Cold region tunnel thermal insulation fortification length calculation method

Abstract

The invention belongs to the technical field of tunnel engineering, and provides a method for calculating the thermal insulation fortification length of a cold region tunnel, which comprises the following steps: A, determining the air pressure and static pressure difference of any point in a tunnel and the winter dominant natural wind pressure and thermal potential difference of the region according to the altitude elevation and air density of a tunnel site region so as to determine the pressure intensity of a wind current mass along a cross section; b, determining the average gradient of the tunnel and the herringbone slope approximation degree # imgabs0 # according to the slope length of the tunnel, and building an air flow mass motion calculation model of the longitudinal unit length of the tunnel according to the average gradient of the tunnel, the cross section area of the tunnel and the pressure intensity of the air flow mass along the cross section; and C, according to the wind current mass movement calculation model of the longitudinal unit length of the tunnel and the average temperature of the coldest month of the tunnel site area, determining a formula of longitudinal temperature field distribution of the tunnel, and calculating to obtain the thermal insulation fortification length of the tunnel in the cold region. The calculation method can ensure that the anti-freezing and anti-freezing design of the tunnel in the cold region is more reasonable and economical, and the application prospect is wide.

Description

Technical Field

[0001] The invention belongs to the technical field of tunnel engineering and relates to a method for calculating the thermal insulation defense length of a cold region tunnel. Background Art

[0002] Cold regions are widely distributed in my country, and there are many tunnels in cold regions. Compared with general temperature regions, the environment in cold regions generally has large positive and negative temperature changes with annual periodic units. The ambient temperature in summer may be above freezing for a long time, and the ambient temperature in winter may be below freezing for a long time. This periodic change in climate and environment has an extremely adverse effect on the insulation and antifreeze of the drainage system and the antifreeze of the structure of the operating cold-region railway tunnels. Under this influence, the drainage system of cold-region tunnels needs to consider the adverse effects of low-temperature freezing blocking and poor drainage; and for the tunnel structure, in addition to considering the temperature stress caused by the large temperature difference in the environment, when the tunnel is in a frost-sensitive stratum and its moisture content exceeds a certain range, or when there are cavities behind the lining due to construction defects and the cavities contain water, the tunnel structure also needs to consider the effects of frost heave force or freeze-thaw cycle. Therefore, tunnels in cold regions should carry out insulation and antifreeze of drainage systems and antifreeze of structures, and determine the insulation length.

[0003] However, the current determination of the insulation fortification length of cold-region tunnels mainly relies on the fortification experience of cold-region traffic tunnels with similar meteorological conditions, without considering the changes in the temperature field distribution in the tunnel. This often leads to unreasonable insulation fortification lengths for cold-region tunnels. Some cold-region tunnel projects may experience different frost damage characteristics after operation due to insufficient measures, while other tunnel projects may increase construction difficulty, project cost, and operation and maintenance costs due to excessive measures. Summary of the invention

[0004] The present invention proposes a method for calculating the insulation fortification length of tunnels in cold regions. The calculation method determines the longitudinal distribution change characteristics of the temperature field in tunnels in cold regions based on influencing factors such as tunnel length, slope and the average temperature of the coldest month at the tunnel entrance, and obtains the insulation fortification length of the tunnel according to the change characteristics of the temperature field in the tunnel in cold regions, which can ensure that the anti-freeze design of tunnels in cold regions is more reasonable and economical.

[0005] The technical solution of the present invention is achieved in this way:

[0006] A method for calculating the insulation fortification length of a cold region tunnel comprises the following steps:

[0007] A. Determine the air pressure and static pressure difference at any point in the tunnel according to the altitude and air density of the tunnel site, as well as the dominant natural wind pressure and thermal potential difference in the region in winter, so as to determine the pressure of the wind flow group along the cross section;

[0008] B. Determine the average slope of the tunnel and the approximation of the herringbone slope ω according to the tunnel slope length. When the tunnel is a single-sided slope, the average slope of the tunnel is the ratio of the relative height difference between the tunnel entrance and the highest point in the tunnel to the tunnel length. Then, based on the average slope of the tunnel, the cross-sectional area of ​​the tunnel and the pressure of the wind flow group along the cross section, establish a calculation model for the movement of the wind flow group per unit length in the longitudinal direction of the tunnel on the single-sided slope of the tunnel;

[0009] When the tunnel is a herringbone slope, the herringbone slope is divided into two single-sided slopes by the slope change point, and the calculation model of wind flow group movement per unit length in the longitudinal direction of the tunnel is established respectively;

[0010] Among them, the herringbone slope approximation L 2 Indicates the length of the short slope where the slope change point is shorter than the hole entrance, L 1 Indicates the length of the long slope with a longer distance from the slope change point to the tunnel entrance, 0≤ω≤1; when 0<ω<0.5, in the calculation model of the wind flow group movement per unit length of the tunnel established by the short slope single-sided slope, the temperature at the slope change point is used as the starting point temperature of the short slope single-sided slope;

[0011] C. According to the calculation model of wind flow group movement per unit length of the tunnel and the average temperature of the coldest month in the tunnel site, the formula for the longitudinal temperature field distribution of the tunnel is determined, and the insulation defense length of the cold zone tunnel is calculated. In this case, the temperature in the formula is set equal to the boundary temperature condition of the defense, and the insulation defense length of the cold zone tunnel can be calculated.

