Considering the uncertainty of the soil mass, extract the node coordinates of the soil mass elements in the finite element model, and generate a three-dimensional lognormal random field of the soil internal friction angle by the modified linear estimation method according to the spatial variability parameters of the soil mass;

[0072] Step S5: Assign the three-dimensional lognormal random field to the nodes of the soil mass elements to obtain non-uniform soil strength, and conduct stability analysis of the tunnel heading face in non-homogeneous soil;

[0073] Step S6: Repeat Step S4 and Step S5, and perform at least 100 Monte Carlo simulations;

[0074] Step S7: When the load factor in non-homogeneous soil is greater than the load factor in homogeneous soil, the heading face is unstable, and obtain the instability probability of the heading face.

[0075] The tunnel face instability risk assessment method considering the uncertainty of soil strength provided by the present invention takes into account the spatial variability of soil strength and the influence of the opening ratio of the shield machine cutter head on the critical support pressure of the tunnel face, and establishes the relationship between the tunnel face instability probability and the traditional safety factor.

[0076] In the step S1, the basic physical and mechanical parameters include the elastic modulus E, Poisson's ratio ν, and unit weight γ of the soil.

[0077] In the step S1, the spatial variability parameters of the soil include the average internal friction angle of the soil, horizontal correlation length ΘH, vertical correlation length ΘV, and coefficient of variation COV;

[0078] In the step S1, the shield machine parameters include the diameter D of the shield machine cutter head and the opening ratio ξ.

[0079] In the present invention, in the step S2, a coupled Euler-Lagrange large deformation finite element model of the shield tunnel is established in the ABAQUS software, and the specific steps are as follows:

[0080] Step S21: According to the burial depth C, diameter D of the tunnel, and the opening ratio ξ of the shield machine cutter head, a geometric model of the shield tunnel is established in the ABAQUS software, where the soil is simulated by the Euler body, and the cutter head and shield body of the shield machine are simulated by the Lagrange body;

[0081] Step S22: Assign material parameters to the soil, cutter head, and shield body in the model. The Mohr-Coulomb model is used to simulate the soil, and the elastic modulus E, Poisson's ratio ν, and unit weight γ of the soil are input. The cutter head and shield body are simulated by rigid bodies;

[0082] Step S23: Set the model boundary conditions. Apply full constraint boundary conditions in three directions to the bottom of the model, apply normal constraint conditions to the sides of the model, and apply fixed constraints to the shield body and cutter head of the shield machine;

[0083] Step S24: Set the model load conditions. Apply the gravitational acceleration g to the entire model, and at the same time apply a support pressure to the tunnel face, and its initial value P0 is equal to the initial ground stress σ0 at the tunnel axis, that is, σ0 = γ(C + D / 2);

[0084] Step S25: Set the element type and divide the mesh. The soil is simulated by three-dimensional eight-node Euler elements, and the shield machine and cutter head are simulated by three-dimensional eight-node solid elements. Set the minimum element size of the soil, shield machine, and cutter head to D / 30, and divide the mesh.

[0085] In the present invention, a coupled Euler-Lagrange large deformation finite element model of a shield tunnel is established in the ABAQUS software, which can truly consider the influence of the cutter head of the shield machine on the stability of the tunnel face and calculate the critical support pressure of the tunnel face under different cutter head opening ratios.

[0086] In the present invention, in step S3, the average soil internal friction angle is input in step S3. By gradually reducing the support pressure P at the tunnel face at the cutter head opening until the tunnel face fails, the relationship curve between the velocity v of the soil on the tunnel face and the normalized support pressure P / P0 is extracted and obtained, and the pressure corresponding to the inflection point of the curve is used as the critical support pressure P of the tunnel face in homogeneous soil. c It can be expressed by the load coefficient Nγ:

[0087] N γ = P c / γD (1)

[0088] Where γ is the unit weight.

[0089] Among them, the average soil internal friction angle input in step S3 is used. At this time, the soil is uniform, so the calculated support pressure is the critical support pressure in homogeneous soil.

