Building seismic motion evaluation system and building seismic motion evaluation method

Abstract

This system evaluates the seismic motion transmitted to buildings with greater accuracy. [Solution] The system calculates the power spectrum of the earthquake observation records at each location and the cross spectrum of the earthquake observation records between the locations from the earthquake observation records of each adjacent location, and calculates the coherence observation value, which is a value of the coherence of earthquake motion that represents the degree of correlation of earthquake motion, based on the earthquake observation records. The system comprises a coherence formulating unit 4 that formulates a coherence formula to express coherence using the horizontal correlation distance and the vertical correlation distance as variables, a correlation distance determination unit 5 that determines the horizontal correlation distance and the vertical correlation distance so that the difference between the value of the coherence formula and the coherence observation value is small, and a building earthquake motion evaluation unit 6 that constructs a surface ground model based on the determined horizontal and vertical correlation distances and evaluates building earthquake motion by inputting earthquake motion into the surface ground model.

Description

[Technical Field]

[0001] The present invention relates to a building seismic motion evaluation system and a building seismic motion evaluation method for evaluating building seismic motion input to a building. [Background technology]

[0002] Conventionally, various seismic response evaluation methods for buildings have been developed to estimate the magnitude of building shaking based on seismic observation records obtained from seismometers and other devices installed on the ground surface during earthquakes. For example, Patent Document 1 discloses a method for estimating earthquake damage to a reinforced concrete building caused by an earthquake. This estimation method includes: a first step to obtain essential information for assuming earthquake damage, such as the seismic characteristics of the reinforced concrete building; a second step which selectively performs, based on the results of the first step, processing required when analyzing a single-mass system, such as measuring microtremors in the reinforced concrete building, and processing that is expected to improve the accuracy of the estimation by utilizing boring data, etc.; a third step which selectively performs, processing a damage assessment matrix based on earthquake records and the results obtained in the second step to estimate the earthquake damage to the reinforced concrete building; and processing an elastoplastic response analysis based on earthquake records and the results obtained in the second step, and estimates the earthquake damage to the reinforced concrete building from the plasticity ratio obtained in the analysis.

[0003] In conventional methods for evaluating the seismic response of buildings, the building is generally modeled as a single-mass system or a multi-mass system, and the seismic motion observed by seismometers installed on the ground surface is directly input to the mass corresponding to the foundation base to evaluate the building's response. However, in real-world phenomena, even between adjacent points separated by only a few meters or tens of meters, spatial variations in phase and amplitude of seismic motion are observed. Such spatial variations in seismic motion between adjacent points are thought to occur due to differences in the propagation speed of seismic motion caused by the heterogeneity of the surface ground, even at close proximity. When spatial variations in seismic motion occur between adjacent points, the seismic motion input to a building may be reduced. It is also thought that this may have the effect of exciting rotation and torsion of the building. Therefore, when evaluating the response of a building as described above, it is desirable to consider the heterogeneity of the surface ground in order to evaluate the seismic motion input to the building more accurately.

[0004] In this regard, Patent Document 2 discloses a ground vibration analysis system that generates a finite element method model of the ground to be analyzed and performs a stability evaluation of the ground. This ground vibration analysis system includes: an average value finite element method model generation means for determining the average value of the ground physical properties and generating a finite element method model using the average value of the ground physical properties; a standard deviation value finite element method model generation means for determining the standard deviation value of the ground physical properties and generating a finite element method model using the standard deviation value of the ground physical properties; an assumed slip line setting means for setting an assumed slip line of the ground to be analyzed; an input seismic motion setting means for setting an input seismic motion that applies an external force to the ground; an average value seismic stress calculation means for calculating the stress during an earthquake using an input seismic motion as an external force and a finite element method model using the average value of the ground physical properties; a standard deviation value seismic stress calculation means for calculating the stress during an earthquake using an input seismic motion as an external force and a finite element method model using the standard deviation value of the ground physical properties; and a force calculation means for calculating the force acting on the assumed slip line by Monte Carlo method based on the seismic stress by the average value and the seismic stress by the standard deviation value. In Patent Document 2, as described above, the average value and standard deviation of the soil properties are used. However, with such a configuration, it may still not be possible to evaluate the seismic motion input to the building with sufficient accuracy.

[0005] In contrast, Patent Document 3 discloses a method for evaluating the magnitude of seismic motion input to a building. This method calculates the average waveform component of the amplitude between waveforms and the variability waveform component representing the residual between the amplitude of each waveform and the average waveform component for waveforms obtained as seismic observation records at each adjacent point, calculates a variability index between waveforms, calculates the variability index, calculates the coefficient of variation of the heterogeneity of S-wave velocity in the surface ground, calculates the wavenumber of the heterogeneous medium and the wavenumber of the seismic wave, which are heterogeneity parameters of a 3D surface ground model, calculates the horizontal correlation distance and the vertical correlation distance of the S-wave velocity in the surface ground, and constructs a 3D surface ground model that reflects the heterogeneity based on the horizontal and vertical correlation distances, and evaluates the magnitude of the seismic motion. In actual surface ground, the velocity structure changes more frequently in the vertical direction than in the horizontal direction. In Patent Document 3, the horizontal correlation distance and the vertical correlation distance appear as separate parameters in the equation, and each is calculated as a separate value. As a result, the characteristics of the ground are represented more accurately in the surface ground model compared to when the surface ground model is constructed isotropically in the horizontal and vertical directions, i.e., when the correlation distances are the same. Therefore, the accuracy of evaluating seismic motion input to buildings is improved.

[0006] However, in Patent Document 3, the index of the degree of variation between waveforms used to determine the horizontal and vertical correlation distances is configured to consider only information related to amplitude. In this respect, there is room to further improve the accuracy of evaluating seismic motion input to buildings. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Japanese Patent Publication No. 2013-120139 [Patent Document 2] Japanese Patent Publication No. 2005-336914 [Patent Document 3] Japanese Patent Publication No. 2023-12586 [Overview of the project] [Problems that the invention aims to solve]

[0008] The problem that this invention aims to solve is to provide a building seismic motion evaluation system and a building seismic motion evaluation method that can evaluate the seismic motion input to a building with higher accuracy. [Means for solving the problem]

