JP4766514B2 - Earthquake risk assessment method and fault model formation program for earthquake risk assessment - Google Patents

Description

  The present invention relates to an earthquake risk evaluation method and a fault model formation program suitable for carrying out this method, and more particularly to an appropriate risk evaluation for an earthquake whose epicenter cannot be specified.

  In recent years, people's interest in earthquakes has increased. Therefore, it is strongly required to predict the damage of buildings due to earthquakes and confirm the safety of the buildings.

  As a method for evaluating the earthquake risk, there is a method using an earthquake hazard curve that represents the relationship between the maximum acceleration on the ground surface and the annual excess probability of the acceleration (Non-patent Document 1). Analysis on the basis of time history is required.

  In order to obtain the time history of acceleration, a ground surface vibration function is generated from the fault surface source function by the Green's function method, and this function is multiplied by the transfer function of the surface layer ground, and further inverse Fourier transform is performed. Here, the Green function method divides the fault plane into, for example, concentric annular or grid-like small faults as shown in FIG. 10, and generates a green function indicating the response of the base plane to the ground motion of those small faults. This is a method of calculating the ground motion by the entire fault plane by superimposing the seismic source function and the Green function arranged on the center and taking the sum of them (Patent Document 1). In other words, the waveform of a large earthquake due to the destruction of the entire fault plane is synthesized by adding the waveforms of small earthquakes due to partial destruction of the fault plane in a predetermined procedure. As the waveform of the small earthquake, the waveform observed in the past can be used, but it can also be theoretically generated using the so-called seismic motion scaling law (similarity law). (See, for example, paragraph 0086 of Patent Document 2). The scaling law is a law that the frequency ω of the ground motion is proportional to the −2 power of the frequency except for the low frequency band. In addition, to calculate the transfer function of the above-mentioned surface layer, it is only necessary to analyze the vibration amplification characteristics of the surface layer. (Patent Document 3).

Furthermore, once the time history of acceleration on the ground surface is obtained, a conventionally known multi-mass point response analysis is performed on each point of the building (see Patent Document 4) to specifically evaluate the influence of the building vibration. The other background art is appropriately cited in the specification.
JP2003-139863 JP2004-362311 JP-A-11-183630 JP-A-11-160144 Endo Akihiko "Operation of Seismic Risk Assessment Method for Reinforced Concrete Pier" Structural Engineering Papers Vol49A Japan Society of Civil Engineers March 2003 Ryosuke Sato "Japanese Earthquake Fault Parameter Handbook" Page 85 Kashima Publishing 1979 Katsuhiro Kamae, Kojiro Irikura, Yasushi Fukuchi "Prediction of strong ground motion during a large earthquake based on the scaling law of earthquakes" Architectural Institute of Japan Structural Systems Proceedings No. 430 pages 1-9 1991 Toshihiro Kakimi “Earthquake structure classification of the Japanese archipelago and surrounding seas”, Vol. 2, Vol. 55, No. 4, 2003, pages 389-406

  In the statistical Green's function method of Patent Document 2, a fault model in which the size and direction are set based on local fault information is formed. However, currently published fault information mainly relates to future ocean-type giant earthquakes, and it has been difficult to form simulated ground motions for medium-scale earthquakes with a seismic intensity of about 4. In addition, it is pointed out that an inland earthquake occurs in a place where the epicenter is not specified, and in this case, an accurate fault model based on detailed data cannot be expected.

  However, for example, in a semiconductor factory, there is a possibility that the operation will stop even if it is subjected to an inland earthquake. As a countermeasure against this, there is a strong demand in the industry for simulating the effect of seismic isolation even for direct earthquakes, which have been difficult to evaluate in the past.

  Therefore, the present invention provides an evaluation method that makes it possible to predict damages such as buildings caused by an earthquake in an area where fault information is not sufficiently known or an epicenter cannot be specified, and for the evaluation The purpose is to propose a program for fault model formation.

