Consideration of the calculation method of stress sharing ratio of underground structure with displacement discontinuity

Abstract

This invention belongs to the field of tunnel engineering technology and relates to a method for calculating the stress sharing ratio of underground structures considering displacement discontinuity. It includes simulating the primary support-secondary lining stress system using an elastic double-layer thick-walled cylinder model. The model consists of the secondary lining and the primary support from the inside out. It assumes that the radial stress between the secondary lining and the primary support is continuous but the radial displacement is discontinuous, setting the radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support as [value missing]. Based on the continuity of radial stress between the secondary lining and the primary support, the radial displacement of the inner wall of the primary support and the radial displacement of the outer wall of the secondary lining are obtained. Based on [value missing], the interface pressure between the secondary lining and the primary support is calculated, and the stress sharing ratio of the secondary lining is calculated using the original rock stress. This invention establishes a calculation model for the stress sharing ratio of the secondary lining under displacement discontinuity, breaking through the limitations of the traditional assumption of continuous displacement. It can guide the design and construction timing of the secondary lining by combining on-site monitoring of radial relative displacement, providing a theoretical tool for dynamic support of soft rock tunnels.

Description

Technical Field

[0001] This invention belongs to the field of tunnel engineering technology, specifically relating to a method for calculating the stress sharing ratio of underground structures that takes into account displacement discontinuity. Background Technology

[0002] For soft rock tunnels, due to the low strength of the surrounding rock and the long duration of deformation, the coordinated stress distribution between the initial support and the secondary lining has always been a core issue in support design. Engineering practice shows that after excavation, the initial support of a soft rock tunnel undergoes a "rapid deformation-slow stabilization" process, while the timing of secondary lining construction is often limited by the construction period and the stability of the surrounding rock. This results in the inability to achieve coordinated deformation between the inner wall of the initial support and the outer wall of the secondary lining, i.e., discontinuous displacement, which mainly occurs in the radial direction of the tunnel. For example, during the construction of the Mozhai Tunnel on the Chongqing-Xiangtan High-speed Railway, after the secondary lining was constructed, the relative displacement of the contact surface reached 4 mm. The calculated stress sharing ratio of the secondary lining based on the traditional displacement continuity model deviated by 35% from the actual measured value, leading to circumferential cracks in the secondary lining.

[0003] Traditional methods for calculating the stress sharing ratio in soft rock tunnels either assume continuous displacement or rely on the absolute displacement of the initial support to derive the sharing ratio. Because they ignore or fail to consider the relative displacement between the initial support and the secondary lining, they lack theoretical significance and are difficult to guide actual engineering projects.

[0004] Currently, research on tunnel support sharing ratio by scholars both domestically and internationally can be divided into three categories, each with its own shortcomings: 1) Analytical methods based on the assumption of displacement continuity, such as deriving the stress formula of circular tunnel lining using the thick-walled cylinder theory, do not consider displacement discontinuity; a calculation model for the initial support-secondary lining sharing ratio is proposed based on this theory, which is only applicable to the scenario where the secondary lining is constructed with a lag and the initial support is completely stable. 2) Numerical simulation-based analysis methods are used to analyze the numerical relationship between the relative displacement increment and the reduction of the secondary lining sharing ratio through FLAC3D simulation, but no analytical formula can be given; considering the creep characteristics of the surrounding rock, the sharing ratio curves at different times are simulated, but it depends on complex parameter input and is difficult to extend to engineering design. 3) Based on empirical methods of field monitoring, a linear empirical formula for the sharing ratio and relative displacement was proposed by statistically analyzing monitoring data from multiple soft rock tunnels, but it lacks theoretical support.

[0005] As can be seen from the above, existing research has two main shortcomings: first, existing models are all based on the assumption of continuous deformation between the initial support and the secondary lining, which does not match the actual construction site; second, the empirical formulas have limited applicability and are difficult to extend to different geological conditions. Therefore, there is an urgent need to develop a complete and engineering-applicable method for calculating the stress sharing ratio of underground structures that considers displacement discontinuities. Summary of the Invention

[0006] In view of the shortcomings of related technologies, the present invention provides a method for calculating the stress sharing ratio of underground structures that takes into account displacement discontinuity, so as to solve the technical problems mentioned in the background art.

