Method for calculating frost heaving force of tunnel in cold region under multi-factor random coupling

Abstract

The invention relates to the technical field of cold region rock mass and cold region tunnel engineering, and discloses a cold region tunnel frost heaving force calculation method under multi-factor random coupling. Comprising the following steps: S1, comprehensively considering the coupling effect of main frost heaving influence factors such as tunnel operation age limit, lining local cavity or defect, surrounding rock porosity and water content condition on the frost heaving force of the tunnel in the cold region; s2, a cold region tunnel frost heaving force calculation formula system under multi-factor random coupling is constructed, and cold region tunnel frost heaving is divided into a single-factor leading frost heaving type, a double-factor coupling frost heaving type and a three-factor coupling frost heaving type; and S3, selecting a corresponding calculation formula of the frost heaving force of the tunnel in the cold region according to different frost heaving types for solving. The method for calculating the frost heaving force of the tunnel in the cold region under multi-factor random coupling, provided by the invention, is suitable for various different types of tunnels in the cold region, has wide applicability, provides a scientific basis for design, construction and maintenance of the tunnel in the cold region, and is beneficial to improving the safety and stability of the tunnel.

Description

Technical Field

[0001] The invention relates to the technical field of cold region rock mass and cold region tunnel engineering, and in particular to a method for calculating frost heave force of cold region tunnel under multi-factor random coupling. Background Art

[0002] Frost heave is one of the main causes of frequent lining structural diseases in cold-region tunnels. The magnitude of frost heave force usually determines the degree of frost heave in cold-region tunnels. The variation law of frost heave force has a great influence on the safety and stability of the lining structure. Therefore, frost heave force is crucial to the design, construction and operation of cold-region tunnels. It has always been the focus and difficult problem that experts and scholars pay the most attention to. However, the frost heave model in the freezing process of cold-region tunnels is established from different perspectives. So far, there is no unified view on the frost heave mechanism and frost heave force. In addition, the frost heave process of cold-region tunnels is often accompanied by complex physical and chemical phenomena, resulting in many factors affecting the frost heave force. The random coupling of frost heave influencing factors leads to a rich variety of frost heave types in cold-region tunnels. Therefore, the classification and derivation of the calculation formula of tunnel frost heave force under the coupling of different factors need to be further improved.

[0003] In addition, when solving the frost heave force of cold-region tunnels, many calculation parameters are involved, such as frost heave rate, geometric parameters, constraint strength, etc. The accuracy, rationality and convenience of these parameter values ​​are directly related to the accuracy and application of the frost heave force calculation formula. Therefore, in order to calculate the frost heave force of cold-region tunnels more accurately and conveniently, it is necessary to systematically analyze, deeply study and reasonably value these calculation parameters. Among them, the elastic resistance coefficient of the surrounding rock is the key indicator for solving the frost heave force. The rationality and accuracy of its value directly affect the stability and safety of the surrounding rock and lining of cold-region tunnels during the frost heave process. At present, the most widely used method for the elastic resistance coefficient of surrounding rock in physical engineering is the indirect calculation method, while there are few studies on the calculation formula of the elastic resistance coefficient of surrounding rock of cold-region tunnels. In particular, the calculation of the elastic resistance coefficient of frozen surrounding rock is relatively complicated, and there are few studies on the calculation of the elastic resistance coefficient of frozen surrounding rock, and there is currently no mature calculation method.

[0004] Therefore, it is necessary to provide a calculation method for frost heave force of tunnels in cold regions under multi-factor random coupling to solve the above technical problems. Summary of the invention

[0005] Since there is no unified view on the frost heave mechanism and frost heave force of tunnels in cold regions, the random coupling of the main frost heave influencing factors leads to the current situation that the types of frost heave in tunnels in cold regions are diverse and there is no relatively systematic and complete frost heave force calculation system. In addition, there are few studies on the calculation formula of the elastic resistance coefficient of the surrounding rock of tunnels in cold regions. The purpose of the present invention is to consider the influence of multiple factors coupling such as local cavity water accumulation behind the lining of tunnels in cold regions, weathering layer and water-rich surrounding rock on the frost heave force, and to provide a calculation system for the frost heave force of tunnels in cold regions and a calculation method for the elastic resistance coefficient of the surrounding rock under practical multiple factors coupling.

