A shield tunnel seismic vulnerability analysis method considering the influence of surface overload

Abstract

The present invention relates to a method for analyzing the seismic vulnerability of shield tunnels taking into account the influence of surface overload, comprising determining the mechanical properties of tunnel materials and the physical and mechanical parameters of soil layers; investigating surface overload cases to determine surface overload conditions; selecting seismic waves and performing a one-dimensional field equivalent linear analysis on soil conditions; establishing a soil-tunnel dynamic finite element numerical model taking into account surface overload; determining earthquake intensity indices, tunnel damage indices, and damage states; and establishing a tunnel seismic probability demand model under the influence of different surface overloads. A seismic vulnerability curve of a tunnel structure under the influence of surface overload is established based on key parameters. Based on a nonlinear incremental dynamic analysis method, this method establishes a soil-tunnel system finite element numerical model taking into account the influence of surface overload, which can quantitatively evaluate the seismic vulnerability and seismic performance of tunnels under the influence of different surface overloads.

Description

Technical Field

[0001] The present invention relates to the field of tunnel structure seismic risk assessment, in particular to a shield tunnel seismic vulnerability analysis method considering the influence of surface overload. Background Art

[0002] With the development of urban civilization and the increasing saturation of spatial resources, the number of underground structures in my country has gradually increased, and their uses are becoming increasingly diverse. They play a vital role in transportation systems, municipal water and power generation, resource extraction, national defense engineering, and other fields. Tunnels for transportation are one of the most important components of these structures. Earthquakes and excessive surface overload can cause severe damage to these structures, resulting in significant losses to cities and even endangering the lives of citizens.

[0003] Seismic vulnerability expresses the probability of a structure exceeding a certain damage state under different earthquake intensities. It can quantitatively analyze the seismic performance of a structure and provide an important reference for the seismic design of urban construction. For the seismic vulnerability analysis of tunnel structures, many scholars have established different research methods, mainly including: (1) vulnerability analysis based on expert judgment; (2) vulnerability analysis based on historical earthquake damage surveys; (3) vulnerability analysis based on numerical methods; (4) vulnerability analysis based on experimental data. In the early days when science and technology and numerical analysis software were not yet developed, vulnerability analysis based on expert judgment and historical earthquake damage surveys was mainly used. Although these two methods can quickly make preliminary judgments, they are relatively subjective and cannot be applied to all geographical areas. They can no longer meet the current vulnerability analysis requirements. With the development of science and technology, scholars have begun to use methods such as numerical analysis to conduct detailed vulnerability analysis, which can perform accurate vulnerability analysis based on a large amount of data and has been used and improved by many scholars.

[0004] Tunnel damage caused by surface overload is a common occurrence in urban development. Because subway line development is often forward-looking and plays a leading role in urban economic development, numerous commercial developments are often located along subway lines, which means that construction-induced surface overload may occur above the subway lines. This suggests that analyzing the impact of surface overload on tunnels has important practical value for urban development. Currently, the main research methods for the impact of surface overload on tunnels include field measurement, model testing, numerical analysis, and theoretical analysis. Field measurement is more effective, but it is also more expensive and time-consuming. While model testing can be difficult to replicate for complex conditions, it is less time-consuming and can account for a wider range of conditions, making it the method of choice for many researchers.

[0005] Under earthquake action, tunnel structures are not only subject to horizontal shear deformation transmitted from the surrounding soil, but also to vertical loads such as surface overloads, which increase the overall structural risk of seismic damage. While surface overload conditions have a significant impact on the seismic performance of tunnel structures, current research has not adequately addressed this factor, and the relationship between surface overload and tunnel seismic performance remains unclear. Further analysis of the changing patterns of seismic vulnerability of tunnel structures under the influence of surface overloads is needed. Therefore, a method for analyzing the seismic vulnerability of tunnels under varying surface overloads is proposed, which can provide recommendations and guidance for optimizing seismic design and reinforcement schemes for tunnel structures, and has important theoretical significance and practical engineering value. Summary of the Invention

[0006] The purpose of this application is to provide a tunnel seismic vulnerability analysis method for situations where surface overload and earthquakes may interact during actual construction. Based on a nonlinear incremental dynamic analysis method, this method establishes a finite element numerical model of the soil-tunnel system that considers the effects of surface overload. This method can quantitatively assess the seismic vulnerability and seismic performance of tunnels under varying surface overload conditions.

