CN110704963A - A fast method to optimize the tunneling parameters of earth pressure balance shield machine - Google Patents

Abstract

The invention relates to a fast method for optimizing the excavation parameters of an earth pressure balance shield machine, and belongs to the technical field of underground tunnel engineering construction. In order to quantitatively optimize the tunneling parameters of the earth pressure balance shield machine, the tunneling efficiency is used as the objective function of optimization analysis, and the prediction equation of tunneling efficiency under limited samples is obtained by performing symbolic regression and linear regression on the measured data. By calculating the continuous function of the coefficient of the tunneling efficiency prediction equation with the variation of the saturated uniaxial compressive strength of the tunneled stratum under the finite sample, the tunneling efficiency prediction equation suitable for the earth pressure balanced shield tunneling in hard rock is obtained. Furthermore, through the step-by-step point-taking method to carry out the optimization calculation in a given definition domain, combined with the check of the driving rate, the optimal driving parameters of the earth pressure balance shield machine suitable for driving hard rock are obtained. Based on engineering survey data and construction data, the invention has the advantages of concise calculation process, reasonable method and strong practicability, and can effectively improve the tunneling efficiency of the earth pressure balance type shield machine.

Description

A fast method to optimize the tunneling parameters of earth pressure balance shield machine

technical field

The invention belongs to the technical field of tunneling parameter optimization of a full-section tunnel boring machine, and particularly relates to a fast method for optimizing the tunneling parameters of an earth pressure balance shield machine.

Background technique

1) A method for predicting the driving efficiency of a hard rock roadheader (application number: 201610755946.8) The method does not provide a specific definition of the driving efficiency, and the influencing factors of the driving efficiency are limited to five types of geological features, and other driving parameters are not considered. The effect of tunneling efficiency.

2) TBM tunneling parameter optimization method (application number: 201910231527.8) This method takes the minimum specific energy consumption as the objective function, the integral variables of the work function are displacement and rotation angle, and the force and torque equations can only be obtained through the existing measured values. Unexplored areas cannot be predicted and optimized ahead of time.

3) Optimization method of shield tunneling parameters in the case of composite strata (application number: 201610003385.6) and 4) "Establishment and optimization of shield tunneling rate model under composite stratum" (Li Jie, Fu Ke, Guo Jingbo, et al. Composite strata The establishment and optimization of the tunneling rate model of the lower shield[J].Modern Tunnel Technology, 2017(3).) There are limitations in applicability and calculation principles. In terms of applicability, the driving rate prediction equation is only applicable to one type of formation, and the equation is no longer equally applicable when the formation conditions change. In terms of calculation principle, compared with reference 3), the driving rate and the cutter head torque are optimized respectively, but the coupling optimization of the driving rate and the cutter head torque is not carried out, that is, the driving parameter group corresponding to the optimal value of the driving rate and the optimal cutter head torque are not carried out. The tunneling parameter groups corresponding to the values are not the same, and the final optimization conclusion that comprehensively considers the tunneling rate and cutterhead torque is not given. Compare with reference 4) simply take the tunneling rate as the optimization object without considering the constraints of equipment loss and load capacity. In addition, the constraints of reference 3) and reference 4) do not give a clear calculation formula, which is difficult to solve by the K-T method.

5) "Establishment of shield tunneling rate model and parameter optimization under complex water-rich strata" (Wang Qiang. Establishment of shield tunneling speed model and parameter optimization under complex water-rich strata [J]. Water Conservancy Planning and Design, 2019(08) :73-78.) Taking the tunneling rate as a single optimization objective function, the constraints of equipment load capacity and loss on tunneling efficiency are not considered, and the tunneling rate prediction equation is only applicable to one kind of formation, which exists in the applicability and the correctness of the principle. limited. In addition, compared with reference 5), the local optimization method is used for the optimization calculation, and the calculation result is greatly affected by the setting of the initial value, resulting in low engineering applicability.

SUMMARY OF THE INVENTION

In order to overcome the above-mentioned defects of the prior art, the present invention proposes a fast method for optimizing the excavation parameters of the earth pressure balance shield machine. As the optimization analysis objective function, it includes the following steps:

Step 1. Establish a statistical sample of driving efficiency

The driving efficiency β is defined as the driving rate v divided by the cutter head torque T, as shown in formula (1). T directly reflects the operating state of the equipment, and β reflects the relationship between the driving rate and the load capacity of the cutter head drive motor.

