JP6997431B2 - How to determine the amount of displacement of a building due to an earthquake - Google Patents

Description

The present invention relates to a method for determining the amount of displacement of a building due to an earthquake.

In recent years, there are an increasing number of cases where seismic structures, seismic isolation structures, or seismic isolation structures are adopted when constructing new detached houses.

On the other hand, for owners of existing detached houses that do not have seismic structures, seismic isolation structures, or seismic isolation structures, how much seismic performance the houses they currently live in have, or the expected occurrence of a large earthquake. There is a lot of desire to know how much damage will be inflicted.

As a method for diagnosing the seismic performance of an existing detached house, a dynamic seismic performance diagnosis method according to Patent Document 1 is provided. The following is a brief description of this method.

A vibration exciter is placed in the house to vibrate in the horizontal direction, and from the relationship between the acceleration detection signals of a plurality of acceleration detectors arranged in the house and the vibration frequency of the exciter, the natural frequency f _h of the house and the said. The acceleration response magnification τ _h at the natural frequency f _h is obtained. Next, the dynamic horizontal rigidity K of the house is calculated based on the first equation predetermined using the weight W _h of the house, the natural frequency f _h , and the acceleration response magnification τ _h . Subsequently, the seismic force Q acting on the house is calculated based on the second predetermined equation. The shear force K _θ is calculated from the calculated dynamic horizontal rigidity K, and the calculated shear force K _θ is compared with the seismic force Q, and it is determined that housing reinforcement is necessary when K _θ <Q.

By the way, when estimating the damage to a house caused by an earthquake, it is desirable to consider not only the information about the house but also the information on the ground on which the house is built. From this point of view, Patent Document 2 proposes a ground exploration device for investigating the ground structure directly under a house.

This ground exploration device detects surface waves generated around the ground surface by vibrating the ground surface up and down with a oscillator, and performs ground exploration, and is sometimes called a surface wave exploration device. The ground exploration device receives two acceleration detectors arranged on the ground at intervals L and detection signals from the two acceleration detectors, and receives acceleration time-series signals A (t) and B (t). The transmission function H (f) is calculated by receiving the time-series signals A (t) and B (t) and performing signal processing based on a predetermined analysis program with the measurement unit including the output seismograph unit. , The phase difference Δθ (f) between the two acceleration detectors and the time difference Δt (f) are calculated from the calculated transmission function H (f), and further calculated from the time difference Δt (f) and the interval L. A signal processing unit for calculating the propagation average velocity V _r (f) and the depth D (f) of the surface wave is provided. In particular, the signal processing unit repeats the process of calculating the propagation average velocity V _r (f) and the depth D (f) to obtain a depth D-propagation average velocity V _r curve (D-V _r dispersion curve). Generate.

Japanese Patent No. 3974858 Japanese Patent No. 3617036

By the way, in the seismic performance diagnosis method of Patent Document 1, it is necessary to introduce various calculation formulas for various numerical calculation, and it is necessary to set it assuming the scale of an earthquake acting on a house. Many of the formulas introduced are general formulas that can be applied to any region of the country. In addition, the scale of the earthquake to be set is uniformly determined in consideration of the seismic intensity of so-called large earthquakes that have been experienced in Japan so far, regardless of the region of the country.

However, the ground structure directly under a house varies widely depending on the region in Japan, and strictly speaking, the ground structure may differ even within a certain region. Also, regarding the scale of earthquakes to be set, earthquakes of the same scale do not occur anywhere in Japan, and there are past major earthquake occurrence histories, ground structures directly under houses, and active faults that are likely to cause major earthquakes. It should be set in consideration of various factors such as whether or not.

Therefore, an object of the present invention is to appropriately assume the scale of a large earthquake occurring at a survey point and to obtain the displacement amount of the building when the assumed large earthquake occurs as a value more realistic. The purpose is to provide a method for determining the amount of displacement of a building that can be performed.