[0009] To solve the above problems, the present invention employs the following means. That is, the present invention is a building seismic motion evaluation system for evaluating building seismic motion input to a building, comprising: a coherence observation value calculation unit that calculates the power spectrum of the seismic observation record at each of the adjacent locations and the cross spectrum of the seismic observation record between the locations from the seismic observation records of each of the adjacent locations, and calculates a coherence observation value which is a value based on the seismic observation record that represents the degree of correlation of seismic motion; and heterogeneity parameters of the surface ground where each of the locations is located, namely the horizontal correlation distance and the vertical The present invention provides a building seismic motion evaluation system comprising: a coherence formulating unit that formulates a coherence formula to express the coherence using the correlation distance in a direction as a variable; a correlation distance determination unit that determines the horizontal correlation distance and the vertical correlation distance so that the difference between the value of the coherence formula and the observed coherence value is small; and a building seismic motion evaluation unit that constructs a surface ground model based on the determined horizontal correlation distance and the vertical correlation distance, and evaluates the building seismic motion by inputting seismic motion into the surface ground model. With the configuration described above, first, a coherence observation value is calculated from the seismic observation records of each adjacent location, representing the degree of correlation between seismic motions between locations. Next, a coherence equation is formulated to express the coherence of seismic motions, using the horizontal correlation distance and vertical correlation distance, which are heterogeneity parameters of the surface ground where each location is situated, as variables. The value of the coherence equation formulated in this way should be the same as or close to the coherence observation value, provided that appropriate values ​​are set for the variables. Therefore, by determining the horizontal and vertical correlation distances so that the difference between the value of the coherence equation and the coherence observation value is small, accurate values ​​for each of the horizontal and vertical correlation distances can be obtained. Based on the horizontal and vertical correlation distances obtained in this way, a surface ground model is constructed, and by inputting seismic motion into the surface ground model, building seismic motion can be evaluated with high accuracy. In particular, in the above embodiment, the coherence observation value, which is the target of calculation as the difference between the coherence formula in which the horizontal correlation distance and the vertical correlation distance are reflected as variables, is calculated based on the power spectrum of the seismic observation record at each location and the cross spectrum of the seismic observation record between locations. Since the cross spectrum of the seismic observation record between locations reflects not only the amplitude but also the phase of the seismic observation record, both amplitude and phase are reflected in the coherence observation value of the seismic motion. Therefore, both amplitude and phase are reflected in both the horizontal correlation distance and the vertical correlation distance, which are calculated based on such coherence observation value of the seismic motion. In this way, by reflecting both amplitude and phase, the accuracy of the horizontal and vertical correlation distances is improved, and the accuracy of the surface ground model in which these horizontal and vertical correlation distances are set is improved. Therefore, the accuracy of the building seismic motion evaluated by inputting seismic motion into the surface ground model is further improved. In this way, it becomes possible to evaluate building ground motion, which is the seismic motion input to a building, with higher accuracy.

[0010] In one aspect of the present invention, the coherence formula unit calculates the propagation velocity of seismic motion and the coefficient of variation of the heterogeneity of said propagation velocity in the surface ground based on the results of a ground investigation, and the coherence formula unit uses the wave number k of the seismic motion calculated based on the propagation velocity, the coefficient of variation μ of the heterogeneity of said propagation velocity, the horizontal correlation distance a1, the vertical correlation distance a3, the distance ρ between the points, the propagation distance l of the seismic motion, the depth z from the ground surface, and the frequency f to calculate the following first formula

number

number

number

[0011] Furthermore, the present invention relates to a building seismic motion evaluation method for evaluating building seismic motion input to a building, comprising: a coherence observation value calculation step, which calculates the power spectrum of the seismic observation record at each of the adjacent locations and the cross spectrum of the seismic observation record between the locations from the respective seismic observation records of the adjacent locations, and calculates a coherence observation value, which is a value based on the seismic observation record that represents the degree of correlation of the seismic motion, and the heterogeneity parameters of the surface ground at each of the locations, which are the horizontal correlation distance and the vertical The present invention provides a method for evaluating building seismic motion, comprising: a coherence formulating step of formulating a coherence formula that expresses the coherence using the correlation distance as a variable; a correlation distance determination step of determining the horizontal correlation distance and the vertical correlation distance such that the difference between the value of the coherence formula and the observed coherence value is small; and a building seismic motion evaluation step of constructing a surface ground model based on the determined horizontal correlation distance and the vertical correlation distance, and evaluating the building seismic motion by inputting seismic motion into the surface ground model. With the configuration described above, as already explained regarding the building seismic motion evaluation system, it becomes possible to evaluate the building seismic motion, which is the seismic motion input to the building, with higher accuracy. [Effects of the Invention]

[0012] According to the present invention, it is possible to provide a building seismic motion evaluation system and a building seismic motion evaluation method that can evaluate the seismic motion input to a building with higher accuracy. [Brief explanation of the drawing]

[0013] [Figure 1] This is a block diagram of a building seismic motion evaluation system according to an embodiment of the present invention. [Figure 2] This is a schematic graph of the coherence observation values ​​calculated by the coherence observation value calculation unit of the above-mentioned building seismic motion evaluation system. [Figure 3]This graph shows the propagation distance L, which is assumed to affect the spatial variation of seismic motion, used when formulating the coherence equation in the coherence equation formulation section of the above-mentioned building seismic motion evaluation system. [Figure 4] This graph relates to the correction coefficient α for the separation distance, which is assumed not to affect the spatial variation of seismic motion, and is used when formulating the coherence equation in the above section on formulating coherence equations. [Figure 5] This is a schematic graph of the coherence formula formulated by the above coherence formula section. [Figure 6] This is a flowchart of the building seismic motion evaluation method using the above-mentioned building seismic motion evaluation system. [Figure 7] This is an explanatory diagram of the surface ground model used in the first verification of the above-mentioned building seismic motion evaluation system. [Figure 8] This figure shows an example of the S-wave velocity distribution on the side and surface of the above surface soil model. [Figure 9] This figure shows the response waves at the ground surface when seismic motion is input to the bottom of the surface ground model described above. [Figure 10] This graph shows the relationship between the coherence observation value, calculated by the coherence observation value calculation unit based on the above response wave, and the frequency. [Figure 11] This figure shows the search range for the horizontal and vertical correlation distances. [Figure 12] This is a graph of the coherence equation into which the horizontal and vertical correlation distances determined by the correlation distance determination unit of the above-mentioned building seismic motion evaluation system have been substituted. [Figure 13] This diagram shows the arrangement of seismometers at the observation facility used in the second verification of the above-mentioned building seismic motion evaluation system. [Figure 14] This figure shows the S-wave velocity structure at the observation facility described above. [Figure 15] This is an explanatory diagram of the earthquake observation records used in the second verification described above. [Figure 16]This graph shows the relationship between the coherence observation value and frequency, calculated by the coherence observation value calculation unit based on the above observation records. [Figure 17] This figure shows the horizontal and vertical correlation distances determined for each layer. [Figure 18] This figure shows an example of a heterogeneous pattern of S-wave velocity in a surface soil model. [Figure 19] This is a coherence graph calculated based on observed results for a surface ground model in which the horizontal and vertical correlation distances estimated in the second verification above were set. [Modes for carrying out the invention]

[0014] This invention is a building seismic motion evaluation system based on the heterogeneity of the surface ground, which is used to evaluate the building seismic motion (input seismic motion) transmitted to the building. The building seismic motion evaluation system evaluates the heterogeneity of the surface ground and estimates the seismic motion transmitted to the ground surface by setting a horizontal correlation distance a1 and a vertical correlation distance a3 that represent the continuity of the ground, based on ground investigation records, so as to match the observed coherence values ​​of seismic motion between adjacent points. Furthermore, the heterogeneity of the surface ground was estimated by calculating the mean shear wave velocity and the coefficient of variation of the shear wave velocity, and by assuming horizontal and vertical correlation distances using scattering theory. Specifically, the correlation (coherence) of seismic observation records between adjacent points was calculated, and the relationship between the heterogeneity of the surface ground and the coherence of seismic motion was formulated based on scattering theory to evaluate the spatial variation characteristics of seismic motion (for example, Ryoichi Tokumitsu, et al.: Construction of a spatial variation model of seismic motion based on seismic motion simulation using a 3D heterogeneous ground model, Journal of Structural Engineering, Architectural Institute of Japan, No. 797, pp. 657-668, 2022.7). In the building seismic motion evaluation system of the present invention, the accuracy of the equations relating to the above relationship is further improved, and these are used in conjunction with observed coherence values ​​to derive the horizontal correlation distance a1 and the vertical correlation distance a3. In this specification, seismic coherence is evaluated based on seismic observation records and ground investigation results as an indicator of how consistent and continuous the shaking of an earthquake is over time.

