Tunnel earthquake vulnerability analysis method based on fuzzy comprehensive evaluation method

Abstract

The invention relates to a tunnel earthquake vulnerability analysis method based on a fuzzy comprehensive evaluation method, and the method comprises the steps: selecting an optimal earthquake intensity index through the fuzzy comprehensive evaluation method, and building a tunnel structure earthquake vulnerability curve through the selected earthquake intensity index. According to the method, the influence of different tunnel burial depths can be considered in the selection process of the seismic oscillation intensity index IM; according to the method, index evaluation optimization can be performed in consideration of four aspects of correlation, effectiveness, practicability and benefit; according to the method, a fuzzy comprehensive evaluation method is adopted, and on the basis of a fuzzy relation comprehensive theory, qualitative factors are converted into quantitative factors for comprehensive evaluation; by using the method, the seismic oscillation intensity index IM can be effectively selected, the calculation result is relatively accurate, and the method has positive significance for accurately analyzing the seismic vulnerability of the underground structure.

Description

Technical Field

[0001] The present invention relates to the field of tunnel seismic performance analysis, and in particular to a method for analyzing tunnel seismic vulnerability based on the fuzzy comprehensive evaluation method. Background Art

[0002] In seismic vulnerability analysis, it is necessary to study the variation law between the structural damage degree and the ground motion intensity. There is a close relationship between the variation of ground motion intensity and structural damage. Therefore, choosing a suitable ground motion intensity index (IM) is crucial for accurately establishing the seismic vulnerability curve. A large number of physical quantities of earthquakes can be used as ground motion intensity indicators. Common ground motion intensity indicators include peak acceleration, peak velocity, peak displacement, and Arias intensity, etc. Among them, peak acceleration, peak velocity, and peak displacement, as the most commonly used indicators, have been widely used in structural analysis. These indicators can all reflect the main characteristics of ground motion. However, due to the randomness of ground motion itself, the results obtained by different IM indicators in structural analysis usually have significant differences. Therefore, how to select a suitable IM indicator to more comprehensively and accurately reflect the variation of ground motion intensity is an important issue in seismic vulnerability analysis. Reasonably selecting the IM indicator can not only reduce the uncertainty of ground motion, but also improve the accuracy and effectiveness of the vulnerability curve. In practical applications, selecting a suitable IM indicator can ensure that under the condition of large uncertainty in ground motion input, the vulnerability analysis of the structure can still provide effective prediction results, thereby providing a more reliable basis for seismic design and structural safety assessment.

[0003] However, there are mainly two current methods for optimizing the selection of seismic intensity indicators: the traditional method for optimizing the selection of seismic intensity indicators and the method for optimizing the selection of seismic intensity indicators based on the artificial neural network method. Among them, the traditional method for optimizing the selection of seismic intensity indicators respectively considers discriminant criteria such as effectiveness, sufficiency, sensitivity, efficiency, practicability, beneficiality, sufficiency, and risk assessability. The evaluation indicators of the traditional method for optimizing the selection of seismic intensity indicators are not unique, the optimization steps are complex, the efficiency is low, and it is a method that cannot quantitatively comprehensively evaluate the performance of each IM indicator. The method for optimizing the selection of seismic intensity indicators based on the artificial neural network method can use the artificial neural network method to construct a probabilistic seismic demand model with multiple IMs. On this basis, the IM is optimized by using the characteristics of the neural network weights. The optimization result is highly similar to the traditional index optimization result, and has the feasibility and universality of practical application, and the evaluation indicator is concise and unique. However, a large amount of data sets are required to train the neural network, the training process is complex, and the interpretability is poor.