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

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

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

[0009] S3. Based on the two-factor coupled frost heave type and the three-factor coupled frost heave type in S2, a two-factor coupled frost heave force calculation model and a three-factor coupled frost heave force calculation model were constructed, and the calculation formulas for the frost heave force of cold-region tunnels under two-factor coupling and three-factor coupling were proposed;

[0010] S4. Select the corresponding calculation formula for frost heave force of cold-region tunnels according to different frost heave types;

[0011] S5. Calculate the elastic resistance coefficient of the surrounding rock of the cold region tunnel, 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 elastic equivalent coefficient of the lining and ice accumulation based on the calculation results;

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

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

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

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

[0016] Elastic resistance coefficient of unfrozen surrounding rock under type II frost heave dominated by single factor;

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

[0018] The elastic resistance coefficient of the unfrozen surrounding rock and the elastic resistance coefficient of the frozen weathering layer under the single factor dominant type I frost heave and the double factor coupled type V frost heave;

[0019] The elastic resistance coefficient of unfrozen surrounding rock, the elastic resistance coefficient of frozen weathering layer, and the elastic resistance coefficient of frozen surrounding rock under two-factor coupling type IV frost heave and three-factor coupling type VII frost heave.

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

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

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

[0023] The method for calculating the frost heave force of 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 multiple influencing factors and their random coupling effects. The classification and derivation of the calculation formula are more systematic and detailed, and can better adapt to cold-region tunnels of different types and conditions.

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

[0025] The calculation method of the present invention not only improves the accuracy of frost heave prediction in cold-region tunnels, but also helps to optimize tunnel design, guide construction and maintenance, thereby effectively preventing and reducing the harm 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 calculation model of frost heave force of tunnels in Class IV cold regions under dual-factor coupling;

[0027] Figure 2 It is a simplified diagram of the calculation model of frost heave force of tunnels in Class V cold regions under dual-factor coupling;

[0028] Figure 3 It is a simplified diagram of the calculation model of frost heave force of Class VI cold zone tunnel under double-factor coupling;

[0029] Figure 4 It is a simplified diagram of the calculation model of frost heave force of Class VII cold zone tunnel under the coupling of three factors;

[0030] Figure 5 It is a simplified diagram for calculating the elastic resistance coefficient of tunnel surrounding rock in cold regions under double-factor coupling type VI frost heave;

[0031] Figure 6 This is a simplified diagram for calculating the elastic resistance coefficient of surrounding rock in cold-region tunnels under double-factor coupling type V (single-factor dominant type I) frost heave;

[0032] Figure 7 This is a simplified diagram for calculating the elastic resistance coefficient of surrounding rock of tunnels in cold regions under frost heaving of three-factor coupling type VII (two-factor coupling type IV). DETAILED DESCRIPTION

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

[0034] Taking into account the coupling effects of the main influencing factors such as tunnel operation life, local voids or defects in lining, porosity and water content of surrounding rocks on the frost heave force of cold-region tunnels, a calculation formula system for the frost heave force of cold-region tunnels under multi-factor random coupling was constructed. The frost heave types of cold-region tunnels were divided into single-factor dominant frost heave type, double-factor coupled frost heave type and three-factor coupled frost heave type. The specific calculation formulas are shown in Table 1.

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

[0036]

[0037]

[0038] Note: The surrounding rock in this table does not include weathered layer.

[0039] Classification of frost heave types dominated by a single factor:

[0040] When the cold-region tunnel has been in operation for a long time and has a significant weathering layer, the weathering layer frost heave plays a leading role in the tunnel frost heave process. Under the dominance of a single factor, the classic weathering layer frost heave model is used to calculate the first type of frost heave force. The commonly used calculation formula is as follows:

[0041]

[0042] Where, P is the frost heave force of tunnel in cold regions; α mr is the frost heave rate of the weathering layer; t mr is the thickness of the weathering layer; K mr is the elastic resistance coefficient of the frozen weathering layer; K l is the elastic equivalent coefficient of the lining.