The method for determining the amount of displacement of a building according to the present invention is
(A) Steps to create a ground model of the survey site by surface wave exploration,
(B) At the above-mentioned survey point, it is assumed that the shaking will be the largest at the time of occurrence among the earthquakes assumed by the publicly announced major active faults and active faults existing in the vicinity, and the earthquakes including the submarine type earthquakes that have occurred in the past. A step of selecting an earthquake as an assumed earthquake and calculating the response spectrum of the ground at the survey point when the assumed earthquake occurs.
(C) Using the calculated response spectrum, a step of creating an earthquake waveform in the engineering base of the survey point at the time of the assumed earthquake, and
(D) A step of calculating at least the surface ground predominant frequency _fg of the survey point using the created ground model and the created seismic waveform, and
(E) A step of calculating the resonance frequency f _h of the building on the ground at the survey point, and
(F) The step of calculating the relative displacement response magnification α of the building from the following formula, and
β = f _g / f _h
α = β ² / {(2hβ) ² + (1-β ² ) ² } ^1/2
However, β is the frequency ratio, h is the damping constant,
including.

According to the present invention, the scale of a large earthquake occurring at a survey point can be appropriately estimated, and the displacement amount of a building when the assumed large earthquake occurs can be obtained as a value more realistic. can.

It is a figure which showed the schematic structure of an example of the ground exploration apparatus applied for carrying out this invention. It is a figure which showed an example of the _{DV r} dispersion curve of the ground of the investigation point obtained at the time of carrying out this invention. It is a figure which showed an example of the ground model of the investigation point obtained at the time of carrying out this invention. It is a figure which showed an example of the monitor screen which is displayed for setting the investigation point at the time of carrying out this invention. It is a figure which showed an example of the monitor screen which is displayed for selecting the big earthquake which is assumed at the investigation point at the time of carrying out this invention. An example of a three-axis diagram of the response spectrum of the ground at the survey point at the time of the assumed earthquake, which is obtained when the present invention is carried out, is shown. It is a figure which showed an example of the seismic waveform in the engineering base of the investigation point obtained at the time of carrying out this invention. It is a figure which showed an example of the monitor screen which is displayed for inputting the information about the ground model of FIG. 3 at the time of carrying out this invention. It is a figure which showed an example of the acceleration transfer function-frequency characteristic obtained at the time of carrying out this invention.

Hereinafter, embodiments of the method for determining the amount of displacement of a building according to the present invention will be described with reference to the drawings. The object of the present invention is a so-called single-family house of about two or three floors, and in the following, for convenience, this type of detached house is collectively referred to as a building.

The method for determining the amount of displacement of a building according to the present invention is realized by a ground survey and a building survey. These investigations will be described step by step below.

(Ground survey)
The ground survey is
(A) Steps to create a ground model of a predetermined point, that is, the survey point where the building to be surveyed is built by surface wave exploration.
(B) Large earthquakes assumed by major domestic active faults announced at the survey points, large earthquakes assumed by active faults existing in the vicinity, and large earthquakes including submarine-type earthquakes that occurred in the past. A step of selecting an earthquake that is expected to have the largest tremor at the time of occurrence as an assumed earthquake and calculating the response spectrum of the ground at the survey point at the time of the assumed earthquake.
(C) Using the calculated response spectrum, a step of creating an earthquake waveform in the engineering base of the survey point at the time of the assumed earthquake, and
(D) The step of calculating at least the surface ground predominant frequency _fg at the survey point by using the created ground model and the created seismic waveform is included.

First, step (a) will be described. In the present embodiment, the surface wave exploration will be described as being carried out by the same apparatus as the ground exploration apparatus disclosed in Patent Document 2, but the method according to the present invention is disclosed in Patent Document 2. It does not mean that it is limited to the equipment having the same configuration as the ground exploration equipment.

The configuration of the ground exploration device will be described with reference to FIG. In FIG. 1, the ground exploration apparatus includes at least two acceleration detectors 11A and 11B, and a measuring unit 12 that receives acceleration detection signals from these acceleration detectors 11A and 11B. The measurement unit 12 includes a seismograph unit 12-1, an A / D conversion unit 12-2, a communication unit 12-3, and an oscillation unit 12-4. The seismograph unit 12-1 has a built-in low-pass filter circuit and generates an acceleration time-series signal from an analog acceleration detection signal. The A / D conversion unit 12-2 is for converting an analog acceleration time-series signal from the seismograph unit 12-1 into a digital acceleration time-series signal, and has an automatic input sensitivity adjustment function. The communication unit 12-3 transmits a digital acceleration time-series signal to a device connected to the measurement unit 12, for example, a personal computer with a monitor (hereinafter, abbreviated as PC) 13. The PC 13 performs signal processing based on the first analysis program installed in advance, and performs ground analysis.