[0012] Furthermore, the method for determining the pressure of the wind flow group along the cross section is as follows:

[0013] ΔP T =ΔP 热 +ΔP 静 +ΔP 风 ;

[0014] Among them, ΔP T It indicates the pressure of the wind flow group along the cross section, unit: Pa;

[0015] ΔP 热 It indicates the thermal pressure difference between the point x meters away from the cave entrance and the cave entrance, unit: Pa;

[0016] ΔP 静 It indicates the static pressure difference between the point x meters away from the cave entrance and the cave entrance, unit: Pa;

[0017] ΔP 风 It represents the natural wind pressure formed by the dominant natural wind in winter in the area x meters away from the cave entrance, unit: Pa.

[0018] Furthermore, the ΔP 热 The method of determining is as follows:

[0019] ΔP热 =(γ out -γ x )·H;

[0020] H = x.tan(artanα);

[0021] Among them, γ out Indicates the air density outside the tunnel, unit: N / m 3 ;

[0022] γ x Indicates the air density inside the tunnel at a distance of x meters from the tunnel entrance, unit: N / m 3 ;

[0023] H represents the relative height difference between the tunnel entrance and the point x meters away from the tunnel entrance, unit: m;

[0024] x represents the distance from any point in the cave to the cave entrance, unit: m;

[0025] α represents the average slope of the tunnel, h represents the relative height difference between the cave entrance and the highest point in the cave, unit: m, L represents the length of the tunnel, unit: m.

[0026] Furthermore, the ΔP 静 The method of determining is as follows:

[0027] ΔP 静 =P x -P out ;

[0028] in,

[0029] P x It indicates the air pressure in the tunnel at a distance of x meters from the entrance, in Pa;

[0030] P x Determined according to the standard atmosphere model:

[0031]

[0032] P out Indicates the air pressure at the tunnel entrance, unit: Pa,

[0033]

[0034] Where H represents the relative height difference between the tunnel entrance and the point x meters away from the tunnel entrance, unit: m;

[0035] H x and H out They represent the altitudes at a point x meters from the tunnel entrance and at the tunnel entrance, respectively, in meters;

[0036] At the same time Hx -H=H x =-x.tan(artanα)=H out ;

[0037] The ΔP 风 The method of determining is as follows:

[0038]

[0039] Where ρ is the air density, unit: kg / m 3 ;

[0040] V a It is the dominant natural wind speed in winter in the region. Here, the meteorologically dominant average wind speed in winter in the area where the tunnel is located is taken, unit: m / s.

[0041] Furthermore, the calculation model of the wind flow group movement per unit length of the tunnel in the single slope is:

[0042] ma=ΔP T .A-mgsin(arctanα);

[0043] m=A·1·ρ=Aρ;

[0044] Among them, m represents the mass of the wind flow group per unit length in the longitudinal direction, unit: kg;

[0045] a represents the acceleration of the wind flow group in the tunnel, unit: m / s 2 ;

[0046] ΔP T It indicates the pressure of the wind flow group along the cross section, unit: Pa;

[0047] A represents the cross-sectional area of ​​the wind flow group, which is equal to the cross-sectional area of ​​the tunnel, unit: m 2 ;

[0048] g represents the acceleration due to gravity, unit: m / s 2 .

[0049] Furthermore, the formula for determining the longitudinal temperature field distribution of the tunnel in step C specifically comprises the following steps:

[0050] S1. Combining the pressure of the wind group along the cross section and the wind group movement calculation model equation per unit length of the tunnel longitudinal direction, the relationship between the wind group movement and temperature change can be obtained:

[0051] ρa=(γ out -γ x ).xtan(artanα)+ΔP 静 +ΔP 风 -ρgsin(arctanα);

[0052] S2. The relationship between air weight, temperature and pressure is obtained:

[0053] S3, the relationship between S1 and S2,

[0054] The relationship between the movement of wind flow group on a single slope and temperature change is:

[0055]

[0056] Taking a = 0, we can get the formula for the longitudinal temperature field distribution of the air flow group in a single slope tunnel;

[0057] The relationship between air weight, temperature and pressure in step S2 is determined as follows:

[0058] According to the ideal gas formula:

[0059] PV = nRT;

[0060] Combined with m = n·M,

[0061] m=ρ·V,

[0062] m=A·1·ρ=Aρ,

[0063] get:

[0064]

[0065] The relationship between air weight and density is: γ=ρg;

[0066] but:

[0067]

[0068] Right now

[0069] In the above formula, T out It indicates the average temperature of the coldest month at the tunnel entrance, unit: Pa;

[0070] T x =T (x) , represents the air flow temperature at a distance of xm from the tunnel entrance, unit: °C;

[0071] P x Indicates the air pressure at a distance of xm from the tunnel entrance, unit: Pa;

[0072] P out Indicates the air pressure at the tunnel entrance, unit: Pa;

[0073] P represents gas pressure, unit: Pa;

[0074] V represents the volume of gas, unit: m 3 ;

[0075] n represents the amount of gaseous substance, unit: mol;

[0076] R represents the gas constant. The gas constant of air under standard conditions is 287 J / (kg·K);

[0077] T represents the gas temperature, unit: °C;

[0078] M represents the average molar mass of air, unit: g / mol, which can be 28.96×10 -3 kg / mol;

[0079] γ represents the air density, unit: N / m 3 .

