JP2011027481A - Method of evaluating earthquake risk - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To evaluate PML adapted to a target building by providing a more appropriate method of evaluating an earthquake risk. <P>SOLUTION: In the method of evaluating the earthquake risk for evaluating an earthquake risk of a building including a plurality of layers to be evaluated by PML, loss distribution of the building to the magnitude of earthquake motion that becomes a basis of the PML is calculated, based on a correlation coefficient of occurrence of losses at respective parts between respective layers and respective parts of the building, based on a correlation coefficient between the magnitude of the earthquake motion and response values for the respective parts between respective layers and respective parts, and a correlation coefficient of yield-strength values for the respective parts between the respective layers and respective parts of the building, and loss distribution at the respective layers and respective parts of the building. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to an earthquake risk evaluation method for evaluating a building loss due to an earthquake.

  It is known to use PML (Earthquake Expected Maximum Loss Rate) as an index of the earthquake risk of a building (see, for example, Patent Document 1). Conventionally, when calculating PML, the loss distribution of each part (frame, finishing, building equipment, etc.) existing in each layer of the building is used, and the loss distribution of each part existing in each layer of the building is The simulation is performed assuming that the correlation of loss occurrence at each part is either independent or complete.

JP 2004-150920 A

  However, as described above, when simulating the loss distribution of each part existing in each layer of the building, assuming that the correlation of the loss occurrence in each part of each layer is independent, the variation of the loss distribution of the entire building is small. Therefore, when the PML is underestimated and assumed to be a complete correlation, there is a problem that the dispersion of the loss distribution of the entire building becomes large and the PML tends to be overestimated.

  This invention is made | formed in view of the said subject, The place made into the objective is to provide the more suitable earthquake risk evaluation method, and to evaluate PML suitable for the object building.

In order to achieve such an object, the earthquake risk evaluation method of the present invention is an earthquake risk evaluation method for evaluating an earthquake risk of a building having a plurality of layers to be evaluated by PML, which is a basis of the PML. The loss distribution of the building with respect to the magnitude of the ground motion, the correlation coefficient between the magnitude of the ground motion and the response value for each part of each layer of the building, and the correlation of the proof stress value for each part of each layer of the building The earthquake risk evaluation method is characterized in that the calculation is based on a correlation coefficient of loss occurrence between each part of the building based on the number and a loss distribution in each part of each layer of the building.
According to such a seismic risk evaluation method, the loss distribution of the building with respect to the magnitude of the ground motion that is the basis of the PML includes the correlation coefficient of the loss occurrence between each part of the building and the loss distribution at each part of the building. Therefore, it is possible to evaluate the seismic risk based on the loss and the probability of occurrence for each magnitude of seismic motion in each part of each layer of the building. At this time, the correlation coefficient of the loss generation between each part of each layer is the correlation coefficient between the magnitude of the earthquake motion and the response value for each part of each layer of the building, and the strength value of each part of each layer of the building. Since it is calculated based on the number of relations, it is possible to arbitrarily set the correlation between each part existing in each layer of the building. For this reason, it is possible to obtain a more accurate PML than when PML is calculated on the assumption that the correlation between each part existing in each layer of the building is independent or complete, and the PML suitable for the building to be evaluated is obtained. Based on this, it is possible to make a more appropriate evaluation.

In this earthquake risk evaluation method, the loss distribution in each part of each layer of the building is preferably an average value of the loss distribution in each part of each layer and a standard deviation of the loss distribution in each part of each layer.
According to such an earthquake risk evaluation method, the loss distribution in each part of each layer is the average value of the loss distribution in each part of each layer and the standard deviation of the loss distribution in each part of each layer. High nature. For this reason, it is possible to obtain a more reliable evaluation result.

In this earthquake risk evaluation method, the response value is a median value of the response values with respect to a plurality of ground motions, and a logarithmic standard deviation of the response values with respect to the plurality of ground motions, and the proof stress value is the proof stress value. And the logarithmic standard deviation of the proof stress value.
According to such an earthquake risk evaluation method, the response value is a median of response values for a plurality of earthquake motions and a logarithmic standard deviation of the response values for a plurality of earthquake motions, and the proof stress is a median of the proof stress values, And since it is the logarithmic standard deviation of the proof stress value, it is possible to obtain a more reliable evaluation result.