[0004] Therefore, in the optimization of seismic intensity indices, it is necessary to adopt an evaluation method that can quantitatively comprehensively evaluate the performance of each IM index. By reasonably selecting the IM index, the impact of ground motion intensity on the structure can be more accurately reflected, thereby effectively improving the safety of structural seismic design and providing scientific data support for earthquake disaster prevention and emergency management. Summary of the Invention

[0005] The purpose of this application is to overcome the deficiency that the existing technology cannot quantitatively comprehensively evaluate each index, and provide a method for optimizing seismic intensity indices and analyzing tunnel seismic vulnerability based on the fuzzy comprehensive evaluation theory. This method comprehensively analyzes the influence of burial depth on the selection of IM indices, and uses the fuzzy comprehensive evaluation method to evaluate and optimize the indices from multiple angles, so as to select a suitable IM to comprehensively reflect the change of ground motion intensity and establish a seismic vulnerability curve.

[0006] The embodiment of this application provides a method for analyzing tunnel seismic vulnerability based on the fuzzy comprehensive evaluation method. The optimal seismic intensity index is selected through the fuzzy comprehensive rating method, and the seismic vulnerability curve of the tunnel structure is established through the selected seismic intensity index;

[0007] The method for selecting the optimal seismic intensity index includes the following steps:

[0008] S1. Establish a numerical analysis model of the soil-tunnel structure system through soil body, tunnel structure and input seismic wave parameters;

[0009] S2. Obtain the relative bending moment ratio through the numerical analysis model of the soil-tunnel structure system, and use the relative bending moment ratio as the tunnel structure failure index;

[0010] S3. Select different ground motion intensity indices and establish a fitting linear regression formula between the tunnel structure failure index and the ground motion intensity index;

[0011] S4. Obtain the regression correlation coefficient, ground motion uncertainty, regression parameters, and effectiveness;

[0012] S5. Establish a factor set U with the indices in S4, and establish an evaluation set V with the ground motion intensity indices in S3;

[0013] S6. Establish a fuzzy matrix R between the factor set and the evaluation set;

[0014]

[0015] Among them, R1 represents the membership degree vector of the evaluation factor u1 belonging to the evaluation set V,

[0016] R1 = {r 11 , r 12 , …, r 1m}, and similarly, the evaluation factors u2, …, un Membership vector;

[0017] S7. Assign a weight vector based on the preference of evaluation factors;

[0018] S8. Perform fuzzy operation based on the fuzzy matrix and the weight vector to obtain the comprehensive evaluation result B, and determine the ranking of the ground motion intensity indicators according to the principle of maximum membership degree. The ones with higher rankings are the most suitable ground motion intensity indicators;

[0019]

[0020] Wherein, W is the evaluation factor weight vector, ° is the fuzzy composition operator, and R is the fuzzy matrix.

[0021] In S1, the parameters of the soil body, tunnel structure and input seismic wave are obtained through one-dimensional site equivalent linear analysis to obtain the soil stiffness and damping parameters, and a numerical analysis model of the soil-tunnel structure system is established using the ABAQUS finite element platform.

[0022] In S2, the structural damage index standard is divided according to the relative bending moment ratio. Among them, the standard grading includes five states: no damage, slight damage, moderate damage, severe damage and collapse. The relative bending moment ratio less than 1.0 is the state of no damage, and greater than 3.5 is the state of collapse.

[0023] In S3, the ground motion intensity indicators include peak ground acceleration, peak ground velocity, peak ground displacement, peak structural acceleration, peak structural velocity, peak structural displacement, peak bedrock acceleration, peak bedrock velocity and peak bedrock displacement.

[0024] In S4, the correlation coefficient R 2 is obtained from the fitting regression curve formula;

[0025] The ground motion uncertainty β D is obtained through the following formula:

[0026]

[0027] Wherein, N is the number of calculated seismic waves; DM j is the structural seismic demand corresponding to the jth seismic wave; m D|IM is the structural seismic resistance corresponding to the ground motion intensity IM calculated from the regression curve;

[0028] The regression parameter a is judged by the following formula:

[0029] ln DM = aln IM + b

[0030] Wherein, a and b are coefficients obtained by fitting according to the calculation results; IM is the ground motion intensity indicator, and DM is the tunnel structure damage indicator;

[0031] The profitability ζ is obtained by the following formula:

[0032]

[0033] where β D is the ground motion uncertainty, and a is the regression parameter.