[0015] Embodiments of the present invention will be described in detail below with reference to the drawings. When evaluating a building's response to an earthquake, the seismic motion input to the building is necessary. The building seismic motion evaluation system in this embodiment constructs a surface ground model corresponding to the surface ground on which the building is located, and evaluates the building seismic motion by inputting the seismic motion into this surface ground model. In particular, the building seismic motion evaluation system in this embodiment appropriately determines the horizontal and vertical correlation distances of the seismic motion in the surface ground, which are heterogeneity parameters of the surface ground, and based on this, constructs a surface ground model that reflects the horizontal and vertical correlation distances, thereby evaluating the building seismic motion with high accuracy. Figure 1 is a block diagram of the building seismic motion evaluation system in this embodiment. The building seismic motion evaluation system 1 can be implemented using information processing equipment such as a personal computer or a server. Functionally, the building seismic motion evaluation system 1 includes a data storage unit 2, a coherence observation value calculation unit 3, a coherence formula unit 4, a correlation distance determination unit 5, a building seismic motion evaluation unit 6, and a results display unit 7.

[0016] The data storage unit 2 stores earthquake observation record data that has been input from an external source. Earthquake observation records are obtained by conducting earthquake observations on the construction site of the building, or within the area including this site, prior to the construction of the building. Earthquake observation records are, for example, waveforms of ground motion obtained from seismometers installed on the ground surface. In particular, in this embodiment, earthquake observation records are acceleration time history waveform data. Earthquake observation records are obtained by installing seismometers on the site and conducting earthquake observations. Earthquake observation records are acquired at multiple points within the construction site of the building, or within the area including this site. Each of these points is located at a distance of several meters to several tens of meters from each other. Hereafter, each of these points located at a short distance from each other within the construction site of the building, or within the area including this site, will be referred to as an adjacent point. In this way, the data storage unit 2 stores earthquake observation records for each of the adjacent locations.

[0017] Data storage unit 2 stores records of surface ground boring surveys that have been input from an external source. Boring survey records of the surface ground are obtained by conducting a boring survey of the surface ground in the area where the building will be constructed, or a certain area including the building site, prior to the construction of the building. The boring survey is conducted at one or more locations within the survey area. For example, if two adjacent locations are selected, it is preferable to conduct the survey at one or more locations midway between these two locations, or around that midway location. For example, if three or more adjacent locations are selected, it is preferable to conduct the survey at one or more locations at the center of these multiple locations, or around that center location.

[0018] The coherence observation calculation unit 3 selects two locations from among several adjacent locations and calculates the coherence of seismic motion between these two locations based on the seismic observation records of each location. Seismic motion coherence is an index that represents the degree of correlation between the shaking of an earthquake at two locations, that is, the degree of correlation of seismic motion between locations. Seismic motion consists of a mixture of multiple frequency components. Seismic motion coherence is determined by calculating the degree of correlation between seismic motion at different locations for each frequency component. The higher the degree of correlation for each frequency component, the more the waveforms of the seismic motion at two locations match, indicating that the vibration patterns are similar. When seismic motion coherence is high, the same frequency components of seismic motion occur at each location, leading to a greater impact on buildings.

[0019] In this embodiment, the coherence observation value calculation unit 3 calculates the coherence of seismic motion as follows. Here, we will describe the case in which coherence is calculated for two adjacent locations A and B. Hereafter, we will assume that multiple earthquake observation records m (m=1 to n, where n is the total number of earthquake observation records) are individually acquired at each of locations A and B by observing multiple earthquakes at each of locations A and B. First, the coherence observation value calculation unit 3 generates a Fourier spectrum for each of the earthquake observation records m at point A by performing a Fourier transform on the earthquake observation record m, for example, as acceleration time history waveform data. Then, for each of the multiple frequency (frequency component) f values, it squares the value of the Fourier spectrum corresponding to that frequency f, thereby generating the power spectrum G for each frequency f. A m Calculate (f). In cases where the seismic observation record m continues for a long period of time, the seismic observation record m is divided into multiple time domains using time windows with a fixed time interval, and after calculating the power spectrum for each time domain as described above, the average value of the power spectrum over different time intervals is calculated to obtain the power spectrum G A m You may calculate (f). The coherence observation value calculation unit 3 similarly calculates the power spectrum G for each frequency f for each earthquake observation record m for location B. B m Calculate (f).

[0020] Next, for each of the seismic observation records m, at each value of a plurality of frequencies f, the coherence observation value calculation unit 3 multiplies the values corresponding to the frequency f of the Fourier spectrum of the seismic observation record m calculated for each of location A and location B, thereby calculating the cross-spectrum G |ρ| m (f) for each frequency f. Here, ρ is the distance between location A and location B, that is, the separation distance. In the case where the seismic observation record m continues for a long time, similar to the case of the power spectrum, the seismic observation record m is divided into a plurality of time regions by time windows having a certain time interval, and after calculating the cross-spectrum for each time region as described above, the average value of the cross-spectrum between different time intervals is calculated, and thus the cross-spectrum G |ρ| m (f) may be calculated. The cross-spectrum G |ρ| m (f) calculated in this way reflects the correlation of both the amplitude and the phase between the seismic observation record m at location A and the seismic observation record m at location B.

[0021] The coherence observation value calculation unit 3 uses the power spectrum G A m (f), G B m (f) and the cross-spectrum G |ρ| m (f) to calculate the coherence Coh O (|ρ|, f) of the ground motion for each of the plurality of frequencies f as shown in the following formula (1).

Equation

[0022] Thus, the coherence observation value calculation unit 3 calculates the cross spectrum G |ρ| m The absolute value of (f) is the power spectrum G A m (f), G B m The value obtained by dividing (f) by each of the square roots is calculated for each seismic observation record m, and the average value of these values ​​among the seismic observation records m is calculated, thereby determining the coherence Coh O Calculate (|ρ|, f). The coherence of seismic motion calculated in this way Coh O (|ρ|, f) is a value calculated based on the seismic observation record m, therefore, from here on, the coherence observation value Coh O It is referred to as (|ρ|, f).

[0023] As shown above, equation (1) above gives cross-spectrum G |ρ| m The absolute value of (f) is the power spectrum G A m (f), G B m Including division by each of the square roots of (f), the coherence observation Coh O The configuration is designed to calculate (|ρ|, f). Therefore, the resulting calculated coherence observation Coh O The value of (|ρ|, f) will be between 0 and 1 (inclusive). Also, as already explained, cross-spectrum G |ρ| m (f) reflects the correlation between both the amplitude and phase of the earthquake observation record m, therefore the coherence observation value Coh O (|ρ|, f) also reflects the correlation between both the amplitude and phase of the seismic observation record m. More specifically, the more similar the phase and amplitude of the seismic observation records m between point A and point B are, and the higher the correlation between the seismic observation records m, the higher the coherence observation value Coh. OThe value of (|ρ|, f) is large and close to 1. Conversely, the phase and amplitude of the earthquake observation records m between point A and point B are not similar and are divergent, and the lower the correlation between the earthquake observation records m, the lower the coherence observation value Coh. O The value of (|ρ|, f) is small and close to 0.

