CN106844942B - Optimization method of tunnel lining design - Google Patents
Optimization method of tunnel lining design Download PDFInfo
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- 238000013461 design Methods 0.000 title claims abstract description 65
- 238000005457 optimization Methods 0.000 title claims abstract description 18
- 238000000034 method Methods 0.000 title claims abstract description 17
- 238000004364 calculation method Methods 0.000 claims abstract description 21
- 238000012545 processing Methods 0.000 claims abstract description 8
- 238000007619 statistical method Methods 0.000 claims abstract description 7
- 238000012360 testing method Methods 0.000 claims abstract description 6
- 238000004458 analytical method Methods 0.000 claims abstract description 4
- 238000012544 monitoring process Methods 0.000 claims abstract description 4
- 238000007781 pre-processing Methods 0.000 claims abstract description 3
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 58
- 239000011435 rock Substances 0.000 claims description 50
- 230000035699 permeability Effects 0.000 claims description 38
- 230000002787 reinforcement Effects 0.000 claims description 13
- 229910000831 Steel Inorganic materials 0.000 claims description 12
- 239000010959 steel Substances 0.000 claims description 12
- 239000004567 concrete Substances 0.000 claims description 11
- 238000009826 distribution Methods 0.000 claims description 10
- 239000000126 substance Substances 0.000 claims description 6
- 238000005520 cutting process Methods 0.000 claims description 4
- 230000001419 dependent effect Effects 0.000 claims description 4
- 238000013507 mapping Methods 0.000 claims description 4
- 239000011159 matrix material Substances 0.000 claims description 4
- 230000002706 hydrostatic effect Effects 0.000 claims description 3
- 230000008569 process Effects 0.000 claims description 3
- 230000005251 gamma ray Effects 0.000 claims description 2
- 238000003825 pressing Methods 0.000 claims description 2
- 238000000746 purification Methods 0.000 claims description 2
- 239000008213 purified water Substances 0.000 claims description 2
- 239000011150 reinforced concrete Substances 0.000 claims description 2
- 229910001294 Reinforcing steel Inorganic materials 0.000 claims 1
- 230000006872 improvement Effects 0.000 abstract description 3
- 238000011160 research Methods 0.000 description 10
- 230000003014 reinforcing effect Effects 0.000 description 5
- 230000000694 effects Effects 0.000 description 4
- 230000002159 abnormal effect Effects 0.000 description 2
- 230000008859 change Effects 0.000 description 2
- 238000010276 construction Methods 0.000 description 2
- 238000012067 mathematical method Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000003204 osmotic effect Effects 0.000 description 2
- 238000000611 regression analysis Methods 0.000 description 2
- 230000003487 anti-permeability effect Effects 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000005336 cracking Methods 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 238000012938 design process Methods 0.000 description 1
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- 238000010586 diagram Methods 0.000 description 1
- 230000008030 elimination Effects 0.000 description 1
- 238000003379 elimination reaction Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000012314 multivariate regression analysis Methods 0.000 description 1
- 238000010606 normalization Methods 0.000 description 1
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Abstract
The invention provides an optimization method of tunnel lining design, which is characterized by comprising the following steps: step 1: calculating the maximum crack width of the lining of different design schemes based on a permeable lining design theory, and taking the calculation parameters and calculation results as an original data set of subsequent mathematical analysis; step 2: preprocessing the original data set in the step 1, and standardizing the original data; performing data anomaly monitoring processing on the data set subjected to the standardized processing by adopting the Mahalanobis distance theory; and step 3: sequentially establishing regression equations of control variables and design parameters by adopting a backward stepwise regression method in multivariate statistical analysis, and selecting the regression equation with the largest significance test value as a final optimization equation of the lining design; the optimization design model comprehensively considers the influence of design parameters on engineering safety, quantitatively analyzes the influence of different optimization design measures on the improvement of lining safety, is simple and clear, improves the design efficiency and has wide applicability.
Description
Technical Field
The invention belongs to the field of hydraulic building structure design, and particularly relates to an optimization method for tunnel lining design.
Background
When a hydraulic tunnel is designed, a concrete lining is generally regarded as a waterproof material, but in a high water-rich engineering environment, the treatment mode often causes the designed lining to have larger thickness and even to be difficult to accept by engineering. With the widespread use of a large number of high-pressure or deep-buried tunnels, the above problems are increasingly highlighted. The concept of designing the lining according to the water permeability is more and more emphasized, and many researches begin to apply the osmotic water pressure to the lining according to the volume force and research the influence of the osmotic flow field and the internal force of the lining.
