JP2011257237A - Earthquake damage prediction method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an earthquake damage prediction method which is capable of performing highly-reliable damage prediction.SOLUTION: The earthquake damage prediction method includes: a seismic deformation calculation step of calculating seismic deformation due to an earthquake in the case where a building is contracted to a single-degree-of-freedom system, by an equivalent linearization method, and calculating the seismic deformation by using a modification coefficient of equivalent linear seismic deformation and a modification coefficient of an attenuation correction coefficient which are defined as random variables; a response drift angle calculation step of calculating a response drift angle of the building from the seismic deformation; a story drift angle calculation step of determining a probability distribution of response story drift angles due to the earthquake on the basis of simulation targeted at a building group; a damage ratio calculation step of determining a relationship between strength of the earthquake and a damage ratio from past earthquake damage results; a limit drift angle calculation step of calculating a limit drift angle of the building on the basis of the probability distribution of response story drift angles and the damage ratio; and a damage prediction step of predicting occurrence of damage of the building by comparing the response drift angle with the limit drift angle.

Description

  The present invention relates to an earthquake damage prediction method.

  In recent years, Business Continuity Management (BCM) has attracted attention, and effective earthquake countermeasures based on earthquake damage prediction of buildings are required. As a method for predicting earthquake damage, for example, in Patent Document 1, a method for predicting building damage to earthquake strength by setting earthquake strength and building attribute data (structure, floor height, building age, seismic performance index, etc.) Has been proposed.

JP 2006-258639 A

  Earthquake damage to a building occurs when the response value of the building caused by the earthquake exceeds the limit value possessed by the building. Therefore, various uncertainties (variations) are appropriately considered in the response value and limit value. Need to be predicted. In particular, the response value of the building varies depending on the spectral characteristics of the ground motion and the building characteristics (building cycle, restoring force characteristics), but the above prediction method does not fully consider these factors, so a highly reliable prediction is performed. It was difficult.

  In addition, from the viewpoint of business continuity, it is necessary to promptly determine the initial response for recovery after an earthquake occurs, and it is important to quickly predict the extent of damage to buildings. There is an equivalent linearization method as a method for quickly predicting the response value of a building, but this method is elastic-plastic by correcting the response value of the elastic system using a coefficient determined according to the degree of plasticization of the building. The response value of the system is predicted. For this reason, uncertainty associated with the prediction error occurs between the response value of the actual elasto-plastic system, and it is difficult to perform highly reliable prediction.

  The present invention has been made in view of the above problems, and an object of the present invention is to provide an earthquake damage prediction method capable of predicting a building damage due to an earthquake with high reliability.

In order to achieve such an object, the earthquake damage prediction method of the present invention is an earthquake damage prediction method for predicting damage to a building due to an earthquake, and the response displacement to an earthquake when the building is reduced to a one-degree-of-freedom system. A response displacement calculating step of calculating the response displacement using a correction coefficient of an equivalent linear response displacement and a correction coefficient of an attenuation correction coefficient determined as a random variable. A response deformation angle calculating step for calculating a response deformation angle of the building from the response displacement; and a response interlayer deformation angle calculating step for obtaining a probability distribution of response interlayer deformation angles due to an earthquake based on a simulation for a group of buildings; A damage rate calculating step for obtaining a relationship between the strength of the earthquake and the damage rate of the building from the past earthquake damage results, and the probability distribution of the response interlayer deformation angle and the previous A critical deformation angle calculating step for calculating a critical deformation angle of the building based on a damage rate, and a damage prediction step for predicting the occurrence of damage to the building by comparing the response deformation angle and the critical deformation angle. It is characterized by having.
According to such an earthquake damage prediction method, it is possible to predict the damage of buildings due to an earthquake with high reliability.

In this earthquake damage prediction method, it is preferable to further use a reduction coefficient of an equivalent attenuation constant of a history element defined as a random variable when calculating the response displacement. Further, it is desirable that the reduction coefficient of the equivalent attenuation constant of the history element is determined according to the restoring force characteristic of the building.
According to such an earthquake damage prediction method, it is possible to further improve the reliability.

In this earthquake damage prediction method, the response deformation angle and the limit deformation angle are each calculated as a lognormal distribution, and in the damage prediction step, an average value of the response deformation angle and an average value of the limit deformation angle May be compared.
According to such an earthquake damage prediction method, it is possible to perform a highly reliable prediction.

