Calculation method for frost heaving force of tunnels in cold regions under multi-factor random coupling

Abstract

The present invention relates to the technical fields of cold region rock masses and cold region tunnel engineering, and discloses a calculation method for frost heaving force of cold region tunnels under multi-factor random coupling, which comprises the following steps: S1. Comprehensively consider the coupling effects of these main frost heaving influencing factors such as the operation life of the tunnel, local cavities or defects in the lining, porosity and water content of the surrounding rock, etc. on the frost heaving force of cold region tunnels; S2. Construct a calculation formula system for frost heaving force of cold region tunnels under multi-factor random coupling, and divide the frost heaving of cold region tunnels into single-factor dominant frost heaving types, two-factor coupling frost heaving types and three-factor coupling frost heaving types; S3. Select the corresponding calculation formula for frost heaving force of cold region tunnels according to different frost heaving types for solution. The calculation method for frost heaving force of cold region tunnels under multi-factor random coupling provided by the present invention is applicable to various different types of cold region tunnels, has wide applicability, provides a scientific basis for the design, construction and maintenance of cold region tunnels, and helps to improve the safety and stability of tunnels.

Description

Technical Field

[0001] The present invention relates to the technical field of cold-region rock masses and cold-region tunnel engineering, and particularly relates to a calculation method for frost heaving force of cold-region tunnels under multi-factor stochastic coupling. Background Art

[0002] Frost heaving is one of the main inducements for frequent diseases of lining structures in cold-region tunnels. The magnitude of the frost heaving force usually determines the degree of frost heaving in cold-region tunnels. The variation law of the frost heaving force has a great impact on the safety and stability of the lining structure. Therefore, the frost heaving force is crucial for the design, construction, and operation of cold-region tunnels and has always been the focus and difficult problem that experts and scholars are most concerned about. However, the frost heaving models during the freezing process of cold-region tunnels are established from different perspectives. So far, no unified view has been formed on the frost heaving mechanism and the frost heaving force. In addition, the frost heaving process of cold-region tunnels is often accompanied by complex physical and chemical phenomena, resulting in numerous influencing factors of frost heaving. The stochastic coupling of the influencing factors of frost heaving leads to a rich variety of frost heaving types in cold-region tunnels. Therefore, the classification and derivation of calculation formulas for frost heaving force of tunnels under the coupling of different factors still need to be further improved.

[0003] In addition, when solving the frost heaving force of cold-region tunnels, many calculation parameters are involved, such as the frost heaving rate, geometric parameters, constraint strength, etc. The accuracy, rationality, and convenience of the values of these parameters directly affect the accuracy and application degree of the frost heaving force calculation formula. Therefore, in order to calculate the frost heaving force of cold-region tunnels more accurately and conveniently, it is necessary to conduct a systematic analysis, in-depth study, and reasonable value-taking of these calculation parameters. Among them, the elastic resistance coefficient of the surrounding rock is a key index for solving the frost heaving force, and its reasonable and accurate value directly affects the stability and safety of the surrounding rock and lining of cold-region tunnels during the frost heaving process. At present, the most widely used method for calculating the elastic resistance coefficient of the surrounding rock in physical projects is the indirect calculation method, and there is relatively little research on the calculation formula for the elastic resistance coefficient of the surrounding rock of cold-region tunnels. Especially, the calculation of the elastic resistance coefficient of frozen surrounding rock is relatively complex, and there is little research on it. Currently, there is no mature calculation method.

[0004] Therefore, it is necessary to provide a calculation method for frost heaving force of cold-region tunnels under multi-factor stochastic coupling to solve the above technical problems. Summary of the Invention

[0005] Since there is currently no unified view on the frost heaving mechanism and the frost heaving force of cold-region tunnels, and in view of the current situation that the stochastic coupling of the main current influencing factors of frost heaving leads to diverse frost heaving types in cold-region tunnels and there is no relatively systematic and perfect frost heaving force calculation system, and in addition, there is relatively little research on the calculation formula for the elastic resistance coefficient of the surrounding rock of cold-region tunnels, the purpose of the present invention is to consider the influence of multi-factor coupling such as local cavity water accumulation, weathered layer, and water-rich surrounding rock behind the lining of cold-region tunnels on the frost heaving force, and provide a practical calculation system for frost heaving force of cold-region tunnels under multi-factor coupling and a calculation method for the elastic resistance coefficient of the surrounding rock.