However, the design theory of the permeable lining is generally complex, and most relevant scholars develop researches on the permeable lining theory in the aspect of influence of single parameter on the lining safety; meanwhile, the current main research directions mostly focus on the qualitative analysis of the design parameters on the safety of the building, and the research conclusion cannot be directly adopted by engineering designers. The permeable lining design in the actual engineering usually considers the comprehensive influence of a plurality of design parameters, and is a typical optimization design problem based on quantitative research.
Therefore, the following problems mainly exist in the research results of the design of tunnel lining: (1) the comprehensive influence of multiple design parameters on the safety of the lining is not considered; (2) the practicability of the research result in the actual engineering is ignored; (3) an intuitive optimization design equation is not abstracted from the aspect of quantitative analysis, and the design efficiency is low.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides an optimal design idea of tunnel lining, which is based on the permeable lining theory, takes the maximum lining crack width as a control variable and combines a multivariate statistical analysis mathematical method to carry out the optimal design of the tunnel lining, and the technical scheme adopted for solving the problems in the prior art is as follows:
a method for optimizing the design of a tunnel lining is characterized by comprising the following steps:
step 2, because the design parameter dimensions of the original data set obtained in the step 1 are not uniform and the data range is large, the original data set obtained in the step 1 is preprocessed, and the preprocessing method comprises the following substeps:
step 2.1, data standardization processing, namely mapping the original data into a value of an interval [0,1], wherein a calculation formula is as follows:
wherein x is
*Is a normalized mapping value, x is the original data value, x
minIs the minimum value, x, of each index in the original data set
maxThe maximum value of each index in the original data set;
step 2.2, performing data anomaly monitoring processing on the standardized data set by adopting the Mahalanobis distance theory, wherein the calculation formula is as follows
Wherein D is
2For mahalanobis distance per sample, X is the normalized data matrix, G
-1Is the inverse of the covariance matrix, and X is the element mean;
D
2the greater the probability density, the smaller the probability density, and when greater to some extent, the probability density of the distribution will be so small that outside this range it is no longer in the range of normal points, and at α confidence levels, the threshold may be determined using the F distribution:
wherein l is the dimension of the sample, n is the sample capacity, F distribution is the common distribution for parameter estimation by mathematical statistics, which evolves from normal distribution, α is the confidence level, and mathematical statistics is a term, and the probability that the sample approaches the population when the population is estimated by the sample is represented by 1- α.
step 3.1, establishing a complete model of multivariate statistical regression, and setting m independent variables x
1,x
2...x
mModels fitted with m independent variables are called full models, i.e.
y＝β
0+β
1x
1+...+β
mx
m+ε (4)
Wherein y is a dependent variable, β
0Is constant, β
1,β
2...β
mIs the regression coefficient, ε is the regression error;
step 3.2, gradually eliminating independent variables and establishing the number of the residual independent variablesA meta statistical regression model; if the argument x is deleted from the m variables
k(k 1, 2.. said., m), then the model fitted with m-1 arguments is called a subtractive model, i.e.
y
k＝β
0+β
1x
1+...+β
k-1x
k-1+β
k+1x
k+1+...+β
mx
m+ε (5)
Step 3.3, calculating the significance difference value of the fitting equation of the full model and all the subtraction models, and taking the significance difference value of the full model as F
0Eliminating independent variable x
kThe difference in significance of the posterior subtraction model is F
k(in the elimination of x)
kThen, the subtraction model has eliminated x
1,x
2...x
k-1k-1 independent variables), the value of the difference in significance of the subtraction model can be expressed as
Wherein the content of the first and second substances,
y
iis the actual value of the dependent variable, i ═ 1, 2.., n;
F
0calculation of the sum of
kThe same;
step 3.4, solving the maximum value F in all the significant difference values
max，F
maxThe corresponding multiple regression equation is the final optimization design equation.