Combined with the excavation parameters automatically recorded by the shield machine during tunnel trial excavation and the excavation parameter data of previous projects, the excavation rate v, cutter head torque T, effective thrust F, soil bin pressure p, cutter head speed n measured at the same time are taken as The same set of excavation parameters. The β, F, p, and n of each recording time in the trial excavation stage are counted as the excavation efficiency statistical samples.

Step 2: Obtain the prediction equation of driving efficiency for finite samples through symbolic regression and linear regression

Symbolic regression is performed on the tunneling efficiency β of the shield machine in each layer with different stratum saturated uniaxial compressive strength _Rc . The computing time on the computer running the symbolic regression algorithm in the background is less than 1 minute and the fitting accuracy ^r2 is high. The fitted equation for β at 0.7 was used as a candidate equation.

The candidate equations of each stratum are counted, and the independent variables n ² , p, np, and pF all coexist in at least one of the candidate equations of each stratum, so n ² , p, np, and pF are taken as the tunneling efficiency under the finite sample. For the independent variable of the prediction equation, such as formula (2), linear regression is performed again on the statistical sample of the driving efficiency through the driving efficiency prediction equation under the finite sample, and the equation coefficients belonging to each stratum are obtained;

β* is the predicted value of the driving efficiency under the finite sample.

β*=a ₁ n ² +a ₂ p+a ₃ np+a ₄ pF+a ₅ (2)

Step 3 Continuation of the prediction equation of tunneling efficiency

The equation coefficients in equation (2) obtained under the condition of finite samples are discrete equation coefficients for finite types of strata, and it is necessary to extend the equations corresponding to the discrete equation coefficients to obtain equations suitable for general strata.

Taking the coefficients of the prediction equations of the tunneling efficiency in different tunneling strata obtained in step 1 as the dependent variable, and with the saturated uniaxial compressive strength R _c of the tunneling stratum as the independent variable, perform linear and nonlinear regression, and the equation coefficients are obtained as a function of R. The continuous function of the variation of _c is shown in formula (3), formula (4), formula (5), formula (6), and formula (7). Because the samples are all obtained from hard rock, the extension of the prediction equation of driving efficiency is also in the range of hard rock, that is, R _c ≥ 30MPa.

a ₁ =116.588-99.614R _c ^0.038 , R _c ≥30MPa (3)

a ₂ =46.522-12.532R _c ^0.313 ,R _c ≥30MPa (4)

a ₃ =0.093R _c -4.414, R _c ≥30MPa (5)

a ₄ =1.135×10 ^-6 R _c -6.976×10 ^-5 , R _c ≥30MPa (6)

As in Equation (8), Substitute Equation (3), Equation (4), Equation (5), Equation (6), Equation (7) into Equation (2) to obtain a hard rock suitable for EPB shield tunneling β** is the predicted value of the tunneling efficiency of the earth pressure balance shield tunneling in hard rock.

Step 4: Determine the optimization formula and boundary conditions

The calculation formula of the tunneling parameter optimization is shown in formula (9), p ^Ω , Θ ^Ω , Ψ ^Ω respectively reflect the allowable fluctuation range of soil bin pressure, effective thrust, and cutter head rotation speed during normal excavation of stratum Ω, namely [p _min , p _max ], [F _min ,F _max ], [n _min ,n _max ].

Step 5: Calculate the maximum value of β** by the point-taking method

The influencing factors of the optimization problem have been quantified and the boundaries are relatively clear. It is advisable to use linear equal division to obtain the optimal value grid of the excavation parameters to be selected, and perform step-by-step point selection method for step-by-step calculation of grid nodes.

Taking p ^Ω , Θ ^Ω , and Ψ ^Ω as the definition domains on the mutually orthogonal x, y, and z coordinate axes of the spatial Cartesian coordinate system, the spatial definition domain of β** is obtained.

代入式(8)，得到β**的空间定义域内各第一步网格节点对应的β**。将β**的空间定义域内各第一步网格节点对应的β**按大小降序排列，得第一步网格节点β**数列。取第一步网格节点β**中最大的前20％的β**所对应的网格节点作为第一步网格优势点。Establish the first step grid, divide p ^Ω , Θ ^Ω , Ψ ^Ω as m ₁ equal parts, and make the normal plane of the coordinate axis where the bisected points are located at all the bisected points, and the intersection of the normal planes form the definition of β** space the first step grid of the domain, any one of the first step grid nodes Equation (10), Equation (11), and Equation (12) are satisfied. After the excavation stratum R _c is determined according to the stratum exploration data, the point

Substitute into formula (8) to obtain the β** corresponding to each first step grid node in the space definition domain of β**. Arrange the β** corresponding to each first-step grid node in the space definition domain of β** in descending order of size to obtain the first-step grid node β** sequence. Take the grid nodes corresponding to the largest top 20% β** of the grid nodes β** in the first step as the grid advantage points of the first step.