[0024] In this way, the coherence observation value calculation unit 3 calculates the power spectrum G of the earthquake observation record m at each of the adjacent locations A and B from the respective earthquake observation records m at locations A and B. A m (f), G B m (f) and the cross-spectrum G of the seismic observation record m between points A and B |ρ| m (f) is calculated, and the power spectrum G A m (f), G B m (f) and cross-spectrum G |ρ| m Based on (f), the coherence value Coh is a value based on the seismic observation record m, which represents the degree of correlation of seismic motion between points A and B. O Calculate (|ρ|, f).

[0025] Figure 2 is a schematic graph of the coherence observations calculated by the coherence observation calculation unit. As described above, the coherence observation value calculation unit 3 calculates the coherence observation value Coh for each of the multiple frequencies f. O We calculate (|ρ|, f). Therefore, the coherence observation Coh O (|ρ|, f) can be expressed as a function of frequency f, as shown in Figure 2.

[0026] Furthermore, regarding equation (1) above, in the processing of the building seismic motion evaluation system 1, if only points A and B are adopted as the combination of adjacent points, the separation distance ρ becomes a fixed value, and therefore the coherence observation value Coh O (|ρ|, f) is a function where only frequency f is a variable. In addition, if there are three or more locations that observe earthquake observation records m, there can be multiple combinations of locations with different distances from each other. Therefore, for each of these multiple combinations, the coherence observation value Coh O Alternatively, we may calculate (|ρ|, f). In this case, the coherence observation Coh O In (|ρ|, f), both f and ρ can be treated as variables.

[0027] Next, the coherence formulating unit 4 formulates a coherence equation that expresses coherence, using the horizontal and vertical correlation distances of seismic motion in the surface ground, which are heterogeneity parameters of the surface ground where points A and B are located, as variables. This coherence equation is used to determine the coherence observed value Coh, which is calculated as described above, as will be explained later in the correlation distance determination unit 5. O The horizontal and vertical correlation distances are determined by comparing them with (|ρ|, f). The correlation distance in heterogeneous ground is an indicator that shows how spatially correlated the physical properties of the ground, such as the propagation speed and attenuation characteristics of seismic motion, are. Seismic motion propagates from the earthquake source through the ground and affects buildings and structures. In heterogeneous ground, there are parts where the propagation speed and attenuation characteristics differ depending on the physical properties of the ground and the arrangement of the geological layers, so the waveform and intensity of seismic motion change within the ground. When the correlation distance is short, the seismic motion is rapidly attenuated due to the heterogeneity of the ground, and the correlation between observation points becomes low. This indicates that the effects of reflection and scattering due to the different properties of the ground strongly influence the seismic motion. Conversely, when the correlation distance is long, the effects of reflection and scattering do not strongly influence the seismic motion. As a result, the seismic motion is not rapidly attenuated, and the correlation between observation points becomes high. In areas with heterogeneous crustal structures and ground characteristics, it is important to understand the characteristics of seismic motion in detail through the evaluation of correlation distance as described above. In this embodiment, the correlation distance is considered separately for the horizontal and vertical directions. More specifically, in the coherence equation formulation section 4 of this embodiment, both the horizontal correlation distance and the vertical correlation distance are used as variables to formulate a coherence equation, and using the coherence equation, the specific values ​​of the horizontal and vertical correlation distances are determined, as will be explained later regarding the correlation distance determination section 5.

[0028] To this end, the coherence formula section 4 first calculates the ground motion propagation velocity v and the coefficient of variation μ of the heterogeneity of said propagation velocity in the surface ground, based on the ground investigation results, using boring survey records of the surface ground. The propagation velocity v of seismic motion in the surface ground is, more specifically, for example, the S-wave velocity v in the surface ground. Furthermore, the coefficient of variation μ of the heterogeneity of propagation velocity in the surface ground is, more specifically, for example, the coefficient of variation μ of the heterogeneity of S-wave velocity in the surface ground. Furthermore, the coherence formula section 4 is the average value of the seismic motion propagation velocity v. <v>Calculate. When the surface ground is composed of multiple layers, the average seismic motion propagation velocity can be calculated for each layer. Therefore, the subsequent processing can be performed for each layer, corresponding to the average seismic motion propagation velocity calculated for each layer. In the following, for the sake of simplicity, we will explain the case where the surface ground is a single layer.

[0029] Coherence formula section 4 is the average value of the seismic motion propagation velocity v calculated as described above. <v>Based on this, the wave number k of the seismic motion is expressed as a function of frequency f using the following equation (2). k=2πf / <v>...(2)

[0030] Next, the coherence formula section 4 uses the wave number k of the seismic motion calculated based on the propagation velocity v as shown in equation (2) above, the coefficient of variation μ of the heterogeneity of the propagation velocity, the horizontal correlation distance a1, the vertical correlation distance a3, the separation distance ρ between points A and B, the propagation distance l of the seismic motion, the depth z from the ground surface, and the frequency f, and based on scattering theory, the following first calculation formula

number

[0031] In equation (3) above, L is calculated using the following second formula

number

number

[0032] Figure 3 is a graph in the coherence equation formulation section that shows the propagation distance L, which is assumed to affect the spatial variation of seismic motion, and is used when formulating the coherence equation. The propagation distance L, which is assumed to influence the spatial variation of seismic motion, was derived as equation (4) above by plotting the results of a simulation analysis using a three-dimensional heterogeneous ground model on a graph with the ratio of the horizontal correlation distance a1 to the vertical correlation distance a3 (a3 / a1) on the horizontal axis and L on the vertical axis, as shown in Figure 3, and then performing regression analysis on this graph.

[0033] Figure 4 is a graph of the correction coefficient α for the separation distance, which is assumed not to affect the spatial variation of seismic motion, and is used when formulating the coherence equation in the coherence equation formulation section. The separation distance correction coefficient α is a coefficient that corrects the separation distance ρ between point A and point B. The separation distance correction coefficient α is derived as equation (5) above by plotting the results of a simulation analysis using a 3D heterogeneous ground model on a graph with the separation distance (absolute value) |ρ| on the horizontal axis and α on the vertical axis, as shown in Figure 4, and then performing regression analysis on this graph.

[0034] In this way, the coherence formula Coh shown as equation (3) above is obtained F (|ρ|, f) is expressed with the horizontal correlation distance a1, the vertical correlation distance a3, and the distance ρ between points A and B as variables. Furthermore, as shown in equation (2) above, the wave number k is expressed using the frequency f as a variable. For this reason, the coherence equation Coh F (|ρ|, f) is expressed with frequency f as an additional variable, as shown schematically in Figure 5, for example. In this way, by setting arbitrary values ​​for the horizontal correlation distance a1, the vertical correlation distance a3, the distance ρ between points, and the frequency f in relation to equation (3) above, the corresponding coherence value can be calculated.

[0035] The correlation distance determination unit 5 calculates the coherence observation value Coh calculated by the coherence observation value calculation unit 3. O (|ρ|, f) and the coherence formula Coh formulated by the coherence formula section 4 F We estimate and determine the values ​​of the horizontal correlation distance a1 and the vertical correlation distance a3 such that the difference between the value of (|ρ|, f) and the given value is small. First, the correlation distance determination unit 5 sets the search range for the horizontal correlation distance a1 and the vertical correlation distance a3. In actual ground conditions, the horizontal correlation distance a1 tends to be larger than the vertical correlation distance a3, so it is desirable to set the search range with the condition a1 ≥ a3.