[0080] Furthermore, when ω=0, the formula for the longitudinal temperature field distribution of the tunnel is:

[0081]

[0082] x represents the distance from any point in the tunnel to the tunnel entrance, that is, the insulation length of the tunnel, unit: m.

[0083] Furthermore, when the herringbone slope approximation ω satisfies the condition of 0.5≤ω≤1, the formula for the longitudinal temperature field distribution of the tunnel airflow group is:

[0084]

[0085] When the herringbone slope approximation ω satisfies the condition of 0.5≤ω≤1, the formula for the longitudinal temperature field distribution of the tunnel is:

[0086]

[0087] When the herringbone slope approximation ω satisfies the condition of 0<ω<0.5, the formula for the longitudinal temperature field distribution of the tunnel air flow group is:

[0088]

[0089] in, Respectively represent the distance from the tunnel entrance to the long slope and short slope in the tunnel m and x' m The wind flow temperature at the location, unit: ℃;

[0090] P x It indicates the air pressure in the tunnel where the long slope is located at a point xm away from the tunnel entrance where the short slope is located, in Pa;

[0091] P' x’ Indicates the distance from the short slope to the long slope in the tunnel.m The air pressure at the location, unit: Pa;

[0092] T out , T' out Respectively represent the coldest monthly average temperature at the entrance of the long slope and short slope, unit: Pa;

[0093] x, x' respectively represent the distance from any point in the tunnel where the long slope and short slope are located to the corresponding tunnel opening, that is, the insulation defense length of the tunnel where the long slope and short slope are located, unit: m;

[0094] α represents the average slope of the tunnel where the long slope is located; β represents the average slope of the tunnel where the short slope is located; h 1 、h 2 Respectively represents the relative height difference between the tunnel entrance and the slope change point where the long slope and short slope are located, unit: m, L 1 , L 2 Respectively represent the length of long slope and short slope, unit: m;

[0095] P out , P' out Respectively represent the air pressure at the tunnel entrance where the long slope and short slope are located, unit: Pa;

[0096] Indicates the air pressure at the highest point in the tunnel, unit: Pa;

[0097] ΔP 静 , ΔP' 静 Respectively represent the distance from the tunnel entrance to the long slope and short slope, x meters and x' m The static pressure difference between the hole and the cave entrance, unit: Pa;

[0098] ΔP 风 , ΔP' 风 Respectively represent the distance from the tunnel entrance to the long slope and short slope, x meters and x' m The natural wind pressure formed by the dominant natural wind in the region in winter, unit: Pa.

[0099] Furthermore, the method for determining the insulation defense length of the cold region tunnel according to the formula of the longitudinal temperature field distribution of the tunnel specifically includes:

[0100] Solve the T(x) equation, set T(x) = -8, and obtain the insulation defense length of the tunnel.

[0101] Furthermore, the method for determining the insulation defense length of the cold region tunnel according to the formula of the longitudinal temperature field distribution of the tunnel specifically includes:

[0102] To T L1 (x) and T L2(x′) equation is solved and T L1 (x) = -8, T L2 (x′)=-8, and the insulation defense length of the tunnel where the long slope and the short slope are located are obtained respectively.

[0103] The working principle and beneficial effects of the present invention are:

[0104] 1. The present invention proposes a method for calculating the insulation defense length of cold-region tunnels. The method derives theoretical formulas based on the kinematic equations of the wind flow group in the tunnel and the basic physical equations, and obtains the longitudinal temperature field distribution formula of the cold-region tunnel based on influencing factors such as tunnel length, slope and the average temperature of the coldest month at the tunnel entrance. The insulation defense length of the tunnel is obtained based on the longitudinal temperature field distribution formula of the cold-region tunnel, which can ensure that the anti-freezing design of the cold-region tunnel is more reasonable and economical, and has broad application prospects.

[0105] 2. In the present invention, the herringbone slope tunnel is divided into different calculation models for analysis, which are compared and verified with field measured data to verify that the formula is reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0107] Figure 1 It is a wind flow motion model in a single slope tunnel;

[0108] Figure 2 It is the wind flow motion model in the tunnel when the herringbone slope approximation satisfies the condition of 0.5≤ω≤1;

[0109] Figure 3 It is the wind flow motion model of the section after the tunnel slope change point when the herringbone slope approximation satisfies the condition of 0<ω<0.5. DETAILED DESCRIPTION

[0110] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0111] The method for calculating the insulation defense length of a cold region tunnel provided by the present invention comprises the following steps:

[0112] A. Determine the air pressure and static pressure difference at any point in the tunnel according to the altitude and air density of the tunnel site, as well as the dominant natural wind pressure and thermal potential difference in the region in winter, so as to determine the pressure of the wind flow group along the cross section;

[0113] B. Determine the average slope of the tunnel and the approximation of the herringbone slope ω according to the tunnel slope length;

[0114] Then, according to the average slope of the tunnel, the cross-sectional area of ​​the tunnel and the pressure of the wind group along the cross section, a calculation model of the wind group movement per unit length in the longitudinal direction of the tunnel is established on the single-sided slope of the tunnel;