  According to the present invention, a more appropriate seismic risk evaluation method is provided to evaluate a PML suitable for a target building.

It is a figure which shows the evaluation flow of the earthquake risk evaluation method which concerns on this invention. It is a figure which shows distribution of a response value and a proof stress value. It is a figure which shows the damage probability function of each site | part of each layer. It is a figure for demonstrating the concept of the correlation coefficient of loss generation. It is a figure which shows the preparation method of an event risk curve. It is a figure for demonstrating the evaluation method of PML based on an event curve. It is a figure which shows distribution of yield strength. It is a figure which shows an example of the correlation diagram of yield strength. It is a figure which shows the comparison with the acceleration response spectrum of a simulated earthquake motion, and a target spectrum. It is a figure which shows an example of the created simulated earthquake motion. It is a figure which shows an example of the correlation diagram of a response interlayer deformation angle when the ground surface maximum speed of an earthquake motion is 50 cm / s. It is a figure which shows an example of the relationship between the ground surface maximum speed and response value in 1st layer, 2nd layer, 5th layer, and 10th layer. It is the graph which showed the earthquake loss curve calculated | required with the invention evaluation method and the conventional evaluation method. It is the graph which showed the event risk curve calculated | required with the invention evaluation method and the conventional evaluation method. It is a figure which shows the comparison of PML of the invention evaluation method, the conventional evaluation method 1, and the conventional evaluation method 2. FIG.

  Hereinafter, an example of the earthquake risk evaluation method of the present embodiment will be described in detail with reference to the drawings.

  FIG. 1 is a diagram showing an evaluation flow of an earthquake risk evaluation method according to the present invention.

<< Summary of Invention >>
The earthquake risk evaluation method of this embodiment is based on the PML shown in the event risk curve indicating the correlation between the occurrence probability of various magnitude earthquakes indicated by the ground surface maximum velocity and the loss rate of the building with respect to the magnitude of the earthquake. evaluate. The loss distribution of the building with respect to the ground surface maximum speed that is the basis of this event risk curve is calculated using the response value and proof value of the building, but the response value and proof value are not uniform throughout the building, There are variations in each part of the building. For this reason, in the seismic risk evaluation method of the present invention, first, the building is modeled as a multi-mass point equivalent shear type fixed to the foundation, and the correlation coefficient between the response value and the proof stress value between each part of each layer of the building is obtained. Next, the correlation coefficient of the loss generation between each part of each layer is obtained based on the correlation coefficient of the response value and the proof stress value between each part of each layer. Then, based on the obtained correlation coefficient of the loss occurrence between each part of each layer and the loss distribution in each part of each layer of the building, the loss distribution of the building with respect to the magnitude of the earthquake motion is obtained to create an event risk curve. Seismic risk is evaluated by PML obtained from the created event risk curve.

That is, the earthquake risk evaluation method of the present invention uses the correlation coefficient and variation of the response value generated for each layer and each part and the yield strength value indicating the limit not to break, and the correlation of loss generation for each layer and each part. The number is calculated, and the earthquake risk is evaluated based on the loss distribution of the entire building calculated based on the correlation coefficient of the loss occurrence for each layer and each part.
Below, the method of calculating | requiring PML used as the parameter | index in the earthquake risk evaluation method of this embodiment is demonstrated based on FIG.

<< How to Obtain PML According to the Present Invention >>
<Modeling of the epicenter>
・ Setting of hypocenter model and probability of earthquake occurrence When evaluating earthquake risk, first set the hypocenter model and probability of earthquake occurrence when evaluating the earthquake risk of the construction site.
In this embodiment, the seismic source model created by the Earthquake Research Promotion Headquarters / Earthquake Investigation Committee is adopted as the seismic source model (S1 in FIG. 1), and the earthquake occurrence probability is determined by the Earthquake Research Promotion Headquarters / Earth Investigation Committee. The proposed one is adopted (S6 in FIG. 1).

・ Calculation of the maximum speed V of the ground surface Calculate the “maximum speed of the ground surface” indicating the magnitude of the earthquake at the construction site when the earthquake occurred.
The maximum speed of the ground surface is also calculated based on the method created by the Earthquake Research Promotion Headquarters and the Earthquake Research Committee.
According to the above method, the maximum speed V of the ground surface can be obtained by multiplying the maximum speed V ₀ on the reference ground by the speed amplification factor amp of the surface ground.