[0036] Next, the correlation distance determination unit 5 determines multiple combinations of values ​​for the horizontal correlation distance a1 and the vertical correlation distance a3. Specifically, the correlation distance determination unit 5 divides the search range, defined by setting a lower limit and an upper limit for the horizontal correlation distance a1, into equal parts, for example, at predetermined intervals. The correlation distance determination unit 5 uses all of the following values ​​as candidate values ​​for the horizontal correlation distance a1: the lower limit, each of the values ​​that became the boundary of each range after dividing the search range, and the upper limit. Furthermore, the correlation distance determination unit 5 divides the search range, which is defined by setting a lower limit and an upper limit for the vertical correlation distance a3, into equal parts, for example, at predetermined intervals. The correlation distance determination unit 5 uses all of the following values ​​as candidate values ​​for the vertical correlation distance a3: the lower limit, each of the values ​​that became the boundary of each range after dividing the search range, and the upper limit. The correlation distance determination unit 5 then derives all possible combinations of multiple candidate values ​​for the horizontal correlation distance a1 and multiple candidate values ​​for the vertical correlation distance a3. In this way, the correlation distance determination unit 5 determines multiple combinations of the values ​​for the horizontal correlation distance a1 and the values ​​for the vertical correlation distance a3.

[0037] The correlation distance determination unit 5 performs the following process for each of the multiple combinations of the horizontal correlation distance a1 value and the vertical correlation distance a3 value. First, the correlation distance determination unit 5 determines the coherence formula Coh for each of the values ​​included in the combination and the separation distance ρ between points A and B. F Substitute this into (|ρ|, f). This gives the coherence formula Coh F (|ρ|, f) represents a state where only frequency f is the variable. Next, each of the multiple frequency f values ​​is given by the coherence formula Coh F Substitute (|ρ|, f) to obtain the coherence formula Coh corresponding to each of the multiple frequencies f in that combination. F Calculate the value of (|ρ|, f). Next, the correlation distance determination unit 5 determines the coherence observed value Coh O (|ρ|, f) and the coherence formula Coh F The difference between the value of (|ρ|, f) and is calculated. Specifically, the correlation distance determination unit 5 calculates the difference as the coherence formula Coh for each of the multiple frequencies f. F The value of (|ρ|, f) and the coherence observation Coh O The sum of squares is calculated by calculating the squares of the residuals of (|ρ|, f) and the sum of the squares of the residuals of each of the multiple frequencies f. In this way, the correlation distance determination unit 5 determines the coherence formula Coh for each of the multiple frequencies f for each of the multiple combinations F The value of (|ρ|, f) and the coherence observation Coh O Calculate the sum of the squares of the residuals of (|ρ|, f) and .

[0038] Then, the correlation distance determination unit 5 extracts the combination from among multiple combinations that minimizes the above sum of squares. The correlation distance determination unit 5 determines the horizontal correlation distance a1 and the vertical correlation distance a3 corresponding to the extracted combinations as the horizontal correlation distance a1 and the vertical correlation distance a3.

[0039] Furthermore, if there are three or more locations where earthquake observation records m are observed, and there are multiple combinations of locations with different separation distances ρ, then the separation distance ρ is not a constant. In this case, for example, multiple combinations of the horizontal correlation distance a1, the vertical correlation distance a3, and the separation distance ρ are generated, and for each of these combinations, the coherence formula Coh is used as described above. F The value of (|ρ|, f) and the coherence observation Coh O Alternatively, the sum of squares of the residuals of (|ρ|, f) and can be calculated, and the values ​​of the horizontal correlation distance a1 and the vertical correlation distance a3 in the combination that minimizes the sum of squares can be determined as the horizontal correlation distance a1 and the vertical correlation distance a3. Furthermore, if the surface ground is composed of multiple layers, the average value of the seismic motion propagation velocity v <v>Since the value differs for each geological layer, the coherence formula Coh F (|ρ|, f) can also be a different equation for each geological layer. In this case, for example, the coherence observation value Coh can be used for each geological layer. O (|ρ|, f) and the coherence formula Coh F Alternatively, the difference between the value of (|ρ|, f) and can be calculated to determine the horizontal correlation distance a1 and the vertical correlation distance a3 for each geological layer.

[0040] The building seismic motion evaluation unit 6 constructs a three-dimensional surface ground model that reflects heterogeneity, based on the horizontal correlation distance a1 and the vertical correlation distance a3 determined as described above. More specifically, when constructing a surface ground model, randomness is added to each of the physical property values ​​of the ground elements to satisfy the horizontal correlation distance a1 and the vertical correlation distance a3, thereby reflecting the values ​​of the horizontal correlation distance a1 and the vertical correlation distance a3 in the 3D surface ground model. The building seismic motion evaluation unit 6 then evaluates the building seismic motion, which is the seismic motion input to a building on the surface ground, by inputting seismic motion into the three-dimensional surface ground model that reflects heterogeneity, constructed as described above, and performing FEM analysis. In this FEM analysis, seismic motion is input to the lowest point of the three-dimensional surface ground model, propagated through the surface ground, and the input seismic motion that reaches the uppermost point of the surface ground is estimated.

[0041] The results display unit 7 displays the building seismic motion evaluated as described above on an output device such as a display (not shown).

[0042] Next, we will explain the building seismic motion evaluation method using the above-described building seismic motion evaluation system with reference to Figures 1 to 5 and Figure 6. Figure 6 is a flowchart of the building seismic motion evaluation method. First, earthquake observation data and surface ground boring survey data are collected and stored in the data storage unit 2 (Step S1: Data collection process). Next, the coherence observation value calculation unit 3 calculates the power spectra G A m (f) and G B m (f) of the seismic observation records at each of the adjacent points A and B, and the cross spectrum G |ρ| m (f) of the seismic observation records between points A and B, and based on the power spectra G A m (f) and G B m (f) and the cross spectrum G |ρ| m (f), calculates the coherence observation value Coh O (|ρ|, f) which is the value of the coherence of the seismic motion representing the degree of correlation of the seismic motion between points A and B based on the seismic observation record m (step S2: coherence observation value calculation step). Also, the coherence formula establishment unit 4 uses, as variables, the horizontal correlation distance a1 and the vertical correlation distance a3 of the seismic motion in the surface ground, which are the inhomogeneous parameters of the surface ground where each of points A and B is located, and establishes the coherence formula Coh F (|ρ|, f) as the first calculation formula (3) as described above (step S3: coherence formula establishment step).

[0043] Subsequently, the correlation distance determination unit 5 determines the horizontal correlation distance a1 and the vertical correlation distance a3 so that the difference between the value of the coherence formula Coh F (|ρ|, f) and the coherence observation value Coh O (|ρ|, f) becomes small (step S4: correlation distance determination step). Then, the building seismic motion evaluation unit 6 constructs a surface ground model based on the determined horizontal correlation distance a1 and vertical correlation distance a3, and inputs seismic motion into the surface ground model to evaluate the building seismic motion (step S5: building seismic motion evaluation step). Finally, the result display unit 7 displays the evaluated building seismic motion on an output device such as a display (not shown) (step S6: result display step).