的长方体并将长方体各边作m₂等分，作各等分点所在坐标轴的法平面，各法平面相交形成该第一步网格优势点的第二步网格，任意一个第二步网格节点

满足式(13)、式(14)、式(15)。根据地层勘查资料确定掘进地层R_c后，将点

代入式(8)，得到所有第二步网格节点对应的β**。The second step grid is established, and for each dominant point of the first step grid, the point is taken as the body center and the projection lengths on the x, y, and z axes are respectively

The rectangular parallelepiped and the sides of the rectangular parallelepiped are divided into m ₂ equal parts as the normal plane of the coordinate axis where each bisected point is located. grid node

Equation (13), Equation (14), and Equation (15) are satisfied. After the excavation stratum R _c is determined according to the stratum exploration data, the point

Substitute into Equation (8) to get β** corresponding to all grid nodes in the second step.

Summarize the β** corresponding to the grid advantage point of the first step and the β** corresponding to all the grid nodes of the second step, and take the grid nodes corresponding to the top 10% with the largest β** as the primary optimization parameter point.

Step 6: Check the driving rate.

There are positive hob and side hob distributed on the cutter head, the positive hob is installed parallel to the driving direction, and there is a non-zero side hob installation angle between the side hob and the driving direction. The effective thrust is approximately equally distributed to each hob and the force parallel to the driving direction is F/N, and the force parallel to the driving direction on the positive hob and the side hob is approximately average F/N, where the number of positive hob is N _fc tools, the number of side hob is N _lc , and the total number of tools is N tools, as shown in formula (16). According to the force balance, the resultant formation resistance force on the cutterhead is equal to the resultant effective thrust force, and the cutterhead torque is equal to the resultant moment of formation resistance on the cutterhead spindle. According to Saint-Venant's principle, the total cutterhead torque on the positive hob is approximately λμ (FN _fc /N)R/2, the cutter head torque can be approximated as the resultant moment of the occlusal force and frictional resistance generated by the effective thrust between the cutter and the face rock, as in formula (17), R is the maximum positive hob Installation radius, r _w is the installation radius of the wth edged hob, θw is the installation angle of the _wth edged hob, μ is the friction coefficient between the steel and the formation, and λ is the empirical correction coefficient.

N=N _fc +N _lc (16)

According to formula (8), the value v** of the driving rate to be determined is shown in formula (18).

Substitute the cutter head speed n, soil bin pressure p, and effective thrust F of the primary optimization parameter point into formula (18) to obtain the v** corresponding to this point, and calculate the corresponding v** for each primary optimization parameter point one by one, take The tunneling parameters of the primary optimization parameter point when v** is the largest are used as the tunneling parameters after optimization.

Further, in step 1: the units of v, T, F, p, and n are mm/min, 10 ⁶ Nm, kN, Bar, and r/min, respectively.

Further, in step 6, λ is an empirical correction coefficient, and λ can be taken as 0.24, 0.21, and 0.2 in granite strata, andesite strata, and limestone strata, respectively.

Description of drawings

Fig. 1 Scatter plots of equation coefficients for different formations under finite samples;

Figure 2 Schematic diagram of the installation angle of the side hob on the cutter head.

Specific implementation method

Aiming at the deficiencies of the prior art, the present invention proposes a fast method for optimizing the tunneling parameters of an earth pressure balance shield machine, which comprises the following steps:

When the shield tunnels into different types of strata, that is, when the stratum distribution on the face changes, the shield tunneling rate and cutter head torque change accordingly. The greater the excavation rate, the shorter the construction period, but the cutter head torque also increases, and the cutter head torque is the most important control parameter for equipment integrity, reflecting the working state of the cutter head spindle. In order to meet the requirements of the construction period and the equipment integrity rate, it is necessary to strike a balance between the driving rate and the torque of the cutterhead, so as to maximize the potential of the equipment and effectively improve the driving rate under the condition of ensuring the equipment is in good condition. Therefore, a shield tunneling parameter control optimization method based on geological segmentation is proposed to realize the dynamic optimal control of shield tunneling parameters based on the tunneling stratum parameters.