[0006] To achieve the above object, the method for calculating frost heaving force of a tunnel in cold region under multi-factor random coupling provided by the present invention includes the following steps:

[0007] S1. Comprehensively consider the coupling effect of main influencing factors of frost heaving on the frost heaving force of the tunnel in cold region, such as the operation years of the tunnel, local cavities or defects in the lining, porosity and water content of the surrounding rock, etc.;

[0008] S2. Construct a calculation formula system for the frost heaving force of the tunnel in cold region under multi-factor random coupling, and divide the frost heaving types of the tunnel in cold region into single-factor dominant frost heaving type, two-factor coupling frost heaving type and three-factor coupling frost heaving type;

[0009] S3. Based on the two-factor coupling frost heaving type and three-factor coupling frost heaving type in S2, construct a two-factor coupling frost heaving force calculation model and a three-factor coupling frost heaving force calculation model, and propose a calculation formula for the frost heaving force of the tunnel in cold region under two-factor coupling and a calculation formula for the frost heaving force of the tunnel in cold region under three-factor coupling;

[0010] S4. Select the corresponding calculation formula for the frost heaving force of the tunnel in cold region according to different frost heaving types;

[0011] S5. Calculate the elastic resistance coefficient of the surrounding rock of the tunnel in cold region, including the elastic resistance coefficient of the unfrozen surrounding rock, the elastic resistance coefficient of the frozen weathered layer, and the elastic resistance coefficient of the frozen surrounding rock, and determine the equivalent elastic coefficient of the lining and ice accretion according to the calculation results;

[0012] S6. Substitute the elastic resistance coefficient of the surrounding rock, the equivalent elastic coefficient of the lining and ice accretion into the calculation formula for the frost heaving force of the tunnel in cold region selected in step S4 to calculate the frost heaving force of the tunnel in cold region.

[0013] Preferably, the calculation of the elastic resistance coefficient of the surrounding rock takes into account the frozen state of the surrounding rock to improve the accuracy of the frost heaving force calculation.

[0014] Preferably, the equivalent elastic coefficient is used to characterize the elastic resistance of the ice accretion and the lining, so as to simplify the calculation of the elastic resistance of the ice accretion and the lining and reduce the calculation complexity.

[0015] Preferably, the calculation of the resistance coefficient of the surrounding rock of the tunnel in cold region under multi-factor random coupling can be further simplified into 4 categories:

[0016] The elastic resistance coefficient of the unfrozen surrounding rock under the single-factor dominant type II frost heaving;

[0017] The elastic resistance coefficient of the unfrozen surrounding rock and the elastic resistance coefficient of the frozen surrounding rock under the three-factor coupling type VI frost heaving;

[0018] The elastic resistance coefficient of unfrozen surrounding rock and the elastic resistance coefficient of frozen weathered layer under the first type of frost heave dominated by single factor and the fifth type of frost heave coupled by two factors;

[0019] The elastic resistance coefficient of unfrozen surrounding rock, the elastic resistance coefficient of frozen weathered layer, and the elastic resistance coefficient of frozen surrounding rock under the fourth type of frost heave coupled by two factors and the seventh type of frost heave coupled by three factors.

[0020] Preferably, the calculation method of frost heave force for cold region tunnels is applicable to various different types of cold region tunnels and has wide applicability.

[0021] Preferably, by calculating the frost heave force, it provides a scientific basis for the design, construction, and maintenance of cold region tunnels, which helps to improve the safety and stability of the tunnels.

[0022] Compared with the related technologies, the calculation method of frost heave force for cold region tunnels under multi-factor random coupling provided by the present invention has the following beneficial effects:

[0023] The calculation method of frost heave force for cold region tunnels under multi-factor random coupling of the present invention provides a more comprehensive and accurate frost heave force calculation system by comprehensively considering various influencing factors and their random coupling effects. The classification and derivation of the calculation formula are more systematic and detailed, and it can better adapt to different types and conditions of cold region tunnels;

[0024] In addition, the calculation method of the elastic resistance coefficient of surrounding rock proposed by the present invention, especially for the calculation of the elastic resistance coefficient of frozen surrounding rock, fills the gap in the existing technology and improves the reliability of frost heave force calculation;

[0025] The calculation method of the present invention not only improves the accuracy of frost heave prediction for cold region tunnels, but also helps to optimize tunnel design, guide construction and maintenance, thereby effectively preventing and reducing the hazards caused by frost heave and ensuring the long-term safe operation of cold region tunnels. By implementing the present invention, the quality and safety performance of cold region tunnel projects can be significantly improved, which has important practical value and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a simplified diagram of the frost heave force calculation model for the fourth type of cold region tunnel under two-factor coupling;

[0027] Figure 2 It is a simplified diagram of the frost heave force calculation model for the fifth type of cold region tunnel under two-factor coupling;

[0028] Figure 3 It is a simplified diagram of the frost heave force calculation model for the sixth type of cold region tunnel under two-factor coupling;

[0029] Figure 4 It is a simplified diagram of the frost heave force calculation model for the seventh type of cold region tunnel under three-factor coupling;

[0030] Figure 5 Schematic diagram for calculating the elastic resistance coefficient of surrounding rock of a cold-region tunnel under the sixth type of frost heave with two-factor coupling

[0031] Figure 6 Schematic diagram for calculating the elastic resistance coefficient of surrounding rock of a cold-region tunnel under the fifth type of frost heave (the first type dominated by a single factor) with two-factor coupling

[0032] Figure 7 Schematic diagram for calculating the elastic resistance coefficient of surrounding rock of a cold-region tunnel under the seventh type of frost heave (the fourth type of frost heave with two-factor coupling) with three-factor coupling Specific implementation manners

[0033] The present invention will be further described below in conjunction with the accompanying drawings and implementation manners.