[0044] The above-described building seismic motion evaluation system 1 is a building seismic motion evaluation system 1 that evaluates the building seismic motion input to a building, and from the seismic observation records of each adjacent point, the power spectrum G of the seismic observation records at each point A m (f), G B m (f) Cross-spectrum G of seismic observation records between the two locations |ρ| m (f) is calculated, and based on these, the coherence value Coh, which is a value based on seismic observation records, represents the degree of correlation of seismic motion. O The coherence observation value calculation unit 3 calculates (|ρ|, f), and the coherence equation Coh expresses coherence using the horizontal correlation distance a1 and the vertical correlation distance a3, which are heterogeneity parameters of the surface ground where each point is located, as variables. F Coherence equation formulation section 4 and coherence equation Coh F The value of (|ρ|, f) and the coherence observation Coh O The system includes a correlation distance determination unit 5 that determines the horizontal correlation distance a1 and the vertical correlation distance a3 so as to minimize the difference with (|ρ|, f), and a building seismic motion evaluation unit 6 that constructs a surface ground model based on the determined horizontal correlation distance a1 and the vertical correlation distance a3, and evaluates the building seismic motion by inputting seismic motion into the surface ground model. According to the above configuration, first, from the seismic observation records of each adjacent location, the coherence observation value Coh, which represents the degree of correlation of seismic motion between locations, is obtained. O The coherence equation Coh is calculated using the horizontal correlation distance a1 and the vertical correlation distance a3, which are heterogeneity parameters of the surface ground at each point, as variables to express the coherence of the seismic motion. F Formulate the equation (|ρ|, f). The coherence equation Coh that is formulated in this way F The value of (|ρ|, f) is the coherence observation Coh if appropriate values ​​are set for the variables. O (|ρ|, f) should take the same or nearly the same value. Therefore, the coherence formula Coh F The value of (|ρ|, f) and the coherence observation Coh O By determining the horizontal correlation distance a1 and the vertical correlation distance a3 such that the difference with (|ρ|, f) is small, accurate values ​​for each of the horizontal and vertical correlation distances a1 and a3 can be obtained. Based on the horizontal and vertical correlation distances a1 and a3 obtained in this way, a surface ground model can be constructed, and by inputting seismic motion into the surface ground model, building seismic motion can be evaluated with high accuracy. In particular, in the above embodiment, the coherence formula Coh reflects the horizontal correlation distance a1 and the vertical correlation distance a3 as variables. F The coherence observation Coh is the one whose difference from (|ρ|, f) is to be calculated. O (|ρ|, f) is the power spectrum G of the seismic observation record at each location. A m (f), G B m (f) Cross-spectrum G of seismic observation records between the two locations |ρ| m (f) is used for calculation. Cross-spectrum G of seismic observation records between locations. |ρ| m (f) reflects not only the amplitude but also the phase of the earthquake observation record, and therefore the coherence observation value of the ground motion Coh O (|ρ|, f) reflects both amplitude and phase. Therefore, the coherence observation value Coh of such seismic motion is O Both the amplitude and phase are reflected in the horizontal correlation distance a1 and the vertical correlation distance a3, which are calculated based on (|ρ|, f). By reflecting both amplitude and phase in this way, the accuracy of the horizontal correlation distance a1 and the vertical correlation distance a3 is improved, and the accuracy of the surface ground model in which these horizontal and vertical correlation distances a1 and a3 are set is improved. Consequently, the accuracy of the building seismic motion evaluated by inputting seismic motion into the surface ground model is further improved. In this way, it becomes possible to evaluate building ground motion, which is the seismic motion input to a building, with higher accuracy.

[0045] Furthermore, the coherence formula section 4 calculates the propagation velocity of seismic motion in the surface ground and the coefficient of variation of the heterogeneity of said propagation velocity based on the results of the ground investigation. The coherence formula section 4 uses the wave number k of the seismic motion calculated based on the propagation velocity, the coefficient of variation μ of the heterogeneity of the propagation velocity, the horizontal correlation distance a1, the vertical correlation distance a3, the distance ρ between points, the propagation distance l of the seismic motion, the depth z from the ground surface, and the frequency f to produce the coherence formula Coh as the first calculation formula (3) above. F Formulate (|ρ|, f), in the first calculation formula, L is the propagation distance that is assumed to affect the spatial variation of the seismic motion, expressed as the second calculation formula (4) above, and α is the correction coefficient for the separation distance that is assumed not to affect the spatial variation of the seismic motion, expressed as the third calculation formula (5) above. According to the above configuration, the coherence formula Coh is shown as the first calculation formula. F The right-hand side of (|ρ|, f) is expressed by the wave number k of the seismic motion, the coefficient of variation μ of the heterogeneity of the propagation speed, the horizontal correlation distance a1, the vertical correlation distance a3, the distance ρ between points, the propagation distance l of the seismic motion, the depth z from the ground surface, the frequency f, the propagation distance L that is assumed to affect the spatial variation of the seismic motion, and the correction coefficient α of the distance that is assumed not to affect the spatial variation of the seismic motion. In this, the wave number k of the seismic motion can be calculated as a function of frequency f, for example, based on the propagation velocity of the seismic motion in the surface ground, which is calculated based on the results of the ground investigation. The coefficient of variation μ of the heterogeneity of the propagation velocity is calculated based on the results of the ground investigation and can be treated as a constant in the same way. The propagation distance l of the seismic motion corresponds to the depth of the surface ground (geological layer), and this can also be treated as a constant by setting its value based on the results of the ground investigation, etc. The depth z from the ground surface is an integral variable. Furthermore, the propagation distance L, which is assumed to affect the spatial variation of the seismic motion, is expressed by the horizontal correlation distance a1 and the vertical correlation distance a3, as shown in the second calculation formula. In addition, the correction coefficient α of the separation distance, which is assumed not to affect the spatial variation of the seismic motion, is expressed by the separation distance ρ between points, as shown in the third calculation formula. In this way, the coherence formula Coh F (|ρ|, f) is a function expressed by variables including the horizontal correlation distance a1, the vertical correlation distance a3, the distance between points ρ, and the frequency f. Thus, in the first calculation formula, the corresponding coherence value can be calculated for any value of the horizontal correlation distance a1, the vertical correlation distance a3, the distance between points ρ, and the frequency f. In this way, the coherence formula Coh F (|ρ|, f) can be appropriately formulated as an equation.

[0046] Furthermore, the coherence observation value calculation unit 3 calculates the coherence observation value Coh of the seismic motion for each of the multiple frequencies f. O (|ρ|, f) is calculated, and coherence formula part 4 expresses the wave number k using frequency f in addition to propagation speed, so that frequency f is further included in the variables, coherence formula Coh F The equation (|ρ|, f) is formulated, and the correlation distance determination unit 5 uses the coherence equation Coh F The values ​​of (|ρ|, f) and the observed coherence values ​​of seismic motion Coh O The difference with (|ρ|, f) is expressed by the coherence formula Coh at each of the multiple frequencies f. F The value of (|ρ|, f) and the coherence observation Coh O The correlation distance determination unit 5 calculates the sum of squares of the residuals with (|ρ|, f) and determines multiple combinations of values ​​for the horizontal correlation distance a1 and the vertical correlation distance a3. Among these multiple combinations, the values ​​included in the combination that minimizes the sum of squares are determined as the horizontal correlation distance a1 and the vertical correlation distance a3. Furthermore, in the coherence observation value calculation unit 3, the coherence observation value Coh of the seismic motion O (|ρ|, f) is the cross-spectrum G |ρ| m The absolute value of (f) is the power spectrum G A m (f), G B m The calculation involves dividing by each of the square roots of (f). With the configuration described above, the building seismic motion evaluation system 1 can be properly implemented.