[0115] Among them, the average slope of a single-slope tunnel is the ratio of the relative height difference between the tunnel entrance and the highest point in the tunnel to the tunnel length. The herringbone slope is divided into two single-slopes by the slope change point. The herringbone slope tunnel has two tunnel average slopes. At this time, the ratio of the relative height difference between the tunnel entrance and the highest point in the tunnel to the tunnel length is the ratio of the relative height difference between the two ends of the tunnel entrance and the slope change point to the length from the tunnel entrance to the slope change point. The approximation of the herringbone slope L 2 Indicates the length of the short slope where the slope change point is shorter than the hole entrance, L 1 Indicates the length of the long slope where the slope change point is far from the tunnel entrance, 0≤ω≤1;

[0116] When ω=0, the tunnel is a single-sided slope (the single-sided slope can be considered as L 2 =0);

[0117] When 0.5≤ω≤1, the tunnel is divided into two single-sided slopes according to the slope change point, and the wind flow group movement calculation model per unit length of the tunnel is established for the two single-sided slopes (when the L of the herringbone slope is 1 =L 2 When ω=1);

[0118] When 0<ω<0.5, the tunnel is divided into two single-sided slopes according to the slope change point. In the calculation model of the wind flow group movement per unit length of the tunnel established by the short slope single-sided slope, the temperature at the slope change point is used as the starting temperature of the short slope single-sided slope.

[0119] C. Based on the calculation model of the wind flow group movement per unit length of the tunnel and the average temperature of the coldest month in the tunnel site, the formula for the longitudinal temperature field distribution of the tunnel is determined, and the insulation defense length of the cold zone tunnel is calculated.

[0120] The pressure of the wind flow group along the cross section in step A is determined as follows:

[0121] ΔP T =ΔP 热 +ΔP 静 +ΔP 风 ;

[0122] Among them, ΔP T It indicates the pressure of the wind flow group along the cross section, unit: Pa;

[0123] ΔP 热 It indicates the thermal pressure difference between the point x meters away from the cave entrance and the cave entrance, unit: Pa;

[0124] ΔP 静 It indicates the static pressure difference between the point x meters away from the cave entrance and the cave entrance, unit: Pa;

[0125] ΔP 风 It represents the natural wind pressure formed by the dominant natural wind in winter in the area x meters away from the cave entrance, unit: Pa.

[0126] The parameters are determined as follows:

[0127] (1)ΔP 静 Determination of:

[0128] ΔP 静 =P x -P out (Formula I);

[0129] in,

[0130] P x It indicates the air pressure in the tunnel at a distance of x meters from the entrance, in Pa;

[0131] P x Determined according to the standard atmosphere model:

[0132]

[0133] P out Indicates the air pressure at the tunnel entrance, unit: Pa,

[0134]

[0135] Where H represents the relative height difference between the tunnel entrance and the point x meters away from the tunnel entrance, unit: m;

[0136] H x and H out They represent the altitudes at a point x meters from the tunnel entrance and at the tunnel entrance, respectively, in meters;

[0137] At the same time H x -H=H x =-x.tan(artanα)=H out ;.

[0138] (2) ΔP 风 Determination of:

[0139]

[0140] Where ρ is the air density, unit: kg / m 3 ;

[0141] V aIt is the dominant natural wind speed in winter in the region. Here, the meteorologically dominant average wind speed in winter in the area where the tunnel is located is taken, unit: m / s.

[0142] (3)ΔP 热 Determination of:

[0143] ΔP 热 =(γ out -γ x )·H;

[0144] H = x.tan(artanα);

[0145] Among them, γ out Indicates the air density outside the tunnel, unit: N / m 3 ;

[0146] γ x Indicates the air density inside the tunnel at a distance of x meters from the tunnel entrance, unit: N / m 3 ;

[0147] H represents the relative height difference between the tunnel entrance and the point x meters away from the tunnel entrance, unit: m;

[0148] x represents the distance from any point in the cave to the cave entrance, unit: m;

[0149] α represents the average slope of the tunnel, h represents the relative height difference between the cave entrance and the highest point in the cave, unit: m, L represents the length of the tunnel, unit: m.

[0150] The steps for establishing the wind flow group movement calculation model per unit length of the tunnel longitudinally on the single slope in step B are as follows:

[0151] (1) When ω = 0, the tunnel is a single-sided slope; Figure 1 is the wind flow motion model of a single slope tunnel. In the figure, γ in That is γ x ;

[0152] Specifically, it is assumed that the cross section of the tunnel is circular, and its radius uses the equivalent hydraulic radius; the average slope is used for calculation in the longitudinal direction of the tunnel; the friction and heat consumption between the natural wind flow and the tunnel wall are ignored; the wind flow in the tunnel is an ideal gas. Considering that the tunnel is a pipeline-like building, the static pressure difference is formed due to the relative height difference between the two end openings, the natural wind pressure is formed due to the regional seasonal dominant natural wind outside the tunnel, and the temperature difference inside and outside the tunnel and the relative height difference of the tunnel opening cause the thermal potential difference, which causes the natural wind outside the tunnel to continuously flow along the tunnel, changing the temperature field distribution in the tunnel in real time. The calculation model formula of the wind flow group movement per unit length in the longitudinal direction of the tunnel is:

[0153] ma=ΔP T.A-mgsin(arctanα);