[0090] Step S3 does not consider the uncertainty of soil strength and assumes the soil to be uniform, so as to obtain the critical support pressure of the tunnel face in homogeneous soil for subsequent comparison with the critical support pressure in non-homogeneous soil.

[0091] In the present invention, in order to consider the uncertainty of soil strength, on the basis of step S2, step S4 extracts the node coordinates of the soil elements in the finite element model, and according to the spatial variability parameters of soil strength, including the average soil internal friction angle the horizontal correlation length ΘH, the vertical correlation length ΘV and the coefficient of variation COV, a three-dimensional lognormal random field of soil internal friction angle is generated by the modified linear estimation method. The specific steps are as follows:

[0092] Step S41, and assign a value to each node with an independent standard normal random vector r;

[0093] Step S42, perform Cholesky decomposition on the cross-correlation matrix, and replace the random vector r in each node with Q, and we can get

[0094] C = L·L T (2)

[0095] Q = L·r (3)

[0096] Among them, \(L\) is a lower triangular matrix. Through the transformation of Equation (3), the uncorrelated random vector \(r\) can be transformed into a correlated random vector with the correlation matrix \(C\). The random vector \(Q\) defined at the element nodes in the three-dimensional space forms the leading random field;

[0097] Step S43: Translate and rotate the leading random field to generate the property field. The position vector is \(y\), and the mapping relationship between the two is as follows:

[0098] \(s = J\cdot y+\varepsilon\) (4)

[0099] \(J = J_3J_2J_1\) (5)

[0100]

[0101]

[0102]

[0103] Among them, \(J\) is the Jacobian matrix, \(\psi_1\), \(\psi_2\), \(\psi_3\) are the rotation angles in three directions, and according to symmetry, their values are uniformly distributed in the interval \([0, \pi / 2]\); \(\varepsilon\) is the translation vector with three direction components. The property field can be obtained through the rotation and translation of Equation (4);

[0104] Step S44: Interpolate any point of the property field using the 8 nodes of the elements of the leading random field, as follows

[0105]

[0106] Among them, \(Q\) j \((y)\) is the \(j\)-th component value of the random vector \(Q\) at point \(y\); is the \(j\)-th component value of the random vector \(Q\) at the \(i\)-th node of element \(k\); \(N\) i \((y)\) is the shape function value of the eight-node element.

[0107] Step S45: Convert the above-generated normal random field into a lognormal random field through an exponential transformation, as follows:

[0108]

[0109]

[0110]

[0111] In the formula, is the internal friction angle of the soil; obeys the lognormal distribution with the mean and standard deviation; are respectively with the mean and variance.

[0112] The present invention can calculate the critical support pressure of the tunnel face considering the spatial variability of soil strength and the instability risk.

[0113] In the present invention, the homogeneous case is equivalent to a deterministic analysis, and the heterogeneous case is equivalent to an uncertain analysis. For the purpose of comparison, the instability probability of the tunnel face is calculated. Therefore, in step S5, in the stability analysis of the tunnel face in heterogeneous soil, the support pressure P at the tunnel face where the cutter head opening is located is gradually reduced ran , until the tunnel face fails, and the velocity of the soil on the tunnel face and the relationship curve of the normalized support pressure P ran / P0 are extracted. The pressure corresponding to the inflection point of the curve is the critical support pressure P of the tunnel face in this random soil sample c,ran , which can be represented by the load factor N γ,ran :

[0114] N γ,ran =P c,ran / γD (13)

[0115] In step S6 of the present invention, steps S4 and S5 are repeated. In order to obtain stable statistical results, at least 100 Monte Carlo simulations are performed to obtain the frequency distribution, mean value γ,ran and standard deviation of the stable load factor (N ) in heterogeneous soil

[0116] In the present invention, in step S7, the calculation formula of the tunnel face instability probability is as follows:

[0117]

[0118] In the formula, k is the safety factor; N γ is the load factor in homogeneous soil calculated in step S3; and are the mean value and standard deviation of the load factor N in heterogeneous soil calculated in step S6; Φ is the cumulative normal function, and its mean value and standard deviation are respectively γ,ran and and

[0119] The method of the present invention can establish the relationship between the tunnel face instability probability and the safety factor.