[0047] Furthermore, the above-described building seismic motion evaluation method is a building seismic motion evaluation method that evaluates the building seismic motion input to the building, and from the seismic observation records of each adjacent point, the power spectrum G of the seismic observation records at each point A m (f), G B m (f) Cross-spectrum G of seismic observation records between the two locations |ρ| m (f) is calculated, and based on these, the coherence value Coh, which is a value based on seismic observation records, represents the degree of correlation of seismic motion. O The coherence observation calculation process S2 calculates (|ρ|, f), and the coherence equation Coh expresses coherence using the horizontal correlation distance a1 and the vertical correlation distance a3, which are heterogeneity parameters of the surface ground where each point is located, as variables. F The coherence equation formulation process S3 involves formulating the equation (|ρ|, f), and the coherence equation Coh F The value of (|ρ|, f) and the coherence observation Coh O The process includes a correlation distance determination step S4, which determines the horizontal correlation distance a1 and the vertical correlation distance a3 such that the difference with (|ρ|, f) is small, and a building seismic motion evaluation step S5, which constructs a surface ground model based on the determined horizontal correlation distance a1 and vertical correlation distance a3, and evaluates the building seismic motion by inputting seismic motion into the surface ground model. With the configuration described above, as already explained with respect to the Building Seismic Motion Evaluation System 1, it becomes possible to evaluate the building seismic motion, which is the seismic motion input to the building, with higher accuracy.

[0048] (First verification example) We have verified the applicability of the above-mentioned building seismic motion evaluation system and building seismic motion evaluation method, and will now explain the content and results of the verification. First, as the first verification, we will explain the verification regarding the estimation of correlation distance using seismic motion simulation waveforms. The coherence value Coh is calculated from the response waves of adjacent locations using seismic motion simulations with a 3D FEM heterogeneous ground model. O Calculate (|ρ|, f) and use the above coherence formula Coh F The results were compared with those of the evaluation of (|ρ|, f). Figure 7 is an explanatory diagram of the surface ground model used in the first verification of the above-mentioned building seismic motion evaluation system. Figure 8 is a diagram showing an example of the distribution of S-wave velocities on the side and surface of the above-mentioned surface ground model. The three-dimensional heterogeneous surface ground model was designed with a horizontal dimension of 300m and a depth dimension of 200m. The mesh size was 1m x 1m. The average S-wave velocity structure of the ground was set to 300 m / s, and the S-wave velocity was varied so that the variation pattern followed a Gaussian autocorrelation function. The horizontal correlation distance a1 of the ground was set to 30 m, and the vertical correlation distance a3 was set to 6 m. The coefficient of variation μ was set to 0.15. In addition, by changing the initial random number, five different surface ground models were created for all cases considered.

[0049] The input ground motion was designed to provide impulsive vibrations, using a trigonometric function displacement waveform with amplitude only in the y-direction and an excitation time of 0.02 seconds. This input ground motion was incident vertically as a plane wave from the bottom of the surface ground model. As shown by the thick line in the center of the surface ground model's surface in Figure 7, response waveform extraction points were set at 1.0 m intervals along a 100 m line in both the x and y directions in the center of the surface ground model's surface, and the time history waveform of the displacement response was extracted. The response wave extraction time was set to approximately 2.5 seconds from the start of input from the bottom of the surface ground model. Figure 9 shows the response waves at the ground surface when seismic motion is input to the bottom of the surface ground model described above. More specifically, Figure 9 shows the time history waveforms of the response waves at 5m intervals at response wave extraction points located on the line x=100~200m, y=150m at the surface, as an example of the time history waveform of the response waves. From Figure 9, it can be confirmed that the initial waveform differs between locations.

[0050] Figure 10 is a graph showing the relationship between the coherence observed value and frequency, calculated by the coherence observed value calculation unit based on the above response wave. More specifically, Figure 10 shows the coherence value Coh for combinations of observation points where the separation distance |ρ| is 10m, 20m, 30m, 40m, and 50m, out of all response waves extracted from the surface of five different surface ground models with different initial random numbers. O Calculate (|ρ|, f) and the frequency f and coherence value Coh O This summarizes the relationship with (|ρ|, f). The higher the frequency f, the higher the coherence value Coh O A tendency is observed for (|ρ|, f) to become smaller. Also, the smaller the distance between observation points, the smaller the coherence value Coh. O We can confirm that (|ρ|, f) becomes large.

[0051] Based on the results shown in Figure 10, the horizontal correlation distance a1 and the vertical correlation distance a3 are estimated from equation (3) above. Figure 11 shows the search range for the horizontal and vertical correlation distances. The search range for the horizontal correlation distance a1 was set in increments of 10m within the range of 10 to 40m. The search range for the vertical correlation distance a3 was set to be 0.1, 0.2, 0.5, 0.7, and 1.0 times the horizontal correlation distance a1. As a result, the horizontal correlation distance a1 was estimated to be 30.0m, and the vertical correlation distance a3 was estimated to be 6.0m. Both the horizontal correlation distance a1 and the vertical correlation distance a3 matched the correlation distances (30m and 6m, respectively) set in the seismic motion simulation. Thus, we were able to accurately estimate the horizontal correlation distance a1 and the vertical correlation distance a3.

[0052] Figure 12 is a graph of the coherence equation into which the horizontal and vertical correlation distances determined by the correlation distance determination unit of the above-mentioned building seismic motion evaluation system have been substituted. In Figure 12, the coherence value Coh shown in Figure 10 is used. O (|ρ|, f) superimposed on the coherence formula Coh F (|ρ|, f) is shown. From Figure 12, the coherence formula Coh F (|ρ|, f) is the value of coherence Coh O It can be seen that (|ρ|, f) is roughly represented.

[0053] (Second verification example) Next, as the second verification, we will explain the verification of the estimation of correlation distance using actual observation records. Figure 13 shows the arrangement of seismometers in the observation facility used in the second verification of the above-mentioned building seismic motion evaluation system. Figure 14 shows the S-wave velocity structure in the above-mentioned observation facility. In this verification, observation records were used for combinations of observation points with separation distances of 5m, 10m, 15m, 21m, and 30m. In addition, in this verification, the coefficient of variation of the S-wave in each layer was evaluated by visually reading the N-value survey results and converting the N-value at each depth into S-wave velocity.

[0054] To estimate the correlation distance of the surface ground, it is important to minimize the influence of noise and nonlinearity, and to extract the waveform from the initial S-wave motion while minimizing the inclusion of P-wave components. Therefore, the following criteria are used: earthquake magnitude (MJ) of 5.0 or higher, focal depth of 80 km or higher, apparent angle of incidence of 40 degrees or less, and maximum acceleration of 100 cm / s². 2 The condition for the target earthquake was that it had to be within a certain range. As a result, observational records of five earthquakes, as shown in Figure 15, were used. Furthermore, the analysis used horizontal waveforms extracted visually for 5.12 seconds from the initial phase of the S wave.