Next, the operation of the ground exploration device will be described. First, the oscillator 15 and the acceleration detectors 11A and 11B are installed in a straight line at the survey point. Let L (m) be the distance between the acceleration detectors 11A and 11B. By vibrating the ground surface in the vertical direction using the exciter 15, a surface wave is generated around the exciter 15. The acceleration detectors 11A and 11B detect the vertical vibration of the surface wave (Rayleigh wave) propagating near the ground surface. The acceleration detection signals from the acceleration detectors 11A and 11B become analog time-series signals A _A (t) and B _A (t) by passing through the low-pass filter circuit of the seismograph unit 12-1, and A / D conversion. It is input to the part 12-2. The digital time-series signals _AD (t) and _BD (t) A / D-converted by the A / D conversion unit 12-2 are transferred from the communication unit 12-3 to the PC 13.

In the PC 13, the power spectra _GAA (f), _GBB (f), cross spectrum _GBA (f), and transfer function of the time series signals _AD (t) and _BD (t) are based on the first analysis program. H (f), coherence function γ ² (f), etc. are calculated. In the PC 13, the phase difference Δθ (f) between the acceleration detection signals of the acceleration detectors 11A and 11B is obtained from the obtained transfer function H (f), and then the time difference Δt (f) is obtained. Further, in the PC 13, the propagation average velocity V _r (f) and the depth D (f) of the surface wave are obtained from the time difference Δt (f) and the interval L between the acceleration detectors 11A and 11B. Then, the DV _r dispersion curve is displayed on the monitor of the PC 13 by the obtained average propagation velocity V _r (f) and the depth D (f).

The above calculation is repeated until the desired _DVr variance curve is obtained. That is, the frequency of the excitation signal given to the oscillator 15 is changed each time the measurement is performed. That is, the phase difference of the transfer function H (f), which has a reciprocal relationship with the propagation speed of the surface wave, is measured for each frequency. Next, the average propagation velocity V _r of the surface wave is calculated from the relationship between the phase difference and the frequency, the depth D is extracted, and as a result of repeated measurement, the DV _r as shown in FIG. 2 is displayed on the monitor. The variance curve is displayed.

According to FIG. 2, it can be seen that the ground at the survey point has a layered structure composed of a plurality of layers (here, 1 to 6 layers and a basement) which are distinguished by the depth D (m) and have different properties. Then, the average propagation velocity V _r (m / s) is calculated for each of the plurality of layers. A detailed operation description of the PC 13 based on the first analysis program is described in Patent Document 2, and is omitted here. Further, the PC 13 in the above-mentioned ground exploration apparatus executes each of the above-mentioned steps (b) to (d) constituting the present invention in addition to the first analysis program for executing the above-mentioned step (a). By mounting the second to fourth analysis programs for this purpose, it can be used as an apparatus for carrying out the present invention.

According to the first analysis program for executing the step (a), the ground model as shown in FIG. 3 is created from the _DVr dispersion curve as shown in FIG. However, before creating the ground model as shown in FIG. 3, inflection points with respect to the _{DV r dispersion} curve in order to distinguish a plurality of strata in the DV r dispersion curve as shown in FIG. Is specified. This is because the inflection point of the _DVr dispersion curve usually appears corresponding to the boundary of the stratum. The operator can specify the inflection point with the touch pen for the _DVr distribution curve displayed on the monitor by the touch panel display, but it is automated by installing a dedicated program that automatically identifies the inflection point. You can also do it. Here, as the items of the ground model, the following 6 items are calculated or extracted for each of a plurality of layers (here, 1 to 6 layers and a basement).

Layer thickness (m): Each layer thickness of the layer structure distinguished by the depth D in FIG. 2, and is extracted from the _DVr dispersion curve by designating an inflection point.
Surface wave velocity (m / s): Calculated for each stratum as the average propagation velocity V _r (m / s).
Shear wave velocity (m / s): The shear wave velocity is converted from the surface wave velocity obtained by surface wave exploration.
Unit volume weight (t / m ³ ): The unit volume weight of soil for each stratum is converted from the shear wave velocity.
Attenuation constant: Here, a constant value (0.05 in this case) is given to all strata, but it may be calculated and set for each stratum.
Soil quality: Apart from the above-mentioned ground exploration, it can be determined for each stratum based on existing survey materials, but the soil quality may be surveyed for each stratum by actual measurement, that is, boring.