Step 1 Establish a statistical sample of driving efficiency

The driving efficiency β is defined as the driving rate v divided by the cutter head torque T, as shown in formula (1). T directly reflects the operating state of the equipment, and β reflects the relationship between the driving rate and the load capacity of the cutter head drive motor.

Combined with the excavation parameters automatically recorded by the shield machine during tunnel trial excavation and the excavation parameter data of previous projects, the excavation rate v, cutter head torque T, effective thrust F, soil bin pressure p, cutter head speed n measured at the same time are taken as The same set of excavation parameters. The β, F, p, and n of each recording time in the trial excavation stage are used as the statistical samples of the excavation efficiency;

The units of v, T, F, p, and n are mm/min (millimeters per minute), 10 ⁶ Nm, kN, Bar, r/min (circles per minute), respectively.

In step 2, the prediction equation of the tunneling efficiency for the finite sample is obtained through symbolic regression and linear regression. The β of the shield machine in each stratum with different stratum saturated uniaxial compressive strength R _c is subjected to symbolic regression, and the symbolic regression algorithm will be run in the background. The fitting equations for β with the computation time on the computer less than 1 minute and the fitting accuracy r ² higher than 0.7 were selected as candidate equations.

The candidate equations of each stratum are counted, and the independent variables n ² , p, np, and pF all coexist in at least one of the candidate equations of each stratum, so n ² , p, np, and pF are taken as the tunneling efficiency under the finite sample. For the independent variable of the prediction equation, as shown in Equation (2), the linear regression is performed again for the statistical sample of the driving efficiency through the driving efficiency prediction equation under the finite sample, and the equation coefficients belonging to each stratum are obtained, as shown in Table 1;

β* is the predicted value of the driving efficiency under the finite sample.

β*=a ₁ n ² +a ₂ p+a ₃ np+a ₄ pF+a ₅ (2)

Table 1 The coefficients of the prediction equation of the driving efficiency of the formation with different saturated uniaxial compressive strength

Step 3 Continuation of the prediction equation of tunneling efficiency

Table 1 shows the equation coefficients obtained by formula (2) under discrete finite sample conditions (the formation saturated uniaxial compressive strengths are 42MPa, 54MPa, 62MPa, 90MPa, and 118MPa, respectively). The corresponding equations can be extended to obtain the equation coefficients suitable for general formations (saturated uniaxial compressive strength is different from the sample value), that is, it can be applied to formations with saturated uniaxial compressive strength not equal to 42MPa, 54MPa, 62MPa, For 90MPa and 118MPa.

Taking the coefficients of the prediction equations of the tunneling efficiency in different tunneling strata obtained in step 1 as the dependent variable, and with the saturated uniaxial compressive strength R _c of the tunneling stratum as the independent variable, the linear and nonlinear regressions are carried out, that is, the equation in Fig. Perform linear and nonlinear regression on the scatter points of , and obtain a continuous function of equation coefficients varying with _Rc , as shown in equations (3), (4), (5), (6), and (7). Because the samples are all obtained from hard rock, the extension of the prediction equation of driving efficiency is also in the range of hard rock, that is, R _c ≥ 30MPa.

a ₁ =116.588-99.614R _c ^0.038 , R _c ≥30MPa (3)

a ₂ =46.522-12.532R _c ^0.313 ,R _c ≥30MPa (4)

a ₃ =0.093R _c -4.414, R _c ≥30MPa (5)

a ₄ =1.135×10 ^-6 R _c -6.976×10 ^-5 , R _c ≥30MPa (6)

As in Equation (8), Substitute Equation (3), Equation (4), Equation (5), Equation (6), Equation (7) into Equation (2) to obtain a hard rock suitable for EPB shield tunneling β** is the predicted value of the tunneling efficiency of the earth pressure balance shield tunneling in hard rock.

Step 4: Determine the optimization formula and boundary conditions

The calculation formula of the tunneling parameter optimization is shown in formula (9), p ^Ω , Θ ^Ω , Ψ ^Ω respectively reflect the allowable fluctuation range of soil bin pressure, effective thrust, and cutter head rotation speed during normal excavation of stratum Ω, namely [p _min , p _max ], [F _min ,F _max ], [n _min ,n _max ].

