Calculation method of annual average loss of external reinforcement structure based on interface shear stress

Abstract

The present invention discloses a method for calculating the annual average loss of the reinforcement of an external attachment structure based on interface shear stress, including establishing a deterministic model for the reinforcement of the external attachment structure, and randomly sampling to generate structural samples and seismic samples; establishing a probabilistic hazard model based on the generated seismic motion; generating a probabilistic vulnerability model based on interface shear stress; establishing a probabilistic total loss expectation model under the seismic motion intensity level; and obtaining the annual average probabilistic seismic loss of the overall reinforcement of the external attachment structure based on interface shear stress based on the probabilistic total loss expectation under the seismic motion intensity level. The present invention proposes an earthquake loss uncertainty that takes into account the randomness and practicality of the destruction, transportation, residual, and maintenance limit states and actual engineering, realizes the classified calculation of earthquake losses, and the calculation process is more efficient, which provides a basis and reference for the loss assessment and promotion and application of the overall reinforcement technology of the external attachment structure in earthquake-prone areas.

Description

Technical Field

[0001] The invention relates to the field of seismic reinforcement and loss assessment of civil engineering structures, and in particular to a method for calculating the annual average loss of external attachment structure reinforcement based on interface shear stress. Background Art

[0002] Probabilistic earthquake loss analysis belongs to the category of probabilistic earthquake risk analysis. It reflects the uncertainty of social and economic losses caused by earthquake disasters and the conditional probability of a structure experiencing or exceeding different degrees of loss under a given structural damage level. Probabilistic earthquake loss analysis is the basis of earthquake risk decision-making and safety management, and is also the ultimate goal of applying probability theory to system decision-making evaluation.

[0003] The overall reinforcement of the external substructure, that is, using the coordinated work of the external overall substructure and the original structure to change the structural system of the original structure, transfer the damage to the external substructure, thereby changing the stress state and deformation mode of the original structure, enhancing the overall seismic resistance of the structure, and thus alleviating the overall seismic demand, is a reinforcement method for the structural system. At present, the calculation of the overall reinforcement loss of the external substructure is often based on a deterministic calculation method, lacking a corresponding probabilistic earthquake loss calculation method. At the same time, the existing calculation method does not consider the influence of limit states such as destruction, transportation, residue, and maintenance. In addition, the existing calculation of the overall reinforcement loss of the external substructure is often based on the overall displacement angle index of the structure, and does not evaluate the loss from the perspective of the shear stress at the interface between the new and old structures, lacking applicable characteristic evaluation indicators. Summary of the invention

[0004] Purpose of the invention: The present invention aims to provide a probability and structural performance based method for calculating the average annual loss of external attachment structure reinforcement based on interface shear stress, which takes into account the uncertainty of destruction, handling, residual, maintenance limit states and earthquake losses.

[0005] Technical solution: The method for calculating the average annual loss of external abutment structure reinforcement based on interface shear stress described in the present invention comprises the following steps:

[0006] (1) Establish a deterministic model for external reinforcement and generate structural samples and ground motion samples by random sampling;

[0007] (2) Establish a probabilistic hazard model based on the generated ground motions;

[0008] (3) Generate a probabilistic vulnerability model based on interface shear stress;

[0009] (4) Establish a probabilistic total loss expectation model under the earthquake intensity level;

[0010] (5) Based on the expected probabilistic total loss under the earthquake intensity level, the annual average probabilistic seismic loss of the overall reinforcement of the external attachment structure based on the interface shear stress is obtained.

[0011] Preferably, the probability risk model H in step (2) IM (x) is

[0012] H IM (x) = P[IM≥x] = k0·x -k

[0013]

[0014]

[0015] Where k0 and k represent shape parameters, IM represents ground motion intensity parameter, and IM DBE and IM MCE They represent the seismic intensity parameters corresponding to the design earthquake and the rare earthquake respectively. The 50-year exceedance probability of the design earthquake DBE is 10%, and the return period is 475 years, that is, the annual exceedance probability p DBE The 50-year exceedance probability of a rare earthquake MCE is 2%, and the return period is 2475 years, that is, the annual exceedance probability p MCE It is 1 / 2475.

[0016] Preferably, the step (3) comprises:

[0017] (3.1) Determine the amplitude modulation interval m of the earthquake intensity parameter and set the interface shear stress of the external attachment structure as the engineering requirement parameter;

[0018] (3.2) Random seismic sample amplitude modulation and circulation, carry out nonlinear dynamic time history response analysis, and obtain the strength parameter IM and interface shear stress under different seismic motion levels;

[0019] (3.3) The interface shear stresses obtained from all earthquake motions under all earthquake motion levels are summarized, and linear regression is performed based on the logarithmic coordinate system and the least squares method to obtain the regression coefficients β1 and β2, and the median value S is calculated. d|IM and log-standard β d |IM is:

[0020] ln d|nM =β0+β1.ln IM

[0021]

[0022] Where n is the number of ground motions under all ground motion levels, D x The data of interface shear stress obtained from the xth analysis result;

[0023] (3.4) Determine the limit state and limit value d of the external reinforcement structure based on interface shear stress; and generate a probabilistic fragility model based on interface shear stress.

[0024] Preferably, the step (3.2) includes setting the initial seismic level x=1, determining the seismic intensity parameter IM_ x , at the x-th level, randomly match n1 and n2, carry out nonlinear dynamic time-history response analysis, and obtain the required interface shear stress τ at the x-th level; judge the size of x and the amplitude modulation interval m, if x is less than m, then x = x + 1, and repeat the above steps; if x is greater than or equal to m, go to the next step (3.3).

[0025] Preferably, the probabilistic vulnerability model P(edp|im) is:

[0026]

[0027] Where Φ is the standard normal distribution function.

[0028] Preferably, the limit states of the external substructure reinforcement include destruction, transportation, residual and maintenance states.

[0029] Preferably, after determining the limit state and limit value d of the external attachment structure reinforcement based on the interface shear stress, it also includes subtracting the generated probabilistic seismic vulnerability models of adjacent limit states from each other to obtain the probabilistic seismic damage model P (DS = ds i |IM):

[0030] P(DS=ds i |IM)=P i (edp|im)-P i+1 (edp|im)

[0031] Among them, P i (edp|im) represents the probabilistic vulnerability model corresponding to the ith limit state, P i+1 (edp|im) represents the probabilistic vulnerability model corresponding to the i+1th limit state.

[0032] Preferably, the probability total loss expectation model in step (4) includes the probability loss expectation values ​​under different limit states, that is, the destruction probability loss expectation value L C , expected value of transport probability loss L T , residual probability loss expected value L NC∩D And the expected value of maintenance probability loss L NC∩R .

[0033] Preferably, at the ground shaking intensity level IM_ x Under this condition, the expected value of the damage probability loss is LC The calculation formula is:

[0034] L c =E[L|C]·P(C P |IM)·P(C T |IM)·α1

[0035] Among them, E[L|C] represents the theoretical expectation of damage loss, E[L|C] is the replacement ratio coefficient corresponding to the damage state, P(C p |IM) represents the probability that the external reinforcement system is in a damaged state under IM, P(C T |IM) represents the probability that the external attachment structure reinforcement system is in the state of transportation damage under IM, and α1 is the damage loss coefficient;

[0036] Expected value of transport probability loss L T The calculation formula is:

[0037] L T =E[L|T]·P(C P |IM)·[1-P(C T |IM)]·α2

[0038] Among them, E[L|T] represents the theoretical expectation of handling loss, E[L|T] is the replacement ratio coefficient corresponding to the handling damage state, and α2 is the handling loss coefficient;

[0039] The expected value of residual probability loss L NC∩D The calculation formula is:

[0040] L NC∩D＝ E[L|NC∩D]·P(C D |NC,IM)·{1-P(C P |IM)}·α3

[0041] Among them, E[L|NC∩D] represents the theoretical expectation of residual loss, E[L|NC∩D] is taken as the replacement ratio coefficient corresponding to the residual damage state of the external attachment structure reinforcement system under non-destructive conditions, P(C D |NC,IM) represents the probability that the external attachment structure reinforcement system is in a residual damage state under IM conditions and non-destructive conditions, and α3 is the residual loss coefficient;

[0042] Maintenance probability loss expected value L NC∩R The calculation formula is:

[0043] L NC∩R =E[L|NC∩R,IM]·{1-P(C D |NC,IM)}·{1-P(C P |IM)}·α4

[0044] Among them, E[L|NC∩R,IM] represents the theoretical expectation of maintenance loss, E[L|NC∩R,IM] is taken as the replacement ratio coefficient corresponding to the maintenance damage state of the external attached structure reinforcement system when the local vibration intensity is IM and under non-destructive conditions, and α4 is the maintenance loss coefficient.

[0045] Preferably, the calculation formula for the annual average probabilistic seismic loss E[L] of the overall reinforcement of the external attachment structure based on the interface shear stress is:

[0046]

[0047] Among them, E[L|IM] is the expected value of the total probabilistic loss.

[0048] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: 1. It takes into account the influence of the limit states of destruction, transportation, residue and maintenance, as well as the transmission process from probabilistic hazard, probabilistic vulnerability to probabilistic risk, realizes the classification calculation of earthquake losses, and can provide more detailed proportion data for different categories of earthquake losses. Compared with the traditional earthquake loss calculation method, the calculation process of the method proposed in the present invention is more efficient, and provides a basis and reference for the loss assessment and promotion and application of the overall reinforcement technology of the external attached structure in earthquake-prone areas; 2. The loss is assessed from the perspective of the shear stress at the interface between the new and old structures. Compared with the traditional loss assessment based on the overall displacement angle of the structure, this assessment method is more characteristic and applicable; 3. It is an earthquake loss uncertainty calculation method based on probability and structural performance. Compared with the traditional deterministic loss assessment, this assessment method fully considers the randomness and practicality of actual engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a flow chart of the method of the present invention;

[0050] Figure 2 It is a schematic diagram of the overall reinforcement scheme of the external attachment structure in an embodiment of the present invention;

[0051] Figure 3 It is a seismic hazard curve diagram of the overall reinforcement of the external attachment structure based on the interface shear stress in the embodiment of the present invention;

[0052] Figure 4 It is a seismic vulnerability curve diagram of the overall reinforcement of the external attachment structure based on the interface shear stress in the embodiment of the present invention;

[0053] Figure 5 It is a probability curve diagram of different limit damage states of the overall reinforcement of the external attachment structure based on the interface shear stress in the embodiment of the present invention;

[0054] Figure 6Graphs of expected probability loss values ​​of the external attachment structure under different limit states based on interface shear stress in the embodiment of the present invention; wherein (a) is a graph of expected probability loss value of destruction; (b) is a graph of expected probability loss value of transportation; (c) is a graph of expected probability loss value of residual; (d) is a graph of expected probability loss value of maintenance;

[0055] Figure 7 It is a graph showing the annual average probability seismic loss of the external attachment structure based on the interface shear stress in an embodiment of the present invention;

[0056] Figure 8 It is a comparison chart of the calculation results of the seismic loss calculation method in the embodiment of the present invention, the classical Monte Carlo benchmark method and the traditional linear regression method. DETAILED DESCRIPTION

[0057] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0058] like Figure 1 As shown, the method for calculating the average annual loss of external attachment structure reinforcement based on interface shear stress of the present invention comprises the following steps:

[0059] (1) Establish a deterministic model for the reinforcement of external auxiliary structures and randomly generate structural samples n1 and seismic motion samples n2.

[0060] (2) Establish a probabilistic hazard model based on the generated ground motions;

[0061] The probabilistic risk model is

[0062] H IM (x) = P[IM≥x] = k0·x -k

[0063]

[0064]

[0065] Where k0 and k represent shape parameters, IM DBE and IM MCE They represent the seismic intensity parameters corresponding to the design earthquake and the rare earthquake respectively. The 50-year exceedance probability corresponding to the design earthquake (DBE) is 10%, and the return period is 475 years, that is, the annual exceedance probability p DBE The 50-year exceedance probability of a rare earthquake (MCE) is 2%, and the return period is 2475 years, that is, the annual exceedance probability p MCE It is 1 / 2475.

[0066] (3) Generate a probabilistic seismic vulnerability model based on interface shear stress. Specifically include:

[0067] (3.1) Determine the random earthquake intensity parameter (IM) and the amplitude modulation interval (m) of the earthquake intensity parameter, and set the interface shear stress of the external attachment structure as the engineering requirement parameter;

[0068] (3.2) Random seismic sample amplitude modulation and circulation, carry out nonlinear dynamic time history response analysis, and obtain the intensity parameter IM and interface shear stress under different seismic levels. Specifically, it includes setting the initial seismic level x = 1 and determining the seismic intensity parameter IM_ x , at the xth level, randomly match n1 and n2, carry out nonlinear dynamic time-history response analysis, and obtain the required interface shear stress τ at the xth level; judge the size of x and the amplitude modulation interval m, if x is less than m, then x = x + 1, repeat the above steps; if x is greater than or equal to m, proceed to the next step;

[0069] (3.3) The interface shear stresses obtained from all earthquake motions under all earthquake motion levels are summarized, and linear regression is performed based on the logarithmic coordinate system and the least squares method to obtain the regression coefficients β1 and β2, and the median value S is calculated. d|IM and log-standard β d |IM is:

[0070] oeLh dIM =β0+β1·lnIM

[0071]

[0072] Where n is the number of ground motions under all ground motion levels, D x The data of interface shear stress obtained from the xth analysis result;

[0073] (3.4) Determine the limit state and limit value d of the external attachment structure reinforcement based on the interface shear stress;

[0074] (3.5) Generate the probabilistic vulnerability model P(edp|im) based on interface shear stress, and the calculation formula is:

[0075]

[0076] Where Φ is the standard normal distribution function.

[0077] (4) Subtract the generated probabilistic seismic vulnerability models of adjacent limit states from each other to obtain the probabilistic seismic damage model.

[0078] Probabilistic damage model P(DS=ds i |IM) is:

[0079] P(DS=ds i |IM)=P i(edp|im)-P i+1 (edp|im)

[0080] Among them, P i (edp|im) represents the probabilistic vulnerability model corresponding to the ith limit state, P i+1 (edp|im) represents the probabilistic vulnerability model corresponding to the i+1th limit state.

[0081] (5) Calculate the expected probability total loss model under the earthquake intensity level. The expected probability total loss model E[L|IM] includes the expected value of the destruction probability loss L C , expected value of transport probability loss L T , the expected value of residual probability loss L NC∩D And the expected value of maintenance probability loss L NC∩R Four parts, namely E[L|IM]=L C +L T +L NC∩D +L NC∩R .

[0082] Ground Motion Intensity Level IM_ x Under this condition, the expected value of the damage probability loss is L C The calculation formula is:

[0083] L C =E[L|C]·P(C P |IM)·P(C T |IM)·αl

[0084] Among them, E[L|C] represents the theoretical expectation of damage loss, E[L|C] is the replacement ratio coefficient corresponding to the damage state, P(C p |IM) represents the probability that the external reinforcement system is in a damaged state under IM, P(C T |IM) represents the probability that the external attachment structure reinforcement system is in the state of transportation damage under IM, and α1 is the damage loss coefficient.

[0085] Ground Motion Intensity Level IM_ x Under this condition, the expected value of the transport probability loss is L T The calculation formula is:

[0086] L T =E[L|T]·P(C P |IM)·[1-P(C T |IM)]·α2

[0087] Among them, E[L|T] represents the theoretical expectation of transportation loss, E[L|T] is the replacement ratio coefficient corresponding to the transportation damage state, and α2 is the transportation loss coefficient.

[0088] Ground Motion Intensity Level IM_ x Under this condition, the expected value of residual probability loss is L NC∩D The calculation formula is:

[0089] L NC∩D =E[L|NC∩D]·P(C D |NC,IM)·{1-P(C P |IM)}·α3

[0090] Among them, E[L|NC∩D] represents the theoretical expectation of residual loss, E[L|NC∩D] is taken as the replacement ratio coefficient corresponding to the residual damage state of the external attachment structure reinforcement system under non-destructive conditions, P(C D |NC,IM) represents the probability that the external attachment structure reinforcement system is in a residual damage state under IM conditions and non-destructive conditions, and α3 is the residual loss coefficient.

[0091] Ground Motion Intensity Level IM_ x Under this condition, the expected value of maintenance probability loss is L NC∩R The calculation formula is:

[0092] L NC∩D =E[L|NC∩R,IM]·{1-P(C D |NC,IM)}·{1-P(C D |NC,IM)}·{1-{(C P |IM)}·α4

[0093] Among them, E[L|NC∩R,IM] represents the theoretical expectation of maintenance loss, E[L|NC∩R,IM] is the replacement ratio coefficient corresponding to the maintenance damage state of the external substructure reinforcement system when the local vibration intensity is IM and under non-destructive conditions, and α4 is the maintenance loss coefficient.

[0094] (6) The seismic intensity level IM_ x E[L|IM] and H under IM (x) By performing convolution integration in all strength parameter IM intervals, the annual average probability seismic loss E[L] of the overall reinforcement of the external attachment structure based on the interface shear stress can be obtained. The calculation formula is:

[0095]

[0096] In order to further illustrate the method of the present invention, a specific reinforcement and renovation project is analyzed. The prototype structure is selected from a five-story office building with a plane size of 27m×15.3m. The structure is located in Class II site soil, the regional fortification intensity is 8 degrees, and the corresponding moderate earthquake peak acceleration is 0.2g. It is planned to use an external frame-support substructure to reinforce the first, third, and fifth spans of the selected frame along the full height of the structure, such as Figure 2 As shown in the figure, a comparative evaluation of the seismic performance is then carried out. In the analysis, the strength index IM is the first cycle spectral acceleration Sa(T1), and the engineering demand parameter EDP is the interface shear stress (τ). Figure 3 The probabilistic seismic hazard curve H of the entire system after reinforcement calculated by the method of the present invention is shown. IM (x), Figure 4 The seismic fragility curve of the reinforced overall system calculated by the method of the present invention, namely P(edp|im), is shown. Figure 5 The probabilistic seismic damage curves of the reinforced overall system under different limit states (destruction, transportation, residual, and maintenance states) calculated using the method of the present invention, namely, P(DS=dsi|IM), are shown. Figure 6 The expected values ​​of probabilistic losses of the overall system after reinforcement under different limit states (destruction, transportation, residual, and maintenance states) calculated by the method of the present invention are shown, where α1, α2, α3, and α4 are taken as 0.84, 0.5, 0.16, and 0.1, respectively, and 100 calculations are performed under each Sa(T1).

[0097] In order to compare and verify the effectiveness and accuracy of the earthquake annual average loss calculation method proposed in the present invention, this embodiment takes the destruction limit state as an example, selects the calculation results of the classic Monte Carlo benchmark method as the benchmark value (10,000 calculations at each Sa(T1)), and selects the traditional linear regression method as a comparison (100 calculations at each Sa(T1)). Figure 7 The regression process of calculating seismic losses using traditional linear regression is shown. Figure 8 The calculation results of the method proposed in the present invention, the classical Monte Carlo benchmark method and the traditional linear regression method are compared. As can be seen from the figure, compared with the traditional linear regression method, the method proposed in the present invention has a better fit with the classical Monte Carlo benchmark method. Therefore, the calculation method of the present invention is more accurate than the traditional linear regression method. At the same time, the classical Monte Carlo benchmark method calculates 10,000 times for each Sa(T1), while the method of the present invention calculates 100 times for each Sa(T1). When obtaining approximate results, the calculation process of the present invention is more efficient, which greatly reduces the calculation workload.

Claims

1. A method for calculating the average annual loss of external abutment structure reinforcement based on interface shear stress, characterized in that: The following steps are involved: (1) Establish a deterministic model for external reinforcement and generate structural samples and ground motion samples by random sampling; (2) Establish a probabilistic hazard model based on the generated ground motions; (3) Generate a probabilistic vulnerability model based on interface shear stress; The step (3) comprises: (3.1) Determine the amplitude modulation interval m of the earthquake intensity parameter and set the interface shear stress of the external attachment structure as the engineering requirement parameter; (3.2) Random seismic sample amplitude modulation and circulation, carry out nonlinear dynamic time history response analysis, and obtain the strength parameter IM and interface shear stress under different seismic motion levels; (3.3) The interface shear stresses obtained from all earthquake motions under all earthquake motion levels are summarized, and linear regression is performed based on the logarithmic coordinate system and the least squares method to obtain the regression coefficients β0 and β1, and the median value S is calculated. d|IM and log-standard β d |IM is: ln S d|IM =β0+β1·ln IM Where n is the number of ground motions under all ground motion levels, D x is the interface shear stress data obtained from the xth analysis result; (3.4) Determine the limit state and limit value d of the external attachment structure reinforcement based on interface shear stress; and generate a probabilistic fragility model based on interface shear stress; The limit states of the external attachment structure reinforcement include destruction, transportation, residual and maintenance states; After determining the limit state and limit value d of the external auxiliary structure reinforcement based on the interface shear stress, the probabilistic seismic vulnerability models of adjacent limit states generated are subtracted from each other to obtain the probabilistic seismic damage model P (DS = ds i |IM): P(DS=ds i |IM)=P i (edp|im)-P i+1 (edp|im) Among them, P i (edp|im) represents the probabilistic vulnerability model corresponding to the ith limit state, P i+1 (edp|im) represents the probabilistic vulnerability model corresponding to the i+1th limit state; (4) Establish a probabilistic total loss expectation model under the earthquake intensity level; The probability total loss expectation model in step (4) includes the probability loss expectation values ​​under different limit states, that is, the destruction probability loss expectation value L C , expected value of transport probability loss LT, expected value of residual probability loss L NC∩D And the expected value of maintenance probability loss L NC∩R ; Under the earthquake intensity level IM_x, the expected value of the damage probability loss L C The calculation formula is: L C =E[L|C]·P(C P |IM)·P(C T |IM)·α1 Among them, E[L|C] represents the theoretical expectation of damage loss, E[L|C] is the replacement ratio coefficient corresponding to the damage state, P(C p |IM) represents the probability that the external reinforcement system is in a damaged state under IM, P(C T |IM) represents the probability that the external attachment structure reinforcement system is in the state of transportation damage under IM, and α1 is the damage loss coefficient; The calculation formula for the expected value of the transport probability loss LT is: L T =E[L|T]·P(C P |IM)·[1-P(C T |IM)]·α2 Among them, E[L|T] represents the theoretical expectation of handling loss, E[L|T] is the replacement ratio coefficient corresponding to the handling damage state, and α2 is the handling loss coefficient; The expected value of residual probability loss L NC∩D The calculation formula is: L NC∩D =E[L|NC∩D]·P(C D |NC,IM)·{1-P(C P |IM)}·α3 Among them, E[L|NC∩D] represents the theoretical expectation of residual loss, E[L|NC∩D] is taken as the replacement ratio coefficient corresponding to the residual damage state of the external attachment structure reinforcement system under non-destructive conditions, P(C D |NC, IM) represents the probability that the external attachment structure reinforcement system is in a residual damage state under IM conditions and non-destructive conditions, and α3 is the residual loss coefficient; Expected value of maintenance probability loss L NC∩R The calculation formula is: L NC∩R =E[L|NC∩R,IM]·{1-P(C D |NC,IM)}·{1-P(C P |IM)}·α4 Among them, E[L|NC∩R,IM] represents the theoretical expectation of maintenance loss, E[L|NC∩R,IM] is taken as the replacement ratio coefficient corresponding to the maintenance damage state of the external attachment structure reinforcement system when the local vibration intensity is IM and under non-destructive conditions, α4 is the maintenance loss coefficient; (5) Based on the expected probabilistic total loss under the earthquake intensity level, the annual average probabilistic seismic loss of the overall reinforcement of the external attachment structure based on the interface shear stress is obtained.

2. The method for calculating the average annual loss of external abutment structure reinforcement based on interface shear stress according to claim 1 is characterized in that: The probability risk model H in step (2) IM (x) is H IM (x)=P[IM≥x]=k0·x -k Where k0 and k represent shape parameters, IM represents ground motion intensity parameter, and IM DBE and IM MCE They represent the seismic intensity parameters corresponding to the design earthquake and the rare earthquake respectively. The 50-year exceedance probability of the design earthquake DBE is 10%, and the return period is 475 years, that is, the annual exceedance probability p DBE The 50-year exceedance probability of a rare earthquake MCE is 2%, and the return period is 2475 years, that is, the annual exceedance probability p MCE It is 1 / 2475.

3. The method for calculating the average annual loss of external abutment structure reinforcement based on interface shear stress according to claim 1 is characterized in that: The step (3.2) includes setting the initial seismic level x=1 and determining the seismic intensity parameter IM_ x , at the x-th level, randomly match the structure sample n1 and the seismic motion sample n2, carry out nonlinear dynamic time-history response analysis, and obtain the required interface shear stress τ at the x-th level; judge the size of x and the amplitude modulation interval m, if x is less than m, then x = x + 1, and repeat the above steps; if x is greater than or equal to m, go to the next step (3.3).

4. The method for calculating the average annual loss of external abutment structure reinforcement based on interface shear stress according to claim 1 is characterized in that: The probabilistic vulnerability model P(edp|im) is: Where Φ is the standard normal distribution function.

5. The method for calculating the average annual loss of external abutment structure reinforcement based on interface shear stress according to claim 1 is characterized in that: The calculation formula for the annual average probability seismic loss E[L] of the overall reinforcement of the external attachment structure based on interface shear stress is: Among them, E[L|IM] is the expected value of the total probabilistic loss.

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