A double-layer beam analysis model and method for stress failure characteristics of a circular tunnel across a fault

Abstract

This invention belongs to the field of disaster prevention and mitigation for underground structures. It discloses a double-layer beam analysis model and method for analyzing the stress and failure characteristics of a circular tunnel spanning a fault. The method constructs a double-layer beam analysis model using the stiffness coefficient of the foundation springs and the calculation parameters of the beam elements. If the limit state of the double-layer beam analysis model meets the criteria, the failure state of the structure can be quickly determined through bending moment and shear force, and the failure location can be identified. Simultaneously, the failure state can be quickly determined by analyzing the proportions of bending moment and shear force terms. This invention achieves high-precision reproduction of fault deformation modes through a load-bearing beam, reproduces the stress and deformation characteristics of a tunnel spanning a fault during fault slippage through the double-layer beam model, and achieves rapid identification of the tunnel structure's failure state and failure mode through the limit state compliance criteria for the bearing capacity of annular reinforced concrete structures.

Description

Technical Field

[0001] This invention belongs to the field of disaster prevention and mitigation of underground structures, and specifically relates to a double-beam analysis model and method for the stress failure characteristics of a circular tunnel spanning a fault. Background Technology

[0002] As long linear structures, tunnels inevitably cross faults during route design. Fault displacement is a major hidden danger to tunnel structural safety, and repairs are extremely difficult once problems occur. How to prevent the relative displacement of the rock and soil on both sides of the fault from affecting structural safety and line operation is the focus of research on the mechanical behavior and disaster mitigation measures of tunnels crossing faults. Among these, how to quickly and efficiently describe the stress and failure characteristics of tunnel structures under fault displacement is a key technical problem hindering the effective implementation of disaster prevention and mitigation work for tunnels crossing faults.

[0003] Currently, researchers typically use model experiments and numerical simulations to discuss the stress, deformation, and failure of tunnel structures under fault displacement conditions. However, the extensive preliminary work and high technical barriers make it difficult to carry out disaster prevention and mitigation work efficiently. In contrast, mechanical models of cross-fault tunnels based on elastic foundation beams meet current needs in terms of computational efficiency and characterization of tunnel structural stress characteristics. Combined with failure criteria for tunnel structures, stress-failure characteristic analysis can be conducted. However, to date, no mechanical model of the stress-failure characteristics of cross-fault tunnels based on elastic foundation beams has been established, and reports on structural failure criteria are also rare. Summary of the Invention

[0004] The purpose of this invention is to overcome the above-mentioned shortcomings and provide a double-beam analysis model and method for the stress and failure characteristics of a circular tunnel across a fault. Based on a simple mechanical model and effective structural failure criteria, it can quickly obtain the stress and failure characteristics of a circular tunnel structure under fault displacement. The calculation accuracy and efficiency can be guaranteed, and it has great potential for widespread application.

[0005] To achieve the above objectives, a double-layer beam analysis method for the stress failure characteristics of a circular tunnel spanning a fault includes:

[0006] The foundation bed coefficient is obtained by measuring the surrounding rock parameters of a circular tunnel spanning a fault, and the stiffness coefficient of the foundation spring is then obtained.

[0007] Based on the structural design parameters of the cross-fault circular tunnel, the calculation parameters of the structural beam elements are obtained, including the structural elastic modulus and moment of inertia.

[0008] Based on the stiffness coefficient of the foundation spring and the calculation parameters of the structural beam unit, a double-layer beam analysis model is constructed, and the width of the fracture zone is determined based on the fault geometric parameters.

[0009] Apply a displacement to the active plate segment of the loaded beam in the double-layer beam analysis model to obtain the longitudinal distribution of bending moment and shear force in the double-layer beam analysis model.

[0010] Determine the failure state of the double-layer beam analysis model;

[0011] The dominant failure term in the analysis model of a double-layer beam is determined by the proportion of shear force and bending moment.