In this earthquake damage prediction method, each of the response deformation angle and the limit deformation angle is calculated as a lognormal distribution, and in the damage prediction step, a predetermined value higher than an average value of the response deformation angles and the limit You may compare with the average value of a deformation angle.
According to such an earthquake damage prediction method, it is possible to make a prediction with a more safety margin.

In this earthquake damage prediction method, it is preferable that a plurality of the limit deformation angles are determined according to the magnitude of damage.
According to such an earthquake damage prediction method, the degree of damage can be predicted.

In this earthquake damage prediction method, it is desirable to predict damage caused by an earthquake for a plurality of buildings distributed over a wide area.
According to such an earthquake damage prediction method, it is possible to appropriately determine the initial response of the restoration priority in the event of an earthquake.

  According to the present invention, it is possible to make a highly reliable prediction of building damage caused by an earthquake.

It is a figure which shows a system configuration. It is a flowchart which shows the concept about the earthquake damage prediction method in this embodiment. 3A and 3B are explanatory diagrams of a method for evaluating the limit interlayer deformation angle. It is a figure which shows the speed response spectrum in 5% of damping constants. 5A and 5B are explanatory diagrams of restoring force characteristics. It is a figure which shows the relationship between a plastic modulus and the equivalent damping constant heq of a hysteresis element. 7A and 7B are diagrams showing the relationship between the plasticity ratio μa and the average attenuation constant hs. 8A and 8B are diagrams showing the distribution shape of the reduction coefficient d of the equivalent attenuation constant of the hysteresis element. 9A and 9B are diagrams showing the distribution shape of the correction coefficient a of the equivalent linear response displacement. It is a figure which shows the distribution shape of the correction coefficient r of an attenuation correction coefficient. 11A and 11B are explanatory diagrams of the relationship between the plasticity ratio μa of the one-degree-of-freedom elastic-plastic system and the plasticity ratio μe of the equivalent one-degree-of-freedom system. It is the figure which showed the relationship between a damage rate and the limit interlayer deformation | transformation angle | corner R 'for every damage degree (a small breakage, a medium breakage, a heavy breakage, collapse). 13A to 13C are diagrams illustrating the relationship between the ground surface maximum speed and the damage level of a building. 14A to 14C are diagrams illustrating the relationship between the measured seismic intensity and the damage level of a building.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In the following, a personal computer will be described as an example of a system (apparatus) for executing the earthquake damage prediction method of the present invention, but the present invention is not particularly limited thereto.

=== System configuration ===
FIG. 1 is a diagram showing a system configuration. The system shown in FIG. 1 includes a computer 10 having a CPU and a memory, a storage device 11, an input device 12, and an output device 13. In the present embodiment, the computer 10 is a personal computer, but is not limited to this. The storage device 11 is, for example, a hard disk or a memory. The storage device 11 stores various programs, for example, a program for causing the computer 10 to execute earthquake damage prediction. The storage device 11 stores data related to past earthquakes, data related to buildings, and the like. The storage device 11 may be built in the computer 10 or may be externally attached to the computer 10. The storage device 11 may be provided in another computer connected to the computer 10 via a network (for example, a local area network (LAN)). The input device 12 is for inputting various conditions and data to the computer 10, and is, for example, a keyboard or a mouse. The output device 13 is for outputting (displaying) the calculation result of the computer 10, and is, for example, a display.

  The above program may be stored in the storage device 11 from the recording medium 14 such as a flexible disk, a CD-ROM, a DVD-ROM, or a semiconductor memory, or via a network (for example, a LAN). It is good also as acquiring from other connected computers.

  In this embodiment, when a response spectrum of earthquake motion and building conditions (construction year, structure type, building floor number, structural seismic index, etc.) are input from the input device 12, the response deformation angle S and the limit deformation are calculated by the computer 10 as will be described later. The angle R is calculated as a lognormal distribution considering uncertainty. The damage is predicted based on the comparison between the response deformation angle S and the limit deformation angle R, and the prediction result is output to the output device 13.

=== Outline of earthquake damage prediction ===
FIG. 2 is a flowchart showing the concept of the earthquake damage prediction method in the present embodiment. An outline of the earthquake damage prediction method of the present embodiment will be described with reference to FIG.