[0034] In S7, the regression correlation coefficient, ground motion uncertainty, regression parameter, and the weight vector selected for profitability are all the same.

[0035] Furthermore, when analyzing the seismic vulnerability of tunnels, establish the correlation between the tunnel structure damage index and the ground motion intensity index, and construct the tunnel structure probabilistic seismic demand model; based on the tunnel structure probabilistic seismic demand model, adopt the two-parameter lognormal model to establish the seismic vulnerability curves of shallow-buried, medium-buried, and deep-buried tunnel structures under different service times

[0036] The beneficial effects of the present invention are as follows: The method of the present invention uses the fuzzy comprehensive evaluation method to conduct index evaluation and optimization from multiple angles, and can select a suitable IM to comprehensively reflect the change of ground motion intensity and establish the seismic vulnerability curve. Compared with other analysis methods, it is specifically manifested as follows:

[0037] (1) The present invention can consider the influence of different tunnel burial depths during the selection process of the ground motion intensity index IM;

[0038] (2) The present invention can consider four aspects of correlation, effectiveness, practicability, and profitability for index evaluation and optimization;

[0039] (3) The present invention adopts the fuzzy comprehensive evaluation method, which is based on the fuzzy relation comprehensive theory, and transforms qualitative factors into quantitative factors for comprehensive evaluation;

[0040] (4) Using the present invention can effectively select the ground motion intensity index IM and the calculation results are relatively accurate, which has positive significance for accurately analyzing the seismic vulnerability of underground structures. Description of the Drawings

[0041] Figure 1 is the technical flow chart of the evaluation method of the present invention.

[0042] Figure 2 is the ABAQUS two-dimensional finite element model in step S1 of the method of the present invention.

[0043] Figure 3 is the fitting regression curve of the relative bending moment ratio of the shallow-buried tunnel structure and different ground motion intensity indexes in step S2 of the method of the present invention.

[0044] Figure 4 is the calculation result of the correlation of different IM indexes in step S4 of the method of the present invention.

[0045] Figure 5 This is the calculation result of the effectiveness of different IM indexes in step S5 of the method of the present invention.

[0046] Figure 6 This is the calculation result of the practicability of different IM indexes in step S6 of the method of the present invention.

[0047] Figure 7 This is the calculation result of the profitability of different IM indexes in step S7 of the method of the present invention.

[0048] Figure 8 This is the ranking of the IM indexes of tunnels with different burial depths based on the fuzzy comprehensive evaluation method in step S8 of the method of the present invention.

[0049] Figure 9 This is the seismic vulnerability curve of tunnel structures with different burial depths established in step S9 of the method of the present invention. Detailed implementation manners

[0050] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0051] In this embodiment, a typical circular tunnel is taken as an example, with a diameter D of 6.2 m, a segment thickness of 0.35 m, a concrete cover thickness of 5 cm, and the concrete material grade adopted is C50. In order to consider the influence of tunnels with different burial depths, three representative burial depths h are selected in this embodiment, which are 10 m, 20 m, and 30 m respectively, and the h / D values of the tunnel burial depth to diameter are 1.61, 3.22, and 4.84 respectively, representing the working conditions of typical shallow-buried tunnels, medium-buried tunnels, and deep-buried tunnels respectively. The cross-sectional reinforcement ratios are 0.46%, 0.72%, and 1.03% respectively, and the segment reinforcements of the lining are HRB400 steel bars with diameters of 16 mm, 20 mm, and 24 mm respectively. A typical geological profile in this area is selected for geotechnical seismic analysis related to soil layers.