The first means is an earthquake risk evaluation method for direct earthquakes,
Forming a fault model having a virtual fault surface in the hypocenter region below the stratum;
Generating a statistical Green's function indicating the response at the base surface of the surface ground to the earthquake motion at each part of the fault plane;
Using this statistical Green's function, obtaining a time history of the ground motion on the basement surface with respect to ground motion for all fault planes;
A step of generating a time history of ground motion on the ground surface from a time history of ground motion of the basement surface by analyzing the vibration amplification characteristics of the surface layer,
Calculating the impact on the structure of the ground surface based on the time history of the ground motion on the ground surface,
At the formation stage of the above fault model,
For the terrain model representing a certain area in common the characteristic of seismic activity, a plurality of reference points 4, adjustably positioned evenly and the position of the reference point group at regular intervals from each other,
Set one virtual fault plane 6 with an area corresponding to the assumed magnitude at the depth of the epicenter area around each reference point,
Unit hypocenter models corresponding to formation start points of the formation are respectively installed at least at two or more outer peripheral portions of the virtual fault plane 6.

  This means is characterized in that a fault model is automatically formed in each stage of the earthquake risk assessment method. Assuming earthquakes in areas where the fault information is not publicly available, and direct earthquakes where the epicenter is not specified, earthquakes such as rules of thumb regarding the relationship between the magnitude of the earthquake and the fault plane, and the frequency of earthquakes by region By making the best use of indirect information about the area, we devise a method for setting the fault plane and conduct risk assessment with the highest possible reliability. The method of the present invention is particularly effective for medium-scale earthquakes, for example, earthquakes having a magnitude of about 5 to 7. Of course, it can also be applied theoretically to large earthquakes and small earthquakes, but since the fault model is published in the former case, analysis using this is possible, and in the latter case This is because there is often no substantial damage to the building.

  The “certain area having the same characteristics of seismic activity” is, for example, a mechanism that shares the earthquake occurrence mechanism and the frequency according to the scale. This frequency of occurrence can be used to predict earthquake damage due to an annual earthquake. For example, in an academic society, it has been proposed to divide the Japanese archipelago and the surrounding sea area into 13 regions (earthquake structure classification) (see Table 2 below). However, an area obtained by further subdividing the area or an area classified separately may be used.

  The “terrain model” may be a real map or a crust model, or a virtual model configured as electronic information.

  The “reference point group” is a set of points arranged in a specific pattern, for example, a point grid pattern, with a constant distance from the nearest neighboring point, and the set as a whole slides arbitrarily on the ground surface. It is desirable to be able to determine the position. By doing so, one of the set of points can be overlapped with an arbitrary observation point on the surface of the earth, in particular, the installation location of the building / equipment to be evaluated. As described above, since the epicenter cannot be identified in a direct earthquake, it is possible to assume a case where the damage of the earthquake is maximized at least for each earthquake scale by overlaying one of the reference points on the observation point. The distance between each reference point is basically free, but can be set to the same size as the average fault size in an earthquake set arbitrarily in the range of magnitude 5 to 7, for example.

  The “virtual tomographic plane” is a tomographic plane surrounded by an arbitrary frame (case), and its size or area can be arbitrarily set. In general, the statistical Green's function method divides the fault plane into small faults in order to form a waveform of a large-scale earthquake due to the destruction of a large fault plane. In the present invention, each part surrounded by a frame independently vibrates. There may be gaps between these virtual tomographic planes, and in some cases, the virtual tomographic planes may overlap. Furthermore, when evaluating the earthquake risk for a single observation point, it is sufficient to form a virtual fault plane around the reference point below that observation point. The virtual fault plane is a model of an actual fault plane having a certain spread. Therefore, at least two, preferably three or more unit source models are arranged at appropriate intervals on the outer periphery of the virtual fault plane. It is good to form by installing it. The shape of the virtual tomographic plane can be changed as appropriate, such as a circle or a polygon.

  The “unit hypocenter model” corresponds to the point at which the first fault rupture on a real seismic source fault has started (fault rupture point). An epicenter fault with a spread is not destroyed at once. First of all, the destruction starts at one point, and spreads to the surrounding area at high speed. Eventually, the expansion of the destruction stops and the formation of the epicenter fault is finished. Various formulas representing the unit hypocenter model have been proposed, and an example is shown in the embodiment.