[0007] The technical solutions provided in this application are as follows:

[0008] A shield tunnel seismic vulnerability analysis method considering the influence of surface overload includes the following steps:

[0009] S1. Determine the mechanical properties of tunnel materials and the physical and mechanical parameters of soil layers;

[0010] S2. Investigate cases where tunnels are affected by surface overloads to determine the appropriate location, size, and extent of the surface overloads;

[0011] S3, selecting a suitable seismic wave and performing a one-dimensional field equivalent linear analysis on the soil conditions obtained in step S1 to obtain the elastic modulus and Rayleigh damping parameter of the soil;

[0012] S4. Based on the physical and mechanical parameters of the tunnel and soil layer determined in steps S1, S2, and S3, as well as the seismic wave and surface overload conditions, a soil-tunnel dynamic finite element numerical model considering the surface overload is established. Different combinations of surface overload and seismic intensity are designed, and the dynamic response of the soil-tunnel system is obtained through a large number of numerical calculations.

[0013] S5. Select the maximum peak acceleration of the input seismic wave as the earthquake intensity index IM; select the diameter deformation rate of the tunnel as the damage index DM; determine the damage state of the tunnel and the damage index threshold corresponding to each damage state;

[0014] S6. Based on the earthquake intensity index IM and the damage index DM selected in step S5, a tunnel seismic resistance probability demand model under different surface overloads is established, as shown in Formula 3:

[0015] lnDM=alnIM+b, formula three

[0016] a and b are obtained through regression analysis; after obtaining the probabilistic demand model, the key parameters for drawing the fragility curve are calculated: the median and logarithmic standard deviation β of the IM values ​​corresponding to each damage state D ;

[0017] S7. Based on the key parameters, establish the seismic vulnerability curve of the tunnel structure under the influence of surface overload, as shown in Formula 5:

[0018]

[0019] Among them, P f When the earthquake is of a certain intensity IM, it exceeds a certain damage state d si The probability of φ represents the standard normal density cumulative probability function; S mi β is the earthquake intensity index threshold corresponding to each damage state obtained in step S6; tot is the total logarithmic standard deviation.

[0020] In S1, the mechanical properties of tunnel materials include tunnel depth, tunnel diameter, lining thickness, and material parameters of concrete and steel bars; the physical and mechanical parameters of the soil layer include soil thickness, soil density, cohesion, internal friction angle, Poisson's ratio, and shear wave velocity.

[0021] In S2, factors to be considered in determining the location of the surface overload include: whether the center of the surface overload deviates from the center of the tunnel, the size of the deviation distance, and the type and range of the load.

[0022] In S3, a one-dimensional site equivalent linear analysis is performed on the soil. A numerical model of the soil layer is established through software. The selected seismic wave is input to calculate the shear modulus of the soil layer, and then the elastic modulus E of the soil is obtained through formula 1. The characteristic period of the soil layer is determined, and the Rayleigh damping parameter of the soil layer is further calculated.

[0023]

[0024] Where G is the shear modulus and μ is the Poisson's ratio of the soil layer.

[0025] In S5, the tunnel diameter deformation rate is calculated as shown in Formula 2:

[0026]

[0027] The tunnel diameter before the earthquake is D, D1, and the tunnel diameter after being affected by surface overload and earthquake is D2, and ΔD is the diameter change.

[0028] In S6, the logarithmic standard deviation β D Calculated by formula 4:

[0029]

[0030] Where n is the number of numerical model calculation results.

[0031] In S7, the total logarithmic standard deviation β tot From formula 6, we can get:

[0032]

[0033] where β ds , β C , β D They represent the uncertainty in the definition of the damage state, the uncertainty in the tunnel seismic response and bearing capacity, and the uncertainty in the ground motion.

[0034] The beneficial effects of the present invention are:

[0035] Previous tunnel seismic vulnerability analyses considered the effects of the tunnel's depth, diameter, material properties, and soil characteristics, but often failed to consider the impact of external factors such as surface overload on the tunnel's seismic performance. Therefore, to quantitatively analyze the impact of surface overload on tunnel seismic performance, it is crucial to adopt a tunnel seismic vulnerability analysis method that considers the influence of surface overload. This method fully considers the impact of changes in the location, size, and scope of surface overload on the tunnel's seismic performance. By establishing a two-dimensional finite element model and conducting extensive numerical simulations, seismic vulnerability curves were plotted under different surface overload conditions, quantitatively analyzing the tunnel's seismic vulnerability. This method has considerable reference value for seismic risk assessment of tunnel structures under the influence of surface overload. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart of the tunnel seismic vulnerability analysis method considering the influence of surface overload in the present invention.

[0037] Figure 2 Schematic diagram of the tunnel location, dimensions and load location for the implementation case.

[0038] Figure 3 Schematic diagram of the seismic probabilistic demand model under the influence of surface overload for the implementation case.

[0039] Figure 4 The seismic vulnerability curve of the tunnel under the influence of surface overload for the implementation case. DETAILED DESCRIPTION

[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0041] like Figure 1 A shield tunnel seismic vulnerability analysis method considering the influence of surface overload is shown, comprising the following steps:

[0042] S1. Determine the mechanical properties of tunnel materials and the physical and mechanical parameters of soil layers.