[0052] As Figure 1 shown, it includes the following steps:

[0053] S1. Determine the parameters including soil body, tunnel structure, and input seismic wave, obtain the soil stiffness and damping parameters through one-dimensional site equivalent linear analysis, and establish a numerical analysis model of the soil-tunnel structure system using the ABAQUS finite element platform, as Figure 2 shown, and carry out a large number of nonlinear dynamic time history analyses.

[0054] S2. Select the relative bending moment ratio DI as the structural damage index (DM), and determine the division criteria for different damage states, as shown in Table 1.

[0055] Table 1 Standard of Tunnel Structure Damage Index

[0056]

[0057] S3. Select nine parameters, namely peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), peak structural acceleration (PSA), peak structural velocity (PSV), peak structural displacement (PSD), peak bedrock acceleration (PBA), peak bedrock velocity (PBV), and peak bedrock displacement (PBD), as the IM index. After taking the natural logarithm of the tunnel structure damage index DM and the nine ground motion intensity indices IM, perform linear regression, establish a relationship diagram between the structural damage index and the ground motion intensity index, and the fitting curve represents the evolution process of the damage index with the increase of seismic intensity. As Figure 3 shown, where the corresponding fitting regression formula has been given in the figure, and the hollow circles represent the data points of the numerical simulation calculation results.

[0058] S4. Obtain the regression correlation coefficient R 2 , ground motion uncertainty β D , regression parameter α, and effectiveness ζ according to the fitting curve in S3.

[0059] The correlation can be represented by the correlation coefficient R 2 in the index fitting regression formula. This index represents the fitting degree between the calculation result and the seismic demand. The larger its value, the better the correlation between the structural damage index DM and the ground motion intensity index IM. As Figure 4 shown.

[0060] The effectiveness refers to the discreteness of structural damage under a given ground motion intensity. As Figure 5 shown, the lower the discreteness of structural damage, the higher the effectiveness of this index. It can be quantitatively analyzed through the magnitude of the ground motion uncertainty β D . The calculation method of βD is shown in the following formula:

[0061]

[0062] where N is the number of calculated seismic waves; DM j is the structural seismic demand corresponding to the jth seismic wave; m D|IM is the structural seismic resistance corresponding to the ground motion intensity IM calculated from the regression curve.

[0063] The practicality refers to the relevant sensitivity between the ground motion intensity and structural damage. As Figure 6As shown, if the degree of association between the two is very low, it indicates that this indicator is not very practical, and it can be judged by the magnitude of the regression parameter a:

[0064] ln DM = aln IM + b

[0065] where a and b are coefficients obtained by fitting according to the calculation results. This formula reflects the relationship between the structural damage index and the ground motion intensity, and based on this, a structural probabilistic seismic demand model is established.

[0066] Benefit represents the uncertainty brought by the change of the IM index to the analysis. For example Figure 7 As shown, the benefit index ζ comprehensively considers the roles of effectiveness and practicality. The lower the ζ value, the smaller the uncertainty brought by the change of this IM index to the analysis, and the higher the benefit of the IM index. Its calculation formula is:

[0067]

[0068] where β D is the ground motion uncertainty and a is the regression parameter.

[0069] S5. Determine the factor set and evaluation set.

[0070] The factor set U includes all evaluation factors. To select the IM index with the optimal performance, the correlation, effectiveness, practicality, and benefit of the index are selected as evaluation factors. Then U = {R 2 , β D , a, ζ}.

[0071] The evaluation set V is the result of evaluating the advantages and disadvantages of the evaluation object and various evaluation factors. In the present invention, only the relative ranking between IM indexes needs to be calculated to select the most suitable IM index. Therefore, it is not necessary to determine the specific evaluation level, but the evaluation set is replaced by all IM indexes. Then V = {PGA, PGV, PGD, PSA, PSV, PSD, PBA, PBV, PBD}.

[0072] S6. Establish the fuzzy matrix R between the factor set U and the evaluation set V.