[0154] m=A·1·ρ=Aρ;

[0155] Among them, m represents the mass of the wind flow group per unit length in the longitudinal direction, unit: kg;

[0156] a represents the acceleration of the wind flow group in the tunnel, unit: m / s 2 ;

[0157] ΔP T It indicates the pressure of the wind flow group along the cross section, unit: Pa;

[0158] A represents the cross-sectional area of ​​the wind flow group, which is equal to the cross-sectional area of ​​the tunnel, unit: m 2 ;

[0159] g represents the acceleration due to gravity, unit: m / s 2 ;

[0160] α represents the average slope of the tunnel, h represents the relative height difference between the cave entrance and the highest point in the cave, in meters, and L represents the length of the tunnel, in meters;

[0161] ρ represents air density, unit: kg / m 3 .

[0162] Furthermore, the formula for determining the longitudinal temperature field distribution of the tunnel in step C specifically comprises the following steps:

[0163] S1. Combining the pressure of the wind group along the cross section and the wind group movement calculation model equation per unit length of the tunnel longitudinal direction, the relationship between the wind group movement and temperature change can be obtained:

[0164] ρa=(γ out -γ x ).xtan(artanα)+ΔP 静 +ΔP 风 -ρgsin(arctanα);

[0165] S2. The relationship between air weight, temperature and pressure is obtained:

[0166] S3, the relationship between S1 and S2,

[0167] The relationship between the movement of wind flow group on a single slope and temperature change is:

[0168]

[0169] Considering that the train passing through the tunnel in the cold region is a short-term effect, the wind speed of the natural wind is independent of time, that is, a = 0, and the formula for the longitudinal temperature field distribution of the wind flow group in the single-slope tunnel is obtained:

[0170]

[0171] The relationship between air weight, temperature and pressure in step S2 is determined as follows:

[0172] According to the ideal gas formula:

[0173] PV = nRT;

[0174] Combined with m = n·M,

[0175] m=ρ·V,

[0176] m=A·1·ρ=Aρ,

[0177] The relationship between density, temperature and pressure is obtained:

[0178]

[0179] The relationship between air weight and density is γ = ρg;

[0180] but:

[0181] Right now

[0182] In the above formula,

[0183] T out Indicates the average temperature of the coldest month at the tunnel entrance, in Pa. If the measured value at the tunnel entrance is lower, the measured value can also be used;

[0184] T x =T (x) , indicating the distance from the tunnel entrance x m The wind flow temperature at the location, unit: ℃;

[0185] P x Indicates the distance from the tunnel entrance x m The air pressure at the location, unit: Pa;

[0186] P out Indicates the air pressure at the tunnel entrance, unit: Pa;

[0187] P represents gas pressure, unit: Pa;

[0188] V represents the volume of gas, unit: m 3 ;

[0189] n represents the amount of gaseous substance, unit: mol;

[0190] R represents the gas constant. The gas constant of air under standard conditions is 287 J / (kg·K);

[0191] T represents the gas temperature, unit: °C;

[0192] M represents the average molar mass of air, unit: g / mol, which can be 28.96×10 -3 kg / mol;

[0193] γ represents the air density, unit: N / m 3 ;

[0194] x represents the distance from any point in the tunnel to the tunnel entrance, that is, the insulation length of the tunnel, unit: m.

[0195] (2) When 0.5≤ω≤1, the tunnel is divided into two single-sided slopes according to the slope change point, and the calculation model of the wind flow group movement per unit length of the tunnel is established for the two single-sided slopes; Figure 2 , is the wind flow motion model in the tunnel when the herringbone slope approximation satisfies the condition of 0.5≤ω≤1; in the figure, γ in That is γ x , γ in ' is γ x ′;

[0196] Similar to the above formula for deriving the longitudinal temperature field distribution of the tunnel for a single slope, the pressure and formula of the wind flow group along the cross section are combined. The formula for obtaining the longitudinal temperature field distribution of the tunnel is:

[0197]

[0198] in, Respectively represent the distance from the tunnel entrance to the long slope and short slope in the tunnel m and x' m The wind flow temperature at the location, unit: ℃;

[0199] P x It represents the air pressure at the point xm from the tunnel entrance where the short slope is located in the tunnel where the long slope is located, in Pa; its determination is based on the same formula II;

[0200] P' x’ Indicates the distance from the short slope to the long slope in the tunnel. m The air pressure at the location, unit: Pa; its determination is based on the same formula II;

[0201] T out , T' out Respectively represent the coldest monthly average temperature at the entrance of the long slope and short slope, unit: Pa;

[0202] x, x' respectively represent the distance from any point in the tunnel where the long slope and short slope are located to the corresponding tunnel opening, that is, the insulation defense length of the tunnel where the long slope and short slope are located, unit: m;

[0203] α represents the average slope of the tunnel where the long slope is located; β represents the average slope of the tunnel where the short slope is located; h 1 、h 2 Respectively represents the relative height difference between the tunnel entrance and the slope change point where the long slope and short slope are located, unit: m, L 1 , L 2 Respectively represent the length of long slope and short slope, unit: m;

[0204] P out , P' out Respectively represent the air pressure at the tunnel entrance where the long slope and the short slope are located, unit: Pa; it is determined according to the standard atmospheric model, the same as formula III, and the actual air pressure parameters collected at the tunnel entrance can also be used;

[0205] ΔP 静 , ΔP' 静 Respectively represent the distance from the tunnel entrance to the long slope and short slope, x meters and x' m The static pressure difference between the point and the opening, unit: Pa; its determination is based on the same formula Ⅰ;

[0206] ΔP 风 , ΔP' 风 Respectively represent the distance from the tunnel entrance to the long slope and short slope, x meters and x' m The natural wind pressure formed by the dominant natural wind in the region in winter, unit: Pa, is determined according to the same formula IV.