≪Evaluation of response deformation angle≫
In this embodiment, a multi-degree-of-freedom building is reduced to a one-degree-of-freedom model (in other words, using a simple model in which the building is replaced with one layer), and the response deformation angle S of the building is converted into an equivalent linearization method. Based on the evaluation. In the equivalent linearization method, the response deformation angle of the elasto-plastic system is predicted using the response deformation angle of the elastic system, so that model uncertainty is generated according to the seismic motion characteristics and the building characteristics. Therefore, as will be described later, the response displacement δe of the equivalent one-degree-of-freedom system is evaluated in consideration of the model uncertainty (S11), and the response deformation angle S using the response displacement δe of the equivalent one-degree-of-freedom system. Is evaluated (S12).

≪Evaluation of limit deformation angle≫
One method for evaluating the limit value of a building in consideration of uncertainties associated with fluctuations in material strength and strength evaluation formulas is to use a damage rate curve created based on past earthquake damage data. However, since the damage rate curve is created for buildings, it includes multiple buildings with different proof stresses, and only the relationship between the seismic intensity and the damage rate of the buildings can be obtained. It is not possible to evaluate the limit deformation angle R of a building by itself. For this reason, in this embodiment, the damage rate of the building group is obtained using the damage rate curve of the past literature (S21), and Monte Carlo simulation is performed on the building group model (S22), and the response interlayer deformation angle is calculated. A probability distribution is obtained (S23). Then, the limit deformation angle R of the building is evaluated based on the reliability theory so that the earthquake damage result can be simulated by combining the probability distribution of the response interlayer deformation angle and the damage rate (S24).

≪Evaluation of disaster damage≫
The damage of the building is evaluated by comparing the response deformation angle S and the limit deformation angle R of the building (S30). In the present embodiment, four critical deformation angles R are set according to the magnitude of damage, and the response deformation angle S is compared with the four critical deformation angles R, so that the degree of damage (small damage, Medium damage, major damage, collapse).
Hereinafter, details of each item of the flow will be described.

=== About Evaluation of Response Deformation Angle S of Building ===
<Evaluation method of response displacement δe of equivalent single-degree-of-freedom system>
As described above, in this embodiment, a multi-degree-of-freedom system (multi-layer) building is contracted to a one-degree-of-freedom system (one layer), and the response displacement of the one-degree-of-freedom elasto-plastic system at the time of earthquake is the maximum point. Evaluate using the equivalent linearization method with stiffness. In the equivalent linearization method, the response displacement of the elasto-plastic system is predicted using the response displacement of the elastic system, so that model uncertainty associated with the prediction error occurs according to the seismic motion characteristics and the building characteristics. Therefore, the response displacement δe of the equivalent one degree of freedom system is evaluated in consideration of the model uncertainty.
In the equation (1), the average value E [he] of the equivalent damping constant he, the correction coefficient a of the equivalent linear response displacement, and the correction coefficient r of the damping correction coefficient are evaluated by the following method.

<Reduction factor of equivalent damping constant of hysteresis element>
Since the equivalent linearization method is strictly established in a steady state with respect to a harmonic external force, when applying the equivalent linearization method to an earthquake in an unsteady state, it is necessary to appropriately set the equivalent stiffness and equivalent damping. For this reason, the equivalent stiffness ke is set using the maximum response displacement δa of the one-degree-of-freedom elastic-plastic system.
(Source: Akinori Shibata: Latest Seismic Structural Analysis, Morikita Publishing, 1981)
The equivalent damping is set using an equivalent damping constant heq of a hysteresis element assuming a steady resonance state.

However, since the response at the time of an earthquake is not in a steady resonance state, if the equivalent damping constant heq in the above equation is used as it is, there is a risk of overestimating the attenuation of the hysteresis element and underestimating the response displacement of the one-degree-of-freedom elastic-plastic system. . Therefore, equivalent damping is obtained by multiplying the hysteresis element equivalent damping constant heq of equation (3) by the reduction factor d so that the response displacement of the one degree of freedom elastic-plastic system can be predicted using the response displacement of the one degree of freedom elastic system. Evaluate as the constant he.

The reduction coefficient d of the hysteresis element equivalent damping constant is determined so that the hysteresis element equivalent damping constant heq matches the average damping characteristic of the one-degree-of-freedom elastic-plastic system during an earthquake.
In addition, the average damping constant hs is evaluated on the assumption that the seismic input energy to the one-degree-of-freedom elastic-plastic system has been converted into the equivalent dashpot damping energy having the equivalent stiffness ke.
(Source: Akinori Shibata: Latest Seismic Structural Analysis, Morikita Publishing, 1981)
The equivalent natural circular frequency ωe is calculated using the equivalent stiffness ke in the equation (2).
However, since the reduction coefficient d of the equivalent attenuation constant of the hysteresis element varies depending on the seismic motion characteristics and the building characteristics, the average value E [he] of the equivalent attenuation constant he is evaluated using the average value E [d] of d. .

