CN110704963A - Rapid method for optimizing tunneling parameters of earth pressure balanced type shield tunneling machine - Google Patents

Rapid method for optimizing tunneling parameters of earth pressure balanced type shield tunneling machine Download PDF

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CN110704963A
CN110704963A CN201910871045.9A CN201910871045A CN110704963A CN 110704963 A CN110704963 A CN 110704963A CN 201910871045 A CN201910871045 A CN 201910871045A CN 110704963 A CN110704963 A CN 110704963A
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tunneling
formula
beta
stratum
efficiency
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CN110704963B (en
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李彤
韩爱民
施烨辉
徐成华
汤国毅
程荷兰
王建军
苏明
王金铭
李闯
李璇
翟维骏
张心远
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NANJING KENTOP CIVIL ENGINEERING TECHNOLOGY Co Ltd
Nanjing Tech University
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Nanjing Tech University
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Abstract

The invention relates to a rapid method for optimizing tunneling parameters of an earth pressure balance type shield tunneling machine, and belongs to the technical field of underground tunnel engineering construction. For quantitatively optimizing the excavation parameters of the earth pressure balanced type shield machine, the excavation efficiency is taken as an optimized analysis target function, and a prediction equation of the excavation efficiency under a limited sample is obtained by performing symbolic regression and linear regression on actually measured data. And obtaining the tunneling efficiency prediction equation suitable for the earth pressure balance type shield tunneling hard rock by calculating a continuous function of the coefficient of the tunneling efficiency prediction equation under the limited sample along with the change of the saturated uniaxial compressive strength of the tunneling stratum. And then, optimal calculation is carried out in a given definition domain through a step-by-step point taking method, and optimal tunneling parameters of the earth pressure balanced type shield tunneling machine suitable for tunneling hard rock are obtained by combining checking of the tunneling rate. The method is based on engineering investigation data and construction data, has simple and clear calculation process, reasonable method and strong practicability, and can effectively improve the tunneling efficiency of the earth pressure balance type shield tunneling machine.

Description

Rapid method for optimizing tunneling parameters of earth pressure balanced type shield tunneling machine
Technical Field
The invention belongs to the technical field of excavation parameter optimization of a full-face tunnel boring machine, and particularly relates to a rapid method for optimizing excavation parameters of an earth pressure balance type shield machine.
Background
1) A method for predicting the tunneling efficiency of a hard rock tunneling machine (application number: 201610755946.8) the method does not give specific definition of the tunneling efficiency, and the influence factors of the tunneling efficiency are limited to five types of geological features, and the influence of other tunneling parameters on the tunneling efficiency is not considered.
2) TBM tunneling parameter optimization method (application number: 201910231527.8) the method uses the minimum specific energy consumption as the objective function, the integral variables of the work function are displacement and rotation angle, the equation of force and torque can only get the broken line equation through the existing measured value, and the non-tunneling area can not be predicted and optimized in advance.
3) Optimization method of shield tunneling parameters under composite stratum condition (application number: 201610003385.6) and 4) establishment and optimization of a shield tunneling rate model under a composite stratum (lige, fuchsia, guojinbo, et al. establishment and optimization of a shield tunneling rate model under a composite stratum [ J ] modern tunneling technology, 2017 (3)) have limitations in applicability and calculation principle. In the aspect of applicability, the tunneling rate prediction equation is only applicable to one stratum, and the equation is not equally applicable when stratum conditions change. In the aspect of calculation principle, in reference 3), the tunneling rate and the cutter head torque are optimized respectively, but coupling optimization of the tunneling rate and the cutter head torque is not performed, that is, the tunneling parameter group corresponding to the optimal tunneling rate value is different from the tunneling parameter group corresponding to the optimal cutter head torque value, and a final optimization conclusion of comprehensively considering the tunneling rate and the cutter head torque is not given; reference 4) is purely based on the tunneling rate as an optimization target without considering the constraints of equipment loss and load capacity. Further, the constraints of the references 3) and 4) do not give a clear calculation formula, and it is difficult to solve the problem by the K-T method.