[0043] The tunnel in this case is buried at a depth of 10m, with a cross-sectional diameter of 6.2m and a reinforced concrete lining thickness of 0.35m. The tunnel structure is located as follows: Figure 2 The material parameters are shown in Table 1:

[0044] Table 1 Material parameters of the tunnel

[0045]

[0046] S2. Investigate surface overload cases and determine appropriate surface overload conditions.

[0047] Research into cases of tunnels affected by surface overloads in the region determined the actual overload location, distance from the tunnel, size, extent, and whether the load was uniformly distributed, providing a reference for subsequent numerical simulations. The selected overload range for this case study was 30 meters, located directly above the tunnel, and the overload conditions were 0 kPa, 25 kPa, 50 kPa, 75 kPa, and 100 kPa.

[0048] S3. Select appropriate seismic waves and perform one-dimensional linear analysis on the soil to supplement the characteristic parameters of the soil.

[0049] Consult the seismic design code for the area to be analyzed and select a dozen or so appropriate seismic waves that are close to the influence coefficient curve of the seismic design code for numerical simulation. Use one-dimensional linear analysis software to perform a one-dimensional site equivalent linear analysis on the soil to obtain the equivalent shear modulus of each soil layer, and then use formula 1 to obtain the elastic modulus E of each soil layer:

[0050]

[0051] Where G is the shear modulus and μ is the Poisson's ratio of the soil layer. After obtaining the elastic modulus, the characteristic period of the soil layer must be determined, and then the Rayleigh damping parameter of the soil layer must be further calculated.

[0052] S4. Establish a finite element model of the soil-tunnel system under the influence of surface overload and perform a large number of calculations.

[0053] Based on the tunnel dimensions and materials used in this case study, a soil-tunnel dynamic finite element numerical model was constructed. A surface surcharge was applied to the soil surface of the model, and the seismic motion selected in step S3 was applied to the bottom of the model. The input seismic motion was amplitude modulated to ensure that earthquakes of various intensities were represented. After the model was established, extensive numerical calculations were performed to determine the dynamic response of the soil-tunnel system, most importantly, the rate of change of the tunnel diameter.

[0054] S5. Determine the earthquake intensity index (IM), tunnel damage index (DM) and damage state (DS).

[0055] In this case, the seismic intensity index (IM) is the maximum peak acceleration of the input seismic wave, and the tunnel damage index (DM) is the diameter deformation rate of the tunnel. The damage state (DS) and the corresponding damage index range are shown in Table 2.

[0056] Table 2 Tunnel damage indicators

[0057]

[0058] The calculation of tunnel diameter deformation rate is shown in Formula 2:

[0059]

[0060] The tunnel diameter before the earthquake is D, D1, and the tunnel diameter after being affected by surface overload and earthquake is D2, and ΔD is the diameter change.

[0061] S6. Establish a probability demand model for seismic resistance of tunnels under different surface overloads and use it to obtain the key parameters of the fragility curve.

[0062] Collect and count the calculation results of the finite element model in step S4, and draw a fitting straight line graph with lnIM as the independent variable and lnDM as the dependent variable (such as Figure 3 ), and thus the seismic probability demand model is obtained as shown in Formula 3:

[0063] lnDM=alnIM+b, formula three

[0064] Where a and b are linear regression parameters. After drawing the probability demand model, the key parameters for drawing the fragility curve are calculated: the IM value corresponding to each damage state (such as Figure 3 As shown, that is, the horizontal coordinate value corresponding to the intersection of the fitting straight line and the damage index threshold) and the logarithmic standard deviation β D , the logarithmic standard deviation is calculated by formula 4.

[0065]

[0066] Where n is the number of numerical model calculation results.

[0067] S7. Establish the seismic vulnerability curve of the tunnel structure under the influence of surface overload based on key parameters.

[0068] The tunnel vulnerability curve under different surface overloads is established by using the two key parameters in the previous step, such as Figure 4 , the vulnerability curve is shown in Formula 5.

[0069]

[0070] Among them, P f When the earthquake is of a certain intensity IM, it exceeds a certain damage state d si The probability of φ represents the standard normal density cumulative probability function; S mi β is the earthquake intensity index threshold corresponding to each damage state obtained in step S6; tot is the total logarithmic standard deviation, which shows the variability of the curve and is obtained by Equation 6.

[0071]

[0072] where β ds , β C , β D They represent the uncertainty of the damage state definition, the uncertainty of the tunnel seismic response and bearing capacity, and the uncertainty of the ground motion. ds and β C Value:

[0073] β ds =0.4, β C =0.3. β D The value of is obtained by step S6.