[0034] Taking into comprehensive consideration the coupling effects of main influencing factors such as the operation life of the tunnel, local cavities or defects in the lining, porosity of the surrounding rock, and water content on the frost heave force of the cold-region tunnel, a calculation formula system for the frost heave force of the cold-region tunnel under multi-factor random coupling is constructed. The frost heave types of the cold-region tunnel are divided into single-factor dominated frost heave types, two-factor coupling frost heave types, and three-factor coupling frost heave types. The specific calculation formulas are shown in Table 1.

[0035] Table 1 Calculation formula system for the frost heave force of the cold-region tunnel under multi-factor random coupling

[0036]

[0037] Note: The surrounding rock referred to in this table does not include the weathered layer.

[0038] Division of single-factor dominated frost heave types

[0039] When there is a significant weathered layer due to the long operation life of the cold-region tunnel, the frost heave of the weathered layer plays a dominant role during the frost heave process of the tunnel. For the first type of frost heave force under single-factor dominance, a classical frost heave model of the weathered layer is selected for calculation. The commonly used calculation formula is as follows:[[]]

[0040]

[0041] In the formula, is the frost heave force of the cold-region tunnel; is the frost heave rate of the weathered layer; is the thickness of the weathered layer; is the elastic resistance coefficient of the frozen weathered layer; is the elastic equivalent coefficient of the lining.

[0042] When there are local cavities or defects behind the lining of a cold-region tunnel, and local water accumulation and frost heaving play a dominant role during the tunnel frost heaving process, the type-II frost heaving force under the dominance of a single factor can be calculated using the classical local water accumulation and frost heaving model. The commonly used calculation formula is as follows:

[0043]

[0044] In the formula, is the phase change frost heaving rate of local water accumulation; is the depth of local water accumulation; is the elastic resistance coefficient of the surrounding rock; is the elastic equivalent coefficient of ice.

[0045] When the porosity of the surrounding rock of a cold-region tunnel is large and water-rich, and the frost heaving of the water-rich surrounding rock plays a dominant role during the tunnel frost heaving process, the type-III frost heaving force under the dominance of a single factor can be calculated using the classical overall frost heaving model of the surrounding rock. The commonly used calculation formula is as follows:

[0046]

[0047] In the formula, is the porosity of the surrounding rock; is the frost heaving rate of the surrounding rock; is the elastic modulus of the lining; is the elastic modulus of the surrounding rock; is the Poisson's ratio of the lining; is the Poisson's ratio of the surrounding rock; p, q, m 1, m 2 are calculation parameters, generally obtained by fitting according to actual on-site data.

[0048] Classification of the two-factor random coupling frost heaving type:

[0049] When the operating years of a cold-region tunnel are long, there is a weathered layer, the porosity of the surrounding rock is large and water-rich, and the frost heaving of the weathered layer and the surrounding rock both play important roles during the tunnel frost heaving process. Therefore, considering the common deformation of the unfrozen surrounding rock, frozen surrounding rock, frozen weathered layer, and lining, the type-IV cold-region tunnel frost heaving model under the coupling of the weathered layer and the surrounding rock is constructed, as shown in Figure 1 . During the freezing process, water migrates towards the frozen surrounding rock and the weathered layer, and negative temperature transfers towards the unfrozen surrounding rock. The frozen volume of the weathered layer and the surrounding rock expands and deforms. The displacements of the lining and the unfrozen surrounding rock are and , respectively. When the weathered layer and the surrounding rock freeze and deform, they are restricted by the lining and the unfrozen surrounding rock, causing the lining and the unfrozen surrounding rock to be subjected to frost heaving forces. Using the differential method, the red area of the frost heaving model is divided into several segments along the circumferential length l. Then, the calculation formula for the type-IV cold-region tunnel frost heaving force under the two-factor coupling is:

[0050]

[0051] When the operation years of cold-region tunnels are long, there are weathered layers, and there are local cavities or defects behind the lining, and during the frost heaving process of the tunnels, the frost heaving of the weathered layer and the frost heaving of local cavity water accumulation both play important roles. Therefore, considering the combined deformation of unfrozen surrounding rock, frozen weathered layer, local water accumulation and icing, and lining, a frost heaving model for Class-V cold-region tunnels under the coupling of two factors of weathered layer and local water accumulation is constructed, as shown in Figure 2 . During the freezing process, water migrates towards the weathered layer and local water accumulation, negative temperature transfers towards the unfrozen surrounding rock, the frozen volume of the weathered layer and local water accumulation expands and undergoes displacement, and the displacements of the lining and unfrozen surrounding rock are respectively and . When frost heaving deformation occurs, it is restricted by the lining and unfrozen surrounding rock, causing the lining and unfrozen surrounding rock to be subjected to frost heaving forces.