Next, step (b) will be described. Step (b) is executed by the second analysis program already installed in the PC 13. In step (b), work is performed to assume the maximum magnitude of an earthquake that will arrive at the survey point as an assumed earthquake. Until now, assumed earthquakes have been determined with reference to past earthquake histories. On the other hand, in this embodiment, the assumed earthquake is determined in consideration of the surrounding conditions of the survey point. In this embodiment, the surrounding conditions of the survey site include large earthquakes assumed by publicly announced major active faults in Japan, large earthquakes assumed by active faults existing in the vicinity, and submarine-type earthquakes that have occurred in the past. List the large earthquakes and select the earthquake that is expected to have the largest tremor when it occurs from among these large earthquakes. To this end, the second analysis program includes large earthquakes assumed by major active faults in Japan that have been published, large earthquakes assumed by active faults existing in the vicinity, and large subduction-zone earthquakes that have occurred in the past. It comes with a database that covers all earthquakes.

The work flow of step (b) is as follows. All the work other than the work such as information input, setting, and designation by the operator is executed by the CPU of the PC 13.

When the operator reads out the second analysis program to the PC 13, a screen prompting the setting of the survey point is displayed on the monitor. The survey point is set by inputting the latitude and longitude. When the desired survey point is input, a map centered on the survey point (here, Ichinomiya City, Aichi Prefecture) as shown in FIG. 4 is displayed.

Then, when the operator specifies the selection of the assumed earthquake, the CPU searches the database and exists in the vicinity of the large earthquake assumed by the publicly announced major active faults in Japan within a predetermined range from the survey point. A list of large earthquakes that are expected due to active faults and large earthquakes that have occurred in the past, including subduction-zone earthquakes. The CPU subsequently calculates and lists the maximum value of the expected shaking at each survey point when it receives the listed large earthquakes, and selects the largest earthquake with the largest shaking from the listed maximum values. The process of selecting is executed.

The calculation of the maximum value of shaking is performed using the following equations (1) and (2).
<Acceleration>
logA _max = 0.50M + 0.0043H + d + 0.61-log (R + 0.0055 × 10 ^0.5M ) -0.003R (1)
However, A _max : maximum acceleration, M: magnitude, H: epicenter depth (km), R: shortest distance from the survey point to the relevant active fault (km), or the above-mentioned past major earthquakes from the survey point. The shortest distance to the epicenter (km), d: coefficient for each type of active fault, and the following values are given. Crustal earthquake: d = 0.0, interplate earthquake: d = 0.01, intraplate earthquake: d = 0.22
<Speed>
logV _{max =} 0.58M + 0.0038H + d-1.29-log (R + 0.0028 × 10 ^0.5M ) -0.002R (2)
However, V _max is the maximum velocity, and here, the following values are given as the coefficient d for each type of active fault. Crustal earthquake: d = 0.0, interplate earthquake: d = -0.02, intraplate earthquake: d = 0.12

List the maximum values using the above equations (1) and (2), and select the earthquake with the maximum value as the assumed earthquake. The above equations (1) and (2) are disclosed in "The distance attenuation equation of maximum acceleration and maximum velocity considering fault type and ground conditions" by Tsukasa Midorikawa et al., Architectural Institute of Japan Structural Papers (1999). ing.

FIG. 5 shows an example of the maximum value calculation result created by the above processing. In the maximum value calculation, the maximum acceleration A _max and the maximum velocity V _max are calculated, but in Fig. 5, for convenience, only the maximum acceleration (cm / s ² ) is displayed as the maximum value, and the Norio earthquake is the maximum value. Is shown. Therefore, from now on, this Norio earthquake will be selected as a hypothetical earthquake, and information about the Norio earthquake will be used to create the response spectrum described later. If the earthquake showing the maximum acceleration and the earthquake showing the maximum velocity are different in the maximum value calculation, the information of the earthquake showing the maximum acceleration is adopted.

In step (b), the response spectrum of the selected ground at the survey point at the time of the assumed earthquake is calculated next.