5) The method comprises the steps of establishing a shield tunneling rate model and optimizing parameters of a shield tunneling machine under a complex water-rich stratum (Wangqiang. establishing a shield tunneling rate model and optimizing parameters of a shield tunneling machine under a complex water-rich stratum [ J ] water conservancy planning and design, 2019(08):73-78.) by taking a tunneling rate as a single optimized objective function, the restriction of equipment load capacity and loss on tunneling efficiency is not considered, a tunneling rate prediction equation is only suitable for one stratum, and the applicability and principle correctness are limited. In addition, in contrast document 5), optimization calculation is performed by a local optimization method, and the calculation result is greatly affected by the setting of an initial value, resulting in low engineering applicability.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a rapid method for optimizing the tunneling parameters of an earth pressure balanced type shield tunneling machine, which is used for quantitatively optimizing the tunneling parameters of the earth pressure balanced type shield tunneling machine and taking the ratio of the tunneling speed to the cutter head torque as an optimized analysis objective function and specifically comprises the following steps:
step one, establishing a tunneling efficiency statistical sample
The tunneling efficiency β is defined as the tunneling rate v divided by the cutter head torque T, as in equation (1). T directly reflects the running state of the equipment, and beta reflects the relationship between the tunneling rate and the load capacity of a cutter head driving motor.
Figure BDA0002202823160000021
And combining the tunneling parameters automatically recorded by the shield tunneling machine during tunneling trial and the tunneling parameter data of the previous engineering, and taking the tunneling speed v, the cutter torque T, the effective thrust F, the soil bin pressure p and the cutter rotating speed n which are actually measured at the same moment as the same group of tunneling parameters. And counting beta, F, p and n at each recording moment in the trial tunneling stage to serve as a tunneling efficiency statistical sample.
Step two, obtaining a tunneling efficiency prediction equation for the limited sample through symbolic regression and linear regression
Uniaxial compressive strength R to formation saturationcPerforming symbol regression on the tunneling efficiency beta of the shield tunneling machine in different strata respectively, and running the symbol regression algorithm on a computer with the computation time of less than 1 minute and the fitting precision r on the background2Fitting equations for β above 0.7 are candidate equations.
Counting candidate equations of each stratum, independent variable n2P, np, pF all co-exist in at least one of the candidate equations for each formation, thus in n2P, np and pF are used as independent variables of the tunneling efficiency prediction equation under the limited sample, as shown in formula (2), linear regression is carried out again on the tunneling efficiency statistical sample through the tunneling efficiency prediction equation under the limited sample, and equation coefficients belonging to each stratum are obtained;
beta is a predicted value of the tunneling efficiency under a limited sample.
β*＝a1n2+a2p+a3np+a4pF+a5(2)
Step three tunneling efficiency prediction equation continuation
The equation coefficients in the formula (2) obtained under the condition of the limited samples are discrete equation coefficients for the limited kinds of strata, and the equations corresponding to the discrete equation coefficients need to be extended to obtain the equations suitable for the general strata.
Taking coefficients of prediction equations of the tunneling efficiency in different tunneling strata under the limited samples obtained in the step one as dependent variables, and taking the saturated uniaxial compressive strength R of the tunneling strata ascLinear and nonlinear regression for independent variables to obtain equation coefficients with RcThe continuous function of the change is shown as formula (3), formula (4), formula (5), formula (6) and formula (7). Because the samples are all obtained from hard rocks, the continuation of the tunneling efficiency prediction equation is also in the hard rock range, namely Rc≥30MPa。
a1＝116.588-99.614Rc 0.038,Rc≥30MPa (3)
a2＝46.522-12.532Rc 0.313,Rc≥30MPa (4)
a3＝0.093Rc-4.414,Rc≥30MPa (5)
a4＝1.135×10-6Rc-6.976×10-5,Rc≥30MPa (6)
Figure BDA0002202823160000031
According to the formula (8), the formula (3), the formula (4), the formula (5), the formula (6) and the formula (7) are replaced by the formula (2), so that a tunneling efficiency prediction equation suitable for the soil pressure balance type shield tunneling hard rock is obtained, and beta is a tunneling efficiency prediction value of the soil pressure balance type shield tunneling hard rock.