[0073] Based on the results of the correlation, effectiveness, practicality, and benefit of different IM indexes, calculate the membership degree vector R1 = {r 11 , r 12 , …, r 1m} of the evaluation factor u1 belonging to V. Similarly, the membership degree vectors of the evaluation factors u2, …, u n can be obtained, and the fuzzy matrix R between the factor set U and the evaluation set V is established as shown in the formula:

[0074]

[0075] Among them, r ij is the membership degree.

[0076] The fuzzy matrices R 浅埋 、R 中埋 、R 深埋 for shallow-buried tunnels, medium-buried tunnels, and deep-buried tunnels can be obtained respectively.

[0077]

[0078] S7. Determine the weight vector W of each evaluation factor.

[0079] The weight vector W gives the importance of each evaluation factor. Different weight values can be assigned to the parameters based on the preference for the evaluation factors. Its expression is:

[0080] W = {w1, w2, …, w n}

[0081] Among them, w i is the weight value of each evaluation factor.

[0082] Considering that the parameters of correlation, effectiveness, practicality, and benefit can all reflect different performances of the IM index, the optimal index assigns the same weight to correlation, effectiveness, practicality, and benefit to reflect the equal importance of the four parameters. The weight vector in this embodiment is: W = [0.25 0.25 0.25 0.25].

[0083] S8. Obtain the comprehensive evaluation result B through complex fuzzy operations on the fuzzy matrix R and the weight vector W, and select the most suitable IM index.

[0084]

[0085] Among them, W is the weight vector of the evaluation factor, ° is the fuzzy composition operator, and R is the fuzzy matrix.

[0086] Substitute the fuzzy matrices R 浅埋 、R 中埋 、R 深埋 into the above formula to obtain the comprehensive evaluation results B of tunnels with different burial depths. According to the principle of the maximum membership degree, the ranking of the IM indexes of tunnels with different burial depths can be determined. The IM index corresponding to b max in the comprehensive evaluation result B of the present invention is the optimal index, as shown in Figure 8 .

[0087] The analysis results show that for shallow - buried tunnels, the top 3 IM indices are PGA > PSA > PGV in sequence; for medium - buried tunnels, the top 3 IM indices are PGA > PGV > PSA in sequence; and for deep - buried tunnels, the top 3 IM indices are PGA > PGV > PSV in sequence. Under the three burial - depth conditions, PGA ranks the highest, and the top 3 indices are all acceleration - type and velocity - type indices, while the displacement - type indices rank among the last 3. Selecting reasonable IM indices plays an important role in establishing the structural seismic vulnerability curve. The above fuzzy comprehensive evaluation results indicate that acceleration - type indices represented by PGA are more suitable for seismic vulnerability analysis of tunnel structures, while displacement - type indices are not suitable for this analysis. Moreover, under the three tunnel burial - depth conditions, PGA is the optimal index among the 9 indices studied and analyzed, and this calculation result is consistent with the results of other similar index analysis studies.

[0088] S9. Establish the correlation between the damage index DM and the ground - motion intensity index IM, and construct the probabilistic seismic demand model of the tunnel structure; based on the probabilistic seismic demand model of the tunnel structure, adopt the two - parameter log - normal model to establish the seismic vulnerability curves of shallow - buried, medium - buried, and deep - buried tunnel structures under different service times, as Figure 9 shown.

[0089] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above - mentioned exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, from any point of view, the embodiments should be regarded as exemplary and non - restrictive.