[0043] When there are local voids or defects behind the lining of a cold-region tunnel, and local water accumulation plays a leading role in the frost heave process of the tunnel, the classic local water accumulation frost heave model can be used to calculate the type II frost heave force under the dominance of a single factor. The commonly used calculation formula is as follows:

[0044]

[0045] In the formula, α i is the freezing and heaving rate of local water phase change; t i is the local water depth; K r is the elastic resistance coefficient of surrounding rock; K i is the elastic equivalent coefficient of ice.

[0046] When the surrounding rock of a tunnel in a cold region has a large porosity and is rich in water, and the frost heaving of the water-rich surrounding rock plays a dominant role in the frost heaving process of the tunnel, the third type of frost heaving force under the dominance of a single factor can be calculated using the classic surrounding rock overall frost heaving model. The commonly used calculation formula is as follows:

[0047]

[0048] Where n is the porosity of the surrounding rock; α fr is the frost heave rate of surrounding rock; E l is the elastic modulus of the lining; E r is the elastic modulus of surrounding rock; μ l is the Poisson's ratio of the lining; μ r is the Poisson's ratio of the surrounding rock; p, q, m1, and m2 are calculation parameters, which are generally obtained by fitting actual on-site data.

[0049] Classification of frost heave types based on double-factor random coupling:

[0050] When the cold zone tunnel has been in operation for a long time and there are weathering layers and surrounding rocks with large porosity and rich water, and the weathering layer and surrounding rock frost heave play an important role in the tunnel frost heave process, the combined deformation of unfrozen surrounding rock, frozen surrounding rock, frozen weathering layer and lining is comprehensively considered, and the cold zone tunnel frost heave model of type IV under the dual-factor coupling of weathering layer and surrounding rock is constructed. Figure 1 During the freezing process, water migrates toward the frozen surrounding rock and weathering layer, negative temperature is transferred toward the unfrozen surrounding rock, the frozen volume of the weathering layer and surrounding rock expands and deforms, the displacements of the lining and unfrozen surrounding rock are Δ and δ respectively, and the weathering layer and surrounding rock are constrained by the lining and unfrozen surrounding rock during frost heaving deformation, so that the lining and unfrozen surrounding rock are subjected to frost heaving force. The red area of ​​the frost heaving model is divided into several sections along the circumferential length l by the differential method, and the calculation formula of the frost heaving force of the Class IV cold zone tunnel under the dual-factor coupling is:

[0051]

[0052] When the cold zone tunnel has been in operation for a long time and there is a weathering layer and local voids or defects behind the lining, the weathering layer frost heave and local void water frost heave play an important role in the tunnel frost heave process. Therefore, considering the joint deformation of unfrozen surrounding rock, frozen weathering layer, local water accumulation and lining, a Class V cold zone tunnel frost heave model under the dual-factor coupling of weathering layer and local water accumulation is constructed. Figure 2 During the freezing process, water migrates toward the weathering layer and local water accumulation, and negative temperature is transmitted toward the unfrozen surrounding rock. The frozen volume of the weathering layer and local water accumulation expands and displaces. The displacements of the lining and unfrozen surrounding rock are Δ and δ, respectively. The frost heave deformation is constrained by the lining and unfrozen surrounding rock, causing the lining and unfrozen surrounding rock to be subject to frost heave force.

[0053] The calculation formula of frost heave force of tunnel in Class V cold region under dual-factor coupling is:

[0054]

[0055] When there are local cavities or defects behind the lining of cold-region tunnels and the surrounding rock has a large porosity and is rich in water, the local cavity water accumulation frost heave and the surrounding rock frost heave play an important role in the tunnel frost heave process. Therefore, considering the joint deformation of tunnel lining, local water accumulation and freezing, frozen surrounding rock and unfrozen surrounding rock, a Class VI cold-region tunnel frost heave model under the dual coupling of local water accumulation and surrounding rock is constructed. Figure 3 During the freezing process, water migrates toward the frozen surrounding rock and local water accumulation, and negative temperature is transferred toward the unfrozen surrounding rock. The surrounding rock and local water accumulation expand and displace due to freezing. The displacements of the lining and unfrozen surrounding rock are Δ and δ, respectively. The frost heave deformation is constrained by the lining and unfrozen surrounding rock, causing the lining and unfrozen surrounding rock to be subjected to frost heave force.