  After the fault model is formed, the generation of statistical green functions, the calculation of the time history of ground motion on the surface of the ground layer, and the analysis of the ground motion amplification analysis on the surface ground are sequentially performed to obtain the maximum ground motion level in the ground motion. Find the acceleration. More preferably, the maximum acceleration in each layer of the building is obtained by multi-mass analysis of the building on the ground surface. Since the procedure of each of these steps is conventionally known, the description thereof is omitted. Once the maximum acceleration is obtained, the damage caused by the earthquake may be calculated by multiplying the above-described earthquake occurrence probability for each region.

  The second means has the first means and is characterized in that unit hypocenter models are respectively installed at at least three locations of the virtual fault plane center and the outer peripheral portion thereof.

  By adopting such a configuration, the unit epicenters can be distributed in a well-balanced manner on the virtual fault plane. For example, when the virtual fault plane is a polygon, a unit source model can be installed at each corner.

The third means is a program suitable for carrying out the earthquake risk evaluation method as the first means or the second means,
On the computer,
Procedure for the terrain model representing a certain area in common the characteristic of seismic activity, arranging a plurality of reference points (4), and evenly each other at regular intervals to allow adjusting the position of the reference point group When,
A procedure for setting the virtual fault plane 6 to the depth of the hypocenter area around each reference point,
A procedure of installing two or more unit source models on the outer periphery of at least one of the virtual fault planes 6;
The area S of the virtual fault plane 6 where the unit hypocenter model is installed corresponds to the magnitude M of the assumed earthquake,
[Equation 1] log ₁₀ S = c × M−d where c and d are similar to a procedure for enlarging or reducing the virtual tomographic plane so as to follow a constant;
It is characterized by letting you do.

  This means is a fault model formation program for earthquake risk assessment. This program may be incorporated as a module in the earthquake risk assessment program. This means is configured to cause the computer to execute a procedure for enlarging / reducing the virtual fault plane according to an empirical rule relating to the relationship between the area of the actual fault plane and the magnitude of the earthquake. Regarding the coefficients c and d in the above formula 1, it is preferable that c = 1 and d = 4.06 to 4.07 (Non-patent Document 2). However, these coefficients vary somewhat depending on the magnitude of the earthquake.

  The fourth means includes the third means, and allows the computer to perform a procedure for rotating the virtual tomographic plane 6 on which the unit epicenter model is installed around a reference point that is the center of the figure. I can do it.

  According to this configuration, the running direction of the virtual fracture layer (the direction of the line of intersection between the formation surface and the horizontal surface) can be arbitrarily set. The rotation angle may be arbitrarily changed, or a plurality of angles may be selected.

    The fifth means includes the third means or the fourth means, and allows the computer to perform a procedure of inclining the virtual fault plane 6 on which the unit source model is installed with respect to the horizontal plane. I have to.

    The inclination angle with respect to the horizontal plane may be arbitrarily changed or may be fixed at a constant angle.

The invention according to the first means has the following effects.
○ Since a fault model is created according to the magnitude of the earthquake and the activity characteristics of the region, the ground motion can be obtained and the specific behavior of the building can be dynamically analyzed even for direct earthquakes where the epicenter is not specified.
○ Even in areas where fault information is not disclosed, it is possible to create a precise hazard curve by analyzing the fault model formed by this means.
○ Since the areas to be evaluated are divided for each earthquake activity characteristic such as the frequency of earthquake occurrence, the damage amount can be evaluated accurately.
○ Easy simulation of earthquake disasters when the location of the epicenter is changed variously because four reference points are set in a certain area with the same earthquake activity characteristics and virtual fault planes are set around each reference point 4. In addition, since the positions of these reference points can be adjusted, the maximum damage can be accurately evaluated for each scale of the earthquake.

  According to the second aspect of the invention, since the unit hypocenter model is installed at each of the center of the virtual fault plane and at least three of the outer periphery thereof, the influence of the variation in distance from the observation point to each unit hypocenter model is affected. An accurate evaluation can be obtained with less.

  According to the third aspect of the invention, the virtual fault plane is similar to the computer so that the area of the virtual fault plane 6 on which the unit hypocenter model is installed follows the rule of thumb corresponding to the magnitude of the assumed earthquake. Therefore, an accurate evaluation can be obtained for each assumed earthquake scale.