<Equivalent linear response displacement correction factor>
Since the response displacement of the one-degree-of-freedom elastic-plastic system is predicted using the response displacement of the equivalent one-degree-of-freedom system, model uncertainty associated with the prediction error occurs between the response displacement of the one-degree-of-freedom elastic-plastic system. For this reason, the correction coefficient a of the equivalent linear response displacement defined by the ratio of both is modeled as a random variable.

<Correction coefficient for attenuation correction coefficient>
The displacement response spectrum with the period T and the attenuation constant h is obtained by multiplying the displacement response spectrum S _D (T, 0.05) with the attenuation constant 5% by the attenuation correction coefficient F (h). However, since the displacement response spectrum predicted by multiplying the attenuation correction coefficient F (h) does not completely match the displacement response spectrum calculated from the seismic response analysis, model uncertainty associated with the prediction error occurs. Therefore, the displacement response spectrum S _D (T, h) of the one-degree-of-freedom elastic system is calculated from the seismic response analysis, the ratio to the attenuation correction coefficient F (h) is set as the correction coefficient r of the attenuation correction coefficient, and r is a random variable. As a model.
The attenuation correction coefficient F (h) is set by the following equation.
(Source: Architectural Institute of Japan: Building Load Guidelines / Comments, 1993)
For example, when h = 0.05, F (h) = 1.

<Building response deformation angle S>
The response deformation angle S of the building is evaluated using the response displacement δe of the equivalent one degree of freedom system of the equation (1).
In Eq. (12), H ₁ is the first-order equivalent height, and when a building is modeled by the uniform mass shear system of the inverted triangular first-order mode, H ₁ is obtained from the following equation.
From equation (12) and equation (1), the response deformation angle S of the building is
When the natural logarithm of both sides is taken, the natural logarithm lnS of the response deformation angle S is expressed by the following equation.

When the correction coefficient a of the equivalent linear response displacement and the correction coefficient r of the attenuation correction coefficient are modeled with a lognormal distribution, the distribution shape of the response deformation angle S of the building also becomes a lognormal distribution, and the probability density function F ( s) is calculated from the following equation.
The logarithmic average value λs of the response deformation angle S is calculated using the equation (15):
The logarithmic standard deviation ζs of the response deformation angle S is given by the following equation.

The logarithmic average value λa and logarithmic standard deviation ζa of the correction coefficient a of the equivalent linear response displacement are calculated from the following equations.
Similarly, the logarithmic average value λr and the logarithmic standard deviation ζr of the correction coefficient r of the attenuation correction coefficient are also calculated.
Thus, in this embodiment, the building is reduced to a one-degree-of-freedom system, and the response displacement δe of the equivalent one-degree-of-freedom system is evaluated using the equivalent linearization method. In this embodiment, uncertainty (variation) is taken into account when evaluating the response displacement δe by the equivalent linearization method. Specifically, the response displacement δe is evaluated using the modeled correction coefficient of the equivalent linear response displacement and the correction coefficient of the attenuation correction coefficient. The response deformation angle S is evaluated based on the response displacement δe.

=== About the evaluation of the limit deformation angle R of the building ===
The critical deformation angle R of the building is a reliability theory that can simulate the earthquake damage result by newly combining Monte Carlo simulation targeting the building group model with the damage rate of the building group obtained from past earthquake damage data. Set based on. First, using the damage rate curve created from the earthquake damage data, the relationship between the seismic intensity and the damage rate of the building group is obtained. Next, a building group model is created and Monte Carlo simulation is performed. The relationship between the seismic intensity and the distribution of the response interlayer deformation angle is calculated, and the damage probability P is analytically obtained assuming the distribution of the critical interlayer deformation angle. The interlayer deformation angle is obtained by standardizing the interlayer displacement by the floor height. And when the seismic intensity is the same value, by dividing the damage rate r of the building group obtained from the damage rate curve and the damage probability P found analytically, Evaluate log standard deviation.