[0056] The calculation formula of frost heave force of tunnel in Class VI cold region under dual-factor coupling is:

[0057]

[0058] Three-factor random coupling frost heave type:

[0059] When the cold zone tunnel has been in operation for a long time and there is a weathering layer, there are local cavities or defects behind the lining, and the surrounding rock has a large porosity and is rich in water, and the weathering layer frost heave, local cavity water frost heave and surrounding rock frost heave all play an important role in the tunnel frost heave process. Therefore, considering the joint deformation of unfrozen surrounding rock, frozen surrounding rock, frozen weathering layer, local water accumulation and lining, a Class VII cold zone tunnel frost heave model under the coupling of local water accumulation, weathering layer and surrounding rock is constructed. Figure 4 .

[0060] Calculation formula of frost heave force of tunnel in Class VII cold region under coupling of three factors:

[0061]

[0062] According to the calculation formula system of frost heave force in cold-region tunnels under multi-factor random coupling, there are 11 main calculation parameters related to frost heave force, which can be divided into three categories, as shown in Table 2. The first category is frost heave rate parameters, including the frost heave rate of surrounding rock, the frost heave rate of weathering layer and the frost heave rate of local water accumulation; the second category is geometric parameters, including the thickness of weathering layer, the thickness of local water accumulation and the freezing depth of tunnel; the third category is 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 weathering layer, the elastic equivalent coefficient of ice and the elastic equivalent coefficient of lining.

[0063] Table 2 Main calculation parameters of frost heave force in cold-region tunnels under multi-factor random coupling

[0064]

[0065] Note: The surrounding rock in this table does not include weathered layer.

[0066] In order to achieve the above object, the present invention adopts the following technical solutions:

[0067] In order to ensure the reliability and accuracy of the calculation of frost heave force in cold-region tunnels under multi-factor random coupling, the frost heave rate parameters, geometric parameters and constraint parameters are preferably obtained based on on-site geological and hydrological conditions, physical engineering monitoring and detection, and indoor test tests. If they cannot be obtained due to actual on-site conditions and test conditions, the following methods can also be used to obtain or calculate them.

[0068] 1. Frost heave rate parameters

[0069] Surrounding rock frost heave rate: The frost heave force calculation model under multi-factor random coupling has a displacement perpendicular to the lining along the radial direction of the tunnel, and the volume increment is the radial volume increment. The freezing of the tunnel is mainly unidirectional freezing along the radial direction of the tunnel. The unidirectional frost heave rate of the surrounding rock is 1 / 3 of the volume frost heave rate. The radial frost heave rate of the surrounding rock under the action of water and heat migration is:

[0070] α fr =0.72%ζn

[0071] Where: α fr is the radial frost heave rate of the surrounding rock under the action of water and heat migration, ζ is the influence coefficient of water and heat migration, which is 1.5846 for frost heave sensitive rocks and 1 for non-frost heave sensitive rocks.

[0072] Frost-heaving rate of weathering layer and local water accumulation: The volume frost-heaving rate of weathering layer under the action of water and heat migration during the freezing process is 6% to 35%, and the volume frost-heaving rate of local water accumulation is 9%.

[0073] 2. Geometric parameters

[0074] Tunnel freezing depth: It is necessary to comprehensively consider factors such as the temperature in the tunnel site, the thermal conductivity of the surrounding rock, the moisture content and latent heat of phase change, and the tunnel insulation measures. The calculation can be carried out using the multi-layer medium method, the classic Stefan freezing depth calculation method, or the numerical simulation method.

[0075] Weathering layer thickness: If the freezing depth of the cold-region tunnel is small, the internal water and heat migration is relatively weak, and the operating period is short, the weathering layer thickness shall be 0-200mm; if the freezing depth of the cold-region tunnel is relatively large, the internal water and heat migration is strong, and the operating period is relatively long, the weathering layer thickness shall be greater than 200mm.