Specifically, the second analysis program performs calculations according to the following equations (3), (4), (5), and (6), and a response spectrum is obtained in the form of a triaxial diagram.
<Acceleration A>
A = 111 × 10 ^0.534M ÷ (Δ ＋ 30) ^1.857 (3)
<Speed V>
V = 2.21 × 10 ^0.545M ÷ (Δ ＋ 30) ^1.636 (4)
<Acceleration response spectrum Sa>
logSa (T) = (1.015-2.29logT-0.644 (logT) ² ) +
0.547M- (1.469-0.492 (logT)) × (log (Δ + 30)) (5)
<Velocity response spectrum Sv>
Sv = Sa (2π / T) (6)
However, M: magnitude, T: period, Δ: epicenter distance (the shortest distance from the epicenter to the survey point measured along the earth's surface). Also, calculate with the attenuation constant h = 0.05. The above equations (3) to (6) are disclosed in the annual report of the Kyoto University Disaster Prevention Research Institute (1984) "Earthquake motion prediction model on an engineering basis" by Goto, Kameda, Sugito, Saito, Otaki and others.

FIG. 6 shows an example of the response spectrum obtained by the above calculation by the second analysis program, and displays the velocity (cm / s), the period (s), and the frequency (Hz) as the numerical values of the three axes. There is. Acceleration and velocity are calculated in this calculation as well, but in FIG. 6, the velocity out of acceleration and velocity is displayed for convenience.

As a second analysis program for selecting the assumed earthquake and calculating the response spectrum as described above, a program called "seismic load setting system: SaleS" is commercially available from Kozo Keikaku Kenkyusho Co., Ltd.

Next, step (c) will be described. In step (c), the response spectrum calculated in step (b) is used to create an earthquake waveform on the engineering basis of the survey point at the time of the assumed earthquake. Step (c) is executed by the third analysis program installed on the PC 13. The creation of seismic waveforms on an engineering basis is realized as follows.

A Fourier amplitude spectrum is created with the response spectrum created in step (b) as a target, and an iterative calculation is performed based on the Fourier amplitude spectrum to match the target spectrum. When the response spectrum created in step (b) and the response spectrum created in step (c) are sufficiently matched, an acceleration waveform (seismic waveform) is created. Then, the time and acceleration (time history response) can be obtained by performing the inverse Fourier transform of the Fourier amplitude spectrum, and the acceleration waveform (earthquake waveform) can be created.

FIG. 7 shows an example of the seismic waveform (Ichinomiya City, Aichi Prefecture) created in step (c).

As a third analysis program for creating the above seismic waveform, a program called "simulated seismic wave creation program: ARTEQ" is commercially available from Kozo Keikaku Kenkyusho Co., Ltd.

Next, step (d) will be described. In step (d), the surface ground predominant frequency _fg at the survey point is calculated here using the data of the ground model created in step (a) and the seismic waveform created in step (c). For this calculation, the data of a plurality of items obtained from the created ground model are input to the PC13, and the seismic waveform created in step (c) is read by the PC13 as follows. Is calculated.

Step (d) is executed by the fourth analysis program installed on the PC 13. The flow of processing by the fourth analysis program is as follows.

First, when the operator reads out the fourth analysis program to the PC 13, a table for inputting the data of the ground model (FIG. 3) as shown in FIG. 8 is displayed on the monitor. When the data input of the ground model to the table on the monitor is completed, the process for calculating the surface ground predominant frequency _fg starts.

The processing here is a calculation of how the vibration caused by an earthquake is transmitted in the surface layer ground represented by the ground model. Simply put, the effects of ground characteristics are reflected in the seismic waves on the engineering foundation, and the effects of ground characteristics when passing through the surface ground are taken into consideration, and the frequency and acceleration transfer function on the ground surface at the survey site. Calculate the relationship. The frequency is common to all layers and indicates a wide range of about 0 to 200 (Hz).

The acceleration transfer function referred to here is to obtain the amplification factor of acceleration in the surface layer ground and the predominant frequency of the surface layer ground, and is based on the idea called the double reflection method. In the double reflection method, when vibration is transmitted through the ground consisting of multiple strata, reflection / scattering occurs at each stratum boundary, further reflection / scattering occurs in the adjacent strata, and finally reaches the ground surface. By the way, the seismic motion transmitted through the engineering base is used to indicate the situation where the dominant frequency and the maximum acceleration change.