  3A and 3B are explanatory diagrams of a method for evaluating the limit interlayer deformation angle. FIG. 3A is a diagram showing a result of an earthquake response analysis for a building group model. Moreover, FIG. 3B is a figure which shows the damage rate curve of a building group. 3A and 3B, the horizontal axis represents the ground surface maximum speed. Moreover, the vertical axis | shaft of FIG. 3A is an interlayer deformation angle, and the vertical axis | shaft of FIG. 3B is a damage rate.

  As shown in FIG. 3A, the limit interlayer deformation angle is constant regardless of the ground surface maximum velocity (in other words, the magnitude of the ground motion), but the response interlayer deformation angle changes in size according to the ground surface maximum velocity. In the same figure, the line which connects the median value of the response interlayer deformation angle for each ground surface maximum velocity (V1, V2,..., Vn) is shown. Thus, the response interlayer deformation angle increases as the ground surface maximum speed increases. Moreover, as can be seen from the damage rate curve in FIG. 3B, the damage rate increases as the ground surface maximum speed increases. Based on this relationship, the critical interlayer deformation angle is evaluated so that the earthquake damage results can be simulated.

The limit state function Z for the building group model is defined using the distribution of the response interlayer deformation angle Q and the distribution of the limit interlayer deformation angle R ′.
When the distributions of the response interlayer deformation angle Q and the limit interlayer deformation angle R ′ are both modeled by a lognormal distribution, the reliability index β corresponding to the limit state function Z is obtained from the following equation.

The logarithmic mean value and logarithmic standard deviation of the response interlayer deformation angle are calculated using the following equations.
At this time, the damage probability P for the building group model is obtained from the following equation.
On the other hand, the damage rate r of the group of buildings is calculated from a damage rate curve created using past earthquake damage data.

When the ground surface maximum speed is v, the damage probability P for the building group model and the damage rate r obtained from the damage rate curve are set to be equal.
In summary, the logarithmic average value λ _R and the logarithmic standard deviation ζ _{R of} the limit interlayer deformation angle R ′ can be obtained from the following equations.

As described above, the limit deformation angle R of the building is evaluated using the limit interlayer deformation angle R ′.
As described above, in this embodiment, the limit deformation angle R is evaluated by combining the damage rate of the building group obtained from the past earthquake damage data with the Monte Carlo simulation for the building group model. .

=== Evaluation of building damage level ===
By evaluating the response deformation angle S and the limit deformation angle R as described above, the distributions of the response deformation angle S and the limit deformation angle R are both modeled in a lognormal distribution. The average value E [S] of the response deformation angle S and the average value E [R _j ] of the limit deformation angle R are calculated from the following equations.

For example, if four levels (j = 1 to 4) of small damage, medium damage, major damage, and collapse are set as the damage degree j of the building, the damage degree is an average value E of response deformation angles as shown in Table 1. It can be evaluated by comparing [S] with the average value E [R _j ] of the critical deformation angle.

Note that since the uncertainty associated with the prediction error is modeled, a predetermined value (for example, a value corresponding to a non-exceeding 90% value) higher than the average value may be used for the determination as the response deformation angle. At this time, the 90% non-excess value S ₉₀ of the response deformation angle is calculated from the following equation.
In equation (34), the coefficient g corresponds to the target non-exceeding value, and when the value is 90% non-exceeding value, g = 1.28.

Table 2 shows the criteria for determining the damage level of a building using a 90% non-excessive value S ₉₀ of the response deformation angle.
In this way, when determining the degree of damage, using the 90% non-excess value S ₉₀ of the response deformation angle S (Table 2), more than when using the average value E [S] (Table 1) Predictions can be made with safety margins in mind.

=== Example of Evaluation of Response Deformation Angle S of Building ===
≪Analysis condition≫
For RC buildings, the reduction coefficient of the equivalent damping constant of the hysteresis element, the correction coefficient of the equivalent linear response displacement, and the correction coefficient of the damping correction coefficient were evaluated.
In this evaluation, two types of restoring force characteristics of a one-degree-of-freedom elasto-plastic system, namely, an origin-oriented type and a rigidity-reduced trilinear type, were set as shown in Table 3.

Here, the above (reduction factor of equivalent damping constant of hysteresis element, correction factor of equivalent linear response displacement, and correction factor of damping correction factor) is examined for the case where the plasticity factor μa falls within the range of Table 4. It was.

In order to take into account the uncertainty of the ground motion characteristics, seismic response analysis was performed for multiple ground motions. Table 5 shows a list of ground motion used for the earthquake response analysis.
FIG. 4 is a diagram showing a velocity response spectrum at a damping constant of 5% in each earthquake motion in Table 5. In addition, the horizontal axis of a figure is a period (sec), and a vertical axis | shaft is a speed response.

