Diagnostic and evaluation method for structures based on ambient microtremors

Abstract

Unlike conventional methods that assess the soundness and safety of structures by directly applying external forces to the object, this method provides a structural diagnostic and evaluation method based on the ambient micro-vibrations of a structure that can diagnose and evaluate the seismic resistance, soundness, and effectiveness of countermeasures and reinforcement work in an inexpensive and rapid manner. [Solution] In a method for evaluating the performance of a structure by observing ambient microtremors, ambient microtremor observation history is observed simultaneously at multiple observation points within the structure, and an estimated value of an index used for seismic design of the structure is calculated using the mean square (RMS) of these time histories, and the seismic performance of the structure based on the observations is evaluated using the ratio of this value to the value of the index used at the time of design.

Description

[Technical Field]

[0001] This invention relates to a diagnostic and evaluation method for structures that diagnoses and evaluates the seismic resistance, soundness, and effectiveness of countermeasures and reinforcement work of a structure based on the constant micro-vibrations of the structure. [Background technology]

[0002] Diagnosing and evaluating the performance of various objects around us, from the human body, machinery, and buildings to cliffs, ground, and trees, is fundamental to living a safe and comfortable life, and many devices and technologies have already been put into practical use. However, diagnosing and evaluating the seismic resistance and soundness of structures such as buildings and infrastructure facilities presents the following difficulties: They are exposed to various natural environmental conditions over long periods of time. Each one has a different shape and material. Destructive testing is not possible. Their size exceeds human scale. They are difficult to move. They cannot be fully described with documents or data. Structures are supported by the ground, and the properties of the ground are more complex than those of man-made structures visible on the surface. There is a high degree of uncertainty regarding the timing, magnitude, and vibration characteristics of sudden external forces such as earthquakes.

[0003] Furthermore, while the conventional method for evaluating the seismic resistance of existing buildings involves calculating the structural seismic index (Is value), this method is time-consuming and costly because it requires experts to interpret information from drawings and other sources and input it into a computer program for complex calculations. Moreover, the calculation method is not unique and involves branching and judgment-based input, which ultimately makes it susceptible to subjective elements, leading to the institutionalization of third-party judgment committees. In short, the above conventional methods were costly, laborious, and time-consuming.

[0004] Diagnostic and evaluation methods for entire structures that have been put into practical use to date include: a) checking consistency with drawings and calculations, b) redoing structural calculations, c) recalculating using a different calculation method, d) measuring the shaking by applying vibrations with a vibrator, e) scoring and compiling scores using a checklist format, and f) based on microtremor observation. Inspections at the time of new construction fall under a) or b), while seismic diagnosis falls under c). However, the calculation methods listed in a) to c) rely on extracting the numerical values ​​that form the basis of the calculations from drawings, etc., so they make assumptions about whether the actual structure and support conditions are as described. Furthermore, even if a 100% accurate judgment can be made by performing detailed calculations on the interior of the structure, the calculation results will be largely influenced by the conditions of the foundation and surrounding ground. Also, the method using vibrators, etc., listed in d), is not very accurate because the energy of the vibrator is too small compared to the potential energy of the structure and surrounding ground, just like when performing structural calculations.

[0005] Constant tremors contain far more comprehensive, detailed, and extensive information about structures and surrounding ground than the information on which the above methods rely. Although the amplitude of constant tremors is small, only a few microns, they possess significant energy because the enormous mass of the structure and surrounding ground is constantly vibrating. Spatially, the vibration occurs at all points in the structure and surrounding ground, and the amount of information is incomparably greater than that from design documents or vibration generators. In particular, being able to measure actual vibrations with the ground as the input source, similar to earthquakes, is important when evaluating the risk from major earthquakes.

[0006] In the past, several methods for diagnosing structures using constant micro-vibrations have been attempted, such as the technology disclosed in Patent Document 1. [Prior art documents] [Patent Documents]

[0007] [Patent Document 1] Patent No. 3876247 [Overview of the Initiative] [Problems that the invention aims to solve]

[0008] However, conventional techniques involved visually determining the prevailing period from the Fourier spectrum and discussing its changes, extracting only a small fraction of the abundant information contained in ambient tremors. Consequently, the diagnostic results were insufficient in both accuracy and content, and could not establish themselves as a method for diagnosing structures. Furthermore, conventional techniques, including Patent Document 1, could not be applied to evaluation or diagnosis within the framework of current standards because the calculated indices were not those used in current design standards or seismic diagnosis standards. Moreover, current design standards do not include any indices that directly evaluate the continued usability of a structure. However, in this specification, current seismic design standards and seismic diagnosis standards for structures will be collectively referred to as "current standards." Also, seismic diagnosis standards will be simply referred to as "diagnosis standards," and seismic design standards will be simply referred to as "design standards."