[0207] (3) When 0<ω<0.5, the tunnel is divided into two single-sided slopes according to the slope change point, and a calculation model of the wind flow group movement per unit length in the longitudinal direction of the tunnel is established on one of the single-sided slopes; Figure 3 is the wind flow motion model of the section after the tunnel slope change point when the herringbone slope approximation satisfies the condition of 0<ω<0.5; in the figure, γ in That is γ x , γ in ' is γ x '

[0208] Similar to the above formula for deriving the longitudinal temperature field distribution of the tunnel for a single slope, the pressure and formula of the wind flow group along the cross section are combined. The formula for the longitudinal temperature field distribution of one side of the tunnel is:

[0209]

[0210] Then the slope change point temperature

[0211] The temperature at the slope change point is used as the starting point temperature of the other side single-sided slope, and a calculation model of the longitudinal wind flow group movement per unit length of the other side single-sided slope is established. The temperature change in the tunnel is a parabolic state with the opening downward. The temperature at the slope change point is the highest, so subtraction is used; the formula for the longitudinal temperature field distribution of the other side tunnel is:

[0212]

[0213] Right now:

[0214]

[0215] The meaning of symbols is the same as (2) when 0.5≤ω≤1, the formula symbol of the longitudinal temperature field distribution of the tunnel, where It represents the air pressure at the highest point in the tunnel, unit: Pa, and can also be determined according to formula II.

[0216] Furthermore, according to the continuity equation, the temperature field calculation formula has the following boundary conditions:

[0217]

[0218] In step C, the method for determining the insulation length of the cold region tunnel according to the formula for the longitudinal temperature field distribution of the tunnel specifically includes: L1 (x) and T L2 (x′) equation is solved, and T(x) = -8, T L1 (x) = -8, T L2 (x′)=-8, and the values ​​of x and x' are obtained respectively, which are the insulation protection length of the tunnel, that is, the insulation protection should be carried out from the tunnel entrance to x meters. Among them, -8 is the existing cold region tunnel design requirement that -8℃ is the boundary condition for protection, and insulation protection should be carried out below -8℃.

[0219] In the above formula, the regional historical meteorological parameters that need to be collected include: the average temperature of the coldest month at the tunnel entrance, air pressure, air density, and the meteorologically average wind speed of the dominant wind in winter in the tunnel area, and the collection period is generally not less than 30 years.

[0220] Example 1

[0221] This example takes a high-speed railway tunnel in a cold region with a total length of 5110m and a single-sided downhill slope of -20‰ (substituting α) from the tunnel entrance to the exit as an example, and uses relevant parameters for calculation and analysis. The tunnel entrance elevation is 3293.6m, the exit elevation is 3193.3m, and the entrance and exit elevation difference is -100.3m. The average temperature of the coldest month in the tunnel site is -10.3℃, and the measured minimum temperature 50m away from the tunnel exit during the test is -16℃ (substituting T out ).

[0222] according to Let T x =-8, where R is 287 J / (kg·K) and M is 28.96×10 -3 kg / mol, g is 9.8m / s 2 , V a Take 1.9m / s and ρ as 1.373kg / m 3 , the insulation length of the tunnel is 1375m, while the actual insulation length of the tunnel is 1350m. The tunnel has not suffered obvious frost damage since it was put into operation in December 2014, indicating that the tunnel defense length is reasonable and feasible. At the same time, the theoretical calculation value of the longitudinal temperature field distribution of the tunnel is compared with the measured temperature value, and the temperature change law is basically consistent.

[0223] Example 2

[0224] This embodiment takes a high-speed railway tunnel with a herringbone slope as an example. The tunnel is 7521 meters long, the tunnel entrance 3444 meters is located at a longitudinal slope of 5.5‰ uphill, the exit 4077 meters is located at a longitudinal slope of -6‰ downhill, the tunnel entrance elevation is 3192.69 meters, and the exit elevation is 3187.09 meters. The calculated herringbone slope approximation is 0.845.

[0225] according to

[0226] And let T x = -8 or T' x = -8, where V a Take 1.9m / s and ρ as 1.357kg / m 3 The insulation lengths of the tunnel entrance and exit are 698m and 371m respectively, while the actual insulation length of the tunnel is 750m. The tunnel has not suffered obvious frost damage since it was put into operation in December 2014, indicating that the tunnel insulation length is reasonable and feasible. At the same time, the theoretical calculation value of the longitudinal temperature field distribution of the tunnel is compared with the measured temperature value, and the temperature change law is basically the same.

[0227] Example 3

[0228] This embodiment takes a high-speed railway tunnel with a herringbone slope as an example. The tunnel is 9490m long. From the entrance to the exit, the tunnel is +6‰ uphill, 5880m long, +9.12‰ uphill, 3500m long, -6‰ downhill, 110m long, the tunnel entrance elevation is 420.99m, and the exit elevation is 487.31m. The calculated herringbone slope approximation is 0.012.