≪Equivalent damping constant heq≫
The restoring force characteristics of RC buildings were set according to the construction year, and the equivalent damping constant heq of the hysteresis element was obtained. As described above, the restoring force characteristics are of two types: the origin-oriented type and the reduced rigidity trilinear type. Table 6 shows the relationship between the construction year and the restoring force characteristics.
5A and 5B are explanatory diagrams of restoring force characteristics. FIG. 5A shows the restoring force characteristic in the case of the origin-oriented type, and FIG. 5B shows the restoring force characteristic of the reduced rigidity trilinear type. In FIGS. 5A and 5B, the horizontal axis is the displacement amount, and the vertical axis is the shearing force.

<Origin-oriented equivalent damping constant (see FIG. 5A)>

<Equivalent damping constant of reduced rigidity trilinear type (see FIG. 5B)>

  FIG. 6 is a diagram showing the relationship between the plasticity factor and the equivalent damping constant (heq) of the hysteresis element. In the figure, the horizontal axis represents the plasticity factor, and the vertical axis represents the equivalent attenuation constant. In the figure, the solid line shows the relationship between the plasticity factor in the origin-oriented type and the equivalent damping of the hysteresis element, and the broken line shows the relationship between the plasticity factor and the equivalent damping of the hysteresis element in the reduced rigidity trilinear type.

≪Relationship between plastic modulus and average damping constant≫
Seismic response analysis of one-degree-of-freedom elastoplastic system was performed, and the average damping constant hs was calculated. Further, the equivalent attenuation constant he was calculated by changing the reduction coefficient d of the equivalent attenuation constant of the hysteresis element from 0.1 to 1.0.
7A and 7B are diagrams showing the relationship between the plasticity ratio μa and the average attenuation constant hs. 7A is a diagram in the case of the origin-oriented type, and FIG. 7B is a diagram in the case of the reduced-rigidity trilinear type.
The figure also shows the equivalent attenuation constant he when the reduction coefficient d of the equivalent attenuation constant of the hysteresis element is changed from 0.1 to 1.0. When the average damping constant hs and the equivalent damping constant he were compared, there was a tendency that he> hs at d = 1.0. For this reason, it can be seen that if the equivalent attenuation constant heq of the history element is used as it is, the history attenuation at the time of earthquake is overestimated.

≪Reduction factor of equivalent damping constant of history element≫
Table 7 shows the calculation result of the reduction coefficient d of the equivalent attenuation constant of the hysteresis element.
8A and 8B are diagrams showing the distribution shape of the reduction coefficient d of the equivalent attenuation constant of the hysteresis element. 8A is a diagram in the case of the origin-oriented type, and FIG. 8B is a diagram in the case of the reduced-rigidity trilinear type.

<< Equivalent linear response displacement correction factor >>
Table 8 shows the calculation result of the correction coefficient a of the equivalent linear response displacement.
9A and 9B are diagrams showing the distribution shape of the correction coefficient a for the equivalent linear response displacement. 9A is a diagram in the case of the origin-oriented type, and FIG. 9B is a diagram in the case of the reduced-rigidity trilinear type.

  Further, in the figure, a curve obtained by modeling the distribution shape with a lognormal distribution is shown. As described above, the distribution of the correction coefficient of the equivalent linear response displacement can be modeled using the lognormal distribution. In addition, the average value of the correction coefficient for the equivalent linear response displacement is about 1.14 for the origin-oriented type, which is slightly larger than 1, but about 1.0 for the low-rigidity trilinear type, and one free using the average value of the equivalent damping constant he. The response displacement of the elastic-plastic system can be roughly predicted.

≪Attenuation correction coefficient correction coefficient≫
Table 9 shows the calculation result of the correction coefficient r of the attenuation correction coefficient.
FIG. 10 is a diagram showing the distribution shape of the correction coefficient r of the attenuation correction coefficient. In the figure, the distribution shape is modeled by a lognormal distribution. As described above, the distribution of the correction coefficient of the attenuation correction coefficient can be modeled using the lognormal distribution.