In calculating the ground surface maximum velocity V, first, the maximum velocity V ₀ in the reference ground (corresponding to S wave velocity 600 m / s) with respect to the earthquake is calculated using the velocity distance attenuation equation (2.2) (FIG. 1). S2, S3).

Next, the speed amplification factor amp by the surface layer ground is calculated using the formula (2.3) by a method based on the fine landform classification (S4 in FIG. 1).
In equation (2.3), the average S wave velocity AVS from the ground surface to 30 m below ground is obtained from equation (2.4).

By the way, as an uncertain factor in calculating the ground surface maximum velocity V, there are an earthquake source characteristic, a propagation characteristic, and a ground characteristic. For this reason, the variation due to these uncertain factors is modeled with a lognormal distribution, and the logarithmic standard deviation ζ _V of the ground surface maximum velocity is set to “Study on Probabilistic Seismic Motion Prediction Map Making Method for the Whole Country” (Disaster Prevention Science) Set to 0.46 based on Technical Research Institute, 2005). Further, as the speed amplitude dependence of the variation, Table 1 is set according to the value of the maximum speed for the region where the maximum speed V _{0 on} the reference ground is 25 cm / s or more (S5 in FIG. 1).

<< Setting of input ground motion >>
In the present embodiment, a method is adopted in which a target spectrum is set as the input seismic motion and the seismic motion is created so as to match the set target spectrum (S7 in FIG. 1). As the target spectrum, the acceleration response spectrum of the building load guideline (1993 version) was adopted in order to easily consider the effects of seismic source characteristics, propagation characteristics, and ground characteristics.

<Target spectrum setting>
In the building load guideline (1993 version), the acceleration response spectrum S _A (T, h) of the ground surface is set by the equations (2.7) to (2.9).

Here, since the reproduction period conversion coefficients _RA and _RV are correction coefficients for the r-year reproduction expected value with respect to the 100-year reproduction expected value, the values are set to 1. Further, the upper limit cycle T _{c of the} section where S _A (T, h) takes a constant value is given by the equation (2.10).

Here, in the standard ground, the ratio of the maximum acceleration to the maximum speed is given by A ₀ / V ₀ = 15 (sec ⁻¹ ). Also, the soil type correction coefficient G _A of maximum acceleration given by 1.2 with respect to the second type ground and the three ground, soil type correction coefficient G _V of maximum speed, (2.3) equation surface layer of Set to the speed amplification factor amp by the ground. Under the above conditions, when the maximum velocity V ₀ of the standard ground is calculated, the acceleration response spectrum S _A (T, h) of the ground surface as the target spectrum is set.

<Setting of envelope function for earthquake motion>
Create a seismic motion that matches the target acceleration response spectrum S _A (T, h). To create the ground motion, first, the Fourier phase spectrum is given by a uniform random number. Then, a time history waveform is created by inverse Fourier transform using the set Fourier amplitude and Fourier phase. Next, given the magnitude of the earthquake, the envelope function E (t) of the ground motion is expressed by the formulas (2.11) to (2.17) by the method of “Introduction to new ground motion spectrum analysis” (Kashima Publishing Co., 2002). Set with.

On the other hand, the duration Td of earthquake motion is given by the following equation.
Ta and Tb are given by the equations (2.16) and (2.17) using the seismic motion duration Td.
Then, the first seismic motion is created by multiplying the time history waveform by E (t). An acceleration response spectrum is calculated for the primary ground motion obtained in this way, and the Fourier amplitude is corrected so as to match the target response spectrum. This operation is repeated to create a ground motion that matches the target acceleration response spectrum.

<Relationship between maximum speed and average magnitude>

<Damage probability function for each part of each layer>
Next, the building is modeled as a foundation fixed multi-mass point equivalent shear type (S8 in FIG. 1), and seismic response analysis is performed using the set seismic motion to calculate the response value of each layer of the building. At this time, in order to evaluate the distribution of response values reflecting the variation in the yield strength of the building and the seismic motion characteristics, a sample value of the yield strength of the building and the seismic motion is extracted to perform a Monte Carlo simulation (S9 in FIG. 1).
Here, the total number of sample values of yield strength is ny, the total number of sample values of ground motion is ng, and the median value Ms (Vg) of the response value to the ground motion g (the ground surface maximum velocity is Vg) and the logarithm of the response value The standard deviation ζ (Vg) is calculated (S10 in FIG. 1).