The theory of calculating the maximum crack width of the lining in step 1 is as follows:
the lining shows for reinforced concrete combined operation before the fracture, along with interior water pressure constantly increases, and lining hoop strain constantly increases, assumes that lining hoop strain is greater than behind the critical axial tensile strain of concrete, and the lining fracture, promptly:
wherein: epsilon
θLIs lining hoop strain; f. of
tDesigning tensile strength for the lining concrete; e
CIs the modulus of elasticity of concrete;
along with interior water pressure constantly increases in the tunnel operation process, the lining cutting shows that earlier fracture breaks away from with the country rock again, and when lining cutting and country rock did not break away from, the hoop strain becomes:
wherein: delta P
wFor tunnel water purification pressure, delta P
w＝P
i-P
0，P
iIs the internal water pressure, P
0Is the underground hydrostatic pressure; v. of
mThe Poisson ratio of the surrounding rock; e
mIs the deformation modulus of the surrounding rock; e
sIs the modulus of elasticity of the steel bar; a is the average radius of the tunnel after lining; t is t
sThe equivalent thickness of the steel bar;
at this time, the equivalent permeability coefficient of the lining is:
wherein: k is a radical of
LIs the equivalent permeability coefficient of the lining; gamma ray
wIs the volume weight of water; u is the kinetic viscosity coefficient of water; s is the crack spacing; the calculation method of the crack spacing S comprises the following steps:
wherein d is the diameter of the tension steel bar, p is the reinforcement ratio, α
1To calculate the coefficient (when the axle center is in tension α
1Taking 0.16, and inquiring the data through the design specification of the hydraulic tunnel); v is a coefficient related to the surface shape of the steel bar (the twisted steel bar v is 0.7, the coefficient represents the surface shape of the steel bar, the steel bar can be divided into plain round steel bars, twisted steel bars and the like according to the surface shape, and the coefficient query can refer to the design specification of hydraulic tunnels);
when the internal water pressure is higher, the water permeability of the lining is also higher, the lining is separated from the surrounding rock, and the hydraulic continuity equation q is used for solving the problem that the water permeability of the lining is higher
L＝q
m：
Wherein: q. q.s
LIs the seepage flow into the lining through the inner surface of the lining; q. q.s
mThe seepage flow rate of the surrounding rock flowing into the outer surface of the lining; k is a radical of
mIs the permeability coefficient of the surrounding rock; h is
0Is an underground water head; h is
iIs a water head in the tunnel; h is
w1Is a lining external water head; h is
0Is an underground water head; b is the outer diameter of the lining; a is
1Is the inner diameter of the lining; l is 2h
0；
From formula (11):
and due to Δ P
L＝γ
wΔh
L，ΔP
w＝γ
wΔh
wIn which Δ P
LNet water pressure, Δ P, for lining
wFor tunnel clean water pressure, the clean external water pressure of the obtained lining in the formula (12) is as follows:
the purified water pressure is transmitted to the pressing force of the surrounding rock through the lining:
wherein the content of the first and second substances,
the conditions for separating the lining from the surrounding rock are as follows:
ΔP
w1＞P
r(15)
substituting formulae (13) and (14) for formula (15) to obtain:
after the lining breaks away from the surrounding rock, the maximum hoop strain borne by the lining becomes:
and (3) driving the result of the formula to obtain the maximum permeability coefficient of the lining:
from the incremental theory, the lining hoop strain becomes:
by bringing the formulas (17) to (19) into the formula (9), the lining equivalent permeability coefficient after the lining is separated from the surrounding rock can be obtained:
substituting the formula (20) into the formula (13) to obtain the quantitative relation of various parameters of the lining after the lining is separated from the surrounding rock:
wherein the content of the first and second substances,
obtaining Δ P from equation (21)
L/ΔP
wReplacing the formula (19) to obtain the circumferential strain epsilon of the lining when the lining is separated from the surrounding rock
θLFurther, the maximum crack width w of the lining can be obtained
maxSee, in particular, formula (22):
w
max＝2ε
θLS (22)
the invention has the following advantages:
(1) based on a tunnel lining design theory, calculation data of different design schemes are fully utilized, rigorous mathematical analysis is combined, an optimization equation of control variables and design parameters is abstracted, and strict logicality is achieved;
(2) the optimization design model comprehensively considers the influence of design parameters on the engineering safety, quantitatively analyzes the influence of different optimization design measures on the improvement of the lining safety, and the research result can be directly used for the actual engineering;
(3) the optimized design model is simple and clear, can be accepted by the engineering technicians, improves the design efficiency and has wide applicability.