≪Comparison of plastic modulus≫
11A and 11B are explanatory diagrams of the relationship between the plasticity ratio μa of the one-degree-of-freedom elastic-plastic system calculated from the seismic response analysis and the plasticity ratio μe (average value and 90% non-exceeding value) of the equivalent one-degree-of-freedom system. It is. 11A is a diagram in the case of the origin-oriented type, and FIG. 11B is a diagram in the case of the reduced-rigidity trilinear type.
When the plastic modulus μe is an average value, μa> μe, which may be a predicted value on the dangerous side, but in the case of a non-exceeding 90% value, except for a relatively large plasticity region, it is almost μe> μa. It has become. Therefore, it can be said that the response displacement of the one-degree-of-freedom elasto-plastic system can be predicted more safely by using the 90% non-exceeding value in consideration of the model uncertainty associated with the prediction error as compared with the case of using the average value.

=== Evaluation example of limit deformation angle R of building ===
Next, an example of evaluating the limit deformation angle R of a building will be described. In this evaluation example, the limit deformation angle R of the building was set so as to simulate the earthquake damage result for the 1995 Hyogoken-Nanbu Earthquake. As described above, the limit deformation angle R of the building was evaluated using the limit interlayer deformation angle R ′.
First, for RC buildings, the building year is set to 5 types, 2 types before 1970 and after 1982, and 3 floors, 3rd floor, 7th floor, 10th floor (only after 1982). RC building group model was created. Then, the logarithmic mean value λ _Q and the logarithmic standard deviation ζ _Q of the response interlayer deformation angle _Q were calculated by the seismic response analysis by Monte Carlo simulation.

Next, the logarithmic mean value λ _R and logarithmic standard deviation ζ _R of the critical interlayer deformation angle R ′ were calculated so as to reproduce the damage rate curve of the RC building group in the Hyogoken-Nanbu Earthquake. Table 10 shows the calculation results of the logarithmic average value λ _R and logarithmic standard deviation ζ _R of the limit interlayer deformation angle R ′.

In RC buildings that have been damaged by the Hyogoken-Nanbu Earthquake, there is a 1: 1 relationship between the number of damaged and collapsed buildings. A deformation angle R ′ was set.
FIG. 12 is a diagram showing the relationship between the damage rate and the limit interlayer deformation angle R ′ for each degree of damage (small damage, medium damage, heavy damage, collapse). In the figure, the horizontal axis is the critical interlayer deformation angle, and the vertical axis is the damage rate. When the limit deformation angle R of the building is evaluated using the limit interlayer deformation angle R ′, the limit deformation angle R for each degree of damage is as shown in FIG.

=== Evaluation example of earthquake damage prediction ===
Next, an evaluation example in which earthquake damage is predicted based on the evaluation result of the response deformation angle S and the evaluation result of the limit deformation angle R described above will be described.

≪About analysis conditions≫
・ Number of building floors: 1 to 15 floors ・ Construction year: before 1970, 1971-1981, after 1982 ・ Structural type: RC building
Table 11 shows the average values of the structural seismic index Is corresponding to the building year and the number of floors when RC buildings are targeted.
(Source: Non-life Insurance Rate Calculation Group: Earthquake Damage Assumptions Collection, 1998)

The elastic period T _{1 of the} building is obtained from the following equation.
The yield shear force coefficient Cy is obtained from the following equation.

The acceleration response spectrum S _A (T, h) of the building load guideline (1993) is set as the response spectrum of earthquake motion.
(Source: Architectural Institute of Japan: Building Load Guidelines / Comments, 1993)

≪Relationship between maximum ground surface speed and damage level of buildings≫
The average value E [S] of the response deformation angle and the average value E [R _j ] of the limit deformation angle were calculated using the above-described conditions. And the damage degree of the building was determined from Table 1.
13A to 13C are diagrams illustrating the relationship between the ground surface maximum speed and the damage level of a building. The horizontal axis in the figure is the maximum ground speed (m / s), and the vertical axis is the degree of damage. 13A shows a case of a building before 1970, FIG. 13B shows a case of a building from 1971 to 1981, and FIG. 13C shows a case of a building after 1982, respectively. In each figure, the relationship between the maximum ground speed and the degree of damage is shown for each of the 1-story to 15-story buildings.

≪Relationship between measured seismic intensity and damage level of buildings≫
The following relational expression is established between the ground surface maximum velocity and the measured seismic intensity.
(Source: National Institute of Science and Technology for Disaster Prevention: Examination of Probabilistic Seismic Ground Motion Prediction Mapping Method for Japan, 2005)
Therefore, it is also possible to obtain the relationship between the measured seismic intensity and the degree of damage.