  According to the fourth aspect of the invention, since the virtual fault plane can be arbitrarily rotated, the direction of the virtual fault plane can be varied with respect to the direction of the building even when information on the fault plane is not obtained. By changing it, it is easy to perform dynamic analysis of the building for each strike and evaluate the maximum damage.

  According to the fifth aspect of the invention, the virtual tomographic plane 6 can be inclined with respect to the horizontal plane, so that accurate evaluation can be performed.

  1 to 6 are explanatory diagrams of a fault model formation program for earthquake risk assessment. In this program, it is desirable that these figures can be displayed on a computer display screen and operated.

  FIG. 1 schematically shows the ground subject to earthquake risk assessment. In the figure, A is the surface ground, C is the source region, and B is the intermediate crust between the base surface D of the surface layer and the source region. Further, point 2 on the ground surface E is an observation point and is a place where a building to be evaluated is installed. In the epicenter region C, a plurality of virtual fault planes 6 are set. These will be described later.

FIG. 2 shows an example in which the crustal structure to be evaluated according to the present invention is divided into a plurality of areas (hereinafter referred to as activity areas) S ₁ , S ₂ . ing. However, the regions shown in the figure are simplified for explanation, and specific division examples will be described later.

3 to 6 show a specific procedure of the fault model formation program of the present invention. The program according to the present embodiment causes a computer to execute the following procedure.
(1) Arrangement of reference points First, as shown in FIG. 2, the operator selects an active area within a certain distance from the observation point 2 among the terrain models corresponding to the actual terrain. Then, the computer arranges a large number of reference points 4 evenly in the activity area Sn selected as shown in FIG. In the example shown in the drawing, the reference points are arranged in the form of a point grid, but the arrangement pattern can be changed as appropriate. The direction of the lattice and the interval between the lattices can be set freely. These reference points 4 group can be adjusted so that one of the reference points 4 is located immediately below the observation point by freely arranging or sliding the position on the terrain model as a whole according to the operation of the operator. It is good to do so.
(2) Setting of Virtual Fault Plane As shown in FIG. 3, a virtual fault plane 6 is set around one reference point 4. The illustrated virtual tomographic plane is a square, but may be changed as appropriate, such as a triangle or a rectangle. This virtual fault plane is a part surrounded by a frame (case) 8 indicated by a solid line in the figure, and is provided so as to include an epicenter of a direct earthquake, particularly an asperity that generates strong ground motion. Yes. Therefore, it is desirable to obtain the area S (km ² ) of the virtual tomographic plane 6 from the formula log ₁₀ S = M− 4.06 . Then, the cross-sectional area for the magnitude M = 5, 6, and 7 and the length of one side when the virtual cross-section is a square are as shown in Table 1. For simplicity, the area of the virtual fault plane at magnitude 5 can be made zero (point epicenter). If the area of the virtual fault plane is too small, the distance between each model is small even if a point source model (described later) is placed on each part of the virtual fault plane. It is because it is not reflected. The depth of the virtual tomographic plane from the ground surface can be set as appropriate by the operator.

(3)単位震源モデルの設置
図示例のように正方形の仮想断層面では、各角部及び図形の中心に単位震源モデルを設置すればよい。単位震源モデルに関しては、前述のスケーリング則に基づいて、次の数式１のモデルが提案されており、これに従うと地震動のＳ波の加速度フーリエスペクトルは数式３のようになる（例えば非特許文献３参照）。

(3) Installation of the unit hypocenter model On the square virtual fault plane as shown in the figure, a unit hypocenter model may be installed at each corner and the center of the figure. Regarding the unit hypocenter model, a model of the following formula 1 has been proposed based on the scaling law described above. According to this, the acceleration Fourier spectrum of the S wave of the ground motion is expressed by the formula 3 (for example, Non-Patent Document 3). reference).

[Formula 2] S (ω) = ω ² / (1+ (ω / ω _c ) ² )
[Formula 3] A (ω) = (R _φθ × M / 4πρβ ³ ) × S (ω) × P (ω) × exp [−ωR / 2QΒ] / r
Where R _φθ is the _radiation coefficient, ρ is the density, β is the S-wave seismic velocity of the medium, and r is the epicenter distance. P (ω) is a high-frequency cutoff function, and is given by, for example, P (ω) = {1+ (ω / ω _c ) ² } ^−1/2 .
(4) Adjustment of virtual tomographic plane The virtual tomographic plane can be subjected to various processes such as enlargement / reduction and rotation by the operation of the operator.