[0052] The calculation formula for the frost heaving force of Class-V cold-region tunnels under the coupling of two factors is:

[0053]

[0054] When there are local cavities or defects behind the lining of cold-region tunnels, the porosity of the surrounding rock is large and water-rich, and during the frost heaving process of the tunnels, the frost heaving of local cavity water accumulation and the frost heaving of the surrounding rock both play important roles. Therefore, considering the combined deformation of tunnel lining, local water accumulation and icing, frozen surrounding rock, and unfrozen surrounding rock, a frost heaving model for Class-VI cold-region tunnels under the coupling of two factors of local water accumulation and surrounding rock is constructed, as shown in Figure 3 . During the freezing process, water migrates towards the frozen surrounding rock and local water accumulation, negative temperature transfers towards the unfrozen surrounding rock, the frozen volume of the surrounding rock and local water accumulation expands and undergoes displacement, and the displacements of the lining and unfrozen surrounding rock are respectively and . When frost heaving deformation occurs, it is restricted by the lining and unfrozen surrounding rock, causing the lining and unfrozen surrounding rock to be subjected to frost heaving forces.

[0055] The calculation formula for the frost heaving force of Class-VI cold-region tunnels under the coupling of two factors is:

[0056]

[0057] Frost heaving types of random coupling of three factors:

[0058] When the operation period of a cold region tunnel is long and there is a weathered layer, there are local cavities or defects behind the lining, the porosity of the surrounding rock is large and water-rich, and during the frost heaving process of the tunnel, the frost heaving of the weathered layer, the frost heaving of local accumulated water, and the frost heaving of the surrounding rock all play important roles. Therefore, considering the combined deformation of unfrozen surrounding rock, frozen surrounding rock, frozen weathered layer, local accumulated water freezing, and the lining, a frost heaving model for Class VII cold region tunnels under the coupling of three factors of local accumulated water, weathered layer, and surrounding rock is constructed, as shown in Figure 4 .

[0059] Frost heaving force calculation formula for Class VII cold region tunnels under the coupling of three factors:

[0060]

[0061] According to the calculation formula system of frost heaving force for cold region tunnels under multi-factor random coupling, there are a total of 11 main calculation parameters related to frost heaving force, which can be divided into three categories, as shown in Table 2. The first category is the frost heaving rate parameters, including the frost heaving rate of the surrounding rock, the frost heaving rate of the weathered layer, and the frost heaving rate of local accumulated water; the second category is the geometric parameters, including the thickness of the weathered layer, the thickness of local accumulated water, and the freezing depth of the tunnel; the third category is the constraint strength parameters, including the elastic resistance coefficient of unfrozen surrounding rock, the elastic resistance coefficient of frozen surrounding rock, the elastic resistance coefficient of the weathered layer, the elastic equivalent coefficient of ice, and the elastic equivalent coefficient of the lining.

[0062] Table 2 Main calculation parameters of frost heaving force for cold region tunnels under multi-factor random coupling

[0063]

[0064] Note: The surrounding rock referred to in this table does not include the weathered layer.

[0065] To achieve the above object, the present invention adopts the following technical solutions to solve it:

[0066] To ensure the reliability and accuracy of the calculation of frost heaving force for cold region tunnels under multi-factor random coupling, the frost heaving rate parameters, geometric parameters, and constraint parameters are preferably selected based on on-site geological and hydrological conditions, monitoring and detection of physical projects, and indoor test measurements. If it is impossible to obtain them due to on-site actual and test conditions, the following methods can also be used to obtain or calculate them.

[0067] 1. Frost heaving rate parameters

[0068] Frost heaving rate of the surrounding rock: In the calculation model of frost heaving force under multi-factor random coupling, the displacement is perpendicular to the lining along the radial direction of the tunnel, and the volume increment is the radial volume increment. Therefore, the freezing of the tunnel is mainly unidirectional freezing along the radial direction of the tunnel, and the unidirectional frost heaving rate of the surrounding rock is 1 / 3 of the volume frost heaving rate. The radial frost heaving rate of the surrounding rock under the action of hydrothermal migration is:

[0069]

[0070] In the formula: is the radial frost heave rate of the surrounding rock under hydrothermal migration,[[]] is the hydrothermal migration influence coefficient, taking 1.5846 for frost - sensitive rocks and 1 for non - frost - sensitive rocks.[[]]

[0071] Frost heave rate of weathered layer and local water accumulation: During the freezing process, the volume frost heave rate of the weathered layer under hydrothermal migration is 6% - 35%, and the volume frost heave rate of local water accumulation is 9%.[[]]

[0072] 2. Geometric parameters

[0073] Freezing depth of the tunnel: Factors such as the air temperature in the tunnel site area, the thermal conductivity of the surrounding rock, the water content and latent heat of phase change, and the tunnel insulation measures need to be comprehensively considered. The multi - layer medium method, the classical Stefan freezing depth calculation method or the numerical simulation method can be used for calculation.[[]]

[0074] Thickness of the weathered layer: When the freezing depth of the tunnel in cold regions is small, the internal hydrothermal migration is weak, and the operation life is short, the thickness of the weathered layer is taken as 0 - 200 mm; when the freezing depth of the tunnel in cold regions is relatively large, the internal hydrothermal migration is strong, and the operation life is relatively long, the thickness of the weathered layer is taken as > 200 mm.[[]]