[0007] This invention provides a method for calculating the stress sharing ratio of underground structures considering displacement discontinuities, comprising the following steps: S1. An elastic double-layer thick-walled cylinder model is used to simulate the initial support-secondary lining stress system, establishing the tunnel stress model. The elastic double-layer thick-walled cylinder model consists of the secondary lining and the initial support, from the inside out. It is assumed that the secondary lining and the initial support satisfy the interlayer contact condition of continuous radial stress but discontinuous radial displacement. The radial relative displacement between the outer wall of the secondary lining and the inner wall of the initial support is set as... ; S2. Based on the continuity of radial stress between the secondary lining and the primary support, and according to the thick-walled cylinder theory and Hooke's law, the radial displacement of the inner wall of the primary support is obtained. radial displacement of the outer wall of the secondary lining ; S3. Based on the discontinuity of radial displacement between the secondary lining and the primary support, utilizing... Solve the interfacial pressure between the secondary lining and the primary support. , expressed as equation (1), where, The original rock stress borne by the outer wall of the initial support. This refers to the internal water pressure borne by the inner wall of the secondary lining. The elastic modulus of the initial support. The elastic modulus of the secondary lining is given by [value]. For the Poisson's ratio of the initial branch, For the Poisson's ratio of the secondary lining, Let be the radius of the inner wall of the secondary lining. Let be the radius of the outer wall of the secondary lining and the inner wall of the initial support. Let be the radius of the initial support outer wall; (1); S4. Calculate the stress sharing ratio of the secondary lining according to formula (2). ; (2).

[0008] In some embodiments, the tunnel stress model in step S1 is also based on the following assumptions: The axisymmetric plane strain condition is as follows: the axial dimension of the tunnel is much larger than the radial dimension, and the stress and displacement only change radially, while the influence of axial stress is ignored. The material properties are as follows: both the secondary lining and the primary support are homogeneous isotropic elastic materials.

[0009] In some embodiments, in step S2, the obtained radial displacement of the inner wall of the initial support is... The radial displacement of the outer wall of the secondary lining is expressed as equation (3); , expressed as equation (4); (3); (4).

[0010] In some embodiments, step S5 is further included, specifically, calculating different parameters based on typical parameters for soft rock tunnel engineering. Stress sharing ratio of the lower lining In order to carry out Impact analysis.

[0011] In some embodiments, step S6 is further included, specifically, using the controlled variable method to analyze the impact of key parameters on the stress sharing ratio of the secondary lining. Sensitivity; key parameters include in-situ stress. , initial support elastic modulus The elastic modulus of the secondary lining Radius of the initial support outer wall Radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support .

[0012] Based on the above technical solutions, the stress sharing ratio calculation method for underground structures considering displacement discontinuity in this invention establishes a calculation model for the stress sharing ratio of the secondary lining under displacement discontinuous conditions, taking into account the discontinuous deformation of the secondary lining and the primary support. This breaks through the limitations of the traditional assumption of continuous displacement, is more consistent with the actual construction site conditions, and clarifies the influence of key parameters such as radial relative displacement on the stress sharing ratio of the secondary lining, thus improving the theoretical system of stress on soft rock tunnel support structures. In practical engineering applications, the radial relative displacement between the secondary lining and the primary support, monitored on-site, can guide the design and timing of secondary lining construction, ensuring a reasonable stress sharing ratio, reducing support defects, and improving the design accuracy of soft rock tunnel support. Therefore, this invention can provide a theoretical tool for dynamic support of soft rock tunnels and has high engineering application and promotion value. Attached Figure Description

[0013] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings: Fig. 1 This is a flowchart of the method for calculating the stress sharing ratio of underground structures considering displacement discontinuity according to the present invention. Fig. 2 This is a schematic diagram of the tunnel stress model in this invention. Detailed Implementation

[0014] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0015] In the description of this invention, it should be understood that the terms "center", "lateral", "longitudinal", "upper", "lower", "top", "bottom", "inner", "outer", "left", "right", "front", "rear", "vertical", "horizontal", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0016] The terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature.

[0017] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0018] refer to Figs. 1-2 As shown, the present invention provides a method for calculating the stress sharing ratio of underground structures considering displacement discontinuity, including the following steps S1 to S4.