Step four, determining an optimized calculation formula and boundary conditions
The optimal calculation formula of the tunneling parameter is shown as a formula (9), pΩ、ΘΩ、ΨΩRespectively reflects the allowable fluctuation range of the soil bin pressure, the effective thrust and the cutter head rotating speed when the stratum is normally tunneled omega, namely [ pmin,pmax]、[Fmin,Fmax]、[nmin,nmax]。
Step five-step dot method for calculating larger value of beta
Influence factors of the optimization problem are quantized, the boundary is clear, linear equal division is adopted to obtain the optimal value grid of the tunneling parameters to be selected, and step-by-step point-taking method gradual operation is carried out on grid nodes.
P is to beΩ、ΘΩ、ΨΩAnd respectively taking the space domain as the domain on the mutually orthogonal x, y and z coordinate axes of the space rectangular coordinate system to obtain the space domain of beta.
Establishing a first step grid, and respectively connecting pΩ、ΘΩ、ΨΩAs m1Dividing equally and making normal planes of coordinate axes of the equally divided points at all equally divided points, intersecting each normal plane to form a first step grid of the beta x space definition domain, and any one node of the first step gridSatisfies the formulas (10), (11) and (12). Determining tunneling stratum R according to stratum investigation datacThen, the points are put
Figure BDA0002202823160000043
And (8) substituting the formula (8) to obtain beta corresponding to each first step grid node in the space definition domain of the beta. And arranging beta corresponding to each first step grid node in the space definition domain of the beta in a descending order according to the size to obtain a first step grid node beta array. And taking the grid nodes corresponding to the maximum first 20% of the grid nodes beta in the first step as the dominant points of the first step grid.
Figure BDA0002202823160000045
Establishing a second step grid, and taking the dominant point of each first step grid as a body center and the projection lengths of the dominant point in the x axis, the y axis and the z axis as
Figure BDA0002202823160000047
The sides of the cuboid are m2Dividing equally, making normal planes of coordinate axes of all equally divided points, intersecting all normal planes to form second step grid of the first step grid dominant point, any one second step grid node
Figure BDA0002202823160000051
Satisfies the formulas (13), (14) and (15). Determining tunneling stratum R according to stratum investigation datacThen, the points are put
Figure BDA0002202823160000052
Figure BDA0002202823160000053
And (4) substituting the formula (8) to obtain beta corresponding to all the second step grid nodes.
Figure BDA0002202823160000055
Figure BDA0002202823160000056
And summarizing beta corresponding to the first-step grid dominant point and beta corresponding to all second-step grid nodes, and taking the grid nodes corresponding to the first 10% of the maximum beta as initial selection optimization parameter points.
And sixthly, checking the tunneling rate.
Positive hobbing cutters are distributed on the cutter headAnd the positive hob is installed in parallel to the tunneling direction, and a non-zero edge hob installation angle exists between the edge hob and the tunneling direction. The effective thrust is approximately evenly distributed to each hob, the force parallel to the tunneling direction is F/N, the forces borne by the positive hob and the side hob and parallel to the tunneling direction are approximately evenly F/N, and the number of the positive hobs is NfcWith a number of edge cutters of NlcThe total number of the cutters is N, and the formula (16) shows. According to the balance of forces, the resultant force of the stratum resistance borne by the cutter head is equal to the resultant force of the effective thrust, the torque of the cutter head is equal to the resultant moment of the stratum resistance to the main shaft of the cutter head, and the sum of the torques of the cutter head borne by the positive hob is approximate to lambda mu (FN) according to the Saint-Venn principlefcR/N) R/2, the cutter head torque can be approximate to the resultant torque of the occlusal force and the frictional resistance generated between the cutter and the rock on the face by the effective thrust, as shown in formula (17), R is the maximum installation radius of the positive hob, and R iswThe mounting radius of the w-th edge hob, thetawThe w-th installation angle of the edge roller cutter is shown, mu is the friction coefficient between steel and the stratum, and lambda is the empirical correction coefficient.