[0075] Depth of local water accumulation: The depth of local cavities can be characterized by the over - excavation depth of the tunnel. The over - excavation depth of smooth - blasting is 5 - 10 cm, and the over - excavation depth is 20 cm when the surrounding rock conditions are poor and the blasting parameters are unreasonable. For other construction methods, the over - excavation depths of class Ⅱ, Ⅲ, and Ⅳ surrounding rocks are taken as 16.14 cm, 15.46 cm, and 9.42 cm respectively.[[]]

[0076] 3. Constraint strength parameters

[0077] Since the size of local water accumulation behind the lining is much smaller than the size of the surrounding rock, the influence of local ice formation on the overall elastic resistance of the surrounding rock is small. The equivalent elastic equivalent coefficient is used to characterize the elastic resistance of the ice formation. Similarly, the equivalent elastic equivalent coefficient is also used for the lining to characterize its elastic resistance. In view of this, the calculation of the resistance coefficient of the surrounding rock of the tunnel in cold regions under multi - factor random coupling can be further simplified into 4 categories, and the specific classification is shown in Table 3.[[]]

[0078] Table 3 Resistance coefficient types of the surrounding rock of the tunnel in cold regions under multi - factor random coupling[[]]

[0079]

[0080] Note: The surrounding rock referred to in this table does not include the weathered layer.[[]]

[0081] (1)Elastic resistance coefficient of unfrozen surrounding rock under the second - type frost heave dominated by a single factor[[]]

[0082] The second type of single-factor frost heave is dominated by local water accumulation, and it is necessary to calculate the elastic resistance coefficient of the unfrozen surrounding rock. The elastic resistance coefficient of the unfrozen surrounding rock The calculation formula is as follows:

[0083]

[0084] In the formula, is the elastic modulus of the unfrozen surrounding rock; is the Poisson's ratio of the unfrozen surrounding rock.

[0085] Given the elastic modulus, Poisson's ratio of the unfrozen surrounding rock, and the tunnel radius, the elastic resistance coefficient of the unfrozen surrounding rock can be calculated through the above formula. Given the surrounding rock grade, the elastic resistance coefficient of the unfrozen surrounding rock can also be estimated according to the surrounding rock grade. See Table 4.

[0086] Table 4 Elastic resistance coefficients of surrounding rocks of different grades

[0087]

[0088] (2)Elastic resistance coefficients of unfrozen and frozen surrounding rocks under the sixth type of double-factor coupled frost heave

[0089] The sixth type of double-factor frost heave is the coupled frost heave of local water accumulation and surrounding rock. Temporarily, the influence of the freezing of local water accumulation on the overall elastic resistance coefficient of the surrounding rock is not considered. Then the frost heave model can be simplified to Figure 5 . After the tunnel in the cold region is frozen, a frozen circle is formed, and the surrounding rock is naturally divided into a frozen area and an unfrozen area. The radius of the frozen circle is , the tunnel radius is , the elastic modulus and Poisson's ratio of the frozen surrounding rock are and , the elastic modulus and Poisson's ratio of the unfrozen surrounding rock are and , the internal of the tunnel is subjected to a uniform pressure , and the pressure on the boundary line of the frozen circle is .

[0090] The calculation formula for the elastic resistance coefficient of the unfrozen surrounding rock is:

[0091]

[0092] The calculation formula for the elastic resistance coefficient of the frozen surrounding rock is:

[0093]

[0094] Given the elastic modulus, Poisson's ratio of the unfrozen and frozen surrounding rocks, the tunnel radius, and the freezing depth, the elastic resistance coefficients of the unfrozen and frozen surrounding rocks can be calculated through the above formula.

[0095] Given the elastic modulus, Poisson's ratio of the unfrozen surrounding rock, the tunnel radius, and the freezing depth, the elastic resistance coefficient of the frozen surrounding rock can also be calculated using the following formula.

[0096]

[0097] In the formula, is the freezing influence coefficient of the elastic modulus, generally taken as 1 - 2.

[0098] Given the surrounding rock grade, the elastic resistance coefficient of the unfrozen surrounding rock and that of the frozen surrounding rock can also be estimated based on the surrounding rock grade.

[0099] (3) Elastic resistance coefficients of the unfrozen surrounding rock and the frozen weathered layer in the single - factor - dominated Type I and double - factor - coupled Type V frost heave models

[0100] Similarly, temporarily ignoring the influence of local water accumulation and ice formation on the overall elastic resistance coefficient of the surrounding rock, the calculation models of the elastic resistance coefficients of the single - factor - dominated Type I and double - factor - coupled Type V frost - heave surrounding rocks can be grouped into one category and simplified to Figure 6 . Among them, the radius of the frozen weathered layer , the elastic modulus and Poisson's ratio of the frozen weathered layer are and respectively, and the demarcation line pressure between the frozen weathered layer and the unfrozen surrounding rock is .

[0101] Calculation formula for the elastic resistance coefficient of the unfrozen surrounding rock:

[0102]

[0103] Calculation formula for the elastic resistance coefficient of the frozen weathered layer:

[0104]

[0105]

[0106] The calculation parameters of the elastic resistance coefficient of the frozen weathered layer need to be determined through on - site investigation according to the actual situation, and then substituted into the above formula to calculate the elastic resistance coefficient of the frozen weathered layer in the cold - region tunnel. If the elastic modulus and Poisson's ratio of the weathered layer cannot be obtained, the elastic modulus of the frozen weathered layer can be taken as 2 times the elastic modulus of ice, and the Poisson's ratio is taken as 0.25 - 0.35.