[0120] In an embodiment of the present invention, as Figure 1 and Figure 2 shown, the method for evaluating the instability risk of the tunnel face considering the uncertainty of soil strength provided by the present invention is implemented as follows:

[0121] Determine the basic physical parameters of the soil mass at the shield construction site and the spatial variability parameters of the soil mass based on in-situ tests and laboratory tests. The basic physical parameters include the elastic modulus of the soil (E = 100 MPa), Poisson's ratio (ν = 0.3), and unit weight (γ = 18 kN / m 3 ), and the spatial variability parameters of the soil mass include the average internal friction angle horizontal correlation length (ΘH = 20 m), vertical correlation length (ΘV = 2 m), and coefficient of variation (COV = 0.2). Obtain the diameter (D = 6 m) and opening ratio (ξ = 30%) of the cutterhead of the shield machine by querying the shield machine parameter table, as shown in Table 1 below;

[0122] Table 1: Cutterhead and Soil Mass Parameter Table of the Shield Machine

[0123]

[0124] Establish a coupled Euler-Lagrange large deformation finite element model of the shield tunnel in the ABAQUS software. The specific steps are as follows:

[0125] (a) Based on the buried depth of the tunnel (C = 6 m), diameter (D = 6 m), and opening ratio of the cutterhead of the shield machine (ξ = 30%), establish a geometric model of the shield tunnel in the ABAQUS software, as shown in Figures 3(a) and 3(b),

[0126] where the soil mass is simulated using the Eulerian body, and the cutterhead and shield body of the shield machine are simulated using the Lagrangian body;

[0127] (b) Assign material parameters to the soil mass, cutterhead, and shield body in the model: Use the Mohr-Coulomb model to simulate the soil mass, input the elastic modulus, Poisson's ratio, and unit weight of the soil mass, and use rigid bodies to simulate the cutterhead and shield body;

[0128] (c) Set the model boundary conditions: Apply fully constrained boundary conditions in three directions to the bottom of the model, apply normal constraint conditions to the sides of the model, and apply fixed constraints to the shield body and cutterhead of the shield machine.

[0129] (d) Set the model load conditions: Apply the gravitational acceleration g = 10 m / s 2 to the entire model, and at the same time apply support pressure to the tunnel face, whose initial value P0 is equal to the initial ground stress at the tunnel axis (i.e., σ0 = 162 kPa);

[0130] (e) Set the element type and divide the mesh: The soil mass is simulated using three-dimensional eight-node Eulerian elements, the shield machine and cutterhead are simulated using three-dimensional eight-node solid elements, set the minimum element size of the soil mass, shield machine, and cutterhead to 0.2 m, and divide the mesh;

[0131] Input the average internal friction angle of the soil mass Analyze the stability of the tunnel face in homogeneous soil. By gradually reducing the support pressure (P) at the tunnel face where the cutter head is opened until the tunnel face fails, extract the relationship curve between the velocity (v) of the soil on the tunnel face and the normalized support pressure (P / P0). As Figure 4 shown, use the pressure corresponding to the inflection point of the curve as the critical support pressure (P c = 0.08P0 = 12.96 kPa) of the tunnel face in homogeneous soil. Using formula (1), the corresponding load factor N γ = P c / γD = 0.12;

[0132] To consider the uncertainty of the soil, based on step S2, extract the node coordinates of the soil elements in the finite element model. According to the spatial variability parameters of the soil, including the average internal friction angle horizontal correlation length (ΘH = 20 m), vertical correlation length (ΘV = 2 m), and coefficient of variation (COV = 0.2), use formula (12) to generate a three-dimensional lognormal random field of the soil internal friction angle and assign the soil internal friction angle to the nodes of the soil elements. As shown in Figures 5(a) and 5(b), the nephogram of the internal friction angle of a typical heterogeneous soil sample is presented, where the dark part indicates a larger internal friction angle and the light part indicates a smaller internal friction angle;

[0133] Analyze the stability of the tunnel face in heterogeneous soil. Gradually reduce the support pressure (P ran ) at the tunnel face where the cutter head is opened until the tunnel face fails, and extract the relationship curve between the velocity of the soil on the tunnel face and the normalized support pressure (P ran / P0). As Figure 6 shown, the pressure corresponding to the inflection point of the curve is the critical support pressure (P c,ran = 0.128P0 = 20.736 kPa) of the tunnel face in this heterogeneous soil sample. Using formula (13), the corresponding load factor N γ,ran = P ran / γD = 0.192.