[0019] Step S1: A stress model of the tunnel is established by simulating the primary support-secondary lining stress system using an elastic double-layer thick-walled cylinder model. The tunnel is theoretically considered circular. The elastic double-layer thick-walled cylinder model consists of the secondary lining and the primary support from the inside out. The outer wall of the secondary lining is in contact with the inner wall of the primary support, and the outer wall of the primary support is in contact with the surrounding rock. The radii of the inner and outer walls of the secondary lining are denoted as... , Let the inner and outer radii of the initial support be denoted as... , , This refers to the tunnel excavation radius. Assuming the secondary lining and primary support satisfy the interlayer contact condition of continuous radial stress but discontinuous radial displacement, the radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support is set as... .

[0020] Furthermore, the tunnel stress model is based on the following assumptions: axisymmetric plane strain condition, specifically, the axial dimension of the tunnel is much larger than the radial dimension, stress and displacement only change radially, and the influence of axial stress is ignored; material property condition, specifically, the secondary lining and the primary support are both homogeneous isotropic elastic materials, and the secondary lining and the primary support are both linear elastic bodies; load condition, specifically, the inner wall of the secondary lining is subjected to internal water pressure (or construction load). The outer wall of the initial support bears the stress of the original rock. .

[0021] Step S2: Based on the continuity of radial stress between the secondary lining and the primary support, and according to the thick-walled cylinder theory and Hooke's law, the radial displacement of the outer wall of the secondary lining is obtained. Radial displacement of the inner wall of the initial support .

[0022] To further explain, the secondary lining is a linear elastic body. Based on the theory of thick-walled cylinders in elastic mechanics, the radial stress of the secondary lining... Satisfying the Lamé equation, expressed as equation (11), where, , The integral constant is determined by the boundary conditions. Radial coordinates, ; (11); Based on boundary conditions, when At this time, the inner wall of the secondary lining is subjected to internal water pressure, and the radial stress of the secondary lining is... ;when At this time, the outer wall of the secondary lining is in contact with the inner wall of the initial support. Because the radial stress between the two is continuous, the radial stress of the secondary lining is... ,in, The radial stress of the initial support, The boundary condition is the interfacial pressure between the secondary lining and the initial support; substituting this boundary condition into equation (11), the integral constant can be solved simultaneously. , , expressed as equation (12); (12); According to Hooke's Law, the radial displacement of the secondary lining... The relationship between stress and force is expressed by equation (13), where, The elastic modulus of the secondary lining is given by [value]. The Poisson's ratio of the secondary lining is given; substituting equations (11) and (12) into equation (13) and simplifying, we obtain the outer wall of the secondary lining ( Radial displacement , expressed as equation (4); (13); (4).

[0023] Similarly, the initial support is a linear elastic body. Based on the thick-walled cylinder theory of elasticity, the radial stress of the initial support... Satisfying the Lamé equation, expressed as equation (21), where, , The integral constant is determined by the boundary conditions. Radial coordinates, ; (twenty one); Based on boundary conditions, when At this time, the outer wall of the secondary lining is in contact with the inner wall of the initial support. Because the radial stress between the two is continuous, the radial stress of the secondary lining is... ;when At that time, the outer wall of the initial support bears the stress of the original rock. At this time, the radial stress of the secondary lining Substituting the boundary condition into equation (21), the integral constant can be solved simultaneously. , , expressed as equation (22); (twenty two); According to Hooke's law, the radial displacement of the initial support... The relationship with stress is expressed by equation (23), where, The elastic modulus of the initial support. The Poisson's ratio of the initial support; substituting equations (21) and (22) into equation (23) and simplifying, we obtain the inner wall of the initial support ( Radial displacement , expressed as equation (3); (twenty three); (3).

[0024] Step S3: Based on the discontinuity of radial displacement between the secondary lining and the initial support, utilize... Substituting equations (3) and (4) into the relation, we obtain the following: The linear equation is then used to solve for the interfacial pressure between the secondary lining and the initial support. , expressed as equation (1); (1).

[0025] Step S4: Define the stress sharing ratio of the secondary lining. For interface pressure With surrounding rock pressure The stress sharing ratio of the secondary lining is calculated according to equation (2). It is understandable that the stress distribution ratio of the initial support is equal to... ; (2).

[0026] The above illustrative embodiment, considering the discontinuous deformation of the secondary lining and the primary support during actual engineering construction, establishes an elastic double-layer thick-walled cylinder model. Based on the thick-walled cylinder theory and Hooke's law, the radial displacement expression between the outer wall of the secondary lining and the inner wall of the primary support is derived. Substituting the radial relative displacement relationship between the two, the interface pressure between the secondary lining and the primary support is calculated, and then the analytical formula for the stress sharing ratio of the secondary lining is derived. Thus, a calculation model for the stress sharing ratio of the primary support and secondary lining under discontinuous displacement is established, breaking through the limitations of the traditional assumption of continuous displacement and improving the stress theory system of soft rock tunnel support structure. In practical engineering applications, the radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support can be monitored on-site to guide the design and timing of secondary lining construction, thereby providing a theoretical tool for the dynamic support design of soft rock tunnels.