Taking a tunnel section of Shenzhen Metro as an example, the saturated uniaxial compressive strength R _c of the excavation stratum is 64.5MPa, then the corresponding excavation efficiency prediction equation of the stratum can be obtained according to formula (8) as β**=-0.115n ² +0.346p +1.585np+3.448×10 ^{- 6} pF+2.739, and according to engineering experience, during normal excavation, the allowable fluctuation range p ^Ω of soil tank pressure in the stratum is [0.05, 0.4], and the allowable fluctuation range of cutter head speed Ψ ^Ω is [ 0.8, 2.2], the allowable range of effective thrust fluctuation Θ ^Ω is [6000, 15000].

Step 5: Calculate the maximum value of β** by the point-taking method

The influencing factors of the optimization problem have been quantified and the boundaries are clear. It is advisable to use linear equal division to obtain the optimal value grid of the tunneling parameters to be selected, and perform step-by-step point selection method for the grid nodes. Because there is no need to set the initial value, so The influence of the initial value selection on the calculation results is avoided.

Taking p ^Ω , Θ ^Ω , and Ψ ^Ω as the definition domains on the mutually orthogonal x, y, and z coordinate axes of the spatial Cartesian coordinate system, the spatial definition domain of β** is obtained.

满足式(10)、式(11)、式(12)。根据地层勘查资料确定掘进地层R_c后，将点

代入式(8)，得到β**的空间定义域内各第一步网格节点对应的β**。将β**的空间定义域内各第一步网格节点对应的β**按大小降序排列，得第一步网格节点β**数列。取第一步网格节点β**中最大的前20％的β**所对应的网格节点作为第一步网格优势点。Establish the first step grid, divide p ^Ω , Θ ^Ω , Ψ ^Ω as m ₁ equal parts, and make the normal plane of the coordinate axis where the bisected points are located at all the bisected points, and the intersection of the normal planes form the definition of β** space the first step grid of the domain, any one of the first step grid nodes

Equation (10), Equation (11), and Equation (12) are satisfied. After the excavation stratum R _c is determined according to the stratum exploration data, the point

Substitute into formula (8) to obtain the β** corresponding to each first step grid node in the space definition domain of β**. Arrange the β** corresponding to each first-step grid node in the space definition domain of β** in descending order of size to obtain the first-step grid node β** sequence. Take the grid nodes corresponding to the largest top 20% β** of the grid nodes β** in the first step as the grid advantage points of the first step.

的长方体并将长方体各边作m₂等分，作各等分点所在坐标轴的法平面，各法平面相交形成该第一步网格优势点的第二步网格，任意一个第二步网格节点

满足式(13)、式(14)、式(15)。根据地层勘查资料确定掘进地层R_c后，将点

代入式(8)，得到所有第二步网格节点对应的β**。The second step grid is established, and for each dominant point of the first step grid, the point is taken as the body center and the projection lengths on the x, y, and z axes are respectively

The rectangular parallelepiped and the sides of the rectangular parallelepiped are divided into m ₂ equal parts as the normal plane of the coordinate axis where each bisected point is located. grid node

Equation (13), Equation (14), and Equation (15) are satisfied. After the excavation stratum R _c is determined according to the stratum exploration data, the point

Substitute into Equation (8) to get β** corresponding to all grid nodes in the second step.

Summarize the β** corresponding to the grid advantage point of the first step and the β** corresponding to all the grid nodes of the second step, and take the grid nodes corresponding to the top 10% with the largest β** as the primary optimization parameter point.

Step 6 Checking the driving rate

As shown in Figure 2, there are positive hob and side hob distributed on the cutter head, the positive hob is installed parallel to the driving direction, and there is a non-zero side hob installation angle between the side hob and the driving direction. The effective thrust is approximately equally distributed to each hob and the force parallel to the driving direction is F/N, and the force parallel to the driving direction on the positive hob and the side hob is approximately average F/N, where the number of positive hob is N _fc tools, the number of side hob is N _lc , and the total number of tools is N tools, as shown in formula (16). According to the force balance, the resultant formation resistance force on the cutterhead is equal to the resultant effective thrust force, and the cutterhead torque is equal to the resultant moment of formation resistance on the cutterhead spindle. According to Saint-Venant's principle, the total cutterhead torque on the positive hob is approximately λμ (FN _fc /N)R/2, the cutter head torque can be approximated as the resultant moment of the occlusal force and frictional resistance generated by the effective thrust between the cutter and the face rock, as in formula (17), R is the maximum positive hob Installation radius, r _w is the installation radius of the wth edge hob (the distance between the contact point between the hob and the face of the hob and the normal line of the cutter head plane passing through the center of the cutter head), θ _w is the wth cutter The installation angle of the side hob, μ is the friction coefficient between the steel and the stratum, λ is the empirical correction coefficient, and λ can be taken as 0.24, 0.21, and 0.2 in the granite stratum, andesite stratum, and limestone stratum, respectively.