[0076] Local water accumulation depth: The local cavity depth can be characterized by the tunnel over-excavation depth. The over-excavation depth of smooth blasting is 5-10cm, and the over-excavation depth of poor surrounding rock conditions and unreasonable blasting parameters is 20cm. For other construction methods, the over-excavation depths of surrounding rock levels II, III, and IV are 16.14cm, 15.46cm, and 9.42cm, respectively.

[0077] 3. Constraint strength parameters

[0078] Since the size of local water accumulation behind the lining is much smaller than that of the surrounding rock, the local ice accumulation has little effect on the overall elastic resistance of the surrounding rock, and the elastic resistance of ice accumulation is characterized by an equivalent elastic equivalent coefficient. Similarly, the lining also uses an equivalent elastic equivalent coefficient to characterize its elastic resistance. In view of this, the calculation of the surrounding rock resistance coefficient of cold-region tunnels under multi-factor random coupling can be further simplified into 4 categories, and the specific classification is shown in Table 3.

[0079] Table 3 Resistance coefficient types of surrounding rock of tunnels in cold regions under multi-factor random coupling

[0080]

[0081] Note: The surrounding rock in this table does not include weathered layer.

[0082] (1) Elastic resistance coefficient of unfrozen surrounding rock under type II frost heave dominated by a single factor

[0083] Single factor type II 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 K ufr The calculation formula is:

[0084]

[0085] In the formula, E ufr is the elastic modulus of the unfrozen surrounding rock; μ ufr is the Poisson's ratio of the unfrozen surrounding rock.

[0086] If the elastic modulus and Poisson's ratio of the unfrozen surrounding rock and the tunnel radius are known, the elastic resistance coefficient of the unfrozen surrounding rock can be calculated by the above formula. If the surrounding rock grade is known, the elastic resistance coefficient of the unfrozen surrounding rock can also be estimated according to the surrounding rock grade, see Table 4.

[0087] Table 4 Elastic resistance coefficients of surrounding rocks of different grades

[0088]

[0089]

[0090] (2) Elastic resistance coefficients of unfrozen surrounding rock and frozen surrounding rock under double-factor coupling type VI frost heave

[0091] The double-factor type VI frost heave is the coupled frost heave of local water accumulation and surrounding rock. The influence of local water accumulation on the overall elastic resistance coefficient of surrounding rock after freezing is temporarily not considered. The frost heave model can be simplified as follows: Figure 5 After freezing, a freezing zone is formed in a cold region tunnel. The surrounding rock is naturally divided into a frozen zone and an unfrozen zone. The radius of the freezing zone is R, and the radius of the tunnel is R. l , the elastic modulus and Poisson's ratio of the frozen surrounding rock are E fr and μ fr , the elastic modulus and Poisson's ratio of the unfrozen surrounding rock are E ufr and μ ufr The interior of the tunnel is subject to a uniform pressure P, and the pressure on the boundary line of the freezing zone is P0.

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

[0093]

[0094] The calculation formula of elastic resistance coefficient of frozen surrounding rock is:

[0095]

[0096] Given the elastic modulus and Poisson's ratio of the unfrozen surrounding rock and the frozen surrounding rock, the tunnel radius and the freezing depth, the elastic resistance coefficient of the unfrozen surrounding rock and the frozen surrounding rock can be calculated using the above formula.

[0097] If the elastic modulus and Poisson's ratio of the unfrozen surrounding rock, the tunnel radius, and the freezing depth are known, the elastic resistance coefficient of the frozen surrounding rock can also be calculated using the following formula.

[0098]

[0099] Where β is the freezing influence coefficient of elastic modulus, which is generally taken as 1 to 2.

[0100] If the surrounding rock grade is known, the elastic resistance coefficient of the unfrozen surrounding rock and the elastic resistance coefficient of the frozen surrounding rock can also be estimated based on the surrounding rock grade.