14A to 14C are diagrams illustrating the relationship between the measured seismic intensity and the damage level of a building. The horizontal axis of the figure shows the measured seismic intensity, and the vertical axis shows the degree of damage. 14A shows the case of a building before 1970, FIG. 14B shows the case of a building from 1971 to 1981, and FIG. 14C shows the case of a building after 1982, respectively. In each figure, the relationship between the measured seismic intensity and the degree of damage is shown for each of the 1-story to 15-story buildings.
If such an evaluation result is displayed on the output device 13, for example, it is possible to easily grasp the degree of damage for each building according to the magnitude of the earthquake.
Note that this embodiment is applied to each of a large number of buildings distributed over a wide area to predict damage (damage level), and the results are output (displayed) to the output device 13 as a distribution map color-coded according to the degree of damage, for example. ). By doing so, it is possible to appropriately determine the initial response of restoration priorities in the event of an earthquake.

  As described above, in this embodiment, the building is reduced to a one-degree-of-freedom system, and the response displacement δe of the one-degree-of-freedom elastic-plastic system at the time of an earthquake is evaluated by the equivalent linearization method. In the present embodiment, when calculating the response displacement δe using the equivalent linearization method, the correction coefficient of the equivalent linear response displacement, the correction coefficient of the attenuation correction coefficient, and the reduction coefficient of the equivalent attenuation constant of the hysteresis element are modeled. Model uncertainties associated with earthquake motion characteristics and building characteristics. Then, the response deformation angle S is evaluated using the response displacement δe.

In addition, the building deformation rate based on the reliability theory is used to simulate the earthquake damage result by combining the damage rate of the building group obtained from past earthquake damage data with Monte Carlo simulation for the building group model. The angle R is evaluated.
The damage degree of the building is evaluated by comparing the response deformation angle S and the limit deformation angle R.
By doing so, since it is possible to make a prediction in consideration of the uncertainty, it is possible to predict the damage level of the building at the time of the earthquake with high reliability.

  The above embodiment is for facilitating the understanding of the present invention, and is not intended to limit the present 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.

10 computers, 11 storage devices, 12 input devices,
13 output device, 14 recording medium

Claims (7)

An earthquake damage prediction method for predicting building damage caused by an earthquake,
A response displacement calculation step of calculating a response displacement with respect to an earthquake when the building is contracted to a one-degree-of-freedom system by an equivalent linearization method, and a correction coefficient and an attenuation correction of an equivalent linear response displacement determined as a random variable A response displacement calculating step of calculating the response displacement using a coefficient correction coefficient;
A response deformation angle calculating step of calculating a response deformation angle of the building from the response displacement;
A response interlayer deformation angle calculation step for obtaining a probability distribution of response interlayer deformation angles due to an earthquake based on a simulation for a building group;
A damage rate calculation step for determining the relationship between the strength of the earthquake and the damage rate of the building from past earthquake damage results;
Based on the probability distribution of the response interlayer deformation angle and the damage rate, a critical deformation angle calculating step for calculating a critical deformation angle of the building;
A damage prediction step for predicting the occurrence of damage to the building by comparing the response deformation angle and the limit deformation angle;
An earthquake damage prediction method characterized by comprising: The earthquake damage prediction method according to claim 1,
An earthquake damage prediction method characterized by further using a reduction factor of an equivalent attenuation constant of a history element defined as a random variable when calculating the response displacement. The earthquake damage prediction method according to claim 2,
A method for predicting earthquake damage, wherein a reduction coefficient of an equivalent attenuation constant of the history element is determined according to a restoring force characteristic of a building. An earthquake damage prediction method according to any one of claims 1 to 3,
The response deformation angle and the limit deformation angle are each calculated as a lognormal distribution,
In the damage prediction step, an average value of the response deformation angles is compared with an average value of the limit deformation angles. An earthquake damage prediction method according to any one of claims 1 to 3,
The response deformation angle and the limit deformation angle are each calculated as a lognormal distribution,
In the damage prediction step, a predetermined value higher than the average value of the response deformation angles is compared with the average value of the limit deformation angles. An earthquake damage prediction method according to any one of claims 1 to 5,
2. A method for predicting earthquake damage, wherein a plurality of said limit deformation angles are determined according to the magnitude of damage. An earthquake damage prediction method according to any one of claims 1 to 6,
An earthquake damage prediction method characterized by predicting damage to a plurality of buildings distributed over a wide area.