N=N _fc +N _lc (16)

According to formula (8), the value v** of the driving rate to be determined is shown in formula (18).

Substitute the cutter head speed n, soil bin pressure p, and effective thrust F of the primary optimization parameter point into formula (18) to obtain the v** corresponding to this point, and calculate the corresponding v** for each primary optimization parameter point one by one, take The tunneling parameters of the primary optimization parameter point when v** is the largest are used as the tunneling parameters after optimization.

Claims (3)

1. a fast method for optimizing the tunneling parameters of earth pressure balance type shield machine, is characterized in that, comprises the steps: Step 1. Establish a statistical sample of driving efficiency The tunneling efficiency β is defined as the tunneling rate v divided by the cutter head torque T, as shown in formula (1); T directly reflects the operation state of the equipment, and β reflects the relationship between the tunneling rate and the load capacity of the cutter head drive motor; Combined with the excavation parameters automatically recorded by the shield machine during tunnel trial excavation and the excavation parameter data of previous projects, the excavation rate v, cutter head torque T, effective thrust F, soil bin pressure p, cutter head speed n measured at the same time are taken as The same set of tunneling parameters; β, F, p, and n at each recording time in the trial tunneling stage are counted as the tunneling efficiency statistical samples; Step 2. Obtain the prediction equation of driving efficiency for finite samples through symbolic regression and linear regression Symbolic regression is performed on the tunneling efficiency β of the shield machine in each layer with different stratum saturated uniaxial compressive strength _Rc . The computing time on the computer running the symbolic regression algorithm in the background is less than 1 minute and the fitting accuracy ^r2 is high. The fitting equation for β at 0.7 is used as a candidate equation; The candidate equations of each stratum are counted, and the independent variables n ² , p, np, and pF all coexist in at least one of the candidate equations of each stratum, so n ² , p, np, and pF are taken as the tunneling efficiency under the finite sample. For the independent variable of the prediction equation, such as formula (2), linear regression is performed again on the statistical sample of the driving efficiency through the driving efficiency prediction equation under the finite sample, and the equation coefficients belonging to each stratum are obtained; β* is the predicted value of the driving efficiency under the finite sample; β*=a ₁ n ² +a ₂ p+a ₃ np+a ₄ pF+a ₅ (2) Step 3. Extension of tunneling efficiency prediction equation The equation coefficients in equation (2) obtained under the condition of finite samples are discrete equation coefficients for finite types of strata, and it is necessary to extend the equations corresponding to the discrete equation coefficients to obtain equations suitable for general strata; Taking the coefficients of the prediction equations of the tunneling efficiency in different tunneling strata obtained in step 1 as the dependent variable, and with the saturated uniaxial compressive strength R _c of the tunneling stratum as the independent variable, perform linear and nonlinear regression, and the equation coefficients are obtained as a function of R. The continuous function of the variation of _c is shown in formula (3), formula (4), formula (5), formula (6), and formula (7). The extension is also in the range of hard rock, that is, R _c ≥ 30MPa; a ₁ =116.588-99.614R _c ^0.038 , R _c ≥30MPa(3) a ₂ =46.522-12.532R _c ^0.313 , R _c ≥30MPa(4) a ₃ =0.093R _c -4.414, R _c ≥30MPa(5) a ₄ =1.135×10 ^-6 R _c -6.976×10 ^-5 , R _c ≥30MPa(6)

As in Equation (8), Substitute Equation (3), Equation (4), Equation (5), Equation (6), Equation (7) into Equation (2) to obtain a hard rock suitable for EPB shield tunneling is the prediction equation of the driving efficiency, β** is the prediction value of the driving efficiency of the earth pressure balance shield tunneling in hard rock;