In step (d), when an earthquake propagates through the surface layer ground, it is calculated how the earthquake propagates for each layer as shown in FIG. At that time, the change in the transmission method is calculated for each frequency to obtain the acceleration transfer function, and the relationship between the frequency and the acceleration transfer function as shown in FIG. 9 is obtained as the acceleration transfer function-frequency characteristic. Then, the acceleration transfer function indicating the peak value is obtained as the surface layer ground amplification factor, and the frequency at that time is obtained as the surface layer ground predominant frequency _fg .

From another point of view, in the case of a stratified structure having a plurality of layers (ordinary ground forms almost this stratified structure), the properties of seismic waves change when propagating in each layer having different physical property values. And since the frequency that is easily transmitted differs from layer to layer, the magnitude of acceleration for each frequency also changes. The above-mentioned calculation is to perform the calculation for each layer including the change such as reflection and scattering, and to summarize it, and to summarize it as the characteristic change of the seismic wave transmitted from the engineering base to the ground surface. .. Here, the stratified structure from the engineering foundation to the ground surface is expressed by the term surface ground, and the surface ground predominant frequency and transfer function (surface ground amplification factor) can be obtained.

As a program for calculating the surface ground predominant frequency _fg as described above, a program called "seismic response analysis program: k-Shake" is commercially available from Kozo Keikaku Kenkyusho Co., Ltd.

(Building survey)
Next, the building survey will be described. In the following, it will be described as a two-story building.

The building survey follows step (d) above and continues.
(E) A step of calculating the resonance frequency f _h of the building on the ground at the survey point, and
(F) The step of calculating the relative displacement response magnification α of the building from the following equations (7) and (8), and
β = f _g / f _h (7)
α = β ² / {(2hβ) ² + (1-β ² ) ² } ^1/2 (8)
However, β is the frequency ratio, h is the damping constant,
including. Of course, the building survey may be carried out before the above-mentioned ground survey, or may be carried out in parallel with the ground survey.

First, step (e) will be described. In this embodiment, step (e) can be realized by utilizing the dynamic seismic performance diagnostic method disclosed in Patent Document 1. However, it does not mean that the method according to the present invention is limited to the dynamic seismic performance diagnostic method disclosed in Patent Document 1.

In the dynamic seismic performance diagnostic method disclosed in Patent Document 1, a measurement system having the same configuration as the ground exploration apparatus shown in FIG. 1 is used. However, in the measurement system used in the dynamic seismic performance diagnosis, the installation form of the oscillator and the installation form of the acceleration detector are different from the case of FIG. That is, in the ground survey, the exciter is installed so as to vibrate in the vertical direction with respect to the ground, and the two acceleration detectors are installed so as to be aligned with the exciter. On the other hand, in the building survey, a oscillating machine equipped with an acceleration detector in the main body of the oscillating machine is used, and at least two acceleration detectors are used in the X-axis direction of the floor surface (of the building facing south). In this case, the survey is usually conducted in the east-west direction (usually in the east-west direction) and in the Y-axis direction (usually in the north-south direction). For this reason, in the case of a two-story building, the exciter is installed on the floor surface of the second floor so as to vibrate horizontally with respect to the floor surface. The detector is installed so as to be aligned with the acceleration detector of the oscillator main body in the Y-axis direction. Further, when the exciter operates in the Y-axis direction, the two acceleration detectors are installed so as to be aligned with the acceleration detector of the exciter main body in the X-axis direction.

(Calculation of resonance frequency _fh of the building)
In the following, the weight of the exciter is We (kN), the weight of the building above a predetermined height from the ground is W _h (kN), and the acceleration detected by the acceleration detector of the _{exciter body is U e .} Let U _h be the acceleration detected by one of the two acceleration detectors. In particular, when the acceleration detected in the X-axis direction by vibrating in the Y-axis direction is U _eX or U _hX , the acceleration response magnification τ _hX in the X-axis direction of the building is expressed by the following equation (9). ..
τ _hX = W _h x U _hX / _{We x U eX (} 9)

The above calculation operation is performed while changing the excitation frequency f of the oscillator, and a graph is created in which the horizontal axis is the oscillation frequency f and the vertical axis is the acceleration response magnification τ _hX in the X-axis direction. The frequency f when τ _hX shows a peak value is obtained as the natural frequency (dominant frequency) f _hX of the building. The dominant frequency is also called the dominant frequency or the resonant frequency. That is, the vibration frequency and the acceleration response magnification here correspond to the frequency and the amplification factor of FIG. 9, respectively.