    For example, it is possible to change from a large virtual fault plane indicated by a solid line in FIG. 4 to a small virtual fault plane indicated by an imaginary line in accordance with Equation 1 corresponding to the magnitude of the assumed earthquake.

  Further, the virtual tomographic plane can be rotated as shown in FIG. At this time, the rotation angle can be increased from 0 to 45 degrees so that the strike direction of the virtual tomographic plane can be arbitrarily selected from eight directions.

  Further, the tomographic model can be in an inclined state drawn with an imaginary line from a horizontal state indicated by a two-dot chain line in FIG. 6 to an inclined state as indicated by a solid line. The inclination angle can be set to 45 degrees, for example.

  When this program is used, the location of the building is designated as observation point 2 as shown in FIG. 2, at least the active area Sn to which this observation point belongs is selected, and the reference point group 4 is set in this active area. In this case, first, one of the reference points is set immediately below the observation point, a virtual fault plane is formed on this point, a point source model is installed, and risk analysis is analyzed by the method described later. By doing so, it is possible to evaluate the impact of the earthquake disaster when the epicenter is directly under the evaluation target. Furthermore, if necessary, the impact of the earthquake disaster when another reference point away from the observation point is used as the epicenter can be evaluated by the same procedure.

7 to 8 are explanatory diagrams of the earthquake risk evaluation method of the present invention. This procedure is as follows.
I. Formation of the fault model The formation of the fault model is basically the same as the contents described as the configuration and usage of the program for forming the fault model, and the description thereof will be omitted.
II. Analysis using a fault model This process is basically known in the art and will be briefly described.
(1) Implementation of Statistical Green Function Method First, a green function is generated between each point source model 10 set on the virtual fault plane and an arbitrary point (intermediate point) 12 on the base plane D. Next, for each of the point source models, an acceleration Fourier spectrum of the ground motion is obtained by Equation 3, and a ground motion function is generated as a sum of the spectra. Assuming that the vibration function in the source region is A _b (ω) and the transfer function of the intermediate crust is H (f), the vibration function at the base surface is A _s (ω) = H (ω) × A _b (ω) (Paragraph 0092 of Patent Document 2). Then, if the integration of these seismic functions and the Green function is performed, the responses at the midpoint 12 to the seismic motions of all point source models are obtained.
(2) Obtain the time history of ground motion on the basement surface.

When the result of the superposition integration is inversely Fourier transformed, the time history of the vibration at the midpoint 12 on the base plane D is obtained.
(3) Analysis of vibration amplification characteristics of surface ground Using the conventional method described above, the characteristics of surface ground A are analyzed, and the earthquake time history at observation point 2 is obtained from this and the vibration time history at intermediate point 12. .
(4) Multi-mass point analysis Analyze the influence on each part of the building from the observation point, that is, the time history of vibrations on the ground surface.
III. Building risk assessment In this process, a probability distribution map as shown in Fig. 8 is created from the maximum acceleration obtained in the above analysis and the frequency of earthquakes by scale given to each active area. Calculate the specific damage on each floor / part of the building.

In addition, the earthquake occurrence frequency according to scale in each activity area is obtained as follows. It is known that the relationship of log ₁₀ N = ab−M (the Gutenberg-Richter rule) is established, where N is the number of earthquakes of magnitude M or more in a certain area. Here, a and b are constants, and the latter is an area-specific numerical value called “b value”. Here, assume that the minimum value of the assumed earthquake is M _min , M _max, and the earthquake occurrence probability at magnitude M = 5, 6 and 7 is P _M (5) = ∫ _5.0 ^5.5 f _M (m) dm, P _M (6) = ∫ _5.5 ^6.5 f _M (m) dm, P _M (7) = ∫ _6.5 ^Mmax f _M (m) dm. However, f _M (m) is a probability density function of an earthquake occurrence, and is derived from the Gutenberg-Richter law as follows.