Drawings
FIG. 1 is a technical flow diagram of the present invention;
FIG. 2 is a schematic view of the tunnel seepage calculation of the present invention;
FIG. 3 shows the variation law of the maximum crack width and the equivalent permeability coefficient of the lining of the present invention;
FIG. 4 is a graph of the maximum crack width of the inventive liner as a function of reinforcement ratio;
FIG. 5 is a graph of the maximum crack width of the inventive liner as a function of reinforcement ratio;
h in FIG. 2
i、h
w1、h
0The water head in the tunnel, the water head outside the lining and the underground water head are arranged in sequence; p
i、P
w1、P
0Sequentially setting the tunnel internal water pressure, the lining external water pressure and the underground hydrostatic pressure; delta P
i、ΔP
w1、ΔP
LThe clean water pressure of the tunnel, the clean outside water pressure of the lining and the clean water pressure born by the lining, gamma
wIs the volume weight of water.
Detailed Description
The technical scheme of the present invention is further specifically described below by way of an embodiment with reference to the accompanying drawings, and a specific embodiment of a method for optimizing a tunnel lining design shown in fig. 1-2 is as follows:
(one) calculation conditions
The embodiment is based on the fact that a pumped storage power station project is practical, the diversion tunnel is of a circular section, the designed internal water pressure is 5.0MPa, and the underground water level is 186m high. The lining concrete is C25, the radius of the excavated tunnel is 2.15m, and the permeability coefficient is 1 multiplied by 10
-9m/s, and a deformation modulus of 28 GPa. The class of the surrounding rock is IV (the Poisson ratio of the surrounding rock is 0.25, and the permeability coefficient is 2-5 multiplied by 10)
-6m/s). The reinforcing bar is arranged by lining concrete inboard, and reinforcing bar protective layer thickness is 50 mm. The reinforcing bar scheme adopts 6 phi 22 (reinforcing bar ratio is 0.57%) and the initial lining thickness is 0.4 m.
In the operation period, the water pressure in the high-pressure tunnel is increased, the lining is cracked, and the permeability coefficient is increased. The large flow loss caused in the process often brings large economic loss to the production operation of the power station, so it is necessary to research the evolution law of the maximum crack width and the equivalent permeability coefficient of the lining, and the result is shown in fig. 3.
As can be seen from fig. 3, during the water-filled operation of the tunnel, the lining seepage field shows three obvious changes along with the increase of the internal water pressure: (1) the lining is not cracked; (2) the lining is cracked but not separated from the surrounding rock; (3) the lining is detached from the surrounding rock. After the lining is cracked, the maximum crack width and the lining permeability coefficient are continuously increased along with the increase of internal water pressure, the change is fastest in the stage (2), and the change rate is obviously slowed down in the stage (3). The main reason is that after the lining is separated from the surrounding rock, the increase of the water pressure difference inside and outside the lining is small, and the development speed of the crack width is limited to a certain extent.
When the internal water pressure reaches about 1.95MPa, the lining is cracked, and when the internal water pressure reaches about 2.38MPa, the lining is separated from the surrounding rock. The difference between the separation load and the cracking load is small and is only 0.43 MPa. After the lining cracks, the lining and the surrounding rock are quickly separated, and the influence of the external seepage of the internal water is large. When the internal water pressure reaches 2.52MPa, the width of the lining crack reaches 0.25mm, which exceeds the crack limiting design requirement. It is therefore necessary to adjust the design.
(II) design step
Keeping the reinforcing bar scheme of 6 phi 22 unchanged, and researching the permeability characteristic k of the surrounding rock
m＝1～50×10
-7And at m/s, the influence of the thickness of the lining on the crack limiting design. The calculation results are shown in fig. 4.
As can be seen from FIG. 4, the permeability coefficient k of the surrounding rock is maintained
mAnd the thickness of the lining is only increased, and the maximum crack width is only slightly reduced. Such as when k
m＝5×10
-6At m/s, the thickness of the lining increases from 0.4m to 0.7m, and the maximum crack width decreases by only 3%. And the thickness of the lining is kept unchanged, the permeability resistance of the surrounding rock is improved, and the maximum crack width of the lining can be reduced to a greater extent. When k is
mFrom 5 × 10
-6m/s is reduced to 1X 10
-7At m/s, the maximum crack width of the lining is greatly reduced and is far below 0.25 mm. The water permeable lining can meet the requirement of the crack limiting design by adopting a single measure for improving the permeability resistance of the surrounding rock, but the situation of redundant design is easy to occur, the problem that the construction grouting quality is difficult to ensure by reducing the permeability of the surrounding rock, and the problems of cost and construction period are caused, so other measures for optimizing the design of the lining are necessary to be further explored.