[0101] (3) Elastic resistance coefficients of unfrozen surrounding rock and frozen weathering layer in the single-factor-dominated type I and double-factor-coupled type V frost heave models

[0102] Similarly, without considering the influence of local water accumulation on the coefficient of elastic resistance of the surrounding rock after freezing, the elastic resistance coefficient calculation model of the frost heave surrounding rock dominated by single factor type I and double factor coupled type V can be classified into one category and simplified as Figure 6 The radius of the frozen weathering layer R mr , the elastic modulus and Poisson's ratio of the frozen weathering layer are E mr and μ mr The boundary pressure between the frozen weathering layer and the unfrozen surrounding rock is P0.

[0103] Calculation formula for elastic resistance coefficient of unfrozen surrounding rock:

[0104]

[0105] The calculation formula of elastic resistance coefficient of frozen weathering layer is:

[0106]

[0107] The calculation parameters of the elastic resistance coefficient of the frozen weathering layer need to be determined according to the actual situation on-site investigation, and then substituted into the above formula to calculate the elastic resistance coefficient of the frozen weathering layer in the cold region tunnel. If the elastic modulus and Poisson's ratio of the weathering layer cannot be obtained, the elastic modulus of the frozen weathering layer can be taken as twice the elastic modulus of ice, and the Poisson's ratio can be taken as 0.25-0.35.

[0108] (4) Elastic resistance coefficients of unfrozen surrounding rock, frozen surrounding rock and frozen weathering layer under two-factor coupling type IV and three-factor coupling type VII frost heave

[0109] Similarly, without considering the influence of local water freezing on the overall elastic resistance coefficient of the surrounding rock, the elastic resistance coefficient calculation models of the double-factor type IV and the three-factor type VII frost heave can be classified into one category and simplified as Figure 7 The uniform pressure inside the tunnel is P, the pressure on the boundary between the frozen weathering layer and the frozen surrounding rock is P1, and the pressure on the boundary of the freezing circle is P0.

[0110] The calculation formula of the elastic resistance coefficient of unfrozen surrounding rock is:

[0111]

[0112] The calculation formula of elastic resistance coefficient of frozen surrounding rock is:

[0113]

[0114] The calculation formula of the elastic resistance coefficient of the frozen weathering layer is:

[0115]

[0116] in:

[0117]

[0118] (5) Elastic equivalent coefficient of lining and ice accumulation

[0119] Up to now, there is no unified calculation method for the elastic equivalent coefficient of lining and ice. The equivalent elastic equivalent coefficient calculation method is usually used in engineering. Since the size of the surrounding rock is much larger than the size of the lining and ice accumulation, the radial displacement caused is relatively small, and the elastic equivalent coefficient of the lining and ice accumulation is equivalent to the average value of the elastic resistance coefficient of the lower level surrounding rock. However, the difference between the maximum elastic resistance coefficient and the minimum elastic resistance coefficient of the same level of surrounding rock is large. If the elastic equivalent coefficient of the lining and ice accumulation tends to the minimum or maximum value of the elastic resistance coefficient, 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:

[0120]

[0121] In the formula, K l (K i ) is the elastic equivalent coefficient of lining or ice accumulation; K2 is the transition elastic equivalent coefficient of lining or ice accumulation; K 2min K is the minimum value of the elastic resistance coefficient of surrounding rock of the same level; 2max is the maximum value of elastic resistance coefficient of surrounding rock of the same level; K 1min K is the minimum value of the elastic resistance coefficient of the lower level surrounding rock; 1max It is the maximum value of the elastic resistance coefficient of the lower level surrounding rock.

[0122] Lining related parameters can be obtained based on on-site engineering data, and the lining elastic equivalent coefficient can be calculated by substituting them into the above formula. If the lining strength is known and the lining elastic modulus and Poisson's ratio are unavailable, the elastic modulus and Poisson's ratio of concrete masonry of different grades can also be obtained by referring to Table 5.

[0123] Table 5 Mechanical parameters of concrete of different grades

[0124]

[0125] The elastic modulus and Poisson's ratio of ice can be obtained through experimental measurement. If actual 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, the elastic equivalent coefficient of ice accumulation can be calculated.

