CN109214102B - Method for calculating cold-proof drainage tunnel length at tunnel portal in severe cold region - Google Patents

Method for calculating cold-proof drainage tunnel length at tunnel portal in severe cold region Download PDF

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CN109214102B
CN109214102B CN201811107580.9A CN201811107580A CN109214102B CN 109214102 B CN109214102 B CN 109214102B CN 201811107580 A CN201811107580 A CN 201811107580A CN 109214102 B CN109214102 B CN 109214102B
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靳宝成
陈霄汉
田鹏
李国良
黄双林
何永旺
谭永庆
符亚鹏
司剑钧
严文翔
徐冲
曹国栋
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Abstract

The invention relates to a method for calculating the length of a cold-proof sluice tunnel at a tunnel portal in a severe cold region, which comprises the steps of analyzing the solar radiation condition of the tunnel portal in the severe cold region and the severe cold region, and calculating the solar radiation index of the tunnel portal; taking a solar radiation index of a tunnel portal, the average temperature of the coldest month of the portal, the actually measured icing length of a drainage channel of a railway tunnel in a severe cold region and the set length of a corresponding cold-proof drainage tunnel as calculation parameters, and drawing up a nonlinear surface equation form; and (3) calculating undetermined parameters of a multi-element nonlinear surface equation by using multi-element nonlinear regression to obtain a calculation formula of the setting length of the cold-proof water drain tunnel in the severe cold region. The invention overcomes the defect that the set length of the cold-proof spillway tunnel in the prior art can not be theoretically, qualitatively and quantitatively analyzed, provides a calculation method with pertinence, and improves the accuracy of the calculation of the set length of the cold-proof spillway tunnel at the tunnel entrance in the severe cold region.

Description

Method for calculating cold-proof drainage tunnel length at tunnel portal in severe cold region
Technical Field
The invention relates to the field of tunnel cold protection, in particular to a method for calculating the length of a tunnel cold-proof spillway at a tunnel entrance in a severe cold region.
Background
According to the survey general of the tunnel freezing injury in severe cold areas established in China, the tunnel freezing injury generally starts from local freezing of drainage channels. Statistics is carried out on a newly-built high-speed railway tunnel in northwest of China, and the condition that a part of the tunnel is frozen after being built exists, so that driving safety is seriously threatened. Particularly, the tunnel portal is positioned in a region with a low temperature on a shade slope of a mountain, the icing problem is more prominent, and the judgment of the shade slope and the sunny slope of the mountain is directly influenced by solar radiation.
The key to prevent freezing injury is to perfect an effective drainage system and reliable cold-proof heat preservation measures. The main measures of the frost-resistant fortification section of the tunnel in severe cold areas in China are a cold-proof sluicing tunnel, a cold-proof sluicing tunnel and an electric tracing system. When the length of the cold-proof drainage tunnel at the tunnel portal is designed, a quantitative calculation method is lacked according to the design experience of designers.
Disclosure of Invention
The invention aims to provide a method for calculating the length of a cold-proof sluice tunnel at a tunnel entrance in a severe cold region, which comprehensively considers the influence factors such as the solar radiation amount, the air temperature at the tunnel entrance and the like and determines the setting length of the cold-proof sluice tunnel in the severe cold region through nonlinear regression.
The technical scheme adopted by the invention is as follows:
the method for calculating the cold-proof spillway length of the tunnel portal in the severe cold region is characterized by comprising the following steps of:
the method comprises the following steps:
the method comprises the following steps: analyzing the influence of solar radiation at the tunnel portal:
analyzing solar radiation conditions of tunnel portals in cold and severe cold areas, and calculating to obtain solar radiation indexes of the tunnel portals through three influence factors, namely azimuth angles of slopes where the tunnel portals are located, natural slopes of the slopes and geographical latitudes;
step two: the equation form is drawn up:
taking a solar radiation index of a tunnel portal and the average temperature of the coldest month of the portal as independent variables, taking the actually measured icing length of a drainage channel of a railway tunnel in a severe cold region and the corresponding setting length of a cold-proof drainage tunnel as dependent variables, and drawing up a multi-element nonlinear surface equation form;
step three: multiple nonlinear regression:
and calculating to obtain undetermined fixed parameters of the multi-element nonlinear surface equation and convergence control coefficients to be regressed, and matching the multi-element nonlinear surface equation to obtain a calculation formula for the cold-proof sluice tunnel setting length of the tunnel in the severe cold region.