Keeping the thickness of the lining unchanged at 0.4m, and researching the influence of the reinforcement ratio increase on the crack limiting design under different surrounding rock permeability characteristics. The calculation results are shown in fig. 5.
As can be seen from figure 5, the improvement of the permeability resistance of the surrounding rock and the increase of the reinforcement ratio of the lining can effectively improve the safety of the lining, and the permeability resistance of the surrounding rock is more obviously improved. From the perspective of optimization design, measures of increasing reinforcement ratio and improving the permeability resistance of surrounding rocks are jointly adopted, and the maximum crack width of the lining can be reduced to be less than 0.25mm, so that the lining can completely meet the requirement of crack limiting design.
In conclusion, when the optimal design of the limited fracture of the lining is carried out, the relatively optimal measure for reducing the maximum fracture width firstly improves the anti-permeability characteristic of the surrounding rock, secondly improves the reinforcement ratio of the lining, and finally can increase the thickness of the lining as an auxiliary means.
After qualitatively discussing the concrete measures of the optimal design of the lining and giving a concrete idea of the optimal design process of the lining, the part is based on the above calculation data,and (3) researching the influence of the reinforcement ratio, the surrounding rock permeability coefficient and the lining thickness on the maximum crack width of the lining by using a mathematical method of multiple stepwise regression. The reinforcement ratio is 0.57%, 0.71%, 0.85% and 0.99%, and the permeability coefficient of the surrounding rock is 5 × 10
-6m/s、1×10
-6m/s、5×10
-7m/s、1×10
-7And m/s, calculating 64 groups of maximum crack widths of the lining thickness according to a scheme of 0.4m, 0.5m, 0.6m and 0.7m as an original data set of multivariate statistical analysis.
And 2, carrying out abnormal value monitoring of the Mahalanobis distance theory on the data set after data standardization processing.
After the 64 groups of original data sets are subjected to standardization processing, the Mahalanobis distance calculation is carried out on the 64 groups of data sets, wherein the maximum value of the Mahalanobis distance is 4.31, and the minimum value of the Mahalanobis distance is 0.64. D
0.01 2Of the (4,60) ═ 3.87, 64 samples, 11 groups belonged to abnormal values. Outliers were removed and 53 sets of data were used for regression analysis.
And 3, sequentially establishing regression equations of the control variables and the design parameters by adopting a backward stepwise regression method in the multivariate statistical analysis, and selecting the regression equation with the maximum significance test value as a final optimization equation of the lining design.
The maximum crack width w
maxReinforcement ratio rho and surrounding rock permeability coefficient k
mThe data after normalization to the lining thickness t are recorded as w
max *、ρ
*、k
m *And t
*. Multivariate regression analysis was performed using a MATLAB stepwise fitting toolbox. First selecting rho
*、k
m *And t
*To w
max *And performing multiple regression. The regression result is shown in the formula (23).
w
max *＝-0.2791ρ
*+0.6733lgk
m *-0.01418t
*+0.1827 (23)
Wherein, the regression coefficient R
20.9575 significance F test value F
1451, residual mean square 0.05711. The fitting degree of the multiple regression analysis is good, and F
1＞F
0.01The regression effect was remarkable when (4,49) was 3.72.
Successively rejecting variables by backward method, rejecting t first
*Selecting rho
*、k
m *To w
max *And performing multiple regression. The regression result is shown in formula (24):
w
max *＝-0.2782ρ
*+0.6720lgk
m *+0.1756 (24)
wherein R is
20.9571 significance F test value F
2682, residual mean square 0.05689. F
2＞F
1And R is
2And the mean square value of the residual error is basically consistent with that of the formula (1), which shows that the multivariate regression effect of the reinforcement ratio and the permeability coefficient of the surrounding rock on the maximum fracture width is obvious. Then select only k
m *To w
max *And (5) performing unary regression. The regression result is shown in formula (25).
w
max *＝0.6613lgk
m *+0.03648 (25)
Wherein R is
20.8080, the fit is poor, suggesting that the effect on the maximum crack width of the lining cannot be explained from a single perspective.