[0027] In some embodiments, the method for calculating the stress sharing ratio of underground structures considering displacement discontinuities further includes step S5, specifically, calculating different... Stress sharing ratio of the lower lining In order to carry out Impact analysis.

[0028] To further illustrate, typical parameters for soft rock tunnel engineering are shown in Table 1. Substituting the parameters in Table 1 into equation (2), different... Stress sharing ratio of the lower lining The calculation results are shown in Table 2.

[0029] Table 1: Typical parameters for soft rock tunnel engineering

[0030] Table 2: Differences Stress sharing ratio of the lower lining Calculation results

[0031] Impact analysis: As can be seen from Table 2, When increasing from -5mm to 5mm, It dropped from 0.91 to 0.73, a decrease of 20%, and The decrease was more significant at that time. From 0 to 5mm, (Decreased by 0.15). The reason is... At that time, the primary support had already deformed and released some of the surrounding rock pressure, leaving the secondary lining to bear the interface pressure. Decrease; When the displacement of the outer wall of the secondary lining is greater than the displacement of the inner wall of the initial support (e.g., if the initial support rebounds after the secondary lining is installed), the secondary lining needs to bear additional pressure. Higher; when That is, when the radial displacement between the secondary lining and the primary support is continuous, This shows that the analytical formula for stress sharing ratio of underground structures considering displacement discontinuity can degenerate into the classical model when displacement is continuous.

[0032] To clarify the stress sharing ratio of key parameters in the secondary lining To determine the degree of influence, in some embodiments, the method for calculating the stress sharing ratio of underground structures considering displacement discontinuities further includes step S6, specifically, using the controlled variable method to analyze the impact of key parameters on the stress sharing ratio of the secondary lining. Sensitivity; key parameters include in-situ stress. , initial support elastic modulus The elastic modulus of the secondary lining Radius of the initial support outer wall Radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support In the controlled variable method, a single parameter changes by 20%, while the remaining parameters are taken as baseline values. , , , , ), calculate the stress sharing ratio of the secondary lining. rate of change ,Will The calculation results are shown in Table 3, which serves as the baseline sharing ratio for the secondary lining.

[0033] Table 3: Results of parameter sensitivity analysis

[0034] As can be seen from Table 3, the stress in the original rock It is a highly sensitive parameter; Each increase Pa, An increase of 0.04, because Increasing the initial support leads to greater compressive deformation, which in turn increases the interfacial pressure transmitted to the secondary lining. Simultaneous increase. High surrounding rock pressure in engineering, such as... Tunnels with high surrounding rock pressure (Pa) require increased secondary lining thickness, such as increasing it to 0.6m, to avoid... Excessive height caused cracks in the secondary lining.

[0035] Radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support and the elastic modulus of the initial support For medium sensitivity parameters; For every 1mm change, The change was 0.01, although The magnitude of the impact is smaller ,but It can be adjusted in real time through on-site monitoring and is a key control parameter for dynamic design; Increase by 20%, The initial support stiffness is reduced by 3.4% because the increased stiffness allows it to withstand more pressure, reducing the transmission to the secondary lining; therefore, in engineering applications, soft rock tunnels should preferably use [this method / approach]. The initial support material of Pa, such as C25 shotcrete + grid arch frame, balances stiffness and deformation capacity.

[0036] Radius of the initial support outer wall As a low-sensitivity parameter, Change of 2%, The change of only 1.1% indicates that the initial support thickness has minimal impact on the stress distribution ratio of the secondary lining, and there is no need to excessively increase the initial support thickness. The elastic modulus of the secondary lining... It is a parameter with extremely low sensitivity. Changes No impact, because Determined by the stress balance between the primary support and the surrounding rock, the stiffness of the secondary lining only affects its own deformation and does not change the pressure sharing ratio. In engineering, C30 to C40 secondary lining concrete can be selected according to economic considerations.