[0012] The subgrade coefficient is obtained by combining surrounding rock parameters with the static finite element method.

[0013] The method for calculating the stiffness coefficient of a foundation spring is as follows:

[0014] k t =KLW

[0015] k1 = 1 / 3k t

[0016] Where, k t denoted as , k1 as , k2 as , k3 as , k4 as , k5 as , k6 as , k7 as , k8 as , k9 as , k1 ...

[0017] The double-layer beam analysis model includes structural beams, load beams, normal foundation springs, and longitudinal foundation springs.

[0018] The total length of a double-beam analysis model is generally greater than 300m or 10 times the width of the fault fracture zone.

[0019] When determining the failure state of a double-layer beam analysis model, the following formula is introduced:

[0020]

[0021] in,

[0022]

[0023]

[0024]

[0025]

[0026] In the formula: V is the shear stress borne by the member; M is the bending moment borne by the member; r cor t is the distance from the shear flow centerline to the center of the cross section; t is the thickness of the annular cross section; f yv f is the yield strength of the stirrup; y Where A is the yield strength of the longitudinal reinforcement; A is the area of ​​the annular cross-section; f c A represents the compressive strength of concrete. stA is the total cross-sectional area of ​​the longitudinal reinforcement; sv is the cross-sectional area of ​​a single stirrup; s is the stirrup spacing;

[0027] when It was then assumed that the double-layer beam analysis model had been corrupted.

[0028] Shear term is The bending moment term is When the shear term accounts for more than half, the failure of the double-layer beam analysis model is considered to be mainly dominated by shear failure. When the bending moment term accounts for more than half, the failure of the double-layer beam analysis model is considered to be mainly dominated by bending failure.

[0029] A double-beam analysis model for the stress failure characteristics of a cross-fault circular tunnel includes a structural beam and a load beam. The load beam is divided into an active plate segment, a fault segment, and a passive plate segment. The structural beam and the load beam are connected by a foundation spring.

[0030] During loading, the ground spring is compressed by moving the active disk, which applies an equivalent load of fault displacement to the structural beam.

[0031] Compared with existing technologies, the method of this invention constructs a double-layer beam analysis model using the stiffness coefficient of the foundation spring and the calculation parameters of the beam elements. If the limit state of the double-layer beam analysis model meets the criteria, the failure state of the structure can be quickly determined and the failure location identified through the bending moment and shear force. Simultaneously, the failure state can be quickly determined by analyzing the proportions of the bending moment and shear force terms. This invention achieves high-precision reproduction of fault deformation modes through a loaded beam, reproduces the stress and deformation characteristics of a tunnel crossing a fault during fault slippage through a double-layer beam model, and achieves rapid identification of the failure state and failure mode of the tunnel structure through the limit state compliance criteria of the bearing capacity of the annular cross-section reinforced concrete structure. This invention has a clear principle, simple structure, high accuracy and efficiency, and can quickly predict the failure state and failure mode of a structure, showing broad application prospects in the construction, design, and research fields of tunnel engineering.

[0032] In the analytical model of this invention, the structural beam and the load beam are connected by a foundation spring. During loading, the foundation spring is compressed by moving the active disk, which applies an equivalent load of fault displacement to the structural beam. The model conforms to the interaction between the surrounding rock and the structure during fault displacement, and can simultaneously reflect the driving effect of stratum deformation on the structure and the constraint effect of the stratum itself. The obtained structural stress and deformation results are more consistent with reality. Attached Figure Description

[0033] Figure 1 This is a structural diagram of the double-layer beam analysis model in this invention;

[0034] Figure 2This is a flowchart of the present invention;

[0035] Figure 3 This is a graph showing the variation of the bearing capacity criterion for the model tunnel in the embodiment;

[0036] Figure 4 This is a diagram showing the variation of the bearing capacity criterion for the prototype tunnel in the embodiment;

[0037] Figure 5 This is a diagram showing the deformation and stress characteristics of the prototype tunnel structure in the embodiment.