In conclusion, the reinforcement ratio and the surrounding rock permeability coefficient have good multivariate regression interpretation effect on the maximum crack width of the lining, the fitting degree is high, and the significance degree is highest. Reducing normalized formula (23) to yield:
w
max＝-0.1759ρ+0.1049lgk
m+0.9706 (26)
wherein, w
maxIn mm, rho units%, k
mThe unit is m/s.
It can be seen that the reinforcement ratio is increased by 0.1%, the maximum lining crack width is reduced by 1.759X 10-2mm, the permeability coefficient of the surrounding rock is reduced by 10 times, and the maximum lining crack width is reduced by 0.1049 mm.
The protective scope of the present invention is not limited to the above-described embodiments, and it is apparent that various modifications and variations can be made to the present invention by those skilled in the art without departing from the scope and spirit of the present invention. It is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.
Claims (2)
1. A method for optimizing the design of a tunnel lining is characterized by comprising the following steps:
step 1: calculating the maximum crack width of the lining of different design schemes based on a permeable lining design theory, and taking the calculation parameters and calculation results as an original data set of subsequent mathematical analysis;
step 2: preprocessing the raw data set of step 1, comprising the following substeps:
step 2.1, data standardization processing, namely mapping the original data into a value of an interval [0,1], wherein a calculation formula is as follows:
wherein x is
*Is a normalized mapping value, x is the original data value, x
minIs the minimum value, x, of each index in the original data set
maxThe maximum value of each index in the original data set;
step 2.2, performing data anomaly monitoring processing on the standardized data set by adopting the Mahalanobis distance theory, wherein the calculation formula is as follows
Wherein D is
2For mahalanobis distance per sample, X is the normalized data matrix, G
-1Is the inverse of the covariance matrix,
is an element average value;
D
2the greater the probability density, the smaller the probability density, and when greater to some extent, the probability density of the distribution will be so small that outside this range it is no longer in the range of normal points, and at α confidence levels, the threshold may be determined using the F distribution:
wherein l is the dimension of the sample, n is the sample capacity, F distribution is the common distribution for parameter estimation by mathematical statistics, which is evolved from normal distribution, α is the confidence level;
and step 3: sequentially establishing regression equations of control variables and design parameters by adopting a backward stepwise regression method in multivariate statistical analysis, and selecting the regression equation with the largest significance test value as a final optimization equation of the lining design; which comprises the following steps:
step 3.1, establishing a complete model of multivariate statistical regression, and setting m independent variables x
1,x
2...x
mModels fitted with m independent variables are called full models, i.e.
y＝β
0+β
1x
1+...+β
mx
m+ε (4)
Wherein y is a dependent variable, β
0Is constant, β
1,β
2...β
mIs the regression coefficient, ε is the regression error;
step 3.2, gradually eliminating independent variables, and establishing a multivariate statistical regression model of the residual independent variables; if the argument x is deleted from the m variables
kK is 1, 2.. times.m, and then the model fitted with m-1 independent variables is called a subtraction model, i.e. k is a model with a constant of zero
y
k＝β
0+β
1x
1+...+β
k-1x
k-1+β
k+1x
k+1+...+β
mx
m+ε (5)
Step 3.3, calculating the significance difference value of the fitting equation of the full model and all the subtraction models, and taking the significance difference value of the full model as F
0Eliminating independent variable x
kThe difference in significance of the posterior subtraction model is F
kThen the value of the difference in significance of the subtraction model can be expressed as:
wherein the content of the first and second substances,
F
0calculation of the sum of
kThe same;
step 3.4, solving the maximum value F in all the significant difference values
max，F
maxThe corresponding multiple regression equation is the final optimization design equation.