Next, the relationship between the ground surface maximum speed Vg (g = 1 to ng) and the median value Ms (Vg) of the response value, and the logarithmic standard deviation ζ of the ground surface maximum speed Vg (g = 1 to ng) and the response value The relationship of (Vg) is obtained, and the relationship between the ground surface maximum velocity V and the median value Ms of response values and the logarithmic standard deviation ζs of the ground surface maximum velocity V and response values are regressed using the following equations.
At this time, the distribution of the proof stress value is set for each part of each layer, and the damage probability P of each part of each layer with respect to the ground surface maximum velocity V is evaluated.

  FIG. 2 is a diagram showing a distribution of response values and proof stress values, and FIG. 3 is a diagram showing a damage probability function of each part of each layer. In FIG. 2, the proof stress value is constant because it is determined by the building regardless of the magnitude of the seismic motion. However, when the response value increases, the distribution of the proof stress value and the distribution of the response value intersect. The probability of this breakage is shown, and it is shown that the probability of breakage increases as the ground surface maximum velocity (earthquake) increases. This is schematically shown in FIG.

Since damage occurs when the response value S exceeds the proof stress value R, the limit state function Z is obtained by subtracting the response value S from the proof stress value R. If Z ≧ 0, there is no damage, and if Z <0, there is damage.

Here, when both the distribution of the response value S and the proof stress value R are modeled by a lognormal distribution, the reliability index β for the limit state function of the equation (2.21) is evaluated by the equation (2.22) (FIG. 1 in S11).
Logarithmic mean value λs of the response value is calculated by taking the natural logarithm of the median M _S of the response value (2.19) below.
When the logarithmic average value λs of the response values of the equation (2.23) and the logarithmic standard deviation ζs of the response values of the equation (2.20) are substituted into the equation (2.22), the reliability index β is (2.24). ).

Therefore, when the logarithmic average value λ _R and logarithmic standard deviation ζ _R of the proof stress values corresponding to the degree of damage (for example, small breakage, medium breakage, etc.) are set, the damage probability function P (V) can be evaluated from the following equation (FIG. 1 in S12).

<Loss distribution of each part of each layer>
In the earthquake risk evaluation method of this embodiment, the earthquake risk is evaluated based on the loss distribution of the entire building based on the correlation coefficient of the loss occurrence for each layer and each part. Here, assuming that the number of layers of the building to be evaluated is i and the number of parts is k, the earthquake risk is evaluated based on the correlation coefficient of the loss occurrence for each layer and each part of k parts of the i-layer building.

In the i layer k region, if the damage probability for the damage level L (L = 1 to n _ik ) is P _{L, ik} (V) and the restoration cost is C _{L, ik} , the average value μ of the loss distribution in the i layer k region _ik (V) and standard deviation σ _ik (V) are obtained using the damage probability function P (V) of equation (2.25) (S13, S14 in FIG. 1).
Here, ΔP _{L, ik} is obtained from the following equation according to the damage level L.

<Distribution of building loss>
Since the building loss is the sum of the loss of each part of each layer, the average value μc (V) and standard deviation σc (V) of the building loss distribution with respect to the ground surface maximum velocity V can be obtained from the following equations. FIG. 4 is a diagram for explaining the concept of the correlation coefficient of loss occurrence.

In the equation (2.31), ρ _{ik, jl} is a correlation coefficient of loss occurrence in the i layer k part and the j layer l part, and as shown in FIG. 4, the correlation coefficient ρ _{Rik, jl} of the proof stress value and The response value correlation coefficient ρ _{Sik, jl} can be used for evaluation (S15 and S16 in FIG. 1).
At this time, since the distribution of the response value and the proof stress value are both modeled by logarithmic normal distribution, the correlation coefficient ρ _{ik, jl} of the loss generation can be calculated from the following equation.

In the equation (2.32), the correlation coefficient ρ _{Rik, jl} of the proof stress value is calculated from the following equation.