[0229] according to

[0230] And let T x = -8 or T'x = -8, where V a Take 1.5m / s and ρ as 1.367kg / m 3 , the insulation lengths of the tunnel entrance and exit are 350m and 0m respectively, while the actual insulation length of the tunnel is 500m. The tunnel has not suffered obvious frost damage since it was put into operation at the end of December 2018, indicating that the tunnel defense length is reasonable and feasible. At the same time, the theoretical calculation value of the longitudinal temperature field distribution of the tunnel is compared with the measured temperature value, and the temperature change law is basically the same.

[0231] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the insulation length of a cold region tunnel, characterized in that: The following steps are involved: A. Determine the air pressure and static pressure difference at any point in the tunnel according to the altitude and air density of the tunnel site, as well as the dominant natural wind pressure and thermal potential difference in the region in winter, so as to determine the pressure of the wind flow group along the cross section; B. Determine the average slope of the tunnel and the approximation of the herringbone slope ω according to the tunnel slope length, and then establish a calculation model of the wind flow group movement per unit length in the tunnel longitudinal direction on the single-sided slope of the tunnel according to the average slope of the tunnel, the cross-sectional area of ​​the tunnel and the pressure of the wind flow group along the cross-section; Among them, when the tunnel is a single-sided slope, the average slope of the tunnel is the ratio of the relative height difference between the tunnel entrance and the highest point in the tunnel to the tunnel length; When the tunnel is a herringbone slope, the herringbone slope is divided into two single-sided slopes by the slope change point, and the calculation model of wind flow group movement per unit length in the longitudinal direction of the tunnel is established respectively; Among them, the herringbone slope approximation L2 represents the length of the short slope where the slope change point is shorter than the tunnel entrance, and L1 represents the length of the long slope where the slope change point is longer than the tunnel entrance, 0≤ω≤1; when 0<ω<0.5, in the calculation model of the wind flow group movement per unit length of the tunnel established by the short slope single-sided slope, the temperature at the slope change point is used as the starting point temperature of the short slope single-sided slope; C. Based on the calculation model of the wind flow group movement per unit length of the tunnel and the average temperature of the coldest month in the tunnel site, the formula for the longitudinal temperature field distribution of the tunnel is determined, and the insulation defense length of the cold zone tunnel is calculated.

2. The method for calculating the insulation fortification length of a cold region tunnel according to claim 1 is characterized in that: The method for determining the pressure of the wind flow group along the cross section is as follows: ΔP T =ΔP 热 +ΔP 静 +ΔP 风 ; Among them, ΔP T = represents the pressure of the wind flow group along the cross section, unit: Pa; ΔP 热 It indicates the thermal pressure difference between the point x meters away from the cave entrance and the cave entrance, unit: Pa; ΔP 静 It indicates the static pressure difference between the point x meters away from the cave entrance and the cave entrance, unit: Pa; ΔP 风 It represents the natural wind pressure formed by the dominant natural wind in winter in the area x meters away from the cave entrance, unit: Pa.

3. The method for calculating the insulation length of a cold region tunnel according to claim 2 is characterized in that: The ΔP 热 The method of determining is as follows: ΔP 热 =(γ out -c x )·H; H = x.tan(artanα); Among them, γ out Indicates the air density outside the tunnel, unit: N / m 3 ; γ x Indicates the air density inside the tunnel at a distance of x meters from the tunnel entrance, unit: N / m 3 ; H represents the relative height difference between the tunnel entrance and the point x meters away from the tunnel entrance, unit: m; x represents the distance from any point in the cave to the cave entrance, unit: m; α represents the average slope of the tunnel, h represents the relative height difference between the cave entrance and the highest point in the cave, unit: m, L represents the length of the tunnel, unit: m.

4. The method for calculating the insulation fortification length of a cold region tunnel according to claim 3 is characterized in that: The ΔP 静 The method of determining is as follows: ΔP 静 =P x -P out ; in, P x It indicates the air pressure in the tunnel at a distance of x meters from the entrance, in Pa; P x Determined according to the standard atmosphere model: P out Indicates the air pressure at the tunnel entrance, unit: Pa, Where H represents the relative height difference between the tunnel entrance and the point x meters away from the tunnel entrance, unit: m; H x and H out They represent the altitudes at a point x meters from the tunnel entrance and at the tunnel entrance, respectively, in meters; At the same time H x -H=H x =-x.tan(artanα)=H out ; The ΔP 风 The method of determining is as follows: Where ρ is the air density, unit: kg / m 3 ; V a It is the dominant natural wind speed in winter in the region. Here, the meteorologically dominant average wind speed in winter in the area where the tunnel is located is taken, unit: m / s.