[0038] Figure 6 The diagram shows the equivalent plastic strain of the prototype tunnel in the embodiment.

[0039] Among them, 1. structural beam; 2. load beam; 3. foundation spring; 4. passive disk; 5. fault; 6. active disk. Detailed Implementation

[0040] The invention will now be further described with reference to the accompanying drawings.

[0041] See Figure 1 A double-beam analysis model for the stress and failure characteristics of a circular tunnel spanning a fault is presented. The model includes a structural beam 1 and a load beam 2. The load beam 2 is divided into an active plate segment 6, a fault segment 5, and a passive plate segment 4. The structural beam 1 and the load beam 2 are connected by a foundation spring 3. During loading, the active plate is moved, causing compression of the foundation spring 3, which applies an equivalent load of fault displacement to the structural beam 1.

[0042] See Figure 2 A method for analyzing the stress and failure characteristics of a circular tunnel spanning a fault using a double-layer beam includes:

[0043] Step 1: Using the surrounding rock parameters of the circular tunnel spanning the fault, and combining this with the static finite element method, the subgrade coefficient is obtained, leading to the stiffness coefficient of the foundation spring. The calculation method for the stiffness coefficient of the foundation spring is as follows:

[0044] k t =KLW

[0045] k1 = 1 / 3k t

[0046] Where, k t , where k is the normal foundation spring stiffness in N / m, k1 is the longitudinal foundation spring stiffness in N / m, K is the subgrade coefficient, L is the concentrated spring spacing of the foundation, and W is the tunnel outer diameter.

[0047] Step 2: Based on the structural design parameters of the circular tunnel spanning the fault, obtain the calculation parameters of the structural beam elements, including the structural elastic modulus and moment of inertia;

[0048] Step 3: Based on the stiffness coefficient of the foundation spring and the calculation parameters of the structural beam unit, construct a double-layer beam analysis model. The double-layer beam analysis model includes structural beams, load beams, normal foundation springs and longitudinal foundation springs. Determine the width of the fracture zone based on the fault geometric parameters. The total length of the double-layer beam analysis model is greater than 300m or 5 times the width of the fault fracture zone.

[0049] Step 4: Apply displacement to the active plate segment of the load beam in the double-layer beam analysis model to obtain the longitudinal distribution of bending moment M and shear force V in the double-layer beam analysis model.

[0050] Step 5: Use the following formula to determine the failure state of the double-layer beam analysis model;

[0051]

[0052] in,

[0053]

[0054]

[0055]

[0056]

[0057] In the formula: V is the shear stress borne by the member; M is the bending moment borne by the member; r cor t is the distance from the shear flow centerline to the center of the cross section; t is the thickness of the annular cross section; f yv f is the yield strength of the stirrup; y Where A is the yield strength of the longitudinal reinforcement; A is the area of ​​the annular cross-section; f c A represents the compressive strength of concrete. st A is the total cross-sectional area of ​​the longitudinal reinforcement; sv is the cross-sectional area of ​​a single stirrup; s is the stirrup spacing;

[0058] when It was then assumed that the double-layer beam analysis model had been corrupted.

[0059] Step 6, based on the shear force term and bending moment term The proportion of shear force is used to determine the dominant failure term in the double-layer beam analysis model. When the proportion of shear force exceeds half, the failure of the double-layer beam analysis model is considered to be mainly dominated by shear failure. When the proportion of bending moment exceeds half, the failure of the double-layer beam analysis model is considered to be mainly dominated by bending failure.