[0107] (4) Elastic resistance coefficients of the unfrozen surrounding rock, frozen surrounding rock, and frozen weathered layer under the double - factor - coupled Type IV and triple - factor - coupled Type VII frost heaves

[0108] Similarly, without considering the impact of local water accumulation and freezing on the overall elastic resistance coefficient of the surrounding rock, the elastic resistance coefficient calculation models for the fourth type of two-factor and the seventh type of three-factor under frost heave can be grouped into one category and simplified to Figure 7 . Among them, the uniform pressure inside the tunnel is , the pressure on the boundary line between the frozen weathered layer and the frozen surrounding rock is , and the pressure on the boundary line of the frozen circle is .

[0109] The calculation formula for the elastic resistance coefficient of the unfrozen surrounding rock is:

[0110]

[0111] The calculation formula for the elastic resistance coefficient of the frozen surrounding rock is:

[0112]

[0113] The calculation formula for the elastic resistance coefficient of the frozen weathered layer is:

[0114]

[0115] Where:

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] (5) Elastic equivalent coefficient of lining and ice accretion

[0122] So far, there is no unified calculation method for the elastic equivalent coefficient of lining and ice. In engineering, the equivalent elastic equivalent coefficient calculation method is usually adopted. Since the size of the surrounding rock is much larger than that of the lining and ice accretion, the resulting radial displacement is relatively small. The elastic equivalent coefficient of the lining and ice accretion is equivalent to the average value of the elastic resistance coefficient of the lower-level surrounding rock. However, the difference between the maximum and minimum elastic resistance coefficients of the same-level surrounding rock is relatively large. If the elastic equivalent coefficient of the lining and ice accretion is biased towards the minimum or maximum value of the elastic resistance coefficient, using the average value method may cause a large deviation. Due to the existence of this potential deviation, an optimized calculation formula is proposed based on the difference calculation method:

[0123]

[0124] In the formula, is the elastic equivalent coefficient of the lining or icing; is the transitional elastic equivalent coefficient of the lining or icing; is the minimum value of the elastic resistance coefficient of the surrounding rock of the same grade; is the maximum value of the elastic resistance coefficient of the surrounding rock of the same grade; is the minimum value of the elastic resistance coefficient of the surrounding rock of the next lower grade; is the maximum value of the elastic resistance coefficient of the surrounding rock of the next lower grade.

[0125] The relevant parameters of the lining can be obtained according to the on-site engineering data. Substituting them into the above formula can calculate the elastic equivalent coefficient of the lining. Given the lining strength and unable to obtain the elastic modulus and Poisson's ratio of the lining, the elastic modulus and Poisson's ratio of different grades of concrete lining can also be taken from Table 5.

[0126] Table 5 Mechanical parameters of concrete of different grades

[0127]

[0128] The elastic modulus and Poisson's ratio of ice can be obtained through experimental measurement. If on-site measurement is inconvenient, the elastic modulus of ice can be taken as 1.0 GPa and the Poisson's ratio can be taken as 0.3. Substituting them into the above formula can calculate the elastic equivalent coefficient of icing.

[0129] The technical effects of the present invention are analyzed and elaborated through specific embodiments below:

[0130] Example 1: The following takes the calculation of the elastic resistance coefficient and the maximum frost heaving force of the surrounding rock of the Kunlun Mountain Railway Tunnel as an example:

[0131] For example, in the calculation of the elastic resistance coefficient and the maximum frost heaving force of the surrounding rock of the Kunlun Mountain Railway Tunnel, due to the cold climate, complex geological structure, broken surrounding rock structure, and well-developed joints and fissures in the tunnel site area of the Kunlun Mountain Railway Tunnel, mainly grade Ⅳ and Ⅴ surrounding rocks, frost damage has occurred several times during operation. Based on the service time, engineering geology, and mechanical parameters of the surrounding rock of the Kunlun Mountain Railway Tunnel, the calculation formula for the elastic resistance coefficient of the surrounding rock of cold-region tunnels under frost heaving of type Ⅶ (type Ⅳ of two factors) of three factors is selected for solution. It can be calculated that the elastic resistance coefficients of the unfrozen surrounding rock, the frozen surrounding rock, the frozen weathered layer, and the elastic equivalent coefficient of the lining structure are 15.90 MPa / m, 7.96 MPa / m, 9.29 MPa / m, and 202.53 MPa / m respectively. Substituting these parameters into the calculation formula for the frost heaving force of type Ⅳ under two-factor coupling, the calculated frost heaving force is 0.32 MPa, while the measured frost heaving force is 0.30 MPa, with a difference of 0.02 MPa between the two. The calculated frost heaving force is quite close to the measured frost heaving force, fully meeting the requirements of the engineering entity.