N＝Nfc+Nlc(16)
Figure BDA0002202823160000057
According to the formula (8), the tunneling rate to-be-determined value v is represented by the formula (18).
Figure BDA0002202823160000061
And substituting the cutter head rotating speed n, the soil bin pressure p and the effective thrust F of the primarily selected optimization parameter points into a formula (18) to obtain v corresponding to the points, calculating the v corresponding to each primarily selected optimization parameter point one by one, and taking the tunneling parameter of the primarily selected optimization parameter point when v is the maximum as the optimized tunneling parameter.
Further, in the step one: v, T, F, p and n are respectively in units of mm/min and 106Nm、kN、Bar、r/min。
Further, in the sixth step, λ is an empirical correction coefficient, and λ can be 0.24, 0.21, and 0.2 in a granite formation, an andesite formation, and a limestone formation, respectively.
Drawings
FIG. 1 is a scatter plot of equation coefficients for different formations under a finite sample;
fig. 2 shows the installation angle of the edge roller on the cutter head.
Detailed description of the invention
Aiming at the defects of the prior art, the invention provides a rapid method for optimizing the tunneling parameters of an earth pressure balance type shield tunneling machine, which comprises the following steps:
when the shield tunnels different types of stratums, namely tunnel face stratum distribution is changed, the shield tunneling speed and cutter head torque are changed accordingly. The tunneling speed is larger, the construction period is shorter, but the cutter head torque is also increased, and the cutter head torque is the most main control parameter of the integrity of equipment and reflects the working state of a cutter head main shaft. In order to meet the requirements of construction period and equipment completeness, balance needs to be obtained between the tunneling rate and the cutter head torque, so that the potential of the equipment is excavated to the maximum extent under the condition that the equipment is guaranteed to be complete, and the tunneling rate is effectively improved. Therefore, the shield tunneling parameter control optimization method based on the geological segmentation is provided, and the shield tunneling parameter dynamic optimization control based on the tunneling stratum parameters is realized.
Step one, establishing a statistical sample of tunneling efficiency
The tunneling efficiency β is defined as the tunneling rate v divided by the cutter head torque T, as in equation (1). T directly reflects the running state of the equipment, and beta reflects the relationship between the tunneling rate and the load capacity of a cutter head driving motor.
Figure BDA0002202823160000071
And combining the tunneling parameters automatically recorded by the shield tunneling machine during tunneling trial and the tunneling parameter data of the previous engineering, and taking the tunneling speed v, the cutter torque T, the effective thrust F, the soil bin pressure p and the cutter rotating speed n which are actually measured at the same moment as the same group of tunneling parameters. Counting beta, F, p and n at each recording moment in the trial excavation stage to be used as a excavation efficiency statistical sample;
v、T、F. the units of p and n are respectively mm/min (millimeter per minute) and 106Nm, kN, Bar, r/min (circles per minute).
Step two, obtaining a prediction equation of the tunneling efficiency for the limited sample through symbolic regression and linear regression to obtain the saturated uniaxial compressive strength R of the stratumcCarrying out symbol regression on beta of the shield tunneling machine in different stratums respectively, and running a symbol regression algorithm on a computer with the operation time of less than 1 minute and the fitting precision r on the background2Fitting equations for β above 0.7 are candidate equations.
Counting candidate equations of each stratum, independent variable n2P, np, pF all co-exist in at least one of the candidate equations for each formation, thus in n2P, np and pF are used as independent variables of the tunneling efficiency prediction equation under the limited sample, as shown in formula (2), linear regression is carried out again on the tunneling efficiency statistical sample through the tunneling efficiency prediction equation under the limited sample, and equation coefficients belonging to each stratum are obtained, and are shown in table 1;
beta is a predicted value of the tunneling efficiency under a limited sample.