[0126] The technical effects of the present invention are analyzed and explained below through specific embodiments:

[0127] Example 1: The following is an example of calculating the surrounding rock resistance coefficient and maximum frost heave force of the Kunlun Mountain Railway Tunnel:

[0128] For example, the calculation of the surrounding rock resistance coefficient and the maximum frost heave force of the Kunlun Mountain Railway Tunnel. Due to the cold climate, complex geological structure, broken surrounding rock structure, and relatively developed joints and fissures in the Kunlun Mountain Railway Tunnel site, which is mainly grade IV and grade V surrounding rock, frost damage occurred several times during operation. According to the service time, engineering geology, surrounding rock mechanical parameters of the Kunlun Mountain Railway Tunnel, the calculation formula for the elastic resistance coefficient of the surrounding rock of cold-zone tunnels under three-factor Class VII (two-factor Class IV) frost heave is selected for solution. The elastic resistance coefficient of the unfrozen surrounding rock, the elastic resistance coefficient of the frozen surrounding rock, the elastic resistance coefficient of the frozen weathering layer and the elastic equivalent coefficient of the lining structure are calculated to be 15.90MPa / m, 7.96MPa / m, 9.29MPa / m and 202.53MPa / m, respectively. These parameters are put into the Class IV frost heave force calculation formula under two-factor coupling, and the calculated frost heave force is 0.32MPa, while the measured frost heave force is 0.30MPa, with a difference of 0.02MPa. The calculated frost heave force and the measured frost heave force are close to each other, which fully meets the requirements of the engineering entity.

[0129] Example 2: The following is an example of calculating the surrounding rock resistance coefficient and maximum frost heave force of the Qingshashan Highway Tunnel:

[0130] For example, the calculation of the resistance coefficient of the surrounding rock and the maximum frost heave force of the Qingshashan Highway Tunnel. Since the Qingshashan Highway Tunnel is located in a high-altitude area with a relatively cold winter climate, the surrounding rock at the test section is loose and broken, cracks are developed, and it is highly sensitive to frost heave. A weathered layer appears inside the surrounding rock, and there are local voids and looseness between the surrounding rock and the lining. The calculation formula for the elastic resistance coefficient of surrounding rock of tunnels in cold regions under double-factor Class V (single-factor Class I) frost heave is selected for solution. The elastic resistance coefficient of unfrozen surrounding rock, the elastic resistance coefficient of frozen weathering layer, the elastic equivalent coefficient of local ice accumulation and lining structure are calculated to be 120.24MPa / m, 61.66MPa / m, 15.31MPa / m and 225.29MPa / m, respectively. These parameters are put into the calculation formula for Class V frost heave force under double-factor coupling, and the calculated frost heave force is 0.39MPa, while the measured frost heave force is 0.35MPa, with a difference of 0.04MPa. The calculated frost heave force and the measured frost heave force are close to each other, which fully meets the requirements of the engineering entity.

[0131] Example 3: The following is an example of calculating the surrounding rock resistance coefficient and maximum frost heave force of the Queershan Highway Tunnel:

[0132] For example, the calculation of the surrounding rock resistance coefficient and the maximum frost heave force of the Queershan Highway Tunnel. Due to the complex topographic and geological conditions and regional faults in the tunnel site of the Queershan Highway Tunnel, some sections of the rock mass are relatively broken, joints and fissures are well developed, groundwater is developed, and the fault fracture zone is rich in water. In the negative temperature section near the entrance of the Queershan Highway Tunnel, there are a large number of voids and defects behind the lining. Local water accumulation and water-to-ice phase change of fissure water in the surrounding rock cause frost heave. Therefore, the calculation formula for the elastic resistance coefficient of surrounding rock of cold zone tunnels under the double-factor Class VI frost heave form is selected for solution. The elastic resistance coefficient of unfrozen surrounding rock, the elastic resistance coefficient of frozen surrounding rock, the elastic equivalent coefficient of local ice accumulation and lining structure are 11.60MPa / m, 7.36MPa / m, 12.66MPa / m and 191.67MPa / m respectively. These parameters are put into the Class VI frost heave force calculation formula under double-factor coupling, and the calculated frost heave force is 1.73MPa, while the measured frost heave force is 1.69MPa, with a difference of 0.04MPa. The calculated frost heave force and the measured frost heave force are close to each other, which fully meets the requirements of the engineering entity.