Claims

1. A method for analyzing the seismic vulnerability of tunnels based on the fuzzy comprehensive evaluation method, characterized in that Select the optimal seismic intensity index by the fuzzy comprehensive evaluation method, and establish the seismic vulnerability curve of the tunnel structure based on the selected seismic intensity index; The method for selecting the optimal seismic intensity index includes the following steps: S1. Establish a numerical analysis model of the soil-tunnel structure system through soil body, tunnel structure and input seismic wave parameters; S2. Obtain the relative bending moment ratio through the numerical analysis model of the soil-tunnel structure system, and use the relative bending moment ratio as the tunnel structure failure index; S3. Select different seismic ground motion intensity indexes, and establish a fitting linear regression formula between the tunnel structure failure index and the seismic ground motion intensity index; S4. Obtain the regression correlation coefficient, seismic ground motion uncertainty, regression parameters, and profitability; S5. Establish a factor set U with the indexes in S4, and establish an evaluation set V with the seismic ground motion intensity indexes in S3; S6. Establish a fuzzy matrix R between the factor set and the evaluation set; Among them, R1 represents the membership degree vector of the evaluation factor u1 belonging to the evaluation set V, R1 = {r 11 , r 12 , …, r 1m}, Similarly, the membership degree vectors of evaluation factors u2, …, u n can be obtained; S7. Assign a weight vector based on the preference of the evaluation factors; S8. Perform fuzzy operation based on the fuzzy matrix and the weight vector to obtain the comprehensive evaluation result B, and determine the ranking of the seismic ground motion intensity indexes according to the principle of the maximum membership degree. The ones with higher rankings are the most suitable seismic ground motion intensity indexes; Among them, W is the evaluation factor weight vector, ° is the fuzzy synthesis operator, and R is the fuzzy matrix.

2. The tunnel seismic vulnerability analysis method based on the fuzzy comprehensive evaluation method according to claim 1, characterized in that In S1, the parameters of the soil body, tunnel structure and input seismic wave obtain the soil stiffness and damping parameters through one-dimensional site equivalent linear analysis, and use the ABAQUS finite element platform to establish a numerical analysis model of the soil-tunnel structure system.

3. The tunnel seismic vulnerability analysis method based on the fuzzy comprehensive evaluation method according to claim 1, characterized in that In S2, divide the structure failure index standard according to the relative bending moment ratio. Among them, the standard grading includes five states: no damage, slight damage, medium damage, severe damage and collapse. The relative bending moment ratio less than 1.0 is the no-damage state, and greater than 3.5 is the collapse state.

4. The method for analyzing the seismic vulnerability of tunnels based on the fuzzy comprehensive evaluation method according to claim 1, wherein In S3, the seismic ground motion intensity indexes include peak ground acceleration, peak ground velocity, peak ground displacement, peak structural acceleration, peak structural velocity, peak structural displacement, peak bedrock acceleration, peak bedrock velocity and peak bedrock displacement.

5. The tunnel seismic vulnerability analysis method based on the fuzzy comprehensive evaluation method according to claim 1, wherein In S4, the correlation coefficient R 2 is obtained from the fitted regression curve formula; Seismic motion uncertainty β D Obtained through the following formula: Where N is the number of calculated seismic waves; DM j is the structural seismic demand corresponding to the j-th seismic wave; m D|IM is the structural seismic capacity corresponding to the ground motion intensity IM calculated from the regression curve; The regression parameter a is judged by the following formula: ln DM = alnIM + b Among them, a and b are coefficients obtained by fitting according to the calculation results; IM is the seismic ground motion intensity index, and DM is the tunnel structure failure index; The profitability ζ is obtained by the following formula: Among them, β D is the uncertainty of ground motion, and a is the regression parameter.

6. The tunnel seismic vulnerability analysis method based on the fuzzy comprehensive evaluation method according to claim 1, wherein In S7, the weight vectors selected for the regression correlation coefficient, seismic ground motion uncertainty, regression parameters and profitability are the same.

7. The tunnel seismic vulnerability analysis method based on the fuzzy comprehensive evaluation method according to claim 1, characterized in that When analyzing the seismic vulnerability of the tunnel, establish the correlation between the tunnel structure failure index and the seismic ground motion intensity index, and construct the probabilistic seismic demand model of the tunnel structure; based on the probabilistic seismic demand model of the tunnel structure, use the two-parameter lognormal model to establish the seismic vulnerability curves of shallow-buried, medium-buried and deep-buried tunnel structures under different service times.

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