β*＝a1n2+a2p+a3np+a4pF+a5(2)
TABLE 1 prediction equation coefficient of tunneling efficiency of different saturated uniaxial compressive strength strata
Figure BDA0002202823160000081
Step three tunneling efficiency prediction equation continuation
Table 1 shows equation coefficients obtained by equation (2) under discrete finite sample conditions (the saturated uniaxial compressive strengths of the formation are 42MPa, 54MPa, 62MPa, 90MPa, and 118MPa, respectively), and the equation corresponding to the discrete equation coefficients under the finite sample conditions needs to be extended to obtain the equation coefficients suitable for general formations (the saturated uniaxial compressive strength is different from the sample value), that is, the equation can be applied to the cases when the saturated uniaxial compressive strength of the formation is not equal to 42MPa, 54MPa, 62MPa, 90MPa, and 118 MPa.
In the first stepThe coefficient of a prediction equation of the tunneling efficiency in different tunneling strata under the limited sample is a dependent variable, and the saturated uniaxial compressive strength R of the tunneling strata is usedcLinear and nonlinear regression for the independent variables, i.e. for the scatter points in FIG. 1, the equation coefficients are obtained as a function of RcThe continuous function of the change is shown as formula (3), formula (4), formula (5), formula (6) and formula (7). Because the samples are all obtained from hard rocks, the continuation of the tunneling efficiency prediction equation is also in the hard rock range, namely Rc≥30MPa。
a1＝116.588-99.614Rc 0.038,Rc≥30MPa (3)
a2＝46.522-12.532Rc 0.313,Rc≥30MPa (4)
a3＝0.093Rc-4.414,Rc≥30MPa (5)
a4＝1.135×10-6Rc-6.976×10-5,Rc≥30MPa (6)
Figure BDA0002202823160000082
According to the formula (8), the formula (3), the formula (4), the formula (5), the formula (6) and the formula (7) are replaced by the formula (2), so that a tunneling efficiency prediction equation suitable for the soil pressure balance type shield tunneling hard rock is obtained, and beta is a tunneling efficiency prediction value of the soil pressure balance type shield tunneling hard rock.
Step four, determining an optimized calculation formula and boundary conditions
The optimal calculation formula of the tunneling parameter is shown as a formula (9), pΩ、ΘΩ、ΨΩRespectively reflects the allowable fluctuation range of the soil bin pressure, the effective thrust and the cutter head rotating speed when the stratum is normally tunneled omega, namely [ pmin,pmax]、[Fmin,Fmax]、[nmin,nmax]。
Taking Shenzhen subway certain tunnel interval as an example, the saturated uniaxial compressive strength R of the tunneling stratumcAnd if the pressure is 64.5MPa, the prediction equation of the tunneling efficiency corresponding to the stratum is obtained as beta, 0.115n according to the formula (8)2+0.346p+1.585np+3.448×10- 6pF +2.739, and according to engineering experience, during normal tunneling, the allowable fluctuation range p of the pressure of the soil bin in the stratumΩIs [0.05,0.4 ]]Allowable fluctuation range psi of cutter head rotation speedΩIs [0.8,2.2 ]]Effective thrust allowable fluctuation range thetaΩIs [6000,15000 ]]。
Step five-step dot method for calculating larger value of beta
Influence factors of the optimization problem are quantized, the boundary is clear, linear equal division is preferably adopted to obtain a mesh with the optimal value of the tunneling parameter to be selected, and step-by-step point taking method gradual operation is carried out on mesh nodes, so that influence of initial value selection on a calculation result is avoided.
P is to beΩ、ΘΩ、ΨΩAnd respectively taking the space domain as the domain on the mutually orthogonal x, y and z coordinate axes of the space rectangular coordinate system to obtain the space domain of beta.
Establishing a first step grid, and respectively connecting pΩ、ΘΩ、ΨΩAs m1Dividing equally and making normal planes of coordinate axes of the equally divided points at all equally divided points, intersecting each normal plane to form a first step grid of the beta x space definition domain, and any one node of the first step grid
Figure BDA0002202823160000101
Satisfies the formulas (10), (11) and (12). Determining tunneling stratum R according to stratum investigation datacThen, the points are put
Figure BDA0002202823160000102
And (8) substituting the formula (8) to obtain beta corresponding to each first step grid node in the space definition domain of the beta. Sorting beta corresponding to each first step grid node in the space definition domain of beta according to descending order of sizeAnd obtaining the first step grid node beta x number sequence. And taking the grid nodes corresponding to the maximum first 20% of the grid nodes beta in the first step as the dominant points of the first step grid.