[0132] Example 2: The following takes the calculation of the elastic resistance coefficient and the maximum frost heaving force of the surrounding rock of the Qingsha Mountain Highway Tunnel as an example:

[0133] For example, in the calculation of the elastic resistance coefficient and the maximum frost heaving force of the surrounding rock of the Qingshashan Highway Tunnel, since the Qingshashan Highway Tunnel is located in a high-altitude area with a relatively cold climate in winter, the surrounding rock at the test section is loose and broken, with developed fissures, strong frost heaving sensitivity, a weathered layer inside the surrounding rock, and defects such as local cavities and non-compaction distributed between the surrounding rock and the lining. The elastic resistance coefficient calculation formula for the surrounding rock of cold-region tunnels under the fifth type of double-factor (first type of single-factor) frost heaving is selected for solution. It can be calculated that the elastic resistance coefficients of the unfrozen surrounding rock, the frozen weathered layer, the local ice accumulation, and the elastic equivalent coefficient of the lining structure are 120.24 MPa / m, 61.66 MPa / m, 15.31 MPa / m, and 225.29 MPa / m respectively. Substituting these parameters into the frost heaving force calculation formula of the fifth type under double-factor coupling, the calculated frost heaving force is 0.39 MPa, while the measured frost heaving force is 0.35 MPa, with a difference of 0.04 MPa between the two. The calculated frost heaving force and the measured frost heaving force are relatively close to each other, fully meeting the requirements of the engineering entity.

[0134] Example 3: The following takes the calculation of the elastic resistance coefficient and the maximum frost heaving force of the surrounding rock of the Que'er Mountain Highway Tunnel as an example:

[0135] For example, in the calculation of the elastic resistance coefficient and the maximum frost heaving force of the surrounding rock of the Que'er Mountain Highway Tunnel, due to the complex topographic and geological conditions in the tunnel site area of the Que'er Mountain Highway Tunnel and the existence of regional fractures, the rock mass in some sections is relatively broken, with developed joint fissures, developed groundwater, and rich water in the fault fracture zone. In the negative temperature section near the entrance of the Que'er Mountain Highway Tunnel, there are quite a number of cavities and defects behind the lining, local water accumulation, and the water-ice phase change of the fissure water in the surrounding rock causes frost heaving. Therefore, the elastic resistance coefficient calculation formula for the surrounding rock of cold-region tunnels under the sixth type of double-factor frost heaving form is selected for solution. It can be calculated that the elastic resistance coefficients of the unfrozen surrounding rock, the frozen surrounding rock, the local ice accumulation, and the elastic equivalent coefficient of the lining structure are 11.60 MPa / m, 7.36 MPa / m, 12.66 MPa / m, and 191.67 MPa / m respectively. Substituting these parameters into the frost heaving force calculation formula of the sixth type under double-factor coupling, the calculated frost heaving force is 1.73 MPa, while the measured frost heaving force is 1.69 MPa, with a difference of 0.04 MPa between the two. The calculated frost heaving force and the measured frost heaving force are relatively close to each other, fully meeting the requirements of the engineering entity.

[0136] Example 4: The following takes the calculation of the elastic resistance coefficient and the maximum frost heaving force of the surrounding rock of the Daban Mountain Highway Tunnel as an example:

[0137] For example, in the calculation of the elastic resistance coefficient and the maximum frost heaving force of the surrounding rock of the Daban Mountain Highway Tunnel, due to the extremely complex geological environment of the Daban Mountain Highway Tunnel, the surrounding rock has a relatively high degree of weathering, well-developed joints and fissures, and geological disasters such as collapse, roof fall, and water inrush occurred during the excavation process. The elastic resistance coefficient calculation formula for the surrounding rock of cold-region tunnels under the frost heaving of the seventh category of three factors (the fourth category of two factors) is selected for solution. The calculated elastic resistance coefficients of the unfrozen surrounding rock, the frozen surrounding rock, the frozen weathered layer, the local ice accumulation, and the elastic equivalent coefficient of the lining structure are 53.01 MPa / m, 30.78 MPa / m, 31.28 MPa / m, 17.00 MPa / m, and 141.12 MPa / m respectively. Substituting these parameters into the frost heaving force calculation formula of the seventh category under the coupling of three factors, the calculated frost heaving force is 0.89 MPa, while the measured frost heaving force is 0.80 MPa, with a difference of 0.09 MPa between the two. The calculated frost heaving force and the measured frost heaving force are relatively close to each other, fully meeting the requirements of the engineering entity.

[0138] The above are only the embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be similarly included in the patent protection scope of the present invention.