Step 4. Determine the optimization formula and boundary conditions The calculation formula of the tunneling parameter optimization is shown in formula (9), p ^Ω , Θ ^Ω , Ψ ^Ω respectively reflect the allowable fluctuation range of soil bin pressure, effective thrust, and cutter head rotation speed during normal excavation of stratum Ω, namely [p _min , p _max ], [F _min ,F _max ], [n _min ,n _max ]; Step 5. Calculate the maximum value of β** by the step-by-step point method The influencing factors of the optimization problem have all been quantified and the boundaries are clear. It is advisable to use linear equal division to obtain the optimal value grid of the tunneling parameters to be selected, and perform step-by-step point selection method for step-by-step calculation of grid nodes; Taking p ^Ω , Θ ^Ω , Ψ ^Ω as the definition domains on the mutually orthogonal x, y, and z coordinate axes of the spatial Cartesian coordinate system, the spatial definition domain of β** is obtained; Establish the first step grid, divide p ^Ω , Θ ^Ω , Ψ ^Ω as m ₁ equal parts, and make the normal plane of the coordinate axis where the bisected points are located at all the bisected points, and the intersection of the normal planes form the definition of β** space the first step grid of the domain, any one of the first step grid nodes

Satisfy formula (10), formula (11), formula (12); after determining the excavation stratum R _c according to the stratum exploration data, the point

Substitute into formula (8) to obtain the β** corresponding to each first step grid node in the spatial definition domain of β**; the β** corresponding to each first step grid node in the spatial definition domain of β** is in descending order of size Arrange to get the first step grid node β** sequence; take the grid node corresponding to the first 20% β** of the first step grid node β** as the first step grid advantage point;

The second step grid is established, and for each dominant point of the first step grid, the point is taken as the body center and the projection lengths on the x, y, and z axes are respectively

The rectangular parallelepiped and the sides of the rectangular parallelepiped are divided into m ₂ equal parts as the normal plane of the coordinate axis where each bisected point is located. grid node

Satisfy formula (13), formula (14), formula (15); after determining the excavation stratum R _c according to the stratum exploration data, the point

Substitute into formula (8) to get the β** corresponding to all the grid nodes in the second step;

Summarize the β** corresponding to the grid advantage point of the first step and the β** corresponding to all the grid nodes of the second step, and take the grid nodes corresponding to the top 10% of the largest β** as the primary selection optimization parameter point; Step 6. Check the driving rate There are positive hob and side hob distributed on the cutter head. The positive hob is installed parallel to the driving direction, and there is a non-zero side hob installation angle between the side hob and the driving direction; the effective thrust is approximately equally distributed to each hob The force on the hob parallel to the heading direction is F/N, and the force parallel to the heading direction on the positive hob and the side hob is approximately F/N on average, in which the number of positive hob is N _fc tools, and the side hob The number is N _lc , and the total number of tools is N, as shown in formula (16); according to the force balance, the resultant formation resistance force on the cutter head is equal to the effective thrust resultant force, and the cutter head torque is equal to the resultant moment of formation resistance to the cutter head spindle, According to Saint-Venant's principle, the sum of the cutter head torque on the positive hob is approximately λμ(FN _fc /N)R/2, and the cutter head torque can be approximated as the bite force generated by the effective thrust between the cutter and the face rock The resultant moment with frictional resistance, such as formula (17), R is the maximum installation radius of the positive hob, rw is the installation radius of the _wth edged hob, θw is the installation angle of the _wth edged hob, μ is Friction coefficient between steel and formation, λ is the empirical correction coefficient; N=N _fc +N _lc (16)

According to Equation (8), the value v** of the driving rate to be determined is shown in Equation (18);

Substitute the cutter head speed n, soil bin pressure p, and effective thrust F of the primary optimization parameter point into formula (18) to obtain the v** corresponding to this point, and calculate the corresponding v** for each primary optimization parameter point one by one, take The tunneling parameters of the primary optimization parameter point when v** is the largest are used as the tunneling parameters after optimization. 2. a kind of fast method for optimizing the tunneling parameters of earth pressure balance type shield machine according to claim 1, is characterized in that, in step 1: the unit of v, T, F, p, n is respectively mm/min, 10 ⁶ Nm, kN, Bar, r/min. 3. a kind of fast method of optimizing earth pressure balance type shield tunneling parameters according to claim 1, is characterized in that, in step 6: λ is empirical correction coefficient, and λ is in granite stratum, andesite stratum, limestone stratum Can be taken as 0.24, 0.21, 0.2 respectively.

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