[0134] Repeat steps S4 and S5, and perform at least 100 Monte Carlo simulations to obtain the frequency distribution, mean value γ,ran and standard deviation of the stable load factor (N in heterogeneous soil. As Figure 7 ;

[0135] Calculate the instability probability p of the tunnel face under different safety factors (k) according to formula (14). The calculation results are shown in Table 2 below. When the safety factor is 1.0, the instability probability of the tunnel face is 64.94%, which does not meet the requirements of engineering safety construction. When the safety factor is 1.7, the instability probability of the tunnel face is reduced to 0.75%, meeting the design requirements of the support pressure of the tunnel face.

[0136] Table 2: Relationship between instability probability p (%) and safety factor

[0137]

[0138] In summary, the tunnel face instability risk assessment method considering the uncertainty of soil strength provided by the present invention can truly consider the influence of the shield cutterhead on the stability of the tunnel face, can calculate the critical support pressure of the tunnel face under different cutterhead opening ratios; can calculate the critical support pressure and instability risk of the tunnel face considering the spatial variability of soil strength; can establish the relationship between the instability probability of the tunnel face and the safety factor.

[0139] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these changes and modifications.

Claims

1. A method for evaluating the instability risk of a tunnel face considering the uncertainty of soil strength, characterized in that, It includes the following steps: Step S1: Determine the basic physical and mechanical parameters of the soil mass at the shield construction site, the spatial variability parameters of the soil mass, and the shield machine parameters based on in-situ tests and laboratory tests; Step S2: Establish a coupled Euler-Lagrange large deformation finite element model of the shield tunnel; Step S3: Conduct stability analysis of the tunnel face in homogeneous soil; in the said step S3, input the average internal friction angle of the soil , by gradually reducing the support pressure P at the tunnel face at the cutter head opening until the tunnel face fails, obtain the relationship curve between the velocity v of the soil on the tunnel face and the normalized support pressure P / P0, and use the pressure corresponding to the inflection point of the curve as the critical support pressure P c of the tunnel face in homogeneous soil, and represent it with the load factor N γ : N γ = P c / γD (1) where, γ is the unit weight, and D is the diameter of the cutterhead of the shield machine; Step S4: Considering the uncertainty of the soil mass, extract the nodal coordinates of the soil elements in the finite element model, and generate a three-dimensional lognormal random field of the soil internal friction angle by the modified linear estimation method according to the spatial variability parameters of the soil mass; Step S5: Assign the three-dimensional lognormal random field to the nodes of the soil elements to obtain the non-uniform soil strength, and conduct the stability analysis of the tunnel face in non-homogeneous soil; Step S6: Repeat Step S4 and Step S5, and perform multiple Monte Carlo simulations; Step S7: When the load factor in non-homogeneous soil is greater than that in homogeneous soil, the tunnel face becomes unstable, and obtain the instability probability of the tunnel face; The calculation formula for the instability probability of the tunnel face is as follows: where k is the safety factor; N γ is the load factor in homogeneous soil; and are the mean and standard deviation of the load factors in 100 heterogeneous soil samples; Φ is the cumulative normal function, and its mean and standard deviation are and .

2. The tunnel face instability risk assessment method considering the uncertainty of soil strength according to claim 1, wherein: In the said Step S1, the basic physical and mechanical parameters include the elastic modulus E, Poisson's ratio ν, and unit weight γ of the soil mass.