[0133] Example 4: The following is an example of calculating the surrounding rock resistance coefficient and maximum frost heave force of the Dabanshan Highway Tunnel:

[0134] For example, the calculation of the resistance coefficient of the surrounding rock and the maximum frost heave force of the Osakayama Highway Tunnel. Due to the extremely complex geological environment of the Osakayama Highway Tunnel, the weathering degree of the surrounding rock is relatively high, the joints and fissures are developed, and geological disasters such as landslides, roof falls, and water gushing occurred during the excavation process. The calculation formula for the elastic resistance coefficient of the surrounding rock of the cold zone tunnel under frost heave of three factors Class VII (double factors Class IV) is selected for solution. The elastic resistance coefficient of the unfrozen surrounding rock, the elastic resistance coefficient of the frozen surrounding rock, the elastic resistance coefficient of the frozen weathered layer, and the local The elastic equivalent coefficients of ice accumulation and lining structure are 53.01MPa / m, 30.78MPa / m, 31.28MPa / m, 17.00MPa / m and 141.12MPa / m respectively. When these parameters are put into the calculation formula of Class VII frost heave force under three-factor coupling, the calculated frost heave force is 0.89MPa, while the measured frost heave force is 0.80MPa, with a difference of 0.09MPa. The calculated frost heave force and the measured frost heave force are close to each other, which fully meets the requirements of the engineering entity.

[0135] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for calculating frost heave force of tunnels in cold regions under multi-factor random coupling, characterized in that: The steps include: S1. Comprehensively consider the coupling effect of the main frost heave influencing factors on the frost heave force of tunnels in cold regions, including tunnel operating years, local voids or defects in the lining, porosity and water content of the surrounding rock; S2. Construct a calculation formula system for frost heave force in cold-region tunnels under multi-factor random coupling, and divide the frost heave types of cold-region tunnels into single-factor dominant frost heave type, double-factor coupled frost heave type and three-factor coupled frost heave type; S3. Based on the two-factor coupled frost heave type and the three-factor coupled frost heave type in S2, a two-factor coupled frost heave force calculation model and a three-factor coupled frost heave force calculation model were constructed, and the calculation formulas for the frost heave force of cold-region tunnels under two-factor coupling and three-factor coupling were proposed; S4. Select the corresponding calculation formula for frost heave force of cold-region tunnels according to different frost heave types; S5. Calculate the elastic resistance coefficient of the surrounding rock of the cold region tunnel, 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 elastic equivalent coefficient of the lining and ice accumulation based on the calculation results; S6. Substitute the elastic resistance coefficient of the surrounding rock, the elastic equivalent coefficient of the lining and the ice accumulation into the calculation formula of the frost heave force of the cold region tunnel selected in step S4 to calculate the frost heave force of the cold region tunnel.

2. The method for calculating frost heave force of cold-region tunnels under multi-factor random coupling according to claim 1 is 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 calculation of the frost heave force.

3. The method for calculating frost heave force of cold-region tunnels under multi-factor random coupling according to claim 1 is characterized in that: The equivalent elastic coefficient is used to characterize the elastic resistance of ice accretion and lining to simplify the calculation of ice accretion and lining elastic resistance and reduce the calculation complexity.

4. The method for calculating frost heave force of cold-region tunnels under multi-factor random coupling according to claim 1 is characterized in that: The calculation of surrounding rock resistance coefficient of tunnels in cold regions under multi-factor random coupling can be simplified into four categories: Elastic resistance coefficient of unfrozen surrounding rock under type II frost heave dominated by single factor; The elastic resistance coefficient of the unfrozen surrounding rock and the elastic resistance coefficient of the frozen surrounding rock under the VI type of frost heave under three-factor coupling; The elastic resistance coefficient of the unfrozen surrounding rock and the elastic resistance coefficient of the frozen weathering layer under the single factor dominant type I frost heave and the double factor coupled type V frost heave; The elastic resistance coefficient of unfrozen surrounding rock, the elastic resistance coefficient of frozen weathering layer, and the elastic resistance coefficient of frozen surrounding rock under two-factor coupling type IV frost heave and three-factor coupling type VII frost heave.

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