In addition, in equation (2.32), the coefficient of variation V _{R, ik} and V _{R, jl} of the proof stress value are calculated from the following equations.
On the other hand, the correlation coefficient ρ _Sik, jl (Vg) of the response value is calculated from the following equation for each ground surface maximum velocity Vg of the ground motion g (g = 1 to ng) (S18 in FIG. 1).

In the equation (2.32), the response value variation coefficients V _{S, ik} (Vg) and V _{S, jl} (Vg) are calculated from the following equations.
In this case, the correlation coefficient of the response values in (2.32) formula [rho _{Sik, jl} is the correlation coefficient of the ground motion g (g = 1~ng) calculated response value for each [rho _{Sik, jl} (Vg) The average value is used for evaluation.

In the above equation, the parameters q and r are obtained using the average value μ _c (V) and standard deviation σ _C (V) of the loss distribution of the building.

On the other hand, the loss C _M (V) corresponding to the 90% non-excess probability is obtained so as to satisfy the following equation.
Similarly, the earthquake loss curve SL _M (V) corresponding to the 90% non-exceeding probability continuously calculates C _M (v) corresponding to the 90% non-exceeding probability of the loss distribution by changing the ground surface maximum velocity. Can be evaluated.

<Event risk curve>

<PML>

<< Comparison of Earthquake Risk Evaluation Method According to the Present Invention and Conventional Earthquake Risk Evaluation Method >>
<Conditions for comparison>
In comparing the results of the earthquake risk evaluation method according to the invention described above (hereinafter referred to as the invention evaluation method) and the results of the conventional earthquake risk evaluation method (hereinafter referred to as the conventional evaluation method), the conditions for the earthquake risk evaluation are as follows: Set as follows. In the invention evaluation method, the correlation of loss occurrence in each part of each layer is arbitrarily set. The conventional evaluation method analyzes two cases. Specifically, one of the conventional seismic risk evaluation methods (hereinafter referred to as “conventional evaluation method 1”) assumes that loss occurs in each part of each layer independently, and the other (hereinafter referred to as “conventional evaluation method 2”) corresponds to each layer. Analysis is performed on the assumption that the loss at each site is completely correlated.
And when the correlation arises between the yield strength of each layer, the earthquake risk result by an invention evaluation method and a conventional evaluation method is compared.

<Setting of building model>
The building model to be evaluated in this earthquake risk evaluation is, for example, RC 10th floor (S8 in FIG. 1). FIG. 7 is a diagram showing the distribution of yield strength.
The yield base shear coefficient is 0.3, and the yield shear force coefficient in the height direction is given by Ai distribution. Restoring force characteristics of each layer, as shown in FIG. 7, the third of the cracking strength _{Q C} the yield strength _{Q y,} set the cracked deformation angle 1/1500, the yield deformation angle 1/150, resilience The characteristic is given by Takeda model. The building attenuation was given as a stiffness proportional type with a primary damping constant of 3%, and when performing an earthquake response analysis, the instantaneous stiffness proportional type was used.

Further, the yield strength distribution is modeled by a logarithmic normal distribution, and the coefficient of variation of the yield strength is set to 0.15 with reference to “Limited State Design Guidelines for Buildings” (Japan Architectural Institute, 2002). Further, the correlation coefficient ρ _Q of the yield strength of each layer is set to 0.8 for all the layers.
At this time, the total number ny of yield strength sample values is 100 cases. FIG. 8 is a diagram illustrating an example of a correlation diagram of yield strength.

On the other hand, the limit interlayer deformation angle is adopted as the proof stress value, and the median value and logarithmic standard deviation of the limit interlayer deformation angle are set as follows (S11 in FIG. 1).

Further, the restoration cost corresponding to the degree of damage is set as follows (S13 in FIG. 1).

<Setting of input earthquake motion>
The construction site is set in Tokyo (latitude: 35.678, longitude: 139.770). At this time, since the speed amplification factor with respect to the reference ground is 2.273, the acceleration response spectrum S _A (T, h) is obtained according to the method described above in <Target spectrum setting> (S7 in FIG. 1). Further, Table 4 shows the relationship between the median of the ground surface maximum speed and the average magnitude.