3. The tunnel face instability risk assessment method considering the uncertainty of soil strength according to claim 1, wherein: In the said Step S1, the spatial variability parameters of the soil mass include the average internal friction angle of the soil mass, the horizontal correlation length ΘH, the vertical correlation length ΘV, and the coefficient of variation COV; The shield machine parameters include the diameter D of the cutterhead of the shield machine and the opening ratio ξ.

4. The tunnel face instability risk assessment method considering the uncertainty of soil strength according to claim 1, characterized in that The said Step S2 specifically includes: Step S21: Establish a geometric model of the shield tunnel according to the buried depth C, diameter D of the tunnel, and the opening ratio ξ of the cutterhead of the shield machine, wherein the soil mass is simulated by the Eulerian body, and the cutterhead and the shield body of the shield machine are simulated by the Lagrangian body; Step S22: Assign material parameters to the soil mass, cutterhead, and shield body in the model, use the Mohr-Coulomb model to simulate the soil mass, input the elastic modulus E, Poisson's ratio ν, and unit weight γ of the soil mass, and use rigid bodies to simulate the cutterhead and the shield body; Step S23: Set the model boundary conditions, apply full restraint boundary conditions in three directions to the bottom of the model, apply normal restraint conditions to the sides of the model, and apply fixed restraints to the shield body and cutterhead of the shield machine; Step S24: Set the model load conditions, apply the gravitational acceleration g to the entire model, and at the same time apply the support pressure to the tunnel face, and its initial value P0 is equal to the initial in-situ stress at the tunnel axis; Step S25: Set the element type and divide the mesh. The soil mass is simulated by three-dimensional eight-node Euler elements, the shield machine and the cutterhead are simulated by three-dimensional eight-node solid elements, set the minimum element size of the soil mass, shield machine, and cutterhead to D / 30, and divide the mesh.

5. The tunnel face instability risk assessment method considering the uncertainty of soil strength according to claim 3, characterized in that The said Step S4 specifically includes: Step S41: Assign a value to each node with an independent standard normal random vector r; Step S42: Conduct Cholesky decomposition on the cross-correlation matrix, and replace the random vector r in each node with Q, and we can get: C = L·L T (2) Q = L·r (3) Among them, L is a lower triangular matrix. Through the transformation of Equation (3), the uncorrelated random vector r can be transformed into a correlated random vector with a correlation matrix C. The random vectors Q defined at the unit nodes in the three-dimensional space form a leading random field; Step S43: Translate and rotate the leading random field to generate an attribute field. The position vector is y, and the mapping relationship between the two is as follows: s = J·y + ε (4) J = J3J2J1 (5) Among them, J is the Jacobian matrix, and J1, J2, and J3 are the components of the Jacobian matrix; ψ1, ψ2, and ψ3 are the rotation angles in three directions, and their values are uniformly distributed in the interval [0, π / 2] according to symmetry; ε is a translation vector with three direction components. The attribute field can be obtained through the rotation and translation of Equation (4); Step S44: Interpolate any point of the attribute field by using the 8 nodes of the elements of the leading random field, as follows: where Q j (y) is the j-th component value of the random vector Q of point y; is the j-th component value of the random vector Q of the i-th node of element k; N i (y) is the shape function value of the eight-node element; Step S45: Convert the generated normal random field into a lognormal random field through an exponential transformation, as follows: In the formula, is the internal friction angle of the soil; are respectively the mean value and variance of 6. The method for evaluating the instability risk of a tunnel face considering the uncertainty of soil strength according to claim 1, characterized in that: In the step S5, in the stability analysis of the tunnel face in heterogeneous soil, gradually reduce the support pressure P at the tunnel face where the cutter head is perforated ran , until the tunnel face fails, and extract the relationship curve between the velocity of the soil mass on the tunnel face and the normalized support pressure P ran / P0. The pressure corresponding to the inflection point of the curve is the critical support pressure P of the tunnel face c，ran , which is represented by the load coefficient N γ，ran : N γ,ran = P c,ran / γD (13).

7. The method for evaluating the instability risk of a tunnel face considering the uncertainty of soil strength according to claim 1, characterized in that: In step S6, at least 100 Monte Carlo simulations are performed.

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