[0055] Figure 16 is a graph showing the relationship between the coherence observation value and frequency, calculated by the coherence observation value calculation unit based on the above observation records. The higher the frequency f and the larger the separation distance |ρ|, the greater the value of coherence Coh. O (|ρ|, f) decreases. This result and the coherence equation Coh in equation (3) above F The horizontal correlation distance a1 and the vertical correlation distance a3 were estimated by grid search so as to minimize the sum of squared errors with (|ρ|, f). The search range for the horizontal correlation distance a1 and the vertical correlation distance a3 was set as shown in Figure 11, similar to the first verification described above. Furthermore, it was permitted that the horizontal correlation distance a1 and the vertical correlation distance a3 would be individual values ​​for each layer. Considering that the above equation (3) does not include the effect of backscattering and is applicable in the range where the degree of scattering of seismic motion is weak, the frequency range to be evaluated in this verification was set to 3 Hz to 8 Hz.

[0056] Figure 17 shows the horizontal and vertical correlation distances determined for each layer. In all layers, the horizontal correlation distance a1 is rated higher than the vertical correlation distance a3. Based on the results in Figure 17, a three-dimensional FEM heterogeneous surface ground model was created, and the spatial variation characteristics of seismic motion between adjacent points on the ground surface were evaluated by seismic motion simulation. The shape of the surface ground model is the same as in the first verification. Figure 18 shows an example of a heterogeneous pattern of S-wave velocity in a surface soil model. A triangular wave with a duration of 0.02 seconds was incident horizontally as a plane wave from the bottom of the surface ground model. Response waves were extracted at 1m intervals along a 100m line parallel to the x and y axes in the center of the ground surface, and coherence between adjacent points was calculated using equation (1).

[0057] Figure 19 is a graph of coherence calculated based on the observed results for a surface ground model in which the horizontal and vertical correlation distances estimated in the second verification above were set. In Figure 19, the coherence value Coh shown in Figure 16 is used. O The result is shown superimposed on (|ρ|, f). Similar to observational records, it can be seen that the tendency for coherence to decrease as the frequency increases and as the distance between the points increases is successfully represented.

[0058] It should be noted that the building seismic motion evaluation system and building seismic motion evaluation method of the present invention are not limited to the embodiments described above with reference to the drawings, and various other modifications are conceivable within their technical scope. For example, in the above embodiment, the correlation distance determination unit 5 determines multiple combinations of values ​​for the horizontal correlation distance a1 and the vertical correlation distance a3, and determines the values ​​included in the combination that minimizes the sum of squares among the multiple combinations as the horizontal correlation distance a1 and the vertical correlation distance a3. However, instead, the horizontal correlation distance a1 and the vertical correlation distance a3 may be determined as follows. First, the correlation distance determination unit 5 sets provisional values ​​for the horizontal correlation distance a1 and the vertical correlation distance a3. Next, the correlation distance determination unit 5, similar to the above embodiment, determines the coherence formula Coh for each of the multiple frequencies f. F The value of (|ρ|, f) and the coherence observation Coh O Calculate the sum of squares of the residuals with (|ρ|, f). The correlation distance determination unit 5 compares the calculated sum of squares with a predetermined judgment threshold. The correlation distance determination unit 5 determines the values ​​of the horizontal correlation distance a1 and the vertical correlation distance a3 that should be ultimately adopted, based on the provisionally set values ​​of the horizontal correlation distance a1 and the vertical correlation distance a3, if the sum of squares is smaller than the judgment threshold. If the sum of squares is greater than or equal to the judgment threshold, the correlation distance determination unit 5 changes and updates the values ​​of the horizontal correlation distance a1 and the vertical correlation distance a3 to different values, calculates the sum of squares for the updated new values, and compares it with the judgment threshold. In this way, the correlation distance determination unit 5 determines the horizontal correlation distance a1 and the vertical correlation distance a3 by repeatedly updating the horizontal correlation distance a1 and the vertical correlation distance a3 and calculating the sum of squares until the sum of squares is less than or equal to the judgment threshold. In this case as well, the horizontal correlation distance a1 and the vertical correlation distance a3 can be appropriately determined.

[0059] In addition to the above, it is possible to select or replace the configurations listed in the above embodiments and modifications, or to change them to other configurations as appropriate. [Explanation of symbols]

[0060] 1. Building seismic motion evaluation system 5. Correlation distance determination unit 2 Data storage unit 6 Building seismic motion evaluation unit 3. Coherence observation value calculation unit 7. Result display unit 4 Coherence Ritual< / v> < / v> < / v> < / v>

Claims

1. A building seismic motion evaluation system that evaluates the seismic motion input to a building, A coherence observation value calculation unit calculates the power spectrum of the earthquake observation record at each of the adjacent locations and the cross spectrum of the earthquake observation record between the locations, and based on these, calculates a coherence observation value, which is a value of the coherence of earthquake motion that represents the degree of correlation of earthquake motion, based on the earthquake observation record. The coherence formulating section formulates a coherence equation that expresses the coherence, using the horizontal correlation distance and the vertical correlation distance, which are heterogeneity parameters of the surface ground at each of the aforementioned points, as variables. A correlation distance determination unit determines the horizontal correlation distance and the vertical correlation distance such that the difference between the value of the coherence formula and the observed coherence value is small. A building seismic motion evaluation unit constructs a surface ground model based on the determined horizontal and vertical correlation distances, and evaluates the building's seismic motion by inputting seismic motion into the surface ground model. A building seismic motion evaluation system characterized by comprising the following features.

2. The aforementioned coherence formula section calculates the propagation velocity of seismic motion in the surface ground and the coefficient of variation of the heterogeneity of said propagation velocity based on the results of the ground investigation. In the coherence formula section, the wave number k of the seismic motion calculated based on the propagation velocity, the coefficient of variation μ of the heterogeneity of the propagation velocity, and the horizontal correlation distance a １ and the vertical correlation distance a ３ Using the distance ρ between the aforementioned points, the propagation distance l of the seismic motion, the depth z from the Earth's surface, and the frequency f, the following first calculation formula is used: [Math 1] The coherence formula is formulated as follows, and in the first calculation formula, L is the second calculation formula below [Math 2] This is the propagation distance that is assumed to affect the spatial variation of seismic motion, and α is expressed as in the third calculation formula below. [Math 3] The building seismic motion evaluation system according to claim 1, characterized in that it is a correction coefficient for separation distance that is assumed not to affect the spatial variation of seismic motion, expressed as follows.

3. A building seismic motion evaluation method for evaluating the seismic motion input to a building, A coherence observation value calculation step, which involves calculating the power spectrum of the earthquake observation record at each of the adjacent locations and the cross spectrum of the earthquake observation record between the locations, and then calculating a coherence observation value, which is a value based on the earthquake observation record that represents the degree of correlation of the seismic motion, based on these, The process involves formulating a coherence equation that expresses the coherence, using the horizontal correlation distance and the vertical correlation distance, which are heterogeneity parameters of the surface ground at each of the aforementioned points, as variables. A correlation distance determination step, in which the horizontal correlation distance and the vertical correlation distance are determined such that the difference between the value of the coherence formula and the observed coherence value is small, A building seismic motion evaluation process is performed, which involves constructing a surface ground model based on the determined horizontal and vertical correlation distances, and evaluating the building's seismic motion by inputting seismic motion into the surface ground model. A method for evaluating building seismic motion, characterized by including the following:

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