The calculation formula of the solar radiation index of the tunnel portal is as follows:
Figure BDA0001808265970000021
wherein, I θ The solar radiation index is the solar radiation index of the tunnel portal; i is Dθ The direct solar radiation intensity at the tunnel portal is obtained; I.C. A dθ The intensity of the solar scattered radiation at the tunnel portal is obtained; I.C. A Rθ Obtaining the ground reflection radiation intensity for the tunnel portal; i is DN The intensity of normal solar radiation refers to the intensity of direct solar radiation in the normal direction of the sun ray, I DN ＝I 0 ×P m ，I 0 Is the solar constant, P is the atmospheric transparency coefficient, m is the atmospheric mass,
Figure BDA0001808265970000031
h is the solar altitude; i is the solar incident angle, cosi = cos θ sinh + sin θ coshcos (α - γ), γ is the bevel azimuth angle; alpha is the sun azimuth; I.C. A DH Intensity of direct solar radiation in horizontal direction, I DH ＝I DN sinh＝I 0 P m sinh；I dH For the intensity of the horizontally directed solar scattered radiation->
Figure BDA0001808265970000032
Theta is the inclination angle of the slope where the tunnel portal is located; rho G The surface reflectivity of the slope where the tunnel is located; i is h Is the total radiation intensity in the horizontal direction,
Figure BDA0001808265970000033
assigning values to a portion of the variables in calculating the solar radiation index, wherein: the solar azimuth angle alpha is 0, which refers to the solar azimuth angle at the moment of 12 hours; the atmospheric transparency coefficient of P is 0.722; surface reflectivity rho of slope where tunnel is located G Is 0.2; solar constant I 0 1 is taken.
Step two, taking the solar radiation index of the tunnel portal and the average temperature of the coldest month of the portal as independent variables, taking the actually measured icing length of the drainage channel of the railway tunnel in the severe cold region and the corresponding setting length of the cold-proof spillway as dependent variables, and drawing up a multivariate nonlinear equation in the following form;
Figure BDA0001808265970000034
wherein T is the average temperature of the coldest month at the hole; i is θ The solar radiation index is the solar radiation index of the tunnel portal; l is the freezing damage length of the high-speed railway tunnel; a. b and c are fixed parameters to be regressed, and d is a convergence control coefficient to be regressed.
In the third step, multivariate nonlinear regression is carried out by utilizing a Marquardt method, undetermined fixed parameters and convergence control coefficients to be regressed of a multivariate nonlinear surface equation are obtained through calculation, and further a calculation formula of the cold-proof sluicehole setting length of the tunnel in the severe cold region is obtained as follows:
Figure BDA0001808265970000041
the calculation result of the calculation formula for the setting length of the cold-proof drainage tunnel in the severe cold region is established on the basis of the average temperature of the coldest month at the tunnel portal and the solar radiation index; and (2) the setting length of the cold-proof water drain tunnel in the severe cold area is also influenced by other factors, when other influencing factors such as the micro-terrain of the tunnel portal, the development degree of underground water, the gradient of the tunnel, the natural wind direction, the wind speed and the running speed of the train are introduced, the independent variable is required to be increased in the step two, the form of a multiple nonlinear equation is newly drawn up, the fixed parameters to be regressed are added in the step three, and the multiple nonlinear regression is newly carried out:
Figure BDA0001808265970000042
wherein m is 1 m 2 ...m n Other factors influencing the calculation result of the length calculation formula set for the cold-proof sluice tunnel in the severe cold region include but are not limited to the micro-topography of the tunnel portal, the development degree of underground water, the gradient of the tunnel, the natural wind direction, the wind speed and the running speed of the train;
Figure BDA0001808265970000043
the method is used for representing the influence mode of each influence factor on the calculation result in the operation process.