[Equation _{4] f M (m) =} b × ln10 × exp {-b × ln10 × (m-M min)} / [1-exp {-b × ln10 × (M max -M min)}]
Then, an occurrence probability P _M5 of an earthquake of magnitude 5 or more at 1 km ² is set, S is an area of an active area, and la is the number of reference points in the active area. Then, since the above P _M is normalized as P _M (5) + P _M (6) + P _M (7) = 1, the occurrence frequency P at each point is as follows.

[Formula 5] P (n) = P _M (n) × P _M5 × (S / la) n = 5, 6, 7

  Non-Patent Document 4 classifies the geological structure of the Japanese archipelago and the surrounding sea area as shown in FIG. 9, and the following Table 2 describes the specific area names. In the present invention, it is desirable to classify the active area based on such crustal information.

It is a perspective view of the ground to which the present invention is applied. It is explanatory drawing which shows one procedure which the tomographic model used for this invention forms. It is explanatory drawing which shows the other procedure which the said tomographic model forms. It is explanatory drawing which shows the further another procedure which the said tomographic model forms. It is explanatory drawing which shows the further another procedure which the said tomographic model forms. It is explanatory drawing which shows the further another procedure which the said tomographic model forms. It is a flowchart of the process of the disaster risk evaluation method of this invention. It is a correlation diagram of the maximum acceleration created by building risk evaluation by the same method and the occurrence probability. It is an example of the area division map used for the method. It is a figure showing the conventional method.

Explanation of symbols

2 ... Observation point 4 ... Reference point 6 ... Virtual fault plane 8 ... Frame 10 ... Point hypocenter 12 ... Middle point A ... Surface ground B ... Middle crustal portion C ... Epitaxial region D ... Basement surface E ... Surface surface Sn ... Region (Activity) Area)

Claims (5)

A method for evaluating earthquake risk for direct earthquakes,
Forming a fault model having a virtual fault surface in the hypocenter region below the stratum;
Generating a statistical Green's function indicating the response at the base surface of the surface ground to the earthquake motion at each part of the fault plane;
Using this statistical Green's function, obtaining a time history of the ground motion on the basement surface with respect to ground motion for all fault planes;
A step of generating a time history of ground motion on the ground surface from a time history of ground motion of the basement surface by analyzing the vibration amplification characteristics of the surface layer,
Calculating the impact on the structure of the ground surface based on the time history of the ground motion on the ground surface,
At the formation stage of the above fault model,
For the terrain model representing a certain area in common the characteristic of seismic activity, a plurality of reference points 4, adjustably positioned evenly and the position of the reference point group at regular intervals from each other,
Set one virtual fault plane (6) with an area corresponding to the assumed magnitude at the depth of the hypocenter area around each reference point,
A method for assessing earthquake risk, characterized in that unit hypocenter models corresponding to the rupture start points of the formation are respectively installed at least at two or more outer peripheral portions of the virtual fault plane ( 6 ) .   The earthquake risk evaluation method according to claim 1, wherein unit hypocenter models are respectively installed at the virtual fault plane center and at least three of the outer periphery thereof. A program suitable for carrying out the earthquake risk assessment method according to claim 1 or 2,
On the computer,
Procedure for the terrain model representing a certain area in common the characteristic of seismic activity, arranging a plurality of reference points (4), and evenly each other at regular intervals to allow adjusting the position of the reference point group When,
Centering on each reference point, setting the virtual fault plane ( 6 ) to the depth of the epicenter area,
A procedure for installing two or more unit source models on the outer periphery of at least one of the virtual fault planes ( 6 ) ,
The area ( S ) of the virtual fault plane ( 6 ) where the unit hypocenter model is installed corresponds to the magnitude M of the assumed earthquake,
[Formula 1] log ₁₀ S = c × M−d where c and d are constants
A procedure for enlarging or reducing the virtual fault plane in a similar manner,
A fault model formation program for earthquake risk assessment, characterized by The computer can be made to perform a procedure of rotating the virtual fault plane ( 6 ) on which the unit hypocenter model is installed about a reference point which is the center of the figure. Fault model formation program for earthquake risk assessment described. The earthquake according to claim 3 or 4, characterized in that the computer can be made to perform a procedure of inclining the virtual fault plane ( 6 ) on which the unit hypocenter model is installed with respect to a horizontal plane. Fault model formation program for disaster risk assessment.

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