S _A (T, h) is set as the target spectrum, and a simulated earthquake motion corresponding to the ground surface maximum speed is created using the relationship between the median value of the ground surface maximum speed and the average magnitude. The maximum speed of the ground surface is set to 20 levels in 5 cm / s increments between 5 and 100 cm / s, and the phase when creating simulated earthquake motion is given by random numbers. A simulated earthquake motion of 10 waves is created for the maximum surface velocity. Therefore, the total number ng of sample values of seismic motion is ng = 20 × 10 = 200 cases. FIG. 9 is a diagram showing a comparison between an acceleration response spectrum of a simulated earthquake motion and a target spectrum, and FIG. 10 is a diagram showing an example of the created simulated earthquake motion.

<Monte Carlo simulation>
The total number of yield strength and ground motion sample values is set as follows, and a combination of the two is used to perform an earthquake response analysis of a total of 100 × 200 = 20000 cases, and the distribution of response values of each layer of the building is calculated (S9 in FIG. 1). The response interlayer deformation angle is employed as the response value.
・ Total number of yield strength samples: ny = 100 cases ・ Total number of earthquake motion samples: ng = 200 cases FIG. 11 is a diagram showing an example of a correlation diagram of response interlayer deformation angles when the ground surface maximum velocity of earthquake motion is 50 cm / s. It is.

<Relationship between ground surface maximum speed and response value>
For each layer of the building, the relationship between the ground surface maximum velocity and the median value of the response value and the relationship between the ground surface maximum velocity and the logarithmic standard deviation of the response value are evaluated (S15 in FIG. 1).
FIG. 12 is a diagram illustrating an example of the relationship between the ground surface maximum speed and the response value in the first layer, the second layer, the fifth layer, and the tenth layer.

<Correlation coefficient of loss occurrence>
The correlation coefficient of the response value, the correlation coefficient of the proof stress value, and the correlation coefficient of loss generation calculated using both values in the invention evaluation method are as follows (S16 and S17 in FIG. 1).

The correlation coefficient of the response value, the correlation coefficient of the proof stress value, and the correlation coefficient of the loss generation calculated using both values in the conventional evaluation method 1 are as follows.

In the conventional evaluation method 2, the correlation coefficient of the response value, the correlation coefficient of the proof stress value, and the correlation coefficient of the loss generation calculated using both values are as follows.

<Comparison of earthquake loss curves>
The invention evaluation method and the conventional evaluation method are compared with the earthquake loss curve based on the correlation of loss occurrence. FIG. 13 is a graph showing earthquake loss curves obtained by the invention evaluation method and the conventional evaluation method. As shown in FIG. 13, the loss rate obtained by the invention evaluation method is between the loss rate of the conventional evaluation method 1 (independent case) and the loss rate of the conventional evaluation method 2 (completely correlated case). The value of is shown. That is, compared with the invention evaluation method, the conventional evaluation method 1 underestimates the loss rate, and conversely, the conventional evaluation method 2 overestimates the loss rate.

<Comparison of event risk curves>
The event risk curve based on the correlation of loss occurrence is compared between the invention evaluation method and the conventional evaluation method. FIG. 14 is a graph showing event risk curves obtained by the invention evaluation method and the conventional evaluation method. As shown in FIG. 14, in the region where the annual excess probability is about 10 ⁻² or less, the loss rate obtained by the invention evaluation method is the loss rate of the conventional evaluation method 1 (independent case) and the conventional evaluation method 2 It shows the value between the loss rate (in the case of perfect correlation). That is, in the region where the annual excess probability is about 10 ⁻² or less, the conventional evaluation method 1 underestimates the loss rate compared to the inventive method, and the conventional evaluation method 2 overestimates the loss rate.

<Comparison of PML>
The PML can be evaluated by a loss C _M (E _K ) for an earthquake E _{K with} an annual excess probability P _K of 1/475.
Therefore, the PML value is obtained from the event risk curve of FIG. 14, and the invention evaluation method and the conventional evaluation method are compared. Compared with the inventive evaluation method, the conventional evaluation method 1 (independent case) underestimates the PML, and the conventional evaluation method 2 (in the case of complete correlation) overestimates the PML.
FIG. 15 is a diagram showing a PML comparison between the invention evaluation method, the conventional evaluation method 1, and the conventional evaluation method 2.