[0037] In summary, the stress sharing ratio calculation method for underground structures considering displacement discontinuity of the present invention takes into account the actual construction situation of discontinuous displacement at the contact surface between the primary support and the secondary lining of soft rock tunnels. Based on the theory of double-layer thick-walled cylinders, a calculation model for the stress sharing ratio of the secondary lining under displacement discontinuity is established, breaking through the limitations of the traditional assumption of continuous displacement and better conforming to the construction site conditions. Furthermore, the present invention verifies the rationality and effectiveness of the analytical formula for the stress sharing ratio of the secondary lining by combining numerical examples and sensitivity analysis, clarifies the influence law of key parameters such as radial relative displacement on the stress sharing ratio of the secondary lining, and improves the stress theory system of soft rock tunnel support structure. The results show that the radial relative displacement between the secondary lining and the primary support has a significant impact on the stress sharing ratio. Therefore, in practical engineering applications, the radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support obtained by on-site monitoring can guide and dynamically adjust the secondary lining design and the timing of secondary lining construction, ensuring a reasonable sharing ratio, reducing support defects, and improving the design accuracy of soft rock tunnel support. Thus, the present invention provides a theoretical tool for dynamic support of soft rock tunnels, has high engineering application and promotion value, and can reliably guide actual engineering construction.

[0038] Finally, it should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0039] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications can still be made to the specific implementation of the present invention or equivalent substitutions can be made to some technical features without departing from the spirit of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the technical solutions claimed in the present invention.

Claims

1. A method for calculating the stress sharing ratio of underground structures considering displacement discontinuity, characterized in that, Includes the following steps: S1. An elastic double-layer thick-walled cylinder model is used to simulate the initial support-secondary lining stress system, establishing a tunnel stress model. The elastic double-layer thick-walled cylinder model consists of the secondary lining and the initial support from the inside out. It is assumed that the secondary lining and the initial support satisfy the interlayer contact condition of continuous radial stress but discontinuous radial displacement. The radial relative displacement between the outer wall of the secondary lining and the inner wall of the initial support is set as... ; S2. Based on the continuity of radial stress between the secondary lining and the primary support, and according to the thick-walled cylinder theory and Hooke's law, the radial displacement of the inner wall of the primary support is obtained. radial displacement of the outer wall of the secondary lining ; S3. Based on the discontinuity of radial displacement between the secondary lining and the primary support, utilizing... Solve the interfacial pressure between the secondary lining and the primary support. , expressed as equation (1), where, The original rock stress borne by the outer wall of the initial support. This refers to the internal water pressure borne by the inner wall of the secondary lining. The elastic modulus of the initial support. The elastic modulus of the secondary lining is given by [value]. For the Poisson's ratio of the initial branch, For the Poisson's ratio of the secondary lining, Let be the radius of the inner wall of the secondary lining. Let be the radius of the outer wall of the secondary lining and the inner wall of the initial support. Let be the radius of the initial support outer wall; (1)； S4. Calculate the stress sharing ratio of the secondary lining according to formula (2). ; (2)。 2. The method for calculating the stress sharing ratio of underground structures considering displacement discontinuity according to claim 1, characterized in that, In step S1, the tunnel stress model is also based on the following assumptions: The axisymmetric plane strain condition is as follows: the axial dimension of the tunnel is much larger than the radial dimension, and the stress and displacement only change radially, while the influence of axial stress is ignored. The material properties are as follows: both the secondary lining and the primary support are homogeneous isotropic elastic materials.

3. The method for calculating the stress sharing ratio of underground structures considering displacement discontinuity according to claim 2, characterized in that, In step S2, the obtained radial displacement of the inner wall of the initial support is... The radial displacement of the outer wall of the secondary lining is expressed as equation (3); , expressed as equation (4); (3)； (4)。 4. The method for calculating the stress sharing ratio of underground structures considering displacement discontinuity according to any one of claims 1 to 3, characterized in that, It also includes step S5, which specifically involves calculating different parameters based on typical parameters for soft rock tunnel engineering. Stress sharing ratio of the lower lining In order to carry out Impact analysis.

5. The method for calculating the stress sharing ratio of underground structures considering displacement discontinuity according to claim 4, characterized in that, The process also includes step S6, which involves using the controlled variable method to analyze the impact of key parameters on the stress distribution ratio of the secondary lining. Sensitivity; the key parameters include in-situ stress. , initial support elastic modulus The elastic modulus of the secondary lining Radius of the initial support outer wall Radial relative displacement between the outer wall of the secondary lining and the inner wall of the primary support .

Images