5. The method for calculating the insulation fortification length of a cold region tunnel according to claim 3 is characterized in that: The calculation model of wind flow group movement per unit length of the single slope tunnel is as follows: ma=ΔP T .A-mgsin(arctanα); m=A·1·ρ=Aρ; Among them, m represents the mass of the wind flow group per unit length in the longitudinal direction, unit: kg; a represents the acceleration of the wind flow group in the tunnel, unit: m / s 2 ; ΔP T It indicates the pressure of the wind flow group along the cross section, unit: Pa; A represents the cross-sectional area of ​​the wind flow group, which is equal to the cross-sectional area of ​​the tunnel, unit: m 2 ; g represents the acceleration due to gravity, unit: m / s 2； α represents the average slope of the tunnel, h represents the relative height difference between the cave entrance and the highest point in the cave, unit: m, L represents the tunnel length, unit: m; ρ is air density, unit: kg / m 3 ;.

6. A method for calculating the insulation fortification length of a cold region tunnel according to claim 5, characterized in that: The formula for determining the longitudinal temperature field distribution of the tunnel in step C specifically comprises the following steps: S1. Combining the pressure of the wind group along the cross section and the wind group movement calculation model equation per unit length of the tunnel longitudinal direction, the relationship between the wind group movement and temperature change can be obtained: ρa=(γ out -c x ).xtan(artanα)+ΔP 静 +ΔP 风 -ρgsin(arctana); S2. The relationship between air weight, temperature and pressure is obtained: S3, the relationship between S1 and S2, The relationship between the movement of wind flow group on a single slope and temperature change is: Taking a = 0, we can get the formula for the longitudinal temperature field distribution of the air flow group in a single slope tunnel; The relationship between air weight, temperature and pressure in step S2 is determined as follows: According to the ideal gas formula: PV = nRT; Combined with m = n·M, m=ρ·V, m=A·1·ρ=Aρ, get: The relationship between air weight and density is: γ =; but: Right now In the above formula, T out It indicates the average temperature of the coldest month at the tunnel entrance, unit: Pa; T x =T (x) , represents the air flow temperature at a distance of xm from the tunnel entrance, unit: °C; P x Indicates the air pressure at a distance of xm from the tunnel entrance, unit: Pa; P out Indicates the air pressure at the tunnel entrance, unit: Pa; P represents gas pressure, unit: Pa; V represents the volume of gas, unit: m 3 ; n represents the amount of gaseous substance, unit: mol; R represents the gas constant. The gas constant of air under standard conditions is 287 J / (kg·K); T represents the gas temperature, unit: °C; M represents the average molar mass of air, unit: g / mol; γ represents the air density, unit: N / m 3 .

7. The method for calculating the insulation fortification length of a cold region tunnel according to claim 6 is characterized in that: When ω=0, the formula for the longitudinal temperature field distribution of the tunnel is: x represents the distance from any point in the tunnel to the tunnel entrance, that is, the insulation length of the tunnel, unit: m.

8. The method for calculating the insulation fortification length of a cold region tunnel according to claim 6 is characterized in that: When the herringbone slope approximation ω satisfies the condition of 0.5≤ω≤1, the formula for the longitudinal temperature field distribution of the tunnel is: When the herringbone slope approximation ω satisfies the condition of 0<ω<0.5, the formula for the longitudinal temperature field distribution of the tunnel air flow group is: in, Respectively represent the wind flow temperature at the distance xm and x′m from the tunnel opening in the tunnel where the long slope and short slope are located, unit: ℃; P x It indicates the air pressure in the tunnel where the long slope is located at a point xm away from the tunnel entrance where the short slope is located, in Pa; P′ x′ It indicates the air pressure in the tunnel where the short slope is located at a distance of x'm from the opening where the long slope is located, in Pa; T out , T′ out Respectively represent the coldest monthly average temperature at the entrance of the long slope and short slope, unit: Pa; x, x′ respectively represent the distance from any point in the tunnel where the long slope and short slope are located to the corresponding tunnel opening, that is, the insulation defense length of the tunnel where the long slope and short slope are located, unit: m; α represents the average slope of the tunnel where the long slope is located; β represents the average slope of the tunnel where the short slope is located; h1 and h2 represent the relative height difference between the tunnel entrance and the slope change point of the long slope and the short slope, respectively, in meters; L1 and L2 represent the length of the long slope and the short slope, respectively, in meters; P out , P o ' ut Respectively represent the air pressure at the tunnel entrance where the long slope and short slope are located, unit: Pa; P L1 Indicates the air pressure at the highest point in the tunnel, unit: Pa; ΔP 静 , ΔP′ 静 Respectively represent the static pressure difference between the tunnel entrance and the position x meters and x'm away from the tunnel entrance where the long slope and the short slope are located, unit: Pa; ΔP 风 , ΔP′ 风 Respectively represent the natural wind pressure formed by the dominant natural wind in winter in the area x meters and x'm away from the tunnel entrance where the long slope and short slope are located, unit: Pa.

9. The method for calculating the insulation fortification length of a cold region tunnel according to claim 7 is characterized in that: The method for determining the insulation defense length of a cold region tunnel according to the formula for the longitudinal temperature field distribution of the tunnel specifically includes: Solve the T(x) equation, set T(x) = -8, and obtain the insulation defense length of the tunnel.

10. The method for calculating the insulation length of a cold region tunnel according to claim 8, characterized in that: The method for determining the insulation defense length of a cold region tunnel according to the formula for the longitudinal temperature field distribution of the tunnel specifically includes: To T L1 (x) and T L2 (x′) equation is solved and T L1 (x) = -8, T L2 (x′)=-8, and the insulation defense length of the tunnel where the long slope and the short slope are located are obtained respectively.

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