  From the above examination results, according to the earthquake risk evaluation method of the above embodiment, as shown in FIG. 15, the conventional evaluation method 1 (independent case) has a PML less than the invention evaluation method, and the conventional evaluation method. It was shown that Method 2 (in the case of complete correlation) overestimates PML compared to the invention evaluation method. Therefore, it is possible to more accurately evaluate the earthquake risk of a building by using the invention evaluation method that reflects the correlation of loss occurrence.

That is, according to the earthquake risk evaluation method of the above embodiment, the loss distributions μc (V) and σc (V) of the building with respect to the magnitude of the ground motion that is the basis of the PML are the phases of the loss generation between the respective portions of the building. Since it is calculated on the basis of the relation number ρ _{ik, jl} and the loss distribution μ _ik (V), σ _ik (V) in each part of the building, the occurrence of each level of earthquake motion in each part of the building It is possible to evaluate the seismic risk based on the loss and probability of occurrence. At this time, the correlation coefficient ρ _{ik, jl} of the loss generation between each part of each layer is the correlation coefficient ρ _{Sik, jl} between the magnitude of the earthquake motion and the response value for each part of each layer of the building, and each layer of the building Since it is calculated based on the correlation coefficient ρ _{Rik, jl} of the proof stress value for each part, it is possible to arbitrarily set the correlation between the parts existing in each layer of the building. For this reason, it is possible to obtain a more accurate PML than when the PML is calculated on the assumption that the correlation between the portions existing in each layer of the building is independent or complete. For this reason, it is possible to perform more appropriate evaluation based on the PML suitable for the building to be evaluated.

Further, since the loss distribution in each part of each layer is the average value μ _ik (V) of the loss distribution in each part of each layer and the standard deviation σ _ik (V) of the loss distribution in each part of each layer, High reliability. For this reason, it is possible to obtain a more reliable evaluation result.

  The response value S is a median value Ms of response values for a plurality of ground motions and a logarithmic standard deviation ζs of response values for a plurality of ground motions. A proof stress value R is a median of proof stress values and a proof stress value. Because of the logarithmic standard deviation, it is possible to obtain a more reliable evaluation result.

  Moreover, the said embodiment is for making an understanding of this invention easy, and is not for limiting and interpreting this invention. The present invention can be changed and improved without departing from the gist thereof, and it is needless to say that the present invention includes equivalents thereof.

For V ground surface maximum speed S response value log mean ζs logarithmic standard deviation [mu] c (V) the magnitude of the earthquake motion logarithmic mean zeta _R proof stress of logarithmic standard deviation lambda _R proof stress response values of R proof stress λs response value Average value of building loss distribution σc (V) Standard deviation of building loss distribution relative to magnitude of ground motion μ _ik (V) Average value of loss distribution at each part of the building relative to magnitude of ground motion σ _ik (V) Ground motion Standard deviation of loss distribution at each part of the building relative to the size of the building ρ _{ik, jl} Correlation coefficient of loss occurrence between each part of the building ρ _{Sik, jl} The magnitude of the earthquake motion and the response value between each part of the building Correlation coefficient with ρ _{Rik, jl} Correlation coefficient with strength value for each part of each layer of building

Claims (3)

An earthquake risk evaluation method for evaluating an earthquake risk of a building having a plurality of layers to be evaluated by PML,
The loss distribution of the building with respect to the magnitude of ground motion, which is the basis of the PML,
Correlation of loss generation between each part of each layer of the building based on a correlation coefficient with a response value for each part of each layer of the building and a correlation coefficient of a proof stress value for each part of each layer of the building Number and
An earthquake risk evaluation method comprising: calculating based on a loss distribution in each part of each layer of the building. The earthquake risk evaluation method according to claim 1,
The loss distribution in each part of each layer of the building is an average value of the loss distribution in each part of each layer and the standard deviation of the loss distribution in each part of each layer. The earthquake risk evaluation method according to claim 1 or 2,
The response value is a median of the response values for a plurality of ground motions, and a logarithmic standard deviation of the response values for the plurality of ground motions,
The method for evaluating earthquake risk, wherein the proof stress value is a median value of the proof stress value and a logarithmic standard deviation of the proof stress value.