The invention has the following advantages:
the invention relates to a method for calculating the setting length of a cold-proof sluice tunnel at a tunnel portal in severe cold regions. The method comprises the steps of analyzing the influence of the solar radiation index of the tunnel portal and the average temperature of the coldest month of the portal on the actually measured drain channel icing length of the railway tunnel in the cold or severe cold region and the corresponding heat preservation ditch setting length, drawing up a multiple nonlinear surface equation form, and providing a calculation formula of the tunnel cold-proof drain tunnel setting length in the severe cold region through multiple nonlinear regression. The method overcomes the defect that the set length of the cold-proof sluicehole at the tunnel entrance in the severe cold region in the prior art cannot be theoretically, qualitatively and quantitatively analyzed, provides a calculation method with pertinence, and improves the accuracy of the calculation of the set length of the cold-proof sluicehole at the tunnel entrance in the severe cold region.
Detailed Description
The present invention will be described in detail with reference to specific embodiments.
The invention relates to a method for calculating the setting length of a cold-proof water drain tunnel at a tunnel portal in a severe cold region, which comprises the following steps:
the method comprises the following steps: and (5) analyzing the influence of solar radiation at the tunnel portal. Analyzing solar radiation conditions of tunnel portals in cold and severe cold areas, and calculating to obtain solar radiation indexes of the tunnel portals through three influence factors, namely azimuth angles of slopes where the tunnel portals are located, natural slopes of the slopes and geographical latitudes;
step two: and (5) drawing up an equation form. Taking a solar radiation index of a tunnel portal and the average temperature of the coldest month of the portal as independent variables, taking the actually measured icing length of a drainage channel of a railway tunnel in a severe cold region and the corresponding cold-proof drainage tunnel setting length of the railway tunnel in China as dependent variables, and drawing up a multi-element nonlinear surface equation form;
step three: multivariate nonlinear regression. And calculating to obtain undetermined fixed parameters of the multi-element nonlinear surface equation and convergence control coefficients to be regressed, and matching the multi-element nonlinear surface equation to obtain a calculation formula of the cold-proof spillway tunnel setting length in the severe cold region.
The first step is that a calculation formula of the solar radiation index of the tunnel portal is as follows:
Figure BDA0001808265970000061
wherein, I θ The solar radiation index is the solar radiation index of the tunnel portal; i is Dθ The direct solar radiation intensity at the tunnel portal is obtained; i is dθ The intensity of the solar scattered radiation at the tunnel portal is obtained; i is Rθ Obtaining the ground reflected radiation intensity for the tunnel portal; i is DN The intensity of normal solar radiation refers to the intensity of direct solar radiation in the normal direction of the sun's rays, I DN ＝I 0 ×P m ，I 0 Is the solar constant, P is the atmospheric transparency coefficient, m is the atmospheric mass,
Figure BDA0001808265970000062
h is the solar altitude; i is the solar incident angle, cosi = cos θ sinh + sin θ coshcos (α - γ), γ is the bevel azimuth angle; alpha is the solar azimuth; i is DH Intensity of direct solar radiation in horizontal direction, I DH ＝I DN sinh＝I 0 P m sinh；I dH For the intensity of the horizontally directed solar scattered radiation->
Figure BDA0001808265970000063
Theta is the inclination angle of the slope where the tunnel portal is located; rho G The surface reflectivity of the slope where the tunnel is located; i is h Is the total radiation intensity in the horizontal direction,
Figure BDA0001808265970000064
in the first step, the solar radiation of the tunnel portal is influenced by factors such as solar ray incidence angle, terrain, cloud cover, portal micro-terrain and the like. China has fewer stations for directly measuring solar radiation, and in many areas, no observed value of solar radiation exists, and indirect calculation is needed, so that a solar radiation calculation model with a simple form and few undetermined parameters needs to be selected in calculation. In order to simplify the calculation process, the invention assigns values to part of variables when calculating the solar radiation index, wherein: the solar azimuth angle alpha is 0, which refers to the solar azimuth angle at the moment of 12 hours; the atmospheric transparency coefficient of P is 0.722; surface reflectivity rho of slope where tunnel is located G Is 0.2; solar constant I 0 1 is taken.