Figure BDA0002202823160000103
Figure BDA0002202823160000104
Figure BDA0002202823160000105
Establishing a second step grid, and taking the dominant point of each first step grid as a body center and the projection lengths of the dominant point in the x axis, the y axis and the z axis as
Figure BDA0002202823160000106
The sides of the cuboid are m2Dividing equally, making normal planes of coordinate axes of all equally divided points, intersecting all normal planes to form second step grid of the first step grid dominant point, any one second step grid node
Figure BDA0002202823160000107
Satisfies the formulas (13), (14) and (15). Determining tunneling stratum R according to stratum investigation datacThen, the points are put
Figure BDA0002202823160000108
Figure BDA0002202823160000109
And (4) substituting the formula (8) to obtain beta corresponding to all the second step grid nodes.
Figure BDA00022028231600001010
Figure BDA0002202823160000111
Figure BDA0002202823160000112
And summarizing beta corresponding to the first-step grid dominant point and beta corresponding to all second-step grid nodes, and taking the grid nodes corresponding to the first 10% of the maximum beta as initial selection optimization parameter points.
Step six tunneling rate check
As shown in fig. 2, a positive hob and an edge hob are distributed on the cutterhead, the positive hob is installed parallel to the tunneling direction, and an edge hob installation angle which is not zero exists between the edge hob and the tunneling direction. The effective thrust is approximately evenly distributed to each hob, the force parallel to the tunneling direction is F/N, the forces borne by the positive hob and the side hob and parallel to the tunneling direction are approximately evenly F/N, and the number of the positive hobs is NfcWith a number of edge cutters of NlcThe total number of the cutters is N, and the formula (16) shows. According to the balance of forces, the resultant force of the stratum resistance borne by the cutter head is equal to the resultant force of the effective thrust, the torque of the cutter head is equal to the resultant moment of the stratum resistance to the main shaft of the cutter head, and the sum of the torques of the cutter head borne by the positive hob is approximate to lambda mu (FN) according to the Saint-Venn principlefcR/N) R/2, the cutter head torque can be approximate to the resultant torque of the occlusal force and the frictional resistance generated between the cutter and the rock on the face by the effective thrust, as shown in formula (17), R is the maximum installation radius of the positive hob, and R iswThe mounting radius of the w-th edge hob (the distance between the contact point between the hob and the tunnel face and the normal line of the cutterhead plane passing through the center of the cutterhead), thetawThe w-th installation angle of the edge hob is set, mu is the friction coefficient between steel and the stratum, lambda is the empirical correction coefficient, and lambda can be respectively 0.24, 0.21 and 0.2 in the granite stratum, the andesite stratum and the limestone stratum.
N＝Nfc+Nlc(16)
Figure BDA0002202823160000113
According to the formula (8), the tunneling rate to-be-determined value v is represented by the formula (18).
Figure BDA0002202823160000121
And substituting the cutter head rotating speed n, the soil bin pressure p and the effective thrust F of the primarily selected optimization parameter points into a formula (18) to obtain v corresponding to the points, calculating the v corresponding to each primarily selected optimization parameter point one by one, and taking the tunneling parameter of the primarily selected optimization parameter point when v is the maximum as the optimized tunneling parameter.