[0009] Furthermore, there was no way to actually measure the distribution coefficient of story shear force in the height direction, the ultimate horizontal bearing capacity, and the product of the cumulative strength index and shape index used in seismic diagnosis, which are currently used in seismic design. The current standards do not specify the assumed seismic motion, and the current calculation method also has the problem of being non-unique and involving inputs based on branching and judgment.

[0010] In view of the problems found in the prior art, including the above-mentioned Patent Document 1, the present invention aims to provide a new method for extracting information about actual structures and surrounding ground systems and using this information for structural design and diagnostic evaluation. This method involves directly obtaining estimated values ​​of cumulative strength indices and structural seismic indices used in the diagnosis and seismic retrofitting design of existing structures, expected values ​​of the distribution coefficient of story shear force in the height direction used in the design of new construction, and damage levels used to directly evaluate the continued usability of structures, all from measured microtremor data. The method of the present invention is referred to as Micro Tremor Diagnosis (MTD). [Means for solving the problem]

[0011] The present invention was made to solve the above problems, and its structural features are that, in a method for evaluating the performance of a structure by observing ambient microtremors, ambient microtremor time histories are observed simultaneously at multiple observation points within the structure, estimated values ​​of an index used for seismic design of the structure are calculated using the mean square (RMS) of these time histories, and the seismic performance of the structure based on the observations is evaluated using the ratio of this value to the index value used at the design stage.

[0012] Furthermore, the continuously measured constant micro-motion time history can be divided, multiple partial time histories can be extracted, the expected value of the index can be calculated for each partial time history, and the sample average can be used as the estimated value of the index. In this case, the duration of the partial time history should preferably be 1 to 2 minutes.

[0013] In the present invention, the observations may be performed after the construction of a new structure, before and after renovation work, and during periodic inspections, and the estimated values ​​at each observation point may be compared with each other to diagnose and evaluate at least one of the changes over time among the seismic performance of the structure, the risk of collapse during a major earthquake, the continuity of use, and the changes before and after renovation work.

[0014] In the present invention, the index can be the distribution coefficient of story shear force in the height direction as defined in the current standards, or the horizontal load-bearing capacity as defined in the current standards.

[0015] Furthermore, in the present invention, the index is the base shear coefficient as defined in the current standards and the current standards A specified acceleration response magnification can also be used.

[0016] Furthermore, in the present invention, the index may be the product of the cumulative strength index and the shape index as defined in the current standards, or it may be the degree of damage or the risk of falling as newly defined in the present invention. [Effects of the Invention]

[0017] According to the present invention, by directly obtaining the expected values ​​of the cumulative strength index and structural seismic index used in the diagnosis and seismic retrofitting design of existing structures, the expected value of the distribution coefficient of story shear force in the height direction used in the design of new construction, and the estimated value of the degree of damage newly defined to directly evaluate the continued usability of structures, from microtremor measurements, it becomes possible to measure the vibration characteristics, strength, degree of damage, etc. of each floor zone by observing with vertical arrays set up in each part of the structure. As a result, it is possible to evaluate the seismic resistance, soundness, or the effectiveness of retrofitting design in a much more detailed, rapid, and inexpensive way than with conventional methods.

[0018] In other words, according to the present invention, by using the above indicators, diagnostic evaluations and inspections can be performed far more cheaply and quickly than current diagnostic evaluation or inspection methods after new construction, after renovation work, and during periodic inspections, thus enabling rational seismic reinforcement design and seismic design of newly constructed structures. [Brief explanation of the drawing]

[0019] [Figure 1] An explanatory diagram showing an example configuration of a diagnostic system to which the method of the present invention is applied. [Figure 2] A flowchart illustrating the basic processing procedure between the microtremometer and the analyzer. [Figure 3] An explanatory diagram showing the factors necessary for calculating the structural seismic index, the ultimate horizontal load-bearing capacity, and the degree of damage in the method of the present invention. [Figure 4] A flowchart illustrating the overall processing steps of the present invention. [Figure 5] A diagram illustrating the processing steps performed within the analyzer, broken down by routine. [Figure 6] This is a schematic diagram illustrating the actual effects and seismic forces of an earthquake. (a) shows the actual effects, (b) shows the spring-mass system, and (c) shows the seismic forces. [Figure 7] Figure 6(b) shows a model (single-mass system) where multiple point masses and a spring are combined into one, as depicted by black dots and lines. [Figure 8] A graph showing the relationship between bilinear cumulative strength index and inter-story drift angle. [Figure 9] A graph showing the relationship between frictional inter-story shear force and support section acceleration. [Figure 10] A graph showing the relationship between frictional inter-layment shear force and inter-layment velocity. [Figure 11] A graph showing the relationship between frictional inter-story shear force and inter-story displacement. [Figure 12] A diagram illustrating the placement of four types of microtremometers on the first floor of a four-story hospital. [Figure 13] This diagram shows the layout of four types of microtremometers on the second floor of a four-story hospital, using the same building as an example. [Figure 14] This diagram shows the layout of four types of microtremometers on the third floor, using a four-story hospital as an example. [Figure 15] This diagram shows the arrangement of four types of microtremometers on the fourth floor, using a four-story hospital as an example. [Figure 16] Layout plan of columns and walls on the first floor and beams on the second floor of Y Hospital. [Figure 17] Layout plan of columns and walls on the second floor and beams on the third floor of Y Hospital. [Figure 18] Assembly diagram of Y Hospital, X direction, 1-way axis. [Figure 19] Drawing of two axes in the X direction at Y Hospital. [Figure 20] Assembly diagram of four axes in the X direction at Y Hospital. [Figure 21] Assembly diagram of the A-axis in the Y direction at Y Hospital. [Figure 22] Drawing of the axis structure of Y Hospital, direction Y, through path B. [Figure 23] A panoramic view of the building for Example 2. [Figure 24] Figure 23 shows the installation status of the A2 measuring instrument on the first floor, corresponding to Figure 25. [Figure 25] An explanatory diagram showing the placement of measuring instruments and reinforcement locations, corresponding to Figure 24. [Figure 26] Micro-displacement trajectories for each floor. [Figure 27] Animation of vibrations on the roof of an 11-story SRC building, measured before reinforcement. [Figure 28]An animation of the vibration of the rooftop of an 11-story SRC building after reinforcement. This figure shows a single moment in the visualization (animation) of the movement of the reinforced rooftop surface, obtained by inputting displacement data (XYZ 3 components) from microtremometers installed at three locations on the rooftop surface into structural analysis result visualization software. [Figure 29] A schematic diagram showing the arrangement of the block wall, foundation, ground, and microtremor sensor. [Figure 30] An explanatory diagram showing the overall view of a concrete block wall in different situations, labeled (a) to (c). [Figure 31] Diagram showing the placement of microtremors on the concrete block wall and at the reference point. [Modes for carrying out the invention]

[0020] The ground surrounding structures is constantly experiencing minute vibrations. Sources of this vibrational energy include tides, traffic vibrations, etc. The amplitude is several microns [10 = -6 It is approximately m. The ambient tremors observed at a certain point in a structure (hereinafter also simply referred to as "tremors") are the result of tremors in the surrounding ground entering the structure from the foundation and being amplified or attenuated as they propagate through the interior of the structure.

[0021] Ambient tremors are observed using accelerometers (micro-tremometers) installed within the structure. These represent the absolute acceleration at a specific point within the structure, and are typically measured in three orthogonal components: a vertical component and two horizontal components. Because the amplitude is small and the duration is short, the structure is a steady-state linear system, and ambient tremors can be mathematically treated as part of a stationaly stochastic process.

[0022] Hereinafter, embodiments of the present invention will be described based on the drawings. Figure 1 is an explanatory diagram showing an example of the configuration of a diagnostic system to which the method of the present invention is applied. According to the figure, the entire diagnostic system consists of a microtremor 1 placed at the layer boundaries 10a, 10b, and 10c of each layer of the structure 10, and an analyzer (e.g., a personal computer) 2 that calculates various vibration characteristic indices, as well as various seismic performance evaluation indices used in current standards and new evaluation indices, based on the data recorded by the microtremor 1.

[0023] Of these, the microtremor meter (for example, the JU410 microtremor meter manufactured by Hakusan Kogyo) 1 incorporates an acceleration sensor, memory, and GPS. The analyzer 2 is equipped with microtremor diagnostic software that receives data recorded by the microtremor meter 1 via USB, LAN, or the internet, and performs calculations using the method of the present invention, which is described in detail below, to calculate various vibration characteristic indices, as well as various seismic resistance evaluation indices used in current standards and new evaluation indices. Furthermore, the microtremor displacement data acquired by the microtremor meters 1, which are installed in, for example, three locations on a certain floor, is sent to the visualization software installed in the analyzer 2, and the movement of the surface is animated in three dimensions and displayed on a display means (display) not shown in the figure of the analyzer 2, so that the vibration mode of the structure 10 can be easily seen and visualized.

[0024] The outline of the present invention method will be described below with reference to Figures 2 to 5. Figure 2 is a flowchart showing the basic processing procedure between the vibration meter 1 and the analyzer 2. According to the figure, the vibration meter 1 measures and records ambient vibrations (acceleration time history of observation points and reference points on the layer boundary). The analyzer 2 filters the received measurement record data in the frequency domain and then obtains the acceleration time history in the frequency band near the natural frequency of the target structure. After obtaining the acceleration time history, it is divided into parts of about 2 minutes in the time domain, and for each part, the time history of interest, energy transfer coefficient, and various indicators are calculated. After calculation, the average value and standard deviation of the vibration characteristic indicator, seismic performance indicator, and seismic damping performance indicator for each part are calculated, and the average value is used as the estimated value of each indicator.

[0025] Furthermore, according to Figure 3, the magnitude of the assumed seismic motion in the present invention method is the maximum acceleration, maximum velocity The performance is expressed in terms of degree, maximum displacement, and duration of strong earthquake. Microtremometers are installed in a vertical array on each floor and reference plane of the target structure. Furthermore, the performance of the target floor of the target structure is expressed in terms of required horizontal bearing capacity, ductility index, age index, and limit cycle count. After the installation of the microtremometers is completed, microtremor measurements are taken using microtremometer 1 and the measurement results are analyzed using analyzer 2, according to the processing procedure shown in Figure 2, and vibration characteristic index (central period, coefficient showing the distribution of story shear force in the height direction), seismic performance evaluation index (product of ultimate cumulative strength index and shape index), and seismic convergence evaluation index (hysteretic absorbed energy, degree of damage). After processing the above, the structural seismic index, ultimate horizontal bearing capacity ratio, and degree of damage are calculated to complete the process.

[0026] Figure 4 is a flowchart showing the overall processing procedure of the present invention method. According to the figure, first, a preliminary survey of the target structure is conducted. Specifically, literature materials such as design drawings, calculations, renovation history, damage history, and past seismic diagnoses are collected, and the possible locations for installing microtremometers are determined through on-site surveys. Next, the measurement time period, measurement duration, placement of microtremometers (instruments), and reference plane are determined as part of the microtremor measurement plan. After formulating the microtremor measurement plan, the microtremor measurement is carried out by setting the absolute time of the instruments, measuring the microtremors, and recording the data, and the analysis is carried out by calculating the time history of interest, vibration characteristic index, and performance index. After completing the above, the diagnosis is carried out. In this case, for a diagnosis in accordance with current standards, the structural seismic index or the ratio of the ultimate horizontal load-bearing capacity is used, and for seismic damping performance evaluation, the degree of damage is used.

[0027] Figure 5 is an explanatory diagram showing the processing performed within analyzer 2 by routine. According to the figure, the input data includes various data as assumed seismic motion parameters, as well as observed microtremor time history, observation time, observation frequency band, analysis time, and analysis frequency band. Various data as observation point attributes and various data as structural parameters are also input.

[0028] The calculation routine performs calculations of the time history of the microtremor of interest, part division, calculation of vibration characteristic index, and calculation of performance index. The preliminary calculation routine performs FFT, filtering, zero-point correction, mean square calculation, center frequency calculation, and bandwidth index calculation.

[0029] The display routine displays input data, observation time history, spectrum, central frequency, bandwidth index, vibration characteristic index, and performance index, as well as time history, power spectrum, trajectory, and surface motion animation. The output and transfer routine is performed via paper, hardware devices, USB, LAN, radio waves, etc.

[0030] The outline of the present invention method has been described above based on Figures 1 to 5, but the present invention method will be described in more detail below. In the present invention method (MTD: Micro Tremor Diagnosis), the mean square (RMS) of the duration, displacement, velocity, and acceleration time history of the microtremor, the peak factor, the zero-crossing period, the central period, the bandwidth index, and the energy transfer coefficient between the microtremor displacement, velocity, and acceleration time history of the reference point and the microtremor time history of the microtremor of interest are used to quantitatively analyze the vibration characteristics of microtremors and structures. This is a characterization of a stochastic process using the second moment and a correlation analysis between input and output.

[0031] In microtremor measurement, several sets of time histories are extracted from the continuous measurement durations for a single microtremor meter setup. For each set, the following quantities are calculated to determine the sample mean and standard deviation. For seismic performance evaluation, the sample mean of each quantity is used as an estimate of the expected value of each quantity.

[0032] Figure 6 is a schematic diagram showing the actual action and seismic force of an earthquake, where (a) shows the actual action, (b) shows the spring / mass point meter, and (c) shows the seismic force. Microtremor diagnosis is performed by modeling the structure's ground system as shown in Figures 6(a) to (c), with the surrounding ground 21 as a rigid floor and the structure 10 as mass points and springs. This is the same as the current seismic standards.

[0033] The ground is constantly subjected to tides, traffic vibrations, etc., and is several microns thick. [10 -6 The vibrations are occurring with an amplitude of approximately m. This is called a microtremor. The surrounding ground 21 of the structure 10, represented by the solid rectangle in Figure 6(a), exhibits the same phenomenon. The microtremors enter the structure 10 from the foundation and propagate within the structure 10, so the structure 10 also experiences microtremors. Since it is subjected to random inputs over a sufficiently long period of time, it is thought that both the surrounding ground 21 and the structure 10 are vibrating in their own unique vibration modes.

[0034] By installing multiple microtremor meters (accelerometers) 1 within the structure 10 as shown in Figure 1, the time history of microtremors can be observed. For example, one accelerometer can be installed in a vertical array at a representative point of each layer, corresponding to modeling each layer of the structure 10 with point masses and springs as shown in Figure 6(b). Since the amplitude of microtremors is minute, the structure 10 is a steady-state linear system over a finite duration, and the constant microtremors can be mathematically treated as part of a stationary stochastic process.

[0035] Seismic motion is a phenomenon in which displacement caused by the fracture of bedrock and ground in the epicenter region becomes a wave that reaches the ground surrounding structures and causes them to vibrate. Therefore, the source of vibrational energy is different from that of ambient tremors, but in the range of small amplitude, it is thought that both the surrounding ground and structures vibrate in their natural modes, so it is thought to vibrate in the same way as ambient tremors. Based on the above, the following indicators will be calculated through microtremor observation to predict the dynamic properties of the structure and its behavior during an earthquake, and the current seismic performance evaluation indicators and new evaluation indicators will be calculated.

[0036] 1. Central Period (Vibration Characteristic Index, Part 1) The central period T of micro-displacement in a certain direction at a certain point within a structure. c [sec] is calculated as follows:

[0037]

number

[0038]

number

[0039] However, ω cy [rad / sec] is the RMS of the time history obtained by differentiating an arbitrary minute time history. The central frequency is calculated by dividing by its own RMS (here, "central" is a translation of the English "central frequency," and does not mean being at a specific center, but rather the expected value of the zero-crossing frequency, which plays a central role in discussing the frequency characteristics of time history in disordered vibration theory), and a (see column a in Table 1) and b (see column b in Table 1) are the displacement time, respectively. This is the RMS of the history and speed-time history.

[0040] [Table 1]

[0041]

number

[0042] Here, [0, t0] is the duration of the micro-motion time history. Velocity, acceleration, and rotation angle. The central period can be similarly defined for the same elements. By calculating the central period of the time history obtained from multiple microtremors installed in a specific part of a structure and comparing them, it is possible to determine whether that part is vibrating in a specific vibration mode.

[0043] 2. Expected value of the coefficient representing the distribution of story shear force in the height direction (Vibration characteristic index, part 2) Current seismic standards and seismic diagnosis standards for buildings are based on the mechanical model shown in Figure 6(b). , seismic force acting on the jth floor of the building (P j ) seismic intensity (k j) and the product of the weight (w j ) of that layer are represented as such.

[0044]

Number

[0045] From the above relationship, when a building consisting of n floors vibrates under the action of an earthquake, the maximum shear force generated in the i-th floor is referred to as the floor shear force a (see column a in Table 2), and is given as the product of the weight b (see column b in Table 2) supported by that floor and the earthquake floor shear force coefficient (C i ) of that floor.

[0046]

Table 2

[0047]

Number

[0048] Furthermore, the earthquake floor shear force coefficