Structure function-oriented risk-oriented aseismic design spectrum construction method

Abstract

The invention discloses a risk-oriented aseismic design spectrum construction method for structure functions, and aims to solve the problems that a method for evaluating the aseismic capacity of a building is limited to the anti-collapse capacity of the structure, higher requirements on the structure functions are not put forward, and the post-earthquake loss of the building is difficult to effectively reduce. The construction method comprises the following steps: 1, determining a first-order approximate earthquake risk function; 2, carrying out the convolution of the earthquake risk function of the site and the vulnerability of each function state of the structure, and determining the annual exceeding risk of each function state of the structure; 3, determining a function vulnerability median value of the target structure; 4, constructing a risk-oriented anti-seismic response spectrum oriented to a structure function; and 5, constructing a structure function-oriented risk-oriented aseismic design spectrum. According to the method, in the process of generating the aseismic design spectrum, the influence of the structure earthquake vulnerability and the field earthquake risk is considered at the same time, and the current structure collapse-oriented risk-oriented aseismic design is expanded to the structure-oriented function. According to the method, more effective design seismic oscillation can be provided for structural aseismic design.

Description

Technical Field

[0001] The present invention belongs to the field of earthquake engineering, and particularly relates to a method for constructing a risk-oriented seismic design spectrum considering the vulnerability of structural functions. Background Technique

[0002] The seismic design spectrum is the basis for determining the seismic ground motion input and an important method for determining the seismic action. The currently widely used design spectrum is in the form of piecewise expression in the natural coordinate system. Its generation method is to calculate the seismic response spectra from a large number of seismic ground motion records under the same site conditions, and perform smoothing processing on the average results of their statistical analysis to obtain the seismic design spectrum. However, the generation of the design spectrum is based on the seismic ground motion intensity with the same exceedance probability, that is, the uniformly hazardous seismic ground motion. The design spectrum generated in this way ignores the uncertainty of the seismic resistance of buildings, resulting in different building damage risks. Therefore, it is necessary to provide a method for constructing a risk-oriented seismic design spectrum considering the seismic resistance of buildings.

[0003] At present, domestic and foreign scholars' consideration of the seismic resistance of buildings mainly focuses on the anti-collapse ability. However, many earthquake damage investigations show that only a small part of the buildings designed by traditional methods collapse. More buildings lose their functions after the earthquake and even need to be demolished and rebuilt, which has an adverse impact on the normal operation of society and economy. In view of this, it is necessary to expand the seismic resistance of structures from collapse-oriented to function-oriented when constructing a risk-oriented seismic design spectrum. Therefore, the present invention proposes a method for constructing a risk-oriented seismic design spectrum for structural functions. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem that the existing methods for evaluating the seismic resistance of buildings are limited to the anti-collapse ability of structures, do not put forward higher requirements for structural functions, and are difficult to effectively reduce the post-earthquake losses of buildings. Furthermore, a method for constructing a risk-oriented seismic design spectrum for structural functions is proposed.

[0005] The method for constructing a risk-oriented seismic design spectrum for structural functions of the present invention is realized according to the following steps:

[0006] Step 1: First-order approximation of the seismic hazard of the target site:

[0007] According to the seismic hazard curve of the target site, through the annual exceedance frequency, 10 times the annual exceedance frequency, and the seismic ground motion intensity corresponding to the target site, determine the first-order approximation seismic hazard function H(x). The expression of the first-order approximation seismic hazard function H(x) is as follows:

[0008] H(x) = k0x -k

[0009] Among them, k and k0 are coefficients related to the slope and intercept of the first-order approximation straight line of the seismic hazard function, H(·) is the first-order approximation seismic hazard function of the target site, representing the relationship between the ground motion intensity of the site and the annual exceedance frequency, and x is the ground motion intensity;

[0010] Step 2: Determine the risk-oriented target parameters of the building function status:

[0011] Let the vulnerability functions of each functional state LS of the structure i follow a lognormal distribution. According to the vulnerability function, by obtaining the basic ground motion and rare ground motion of the site where the structure with vulnerability data is located, determine the conditional exceedance probability p of each functional state of the structure under the basic ground motion LSi|DBE and the conditional exceedance probability p of each functional state of the structure under the rare ground motion LSi|MCE , and then convolve the seismic hazard function of the site with the vulnerability of each functional state of the structure to determine the annual exceedance risk λ of each functional state of the structure LSi , the annual exceedance risk λ of each functional state of the structure LSi is expressed as follows:

[0012]

[0013] Where: λ LSi is the annual exceedance risk of the structural functional state LS i , C 12 is the correction factor considering the physical inconsistency of the upper and lower limits of the ground motion intensity when calculating λ LSi , is the logarithmic standard deviation of the vulnerability of the structural functional state LS i , is the median value of the vulnerability function of the structural functional state LS i ;

[0014] Taking the annual exceedance risk λ of each functional state of the structure LSi as the reference value, determine the target annual exceedance risk λ of each functional state of the structure LSia ;

[0015] Step 3: Determine the median value of the target structural functional vulnerability:

[0016] According to the first-order approximation seismic hazard function H(x) in Step 1 and the target annual exceedance risk determined in Step 2, obtain the median value of the vulnerability of each functional state LS of the structure that meets the risk requirements i

[0017]

[0018] Where, λ LSia is the annual exceedance risk of each functional state LS of the structurei Annual exceedance risk of the target year, Structural functional state LS to meet the target risk requirement i Median value of the vulnerability function;

[0019] Step 4: Construct a risk - oriented seismic response spectrum for structural function:

[0020] Based on the structural functional states LS determined in Step 3 i Median vulnerability, and the annual exceedance risk of each functional state calculated in Step 2, calculate the risk - oriented ground motion. The risk - oriented ground motion is determined by the following formula, and then construct the risk - oriented seismic response spectrum;

[0021]

[0022] where S aDBE,R is the risk - oriented ground motion of the structure under the basic ground motion, S aMCE,R is the risk - oriented ground motion of the structure under the rare ground motion, and Φ(·) is the standard normal distribution function;

[0023] Step 5: Construct a risk - oriented seismic design spectrum for structural function:

[0024] Calibrate the risk - oriented seismic response spectrum obtained in Step 4, and then construct a risk - oriented seismic design spectrum for structural function.

[0025] The present invention provides a method for constructing a risk - oriented seismic design spectrum for structural function, which simultaneously considers the influence of structural seismic vulnerability and site seismic hazard during the generation of the seismic design spectrum, and extends the current risk - oriented seismic design for structural collapse to the seismic design for structural function in the form of a structural functional vulnerability function.

[0026] Compared with the traditional uniform - hazard seismic design method, the present invention considers the influence of the uncertainties of the structure and the site on seismic design; compared with the latest research on uniform - risk seismic design, the present invention considers structural function in the seismic design spectrum, and the considered structural seismic capacity is more comprehensive, providing a more effective design ground motion for structural seismic design and realizing the uniform functional seismic design of regional buildings. Description of the Drawings

[0027] Figure 1 is a flow chart of the method for constructing a risk - oriented seismic design spectrum for structural function of the present invention;

[0028] Figure 2The risk - oriented seismic response spectrum for structural functions in the embodiment; in the figure, UHS is the uniform hazard seismic response spectrum, UFS is the uniform function seismic response spectrum, LS1, LS3, LS4, LS5 are respectively four functional states of the structure, the abscissa T is the natural vibration period of the structure, and the ordinate S a is the spectral acceleration;

[0029] Figure 3 is the risk - oriented seismic design spectrum for structural functions in the embodiment. Specific implementation manners

[0030] Specific implementation manner 1: The construction method of the risk - oriented seismic design spectrum for structural functions in this implementation manner is carried out according to the following steps:

[0031] Step 1: First - order approximation of the seismic hazard of the target site:

[0032] According to the seismic hazard curve of the target site, through the annual exceedance frequency, 10 times the annual exceedance frequency and the ground motion intensity corresponding to the target site, determine the first - order approximation seismic hazard function H(x). The expression of the first - order approximation seismic hazard function H(x) is as follows:

[0033] H(x)=k0x -k

[0034] where k and k0 are coefficients related to the slope and intercept of the first - order approximation straight line of the seismic hazard function, H(·) is the first - order approximation seismic hazard function of the target site, representing the relationship between the ground motion intensity of the site and the annual exceedance frequency, and x is the ground motion intensity;

[0035] Step 2: Determine the risk - oriented target parameters of the building functional state:

[0036] Suppose the vulnerability functions of each functional state LS i of the structure follow a log - normal distribution. According to the vulnerability function, by obtaining the basic ground motion and rare - event ground motion of the site where the structure is located with vulnerability data, determine the conditional exceedance probability p LSi|DBE of each functional state of the structure under the basic ground motion and the conditional exceedance probability p LSi|MCE under the rare - event ground motion. Then convolve the seismic hazard function of the site with the vulnerability of each functional state of the structure to determine the annual exceedance risk λ LSi of each functional state of the structure. The expression of the annual exceedance risk λ LSi of each functional state of the structure is as follows:

[0037]

[0038] where: λ LSi is the annual exceedance risk of the structural functional state LS i and C12 To consider the correction factor for the physical inconsistency between the upper and lower limits of ground motion intensity when calculating λ LSi ; Let the logarithmic standard deviation of the vulnerability of the structural functional state LS i be Let the median value of the vulnerability function of the structural functional state LS i be

[0039] Taking the annual exceedance risk λ LSi of each structural functional state as the reference value, determine the target annual exceedance risk λ LSia ;

[0040] Step 3: Determine the median value of the target structural functional vulnerability:

[0041] According to the first-order approximate seismic hazard function H(x) in Step 1 and the target annual exceedance risk determined in Step 2, obtain the median value of the vulnerability of each structural functional state LS i ;

[0042]

[0043] where λ LSia is the target annual exceedance risk of each structural functional state LS i ; is the median value of the vulnerability function of the structural functional state LS i that meets the target risk requirement;

[0044] Step 4: Construct a risk-oriented seismic response spectrum for structural functions:

[0045] Based on the median value of the vulnerability of each structural functional state LS i determined in Step 3 and the annual exceedance risk of each functional state calculated in Step 2, calculate the risk-oriented ground motion. The risk-oriented ground motion is determined by the following formula, and then construct a risk-oriented seismic response spectrum;

[0046]

[0047] where S aDBE,R is the risk-oriented ground motion of the structure under the basic ground motion, S aMCE,R is the risk-oriented ground motion of the structure under the rare ground motion, and Φ(·) is the standard normal distribution function;

[0048] Step 5: Construct a risk-oriented seismic design spectrum for structural functions:

[0049] Calibrate the risk-oriented seismic response spectrum obtained in Step 4, and then construct a risk-oriented seismic design spectrum for structural functions.

[0050] Embodiment 2: The difference between this embodiment and Embodiment 1 is that in Step 1, the calculation formulas of k and k0 are as follows:

[0051]

[0052] where ν is the selected annual exceedance frequency, and S a,1 is the ground motion intensity corresponding to the selected annual exceedance frequency, and S a,10 is the ground motion intensity corresponding to 10 times the annual exceedance frequency.

[0053] Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is that in Step 2, the functional state LS of the structure i is divided into five stages, namely LS1, LS2, LS3, LS4, and LS5, where LS1 represents that the building can be safely used with complete functions; LS2 represents that the building can be safely used with partial loss of functions; LS3 represents that the building cannot be safely used; LS4 represents that the building cannot be repaired; LS5 represents that the building collapses.

[0054] Embodiment 4: The difference between this embodiment and any one of Embodiments 1 to 3 is that in Step 2, the conditional exceedance probability p LSi|DBE of each functional state of the structure under the basic ground motion, and the conditional exceedance probability p LSi|MCE of each functional state of the structure under the rare ground motion are determined respectively according to the following formulas:

[0055]

[0056] where: DBE is the basic ground motion intensity, MCE is the rare ground motion intensity, is the median value of the vulnerability function of the structural functional state LS i , is the logarithmic standard deviation of the vulnerability of the structural functional state LS i , Φ(·) is the standard normal distribution function, p LSi|DBE is the conditional exceedance probability of the structural functional state LS i under the basic ground motion, and p LSi|MCE is the conditional exceedance probability of the structural functional state LS i under the rare ground motion.

[0057] Embodiment 5: The difference between this embodiment and any one of Embodiments 1 to 4 is that the logarithmic standard deviation i of the vulnerability of the structural functional state LS takes a value of 0.8.

[0058] Embodiment Six: The difference between this embodiment and any one of Embodiments One to Five lies in the annual exceedance risk λ of each functional state of the structure in Step 2 LSi in the expression of C 12 The calculation formula is as follows:

[0059]

[0060]

[0061] where erf(·) is the error function, im1 is the lower limit of ground motion intensity, im2 is the upper limit of ground motion intensity, and Δim1 and Δim2 are the coefficients for considering the upper limit and lower limit of ground motion intensity respectively.

[0062] Embodiment Seven: The difference between this embodiment and Embodiment Six lies in that the calculation formula for the coefficient Δim1 for considering the upper limit of ground motion intensity is as follows:

[0063]

[0064] The calculation formula for the coefficient Δim2 for considering the lower limit of ground motion intensity is as follows:

[0065]

[0066] Embodiment Eight: The difference between this embodiment and any one of Embodiments One to Seven lies in that the value of the target annual exceedance risk λ of each functional state of the structure in Step 2 LSia is less than or equal to the value of the annual exceedance risk λ LSi of each functional state of the structure in Step 2.

[0067] Embodiment Nine: The difference between this embodiment and any one of Embodiments One to Eight lies in that the risk-oriented seismic response spectrum in Step 4 is composed of the connection lines of the calculation results of risk-oriented ground motions for structures with different periods.

[0068] Embodiment Ten: The difference between this embodiment and any one of Embodiments One to Nine lies in that the calibration of the risk-oriented seismic response spectrum in Step 5 uses the differential evolution algorithm to obtain the optimal values of the characteristic parameters of the risk-oriented seismic design spectrum.

[0069] Example: The method for constructing a risk-oriented seismic design spectrum for structural functions in this example is implemented according to the following steps:

[0070] Step One, First-order approximation of the seismic hazard of the target site:

[0071] In this example, it is assumed that the virtual site is located at 57.792N, 139.389W, the site soil is of type B, and its seismic hazard curve is approximately expressed by the following formula:

[0072] H(x) = k0x -k

[0073]

[0074] Wherein, H(·) is the seismic hazard function of the target site, representing the relationship between the seismic ground motion intensity and the annual exceedance frequency. x is the seismic ground motion intensity. In this embodiment, the spectral acceleration is selected as the seismic ground motion intensity. ν is the selected annual exceedance frequency, which is taken as 4.04×10 -4 , S a,1 is the seismic ground motion intensity corresponding to the selected annual exceedance frequency, and S a,10 is the seismic ground motion intensity corresponding to 10 times the annual exceedance frequency. k and k0 are coefficients related to the slope and intercept of the first-order approximation straight line of the seismic hazard function. Taking 0s, 0.1s, 0.5s, 1s, and 5s as examples, the values of S a,1 and S a,10 and the calculation results of k and k0 are shown in Table 1.

[0075] Table 1 k and k0 of the first-order approximation of the seismic hazard of the target site

[0076]

[0077] Step 2: Determine the risk-oriented target parameters of the building functional state:

[0078] Assume that the vulnerability functions of each structural functional state follow a lognormal distribution and can be expressed as the following formula:

[0079]

[0080] Wherein, and are the median value and the logarithmic standard deviation of the structural functional state LS i respectively. The division of the structural functional vulnerability function stage LS i adopted in this embodiment is shown in Table 2.

[0081] Table 2 Division of the structural functional vulnerability function stage LS i Division

[0082]

[0083] The structural functional vulnerability parameters (i.e., and )Using the data obtained from the literature Burton et al., Measuring the Impact of Enhanced Building Performance on the Seismic Resilience of a Residential Community. Earthquake Spectra 2017; 33: 1347–67., the conditional exceedance probabilities of each structural functional state under the basic ground motion and the rare ground motion are determined according to the following formula:

[0084]

[0085] Where: DBE is the basic ground motion spectral acceleration, MCE is the rare ground motion spectral acceleration, is the median value of the vulnerability function of the structural functional state LS i and is the logarithmic standard deviation of the vulnerability of the structural functional state LS i , which is uniformly taken as 0.8 in this embodiment. Φ(·) is the standard normal distribution function, p LSi|DBE is the conditional exceedance probability of the structural functional state LSi under the basic ground motion, and p LSi|MCE is the conditional exceedance probability of the structural functional state LS i under the rare ground motion. For the functional states LS1, LS3, LS4, and LS5, the calculation results of the conditional exceedance probabilities are shown in Table 3.

[0086] Table 3 Conditional Exceedance Probabilities

[0087]

[0088] The annual exceedance risk of each structural functional state is determined according to the following formula

[0089]

[0090] Where: λ LSi is the annual exceedance risk of the structural functional state LS i , C 12 is the correction factor considering the physical inconsistency between the upper and lower limits of the ground motion intensity when calculating λ LSi , erf(·) is the error function, im1 is the lower limit of the ground motion intensity, im2 is the upper limit of the ground motion intensity, and Δim1, Δim2 are the coefficients considering the upper and lower limits of the ground motion intensity. The conversion between the annual exceedance risk and the 50-year exceedance risk is as follows:

[0091] λ LSi,50 = 1 - (1 - λ LSi ) 50

[0092] where λ LSi,50 is the 50-year exceedance risk of the structural functional state LS i . The calculation results of the 50-year exceedance probability for the functional states LS1, LS3, LS4, and LS5 are shown in Table 4.

[0093] Table 4 50-year exceedance probability

[0094]

[0095] Taking the annual exceedance risk λ LSi of each structural functional state as the reference value, determine the target annual exceedance risk λ LSia of each structural functional state. In this embodiment, take λ LSia = λ LSi .

[0096] Step 3. Determine the median value of the target structural functional vulnerability:

[0097] According to the first-order approximate analytical formula of the seismic risk obtained by convolving the seismic hazard function in Step 1 with the structural functional vulnerability, determine the median value of the vulnerability of each structural functional state that meets the risk requirements according to the following formula:

[0098]

[0099] where λ LSia is the target annual exceedance risk of the structural functional state LS i , and m RLSi,a is the median value of the vulnerability function of the structural functional state LS i that meets the target risk requirements.

[0100] Step 4. Construct a risk-oriented seismic response spectrum for structural functions:

[0101] Combining the median value of the vulnerability function of the structural functional state LS i determined in Step 3 and the annual exceedance risk of each functional state calculated in Step 2, determine the risk-oriented ground motion according to the following formula:

[0102]

[0103] where S aDBE,R is the risk-oriented ground motion of the structure under the basic ground motion, and S aMCE,R is the risk-oriented ground motion of the structure under the rare ground motion.

[0104] For the natural vibration periods of different structures, repeat the above steps 1 to 4 to calculate the risk-oriented ground motions for different natural vibration periods of structures, thereby constructing a risk-oriented seismic response spectrum. In this embodiment, the risk-oriented ground motions of uniform hazard, LS1, LS3, LS4, and LS5 are calculated, and the constructed risk-oriented seismic response spectrum is as Figure 2 shown.

[0105] Step 5: Construct a risk-oriented seismic design spectrum for structural functions:

[0106] Calibrate the risk-oriented seismic response spectrum obtained in Step 4 using the differential evolution algorithm, and then construct a risk-oriented seismic design spectrum for structural functions, as Figure 3 shown.

[0107] In summary, based on the uniform hazard design principle, the present invention proposes a method for constructing a risk-oriented seismic design spectrum for structural functions, and performs a first-order approximation of seismic hazard for a virtual site based on the present invention. According to the selected vulnerability data of structural functions, the conditional exceedance probabilities and annual exceedance risks of each functional state under the basic ground motion and rare ground motion are calculated, the median vulnerability values of each functional state that meet the target risk requirements are determined, a risk-oriented seismic response spectrum for structural functional states is constructed, and the risk-oriented seismic design spectrum for structural functions is calibrated by the differential evolution algorithm. The present invention has sufficient theoretical basis, comprehensively considers the seismic capacity of structures, and provides an effective basis for structural seismic design.

Claims

1. A risk-oriented seismic design spectrum construction method for structural functions, characterized by The risk-oriented seismic design spectrum construction method for structural functions is implemented in the following steps: Step 1: First-order approximation of the seismic hazard of the target site: According to the seismic hazard curve of the target site, the first-order approximate seismic hazard function H(x) is determined by the annual exceedance frequency and 10 times the annual exceedance frequency and the seismic intensity corresponding to the target site. The expression of the first-order approximate seismic hazard function H(x) is as follows: H(x)=k0x -k Where k and k0 are coefficients related to the slope and intercept of the first-order approximate straight line of the seismic hazard function, H(·) is the first-order approximate seismic hazard function of the target site, which represents the relationship between the site seismic motion intensity and the annual exceedance frequency, and x is the seismic motion intensity; Step 2: Determine the risk-oriented target parameters for the functional status of the building: Assume that each functional state of the structure is LS i The vulnerability function of the structure follows a log-normal distribution. Based on the vulnerability function, the conditional exceedance probability p of each functional state of the structure under the basic earthquake motion is determined by obtaining the basic earthquake motion and rare earthquake motion of the structure where the vulnerability data is located. LSi|DBE and the conditional exceedance probability p under rare earthquake motion LSi|MCE Then the seismic hazard function of the site is convolved with the vulnerability of each functional state of the structure to determine the annual exceedance risk λ of each functional state of the structure LSi , the annual exceedance risk λ of each functional state of the structure LSi The expression is as follows: Where: LSi LS is the structural function status i The year exceeds the risk, C 12 To consider the calculation of λ LSi Correction factor for physical inconsistency of upper and lower limits of ground motion intensity, LS is the structural function status i The logarithmic standard deviation of vulnerability, LS is the structural function status i The median value of the vulnerability function; the annual exceedance risk λ of each functional state of the structure LSi As a reference value, to determine the target annual exceedance risk λ for each functional state of the structure LSia ; Step 3: Determine the median value of the target structure and function vulnerability: According to the first-order approximate earthquake hazard function H(x) in step 1 and the target annual exceedance risk determined in step 2, the functional states LS of the structure that meet the risk requirements are obtained. i Median vulnerability Among them, λ LSia LS for each functional state of the structure i The goal of the year is to exceed risk, To meet the target risk requirements of the structural function state LS i The median value of the vulnerability function; Step 4: Construct a risk-oriented seismic response spectrum for structural functions: Based on the functional states LS of the structure determined in step 3 i The median value of vulnerability is used to calculate the risk-oriented seismic motion according to the annual exceedance risk of each functional state calculated in step 2. The risk-oriented seismic motion is determined according to the following formula, and then the risk-oriented seismic response spectrum is constructed; Among them, S aDBE,R is the risk-oriented ground motion of the structure under the basic ground motion, S aMCE,R is the risk-oriented seismic motion of the structure under rare seismic motion, Φ(·) is the standard normal distribution function; Step 5: Construct a risk-oriented seismic design spectrum for structural functions: The risk-oriented seismic response spectrum obtained in step 4 is calibrated to construct a risk-oriented seismic design spectrum oriented to structural functions.

2. The method for constructing a risk-oriented seismic design spectrum for structural functions according to claim 1 is characterized in that The calculation formulas for k and k0 in step 1 are as follows: Where ν is the selected annual exceedance frequency, S a,1 To select the seismic intensity corresponding to the annual exceedance frequency, S a,10 It is the seismic intensity corresponding to 10 times the annual exceedance frequency.

3. The method for constructing a risk-oriented seismic design spectrum for structural functions according to claim 1 is characterized in that The functional state LS of the structure in step 2 i It is divided into five stages: LS1, LS2, LS3, LS4 and LS5, where LS1 means the building can be used safely and has complete functions; LS2 means the building can be used safely but has some functions lost; LS3 means the building cannot be used safely; LS4 means the building cannot be repaired; and LS5 means the building has collapsed.

4. The method for constructing a risk-oriented seismic design spectrum for structural functions according to claim 1 is characterized in that The conditional exceedance probability p of each functional state of the structure under the basic ground motion in step 2 LSi|DBE , and the conditional exceedance probability p of each functional state of the structure under rare earthquake motion LSi|MCE Determine according to the following formula: Among them: DBE is the basic earthquake intensity, MCE is the rare earthquake intensity, LS is the structural function status i The median value of the vulnerability function, LS is the structural function status i is the logarithmic standard deviation of the vulnerability, and Φ(·) is the standard normal distribution function.

5. The method for constructing a risk-oriented seismic design spectrum for structural functions according to claim 1 is characterized in that Structural functional status LS i The logarithmic standard deviation of vulnerability The value of is 0.

8.

6. The method for constructing a risk-oriented seismic design spectrum for structural functions according to claim 1 is characterized in that The annual exceedance risk λ of each functional state of the structure in step 2 LSi In the expression C 12 The calculation formula is as follows: Wherein, erf(·) is the error function, im1 is the lower limit of the earthquake intensity, im2 is the upper limit of the earthquake intensity, Δim1 and Δim2 are the coefficients considering the upper limit and lower limit of the earthquake intensity, respectively.

7. The method for constructing a risk-oriented seismic design spectrum for structural functions according to claim 6 is characterized in that The calculation formula of the coefficient Δim1 considering the upper limit of earthquake intensity is as follows: The calculation formula of the coefficient Δim2 considering the lower limit of earthquake intensity is as follows:

8. The method for constructing a risk-oriented seismic design spectrum for structural functions according to claim 1 is characterized in that The target annual exceedance risk λ of each functional state of the structure in step 2 LSia The value of is less than or equal to the annual exceedance risk λ of each functional state of the structure in step 2 LSi The value of .

9. The method for constructing a risk-oriented seismic design spectrum for structural functions according to claim 1 is characterized in that The risk-oriented seismic response spectrum in step 4 is composed of the lines connecting the risk-oriented seismic motion calculation results of structures with different periods.

10. The method for constructing a risk-oriented seismic design spectrum for structural functions according to claim 1, characterized in that In step 5, the risk-oriented seismic response spectrum is calibrated using a differential evolution algorithm to obtain the optimal values ​​of the characteristic parameters of the risk-oriented seismic design spectrum.

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