[0074] pass Figure 4This method can be used to analyze the seismic vulnerability of tunnels under the influence of surface overload. The results show that in the region where the case study was conducted, when the tunnel cover thickness is low, the seismic performance of the tunnel decreases rapidly as the surface overload increases. When the seismic intensity index is approximately 0.2g, the probability of minor damage increases by approximately 3.5 times, the probability of moderate damage increases by nearly 6 times, and the probability of severe damage increases by nearly 9 times as the surface overload increases from 0 kPa to 100 kPa. This case study demonstrates that the tunnel vulnerability curve constructed using this method can quantify the strength and degree of seismic performance of a tunnel under different surface overloads, allowing for a reasonable assessment of the tunnel's seismic risk. This method is particularly suitable for earthquake-prone areas and for construction projects above existing tunnels that result in surface overloads such as soil piling. It provides important guidance and practical value for seismic vulnerability analysis, seismic design, and construction of urban tunnels.

[0075] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive.

Claims

1. A shield tunnel seismic vulnerability analysis method considering the influence of surface overload, characterized by: The following steps are involved: S1. Determine the mechanical properties of tunnel materials and the physical and mechanical parameters of soil layers; S2. Investigate cases where tunnels are affected by surface overloads to determine the appropriate location, size, and extent of the surface overloads; S3, selecting a suitable seismic wave and performing a one-dimensional field equivalent linear analysis on the soil conditions obtained in step S1 to obtain the elastic modulus and Rayleigh damping parameter of the soil; S4. Based on the physical and mechanical parameters of the tunnel and soil layer determined in steps S1, S2, and S3, as well as the seismic wave and surface overload conditions, a soil-tunnel dynamic finite element numerical model considering the surface overload is established. Different combinations of surface overload and seismic intensity are designed, and the dynamic response of the soil-tunnel system is obtained through a large number of numerical calculations. S5. Select the maximum peak acceleration of the input seismic wave as the earthquake intensity index IM; select the diameter deformation rate of the tunnel as the damage index DM; determine the damage state of the tunnel and the damage index threshold corresponding to each damage state; S6. Based on the earthquake intensity index IM and the damage index DM selected in step S5, a tunnel seismic resistance probability demand model under different surface overloads is established, as shown in Formula 3: lnDM=alnIM+b, formula three Where a and b are obtained through regression analysis; After obtaining the probabilistic demand model, the key parameters for drawing the fragility curve are calculated: the median and logarithmic standard deviation β of the IM value corresponding to each damage state D ; S7. Based on the key parameters, establish the seismic vulnerability curve of the tunnel structure under the influence of surface overload, as shown in Formula 5: Among them, P f When the earthquake is of a certain intensity IM, it exceeds a certain damage state d si The probability of φ represents the standard normal density cumulative probability function; S mi β is the earthquake intensity index threshold corresponding to each damage state obtained in step S6; tot is the total logarithmic standard deviation.

2. The shield tunnel seismic vulnerability analysis method considering the influence of surface overload according to claim 1 is characterized in that: In S1, the mechanical properties of tunnel materials include tunnel depth, tunnel diameter, lining thickness, and material parameters of concrete and steel bars; the physical and mechanical parameters of the soil layer include soil thickness, soil density, cohesion, internal friction angle, Poisson's ratio, and shear wave velocity.

3. The shield tunnel seismic vulnerability analysis method considering the influence of surface overload according to claim 1 is characterized in that: In S2, factors to be considered in determining the location of the surface overload include: whether the center of the surface overload deviates from the center of the tunnel, the size of the deviation distance, and the type and range of the load.

4. The shield tunnel seismic vulnerability analysis method considering the influence of surface overload according to claim 1 is characterized in that: In S3, a one-dimensional site equivalent linear analysis is performed on the soil. A numerical model of the soil layer is established through software. The selected seismic wave is input to calculate the shear modulus of the soil layer, and then the elastic modulus E of the soil is obtained through formula 1. The characteristic period of the soil layer is determined, and the Rayleigh damping parameter of the soil layer is further calculated. Where G is the shear modulus and μ is the Poisson's ratio of the soil layer.

5. The shield tunnel seismic vulnerability analysis method considering the influence of surface overload according to claim 1 is characterized in that: In S5, the tunnel diameter deformation rate is calculated as shown in Formula 2: The tunnel diameter before the earthquake is D, D1, and the tunnel diameter after being affected by surface overload and earthquake is D2, and ΔD is the diameter change.

6. The shield tunnel seismic vulnerability analysis method considering the influence of surface overload according to claim 1 is characterized in that: In S6, the logarithmic standard deviation β D Calculated by formula 4: Where n is the number of numerical model calculation results.

7. The shield tunnel seismic vulnerability analysis method considering the influence of surface overload according to claim 1 is characterized in that: In S7, the total logarithmic standard deviation β tot From formula 6, we can get: where β ds , β C , β D They represent the uncertainty in the definition of the damage state, the uncertainty in the tunnel seismic response and bearing capacity, and the uncertainty in the ground motion.

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