The acceleration response magnification τ _hY and the resonance frequency f _hY in the Y-axis direction of the building are also obtained in the same manner.

The calculation operation of step (e) as described above can also be realized by the analysis program (fifth analysis program) pre-installed in the PC 13.

Next, in step (f), the relative displacement response magnification α of the building is calculated. Here, the relative displacement response magnification α of the building is a numerical value indicating how much the building is displaced when the assumed earthquake selected in step (b) above occurs, and is a numerical value indicating how much the building is displaced in each of the X-axis direction and the Y-axis direction. It is calculated.

Speaking of the relative displacement response magnification α _X in the X-axis direction of the building, it is calculated by the following equations (10) and (11).
β _X = f _g / f _hX (10)
α _X = β _X ² / {(2hβ _X ) ² + (1-β _X ² ) ² } ^1/2 (11)
The relative displacement response magnification α _Y of the building in the Y-axis direction is also calculated in the same manner.

The calculation operation of step (f) as described above can also be realized by the analysis program (sixth analysis program) pre-installed in the PC 13.

By the way, the degree of damage to the building at the time of an earthquake is undamaged (D <2.5 cm), minor damage (small damage) (2.5 cm ≤ D <5.0 cm), medium, depending on the displacement D of the building. It is classified into damage (medium damage) (5.0 cm ≤ D <7.5 cm), major damage (major damage) (7.5 cm ≤ D <10 cm), and total damage (including collapse) (10 cm ≤ D).

As described above, the relative displacement response magnification α of the building is a numerical value indicating how much the building is displaced when the assumed earthquake selected in the above step (b) occurs, that is, the displacement amount D of the building. Therefore, the degree of damage to the building at the time of the assumed earthquake can be determined based on the relative displacement response magnifications α _X and α _Y of the building obtained as described above. In other words, if it is determined that the displacement of the building, that is, the relative displacement response factors α _X and α _Y , is greater than or equal to minor damage, the proposal to the building owner should reinforce the building. Will be able to.

Therefore, as an additional step (g), if necessary,
(G) Based on the calculated relative displacement response magnification α, a step of determining whether or not reinforcement is necessary for the building so that the displacement amount is equal to or less than a predetermined value even when the assumed earthquake occurs. May be included.

According to the embodiment of the present invention described above, the scale of a large earthquake occurring at a survey point can be appropriately estimated, and the displacement amount of the building when the assumed large earthquake occurs can be more realistically determined. It can be obtained as a value.

11A, 11B Acceleration detector 12 Measuring unit 13 PC (personal computer)

Claims (2)

(A) Based on the results of surface wave exploration, the ground structure of the surface layer directly under the detached house, which is a building on the ground at the survey site, is divided into multiple layers, layer thickness, surface wave velocity, shear wave velocity, and unit. Steps to create a ground model containing data for multiple items of volume weight, decay constant, and soil quality for each layer,
(B) At the above-mentioned survey point, it is assumed that the shaking will be the largest at the time of occurrence among the earthquakes assumed by the publicly announced major active faults and active faults existing in the vicinity, and the earthquakes including the submarine type earthquakes that have occurred in the past. A step of selecting an earthquake as an assumed earthquake and calculating the response spectrum of the ground at the survey point when the assumed earthquake occurs.
(C) Using the calculated response spectrum, a step of creating an earthquake waveform in the engineering base of the survey point at the time of the assumed earthquake, and
(D) A step of calculating at least the surface ground predominant frequency _fg of the survey point using the data of the plurality of items in the created ground model and the created seismic waveform.
(E) A step of calculating the resonance frequency f _h of the building on the ground at the survey point, and
(F) The step of calculating the relative displacement response magnification α of the building from the following formula, and
β = f _g / f _h
α = β ² / {(2hβ) ² + (1-β ² ) ² } ^1/2
However, β is the frequency ratio, h is the damping constant,
A method for determining the amount of displacement of a building, including. (G) Based on the calculated relative displacement response magnification α, a step of further determining whether or not reinforcement is necessary for the building so that the displacement amount is equal to or less than a predetermined value even when the assumed earthquake occurs is further performed. The method for determining the amount of displacement of a building according to claim 1, which includes.

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