Taking the solar radiation index of the tunnel portal and the average temperature of the coldest month of the portal as independent variables, taking the actually measured icing length of a drainage channel and the corresponding setting length of a cold-proof spillway tunnel of a railway tunnel in a severe cold region built in China as dependent variables, and drawing up a multivariate nonlinear equation in the following form;
Figure BDA0001808265970000071
wherein T is the average temperature of the coldest month at the hole; i is θ The solar radiation index is the solar radiation index of the tunnel portal; l is the freezing damage length of the high-speed railway tunnel; a. b and c are fixed parameters to be regressed, and d is a convergence control coefficient to be regressed.
Performing multivariate nonlinear regression by using a Levenberg-Marquardt method, and calculating to obtain undetermined fixed parameters and convergence control coefficients to be regressed of a multivariate nonlinear surface equation, thereby obtaining a calculation formula of the cold-proof sluicehole setting length of the tunnel in the severe cold region as follows:
Figure BDA0001808265970000072
the calculation result of the calculation formula for the setting length of the cold-proof drain hole in the tunnel in the severe cold region is established on the basis of the average temperature of the coldest month at the tunnel entrance and the solar radiation index. And (2) the setting length of the cold-proof water drain tunnel in the severe cold area is also influenced by other factors, when introducing other influencing factors such as the micro-topography of the tunnel portal, the development degree of underground water, the gradient of the tunnel, the natural wind direction, the wind speed, the running speed of the train and the like, the independent variable is required to be increased in the step two, the form of a multiple nonlinear equation is newly drawn up, the fixed parameters to be regressed are added in the step three, and the multiple nonlinear regression is carried out again:
Figure BDA0001808265970000081
wherein m is 1 m 2 ...m n And setting other factors of the calculation result of the length calculation formula for the cold-proof water drain tunnel in the severe cold area, including but not limited to the micro-topography of the tunnel entrance, the development degree of underground water, the gradient of the tunnel, the natural wind direction, the wind speed and the running speed of the train.
Figure BDA0001808265970000082
The method is an operation process and represents the influence mode of each influence factor on the calculation result.
The fitting process of the calculation formula for the setting length of the cold-proof sluiceway of the tunnel in the severe cold region is established on the basis of the actually measured freezing length of the drainage channel of the railway tunnel in the severe cold region and the corresponding setting length of the cold-proof sluiceway in China, the tunnel is positioned in a high-altitude area with lower temperature in the northwest of China, and the applicability of tunnels in other severe cold regions such as the northeast of China needs to be further demonstrated;
limited by the measured data, the calculation formula of the tunnel cold-proof sluicing tunnel setting length in the severe cold region is only suitable for the tunnel with the cold-proof sluicing tunnel, the average temperature of the coldest month at the tunnel entrance is between minus 7.55 ℃ and minus 18.0 ℃, and the adaptability of the tunnel entrance with the average temperature of the coldest month lower than minus 18.0 ℃ needs to be further verified.
The invention relates to a method for calculating the setting length of a cold-proof drainage tunnel at a tunnel portal in a severe cold region, which is used for calculating the solar radiation index of the tunnel portal according to the characteristics of the tunnel portal, three influence factors of the azimuth angle of the slope where the tunnel portal is located, the natural gradient of the slope and the geographical latitude, and evaluating the size of the solar radiation received by the tunnel portal. The method comprises the steps of analyzing the influence of the solar radiation index of the tunnel portal and the average temperature of the coldest month of the portal on the actually measured drain channel icing length of the railway tunnel in the cold or severe cold region and the corresponding heat preservation ditch setting length, drawing up a multiple nonlinear surface equation form, and providing a calculation formula of the tunnel cold-proof drain tunnel setting length in the severe cold region through multiple nonlinear regression. The method overcomes the defect that the set length of the cold-proof sluicehole at the tunnel entrance in the severe cold region in the prior art cannot be theoretically, qualitatively and quantitatively analyzed, provides a calculation method with pertinence, and improves the accuracy of the calculation of the set length of the cold-proof sluicehole at the tunnel entrance in the severe cold region.
The invention is not limited to the examples, and any equivalent changes to the technical solution of the invention by a person skilled in the art after reading the description of the invention are covered by the claims of the invention.

Claims (1)

1. The method for calculating the cold-proof sluice tunnel length at the tunnel portal in the severe cold region is characterized by comprising the following steps of:
the method comprises the following steps:
the method comprises the following steps: analyzing the influence of solar radiation at the tunnel portal:
analyzing solar radiation conditions of tunnel portals in cold and severe cold areas, and calculating to obtain solar radiation indexes of the tunnel portals through three influence factors, namely azimuth angles of slopes where the tunnel portals are located, natural slopes of the slopes and geographical latitudes; the calculation formula of the solar radiation index of the tunnel portal is as follows:
Figure FDA0003946503460000011
wherein, I θ The solar radiation index is the solar radiation index of the tunnel portal; i is Dθ The intensity of direct solar radiation at the tunnel portal is obtained; i is dθ The intensity of the solar scattered radiation at the tunnel portal is obtained; i is Rθ Obtaining the ground reflected radiation intensity for the tunnel portal; i is DN The intensity of normal solar radiation refers to the intensity of direct solar radiation in the normal direction of the sun's rays, I DN ＝I 0 ×P m ，I 0 Is the solar constant, P is the atmospheric transparency coefficient, m is the atmospheric mass,
Figure FDA0003946503460000012
h is the solar altitude; i is the solar incident angle, cosi = cos θ sinh + sin θ coshcos (α - γ), γ is the bevel azimuth angle; alpha is the solar azimuth; i is DH Intensity of direct solar radiation in horizontal direction, I DH ＝I DN sinh＝I 0 P m sinh；I dH For the intensity of the horizontally directed solar scattered radiation->
Figure FDA0003946503460000021
Theta is the inclination angle of the slope where the tunnel portal is located; rho G The surface reflectivity of the slope where the tunnel is located; i is h Is the total radiation intensity in the horizontal direction,
Figure FDA0003946503460000022
assigning values to a portion of the variables in calculating the solar radiation index, wherein: the solar azimuth angle alpha is 0, which refers to the solar azimuth angle at the moment of 12 hours; the atmospheric transparency coefficient of P is 0.722; surface reflectivity rho of slope where tunnel is located G Is 0.2; solar constant I 0 Taking 1;
step two: drawing up an equation form:
taking a tunnel portal solar radiation index and a tunnel portal coldest month average temperature as independent variables, taking a drainage channel icing length and a corresponding cold-proof drainage tunnel setting length which are actually measured by a railway tunnel in a severe cold region as dependent variables, and drawing up a multivariate nonlinear surface equation form as follows:
Figure FDA0003946503460000023
wherein T is the average temperature of the coldest month at the hole; i is θ The solar radiation index is the solar radiation index of the tunnel portal; l is the freezing damage length of the high-speed railway tunnel; a. b and c are fixed parameters to be regressed, and d is a convergence control coefficient to be regressed;
step three: multiple nonlinear regression:
performing multiple nonlinear regression by using a Marquardt method, calculating to obtain undetermined fixed parameters of a multiple nonlinear surface equation and a convergence control coefficient to be regressed, matching the multiple nonlinear surface equation to obtain a calculation formula for the cold-proof sluice tunnel setting length of the tunnel in the severe cold region as follows:
Figure FDA0003946503460000024
the calculation result of the calculation formula for the setting length of the cold-proof drain hole in the tunnel in the severe cold region is established on the basis of the average temperature of the coldest month at the tunnel entrance and the solar radiation index; and (2) the setting length of the cold-proof water drain tunnel in the severe cold area is also influenced by other factors, when other influencing factors such as the micro-terrain of the tunnel portal, the development degree of underground water, the gradient of the tunnel, the natural wind direction, the wind speed and the running speed of the train are introduced, the independent variable is required to be increased in the step two, the form of a multiple nonlinear equation is newly drawn up, the fixed parameters to be regressed are added in the step three, and the multiple nonlinear regression is newly carried out:
Figure FDA0003946503460000031
wherein m is 1 m 2 ...m n Other factors influencing the calculation result of the length calculation formula set for the cold-proof sluice tunnel in the severe cold region include but are not limited to the micro-topography of the tunnel portal, the development degree of underground water, the gradient of the tunnel, the natural wind direction, the wind speed and the running speed of the train;
Figure FDA0003946503460000032
the method is an operation process and represents the influence mode of each influence factor on the calculation result. />
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Publication number Priority date Publication date Assignee Title
CN103410563A (en) * 2013-07-23 2013-11-27 同济大学 Cold-proof draining tunnel

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