2. The method of claim 1 for optimizing a tunnel lining design, wherein: the theory of calculating the maximum crack width of the lining in the step 1 is as follows:
the lining shows for reinforced concrete combined operation before the fracture, along with interior water pressure constantly increases, and lining hoop strain constantly increases, assumes that lining hoop strain is greater than behind the critical axial tensile strain of concrete, and the lining fracture, promptly:
wherein: epsilon
θLIs lining hoop strain; f. of
tDesigning tensile strength for the lining concrete; e
CIs the modulus of elasticity of concrete;
along with interior water pressure constantly increases in the tunnel operation process, the lining cutting shows that earlier fracture breaks away from with the country rock again, and when lining cutting and country rock did not break away from, the hoop strain becomes:
wherein: delta P
wFor tunnel water purification pressure, delta P
w＝P
i-P
0，P
iIs the internal water pressure, P
0Is the underground hydrostatic pressure; v. of
mThe Poisson ratio of the surrounding rock; e
mIs the deformation modulus of the surrounding rock; e
sIs the modulus of elasticity of the steel bar; a is the average radius of the tunnel after lining; t is t
sThe equivalent thickness of the steel bar;
at this time, the equivalent permeability coefficient of the lining is:
wherein: k is a radical of
LIs the equivalent permeability coefficient of the lining; gamma ray
wIs the volume weight of water; u is the kinetic viscosity coefficient of water; s is the crack spacing; the calculation method of the crack spacing S comprises the following steps:
wherein d is the diameter of the tensioned steel bar, rho is the reinforcement ratio, α
1To calculate the coefficients; v is a coefficient related to the surface shape of the reinforcing steel bar;
when the internal water pressure is higher, the water permeability of the lining is also higher, the lining is separated from the surrounding rock, and the hydraulic continuity equation q is used for solving the problem that the water permeability of the lining is higher
L＝q
m：
Wherein: q. q.s
LIs the seepage flow into the lining through the inner surface of the lining; q. q.s
mThe seepage flow rate of the surrounding rock flowing into the outer surface of the lining; k is a radical of
mIs the permeability coefficient of the surrounding rock; k is a radical of
LLining permeability coefficient is the permeability coefficient of the surrounding rock; h is
0Is an underground water head; h is
iIs a water head in the tunnel; h is
w1Is a lining external water head; h is
0Is an underground water head; b is the outer diameter of the lining; a is
1Is the inner diameter of the lining; l is 2h
0；
From formula (11):
and due to Δ P
L＝γ
wΔh
L，ΔP
w＝γ
wΔh
wIn which Δ P
LNet water pressure, Δ P, for lining
wFor tunnel clean water pressure, the clean external water pressure of the obtained lining in the formula (12) is as follows:
the purified water pressure is transmitted to the pressing force of the surrounding rock through the lining:
wherein the content of the first and second substances,
the conditions for separating the lining from the surrounding rock are as follows:
ΔP
w1＞P
r(15)
substituting formulae (13) and (14) for formula (15) to obtain:
after the lining breaks away from the surrounding rock, the maximum hoop strain borne by the lining becomes:
and (3) driving the result of the formula to obtain the maximum permeability coefficient of the lining:
from the incremental theory, the lining hoop strain becomes:
by bringing the formulas (17) to (19) into the formula (9), the lining equivalent permeability coefficient after the lining is separated from the surrounding rock can be obtained:
substituting the formula (20) into the formula (13) to obtain the quantitative relation of various parameters of the lining after the lining is separated from the surrounding rock:
wherein the content of the first and second substances,
obtaining Δ P from equation (21)
L/ΔP
wReplacing the formula (19) to obtain the circumferential strain epsilon of the lining when the lining is separated from the surrounding rock
θLFurther, the maximum crack width w of the lining can be obtained
maxSee, in particular, formula (22):
w
max＝2ε
θLS (22) 。
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| CN113505428B (en) * | 2021-08-17 | 2023-11-07 | 中国电建集团成都勘测设计研究院有限公司 | Comprehensive quantitative design method for circular water passing tunnel lining structure |
| CN115994494A (en) * | 2022-11-21 | 2023-04-21 | 长江三峡勘测研究院有限公司（武汉） | Method and system for estimating diving high external water pressure of multilayer slowly-inclined rock-soil body deep-buried tunnel |
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| CN105804766A (en) * | 2016-05-19 | 2016-07-27 | 武汉大学 | Calculation method of tunnel lining design |
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| CN105804766A (en) * | 2016-05-19 | 2016-07-27 | 武汉大学 | Calculation method of tunnel lining design |
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| 《Stresses around pressure tunnels with semi-permeable liners》;BOBET A ， NAM S W;《 Rock Mechanics and Rock Engineering》;20070630(第3期);287–315 * |
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