Claims

1. A calculation method for frost heaving force of tunnels in cold regions under multi-factor random coupling, characterized in that, It includes the following steps: S1. Comprehensively consider the coupling effect of the main frost heaving influencing factors such as the tunnel operation life, local cavities or defects in the lining, porosity of surrounding rock, and water content on the frost heaving force of tunnels in cold regions; S2. Construct a calculation formula system for the frost heaving force of tunnels in cold regions under multi-factor random coupling, and classify the frost heaving types of tunnels in cold regions into single-factor dominant frost heaving types, two-factor coupling frost heaving types, and three-factor coupling frost heaving types; S3. Based on the two-factor coupling frost heaving type and three-factor coupling frost heaving type in S2, construct a two-factor coupling frost heaving force calculation model and a three-factor coupling frost heaving force calculation model, and propose a calculation formula for the frost heaving force of tunnels in cold regions under two-factor coupling and a calculation formula for the frost heaving force of tunnels in cold regions under three-factor coupling; S4. Select the corresponding calculation formula for the frost heaving force of tunnels in cold regions according to different frost heaving types; The calculation formulas for the frost heaving force of tunnels in cold regions under single-factor, two-factor, and three-factor coupling are respectively: Class Ⅰ, weathered layer: ; Type II, local waterlogging: ; Class III, surrounding rock: ; Class IV, weathered layer and surrounding rock: ; Class V, weathered layer and local water accumulation: ; Class VI, local water accumulation and surrounding rock: ; Class VII, weathered layer, local water accumulation and surrounding rock: ; In the formula, is the frost heaving force of the tunnel in cold regions; is the frost heaving rate of the weathered layer; is the thickness of the weathered layer; is the elastic resistance coefficient of the frozen weathered layer; is the equivalent elastic coefficient of the lining; In the formula, is the frost heave rate of local water accumulation phase change; is the local water accumulation depth; is the elastic resistance coefficient of surrounding rock; is the elastic equivalent coefficient of ice; Wherein, is the porosity of surrounding rock; is the frost heave rate of surrounding rock; is the elastic modulus of lining; is the elastic modulus of surrounding rock; is the Poisson's ratio of lining; is the Poisson's ratio of surrounding rock; p, q, m 1, m 2 are calculation parameters obtained by fitting according to actual on-site data; S5. Calculate the elastic resistance coefficient of the surrounding rock of the tunnel in cold regions, including the elastic resistance coefficient of unfrozen surrounding rock, the elastic resistance coefficient of frozen weathered layer, and the elastic resistance coefficient of frozen surrounding rock, and determine the elastic equivalent coefficient of the lining and ice accumulation according to the calculation results; Elastic resistance coefficient of unfrozen surrounding rock under the second type of frost heave dominated by single factor The calculation formula is as follows: , where is the elastic modulus of unfrozen surrounding rock; is the Poisson's ratio of unfrozen surrounding rock; The calculation formula for the elastic resistance coefficient of unfrozen surrounding rock under the coupling of double factors and the sixth type of frost heave is as follows: The calculation formula for the elastic resistance coefficient of frozen surrounding rock is as follows: where the radius of the frozen circle is the radius of the tunnel is the elastic modulus and Poisson's ratio of frozen surrounding rock are and the elastic modulus and Poisson's ratio of unfrozen surrounding rock are and the tunnel is subjected to uniform pressure and the pressure on the boundary line of the frozen circle is ; Calculation formulas for the elastic resistance coefficient of unfrozen surrounding rock in the single-factor-dominated Type I and two-factor-coupled Type V frost heave models: , calculation formula for the elastic resistance coefficient of frozen weathered layer: , ， where the radius of the frozen weathered layer , the elastic modulus and Poisson's ratio of the frozen weathered layer are respectively and , and the boundary pressure between the frozen weathered layer and the unfrozen surrounding rock is ; The calculation formula for the elastic resistance coefficient of unfrozen surrounding rock under the coupling of two factors in the fourth category and the coupling of three factors in the seventh category of frost heaving is as follows: The calculation formula for the elastic resistance coefficient of frozen surrounding rock is as follows: The calculation formula for the elastic resistance coefficient of frozen weathered layer is as follows: , Among them: ， ， ， ， ， Among them, the internal pressure of the tunnel is uniform as , the pressure on the demarcation line between the frozen weathered layer and the frozen surrounding rock is , and the pressure on the demarcation line of the frozen circle is ; The calculation formula for the elastic equivalent coefficient of the lining and ice accumulation is: ， Wherein, is the elastic equivalent coefficient of the lining or ice accretion; is the transitional elastic equivalent coefficient of the lining or ice accretion; is the minimum value of the elastic resistance coefficient of the surrounding rock of the same level; is the maximum value of the elastic resistance coefficient of the surrounding rock of the same level; is the minimum value of the elastic resistance coefficient of the surrounding rock of the next lower level; is the maximum value of the elastic resistance coefficient of the surrounding rock of the next lower level; S6. Substitute the elastic resistance coefficient of the surrounding rock and the elastic equivalent coefficient of the lining and ice accumulation into the calculation formula for the frost heaving force of the tunnel in cold regions selected in step S4 to calculate the frost heaving force of the tunnel in cold regions.

2. The calculation method of frost heaving force for cold-region tunnels under multi-factor random coupling according to claim 1, characterized in that The calculation of the elastic resistance coefficient of the surrounding rock takes into account the frozen state of the surrounding rock to improve the accuracy of the frost heaving force calculation.

3. The calculation method of frost heaving force for cold region tunnels under multi-factor random coupling according to claim 1, characterized in that Use the equivalent elastic equivalent coefficient to characterize the elastic resistance of ice accumulation and lining, so as to simplify the calculation of the elastic resistance of ice accumulation and lining and reduce the calculation complexity.

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