[0060] Example 1:

[0061] Established via ABAQUS Figure 1The double-layer beam model shown uses mechanical parameters and structural section parameters of similar materials to determine the calculation parameters of the beam elements. The bending stiffness of the loaded beam is taken as 10,000 times that of the tunnel structure, equivalent to infinite stiffness. The stiffness of the foundation spring is obtained using the following formula:

[0062] k t =KLW

[0063] k1 = 1 / 3k t

[0064] In the formula: k1 is the shear spring stiffness of the foundation along the longitudinal sidewall of the structure, in N / m; k t The spring stiffness of the foundation under tension and compression along the longitudinal sidewalls of the structure is given in N / m; K is the subgrade coefficient, calculated using the static finite element method according to the "Code for Seismic Design of Urban Rail Transit Structures" GB 50909-2014, where K = 1.2 × 10⁻⁶. 9 N / m 3 L is the spacing between the concentrated springs of the foundation, which is 0.01m in this application; W is the average transverse width or diameter of the tunnel, which is 0.3m in this application.

[0065] Using the intersection of the structural centerline and the fault plane in the model test as the boundary, the length of the active disk side beam structure was determined to be 1360 mm, and the length of the passive disk side beam structure was determined to be 1680 mm. Fault displacement was simulated by applying forced displacement to the active disk side load beam.

[0066] Based on the actual situation, the calculation parameters of the ultimate bearing capacity of the model tunnel were determined (Table 1), and then the ultimate bearing capacity criterion parameters M0 = 754 N·m and V0 = 5829 N were obtained.

[0067] Table 1 Calculation parameters of the ultimate bearing capacity of the model tunnel

[0068]

[0069] The variation law of the structural ultimate bearing capacity criterion is as follows Figure 3 As shown, the bearing capacity criterion of the structure in the initial state during fault displacement exhibits an approximately hump-shaped distribution, being larger on both sides of the fault, where the shear term is almost negligible; and smaller at the fault itself, dominated by the shear term. This indicates that at this point, the structure is primarily subjected to bending on both sides of the fault, and primarily to shear at the fault, with the bearing capacity mainly controlled by bending moment. Furthermore, the criterion is not symmetrically distributed; the bearing capacity criterion for the passive panel side structure is larger, suggesting that the tunnel may first experience bending failure on the passive panel side.

[0070] Based on the comparative experimental results, it can be concluded that the analytical model in this paper can well reflect the stress failure characteristics of the structure, especially the failure mode, failure location and failure sequence of the structure.

[0071] Taking the Kangding No. 1 Tunnel of the Zheduo Mountain section of the Sichuan-Tibet Railway, which traverses the Selaha Fault, as the object of analysis, an analytical model was established. The calculation parameters for the structure and surrounding rock were determined based on the prototype parameters in Table 2. The subgrade coefficient was obtained using the static finite element method recommended by the specifications. The initial tunnel calculation length was taken as 30 times the tunnel outer diameter, i.e., 300m. The fault zone was located in the middle of the structure, with a width of 1m. The subgrade coefficient was calculated by multiplying the surrounding rock parameters by a reduction factor of 0.2, with a maximum displacement of 0.5m. Four loading levels were applied: 0.05m, 0.125m, 0.25m, and 0.50m.

[0072] Table 2 Physical and mechanical parameters of prototype and similar materials

[0073]

[0074] The calculation parameters of the ultimate bearing capacity of the single-track circular tunnel of the Sichuan-Tibet Railway are shown in Table 2. Based on this, the ultimate bearing capacity parameters of the prototype tunnel are determined to be M0 = 86.4MN·m and V0 = 18.5MN.

[0075] Table 2 Calculation parameters of ultimate bearing capacity of prototype tunnel

[0076]

[0077] Extracting the bearing capacity criteria, deformation, and stress patterns of the tunnel structure during loading, as follows: Figure 4 and Figure 5 As shown, the criterion increases rapidly and abruptly at the fault location, and is dominated by shear force. Furthermore, the deformation and stress of the prototype tunnel are concentrated within a range of 1–1.5D near the fault; beyond this range, the stress rapidly decreases.

[0078] This indicates that the prototype tunnel exhibits strong interaction with the surrounding rock at the fault location, and its failure is dominated by shear force, likely due to the strong constraint of the surrounding rock on the tunnel structure. It can be predicted that during fault displacement, the structure will experience direct shear failure near the fault plane.

[0079] To verify the analysis results, a three-dimensional nonlinear finite element analysis model of the prototype tunnel was established. The mechanical parameters of the materials were determined according to Table 2. The stress-deformation relationships of the surrounding rock, fault zone, and tunnel structure were described using linear elastic constitutive model, Mohr-Coulomb constitutive model, and concrete plastic damage model (CDP model), respectively. The CDP model parameters and loading process are referenced.

[0080] The equivalent plastic strain contour map of the fault-slip tunnel structure when the fault strike-slip displacement is 0.05m is shown below. Figure 6 As shown, the plastic deformation of the tunnel structure during fault displacement is mainly concentrated within a 1D range near the fault. Therefore, the analytical model and criteria constructed in this invention can accurately describe the failure characteristics of tunnels spanning fault sections.

Claims

1. A double-layer beam analysis method for the stress failure characteristics of a circular tunnel spanning a fault, characterized in that, include: The foundation bed coefficient is obtained by measuring the surrounding rock parameters of a circular tunnel spanning a fault, and the stiffness coefficient of the foundation spring is then obtained. Based on the structural design parameters of the cross-fault circular tunnel, the calculation parameters of the structural beam elements are obtained, including the structural elastic modulus and moment of inertia. Based on the stiffness coefficient of the foundation spring and the calculation parameters of the structural beam unit, a double-layer beam analysis model is constructed, and the width of the fracture zone is determined based on the fault geometric parameters. A displacement is applied to the active disk end of the load beam in the double-layer beam analysis model to obtain the longitudinal distribution of bending moment and shear force in the double-layer beam analysis model. To determine the failure state of a double-layer beam analysis model, the following formula is introduced: in, In the formula: V The shear stress borne by the component; M The bending moment borne by the component; r cor This is the distance from the shear flow centerline to the center of the cross section. t The thickness of the annular section; f yv The yield strength of the stirrup; f y The yield strength of the longitudinal reinforcement; A The area of ​​the annular cross-section; f c This refers to the compressive strength of concrete. A st This represents the total cross-sectional area of ​​the longitudinal reinforcement. A sv This represents the cross-sectional area of ​​a single-limb stirrup; s This refers to the spacing between the stirrups; when It was then assumed that the double-layer beam analysis model had been corrupted; Shear term is The bending moment term is When the shear term accounts for more than half, it is considered that the failure of the double-layer beam analysis model is mainly dominated by shear failure; when the bending moment term accounts for more than half, it is considered that the failure of the double-layer beam analysis model is mainly dominated by bending failure. The dominant failure term in the analysis model of a double-layer beam is determined by the proportion of shear force and bending moment.

2. The double-layer beam analysis method for stress failure characteristics of a cross-fault circular tunnel according to claim 1, characterized in that, The subgrade coefficient is obtained by combining surrounding rock parameters with the static finite element method.

3. The double-layer beam analysis method for stress failure characteristics of a cross-fault circular tunnel according to claim 1, characterized in that, The method for calculating the stiffness coefficient of a foundation spring is as follows: k t ＝ KLW k 1＝1 / 3 k t in, k t The normal foundation spring stiffness, k 1 represents the longitudinal foundation spring stiffness. K For the bed coefficient, L The concentrated spring spacing of the foundation. W This refers to the outer diameter of the tunnel.

4. The double-layer beam analysis method for stress failure characteristics of a cross-fault circular tunnel according to claim 1, characterized in that, The double-layer beam analysis model includes structural beams, load beams, normal foundation springs, and longitudinal foundation springs.

5. The double-layer beam analysis method for stress failure characteristics of a cross-fault circular tunnel according to claim 1, characterized in that, The total length of the double-beam analysis model is greater than 300m or 10 times the width of the fault fracture zone.

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