Claims (3)

1. A rapid method for optimizing the tunneling parameters of an earth pressure balance type shield tunneling machine is characterized by comprising the following steps:
step one, establishing a tunneling efficiency statistical sample
Defining the tunneling efficiency beta as the tunneling speed v divided by the cutter head torque T, as shown in the formula (1); t directly reflects the running state of equipment, and beta represents the relationship between the tunneling rate and the load capacity of a cutter head driving motor;
combining tunneling parameters automatically recorded by a shield machine during tunnel trial tunneling and tunneling parameter data of a previous project, and taking a tunneling speed v, a cutter torque T, an effective thrust F, a soil bin pressure p and a cutter rotating speed n which are actually measured at the same moment as a same group of tunneling parameters; counting beta, F, p and n at each recording moment in the trial excavation stage to be used as a excavation efficiency statistical sample;
step two, obtaining a tunneling efficiency prediction equation for the limited sample through symbolic regression and linear regression
Uniaxial compressive strength R to formation saturationcPerforming symbol regression on the tunneling efficiency beta of the shield tunneling machine in different strata respectively, and running the symbol regression algorithm on a computer with the computation time of less than 1 minute and the fitting precision r on the background2Fitting equations for β higher than 0.7 as candidate equations;
counting candidate equations of each stratum, independent variable n2P, np, pF all co-exist in at least one of the candidate equations for each formationIn the equation, therefore in n2P, np and pF are used as independent variables of the tunneling efficiency prediction equation under the limited sample, as shown in formula (2), linear regression is carried out again on the tunneling efficiency statistical sample through the tunneling efficiency prediction equation under the limited sample, and equation coefficients belonging to each stratum are obtained;
beta is a predicted value of the tunneling efficiency under a limited sample;
β*＝a1n2+a2p+a3np+a4pF+a5(2)
step three, tunneling efficiency prediction equation continuation
The equation coefficients in the formula (2) obtained under the condition of the limited samples are discrete equation coefficients for the limited kinds of strata, and the equations corresponding to the discrete equation coefficients need to be extended to obtain the equations suitable for the general strata;
taking coefficients of prediction equations of the tunneling efficiency in different tunneling strata under the limited samples obtained in the step one as dependent variables, and taking the saturated uniaxial compressive strength R of the tunneling strata ascLinear and nonlinear regression for independent variables to obtain equation coefficients with RcThe continuous function of the change is shown as formula (3), formula (4), formula (5), formula (6) and formula (7); because the samples are all obtained from hard rocks, the continuation of the tunneling efficiency prediction equation is also in the hard rock range, namely Rc≥30MPa；
a1＝116.588-99.614Rc 0.038,Rc≥30MPa(3)
a2＝46.522-12.532Rc 0.313,Rc≥30MPa(4)
a3＝0.093Rc-4.414,Rc≥30MPa(5)
a4＝1.135×10-6Rc-6.976×10-5,Rc≥30MPa(6)
Figure FDA0002202823150000021
According to the formula (8), the formula (3), the formula (4), the formula (5), the formula (6) and the formula (7) are replaced by the formula (2), so that a tunneling efficiency prediction equation suitable for the soil pressure balance type shield tunneling hard rock is obtained, and beta is a tunneling efficiency prediction value of the soil pressure balance type shield tunneling hard rock;
Figure FDA0002202823150000022
step four, determining an optimized calculation formula and boundary conditions
The optimal calculation formula of the tunneling parameter is shown as a formula (9), pΩ、ΘΩ、ΨΩRespectively reflects the allowable fluctuation range of the soil bin pressure, the effective thrust and the cutter head rotating speed when the stratum is normally tunneled omega, namely [ pmin,pmax]、[Fmin,Fmax]、[nmin,nmax]；
Step five, calculating a larger value of beta by a step-by-step point-taking method
Influence factors of the optimization problem are quantized, the boundary is clear, linear equal division is adopted to obtain a mesh with the optimal value of the tunneling parameter to be selected, and step-by-step point-taking method gradual operation is carried out on mesh nodes;
p is to beΩ、ΘΩ、ΨΩRespectively serving as definition domains on the mutually orthogonal x, y and z coordinate axes of the space rectangular coordinate system to obtain a space definition domain of beta;
establishing a first step grid, and respectively connecting pΩ、ΘΩ、ΨΩAs m1Dividing equally and making normal planes of coordinate axes of the equally divided points at all equally divided points, intersecting each normal plane to form a first step grid of the beta x space definition domain, and any one node of the first step grid
Figure FDA0002202823150000031
Satisfies formula (10), formula (11), formula (12); determining tunneling stratum R according to stratum investigation datacThen, the points are put
Figure FDA0002202823150000032
Substituting formula (8) to obtain beta corresponding to each first step grid node in the space definition domain of beta; arranging beta corresponding to each first step grid node in the space definition domain of the beta in a descending order according to the size to obtain a first step grid node beta sequence; taking the grid nodes corresponding to the largest first 20% beta in the first step grid nodes beta as the first step grid dominant points;
Figure FDA0002202823150000033
Figure FDA0002202823150000034
Figure FDA0002202823150000035
establishing a second step grid, and taking the dominant point of each first step grid as a body center and the projection lengths of the dominant point in the x axis, the y axis and the z axis as
Figure FDA0002202823150000036
The sides of the cuboid are m2Dividing equally, making normal planes of coordinate axes of all equally divided points, intersecting all normal planes to form second step grid of the first step grid dominant point, any one second step grid node
Figure FDA0002202823150000037
Satisfies formula (13), formula (14), formula (15); determining tunneling stratum R according to stratum investigation datacThen, the points are put
Figure FDA0002202823150000038
Figure FDA0002202823150000039
Substituting an equation (8) to obtain beta corresponding to all the second step grid nodes;
Figure FDA0002202823150000041
Figure FDA0002202823150000042
Figure FDA0002202823150000043
summarizing beta corresponding to the first-step grid dominant point and beta corresponding to all second-step grid nodes, and taking the grid nodes corresponding to the first 10% of the maximum beta as initial selection optimization parameter points;
sixthly, checking the tunneling rate
A positive hob and an edge hob are distributed on the cutterhead, the positive hob is installed in parallel to the tunneling direction, and an edge hob installation angle which is not zero exists between the edge hob and the tunneling direction; the effective thrust is approximately evenly distributed to each hob, the force parallel to the tunneling direction is F/N, the forces borne by the positive hob and the side hob and parallel to the tunneling direction are approximately evenly F/N, and the number of the positive hobs is NfcWith a number of edge cutters of NlcThe total number of the cutters is N, and the formula (16) shows; according to the balance of forces, the resultant force of the stratum resistance borne by the cutter head is equal to the resultant force of the effective thrust, the torque of the cutter head is equal to the resultant moment of the stratum resistance to the main shaft of the cutter head, and the sum of the torques of the cutter head borne by the positive hob is approximate to lambda mu (FN) according to the Saint-Venn principlefcR/N) R/2, the cutter head torque can be approximate to the resultant torque of the occlusal force and the frictional resistance generated between the cutter and the rock on the face by the effective thrust, as shown in formula (17), R is the maximum installation radius of the positive hob, and R iswThe mounting radius of the w-th edge hob, thetawSetting the installation angle of the w-th edge hob, wherein mu is the friction coefficient between steel and the stratum, and lambda is the empirical correction coefficient;
N＝Nfc+Nlc(16)
Figure FDA0002202823150000044
according to the formula (8), the tunneling rate to-be-determined value v is shown as the formula (18);
Figure FDA0002202823150000051
and substituting the cutter head rotating speed n, the soil bin pressure p and the effective thrust F of the primarily selected optimization parameter points into a formula (18) to obtain v corresponding to the points, calculating the v corresponding to each primarily selected optimization parameter point one by one, and taking the tunneling parameter of the primarily selected optimization parameter point when v is the maximum as the optimized tunneling parameter.
2. The rapid method for optimizing the tunneling parameters of the earth pressure balance type shield tunneling machine according to claim 1, characterized in that in the first step: v, T, F, p and n are respectively in units of mm/min and 106Nm、kN、Bar、r/min。
3. The rapid method for optimizing the tunneling parameters of the earth pressure balance type shield tunneling machine according to claim 1, characterized in that in the sixth step: lambda is an empirical correction coefficient, and can be respectively 0.24, 0.21 and 0.2 in a granite stratum, an andesite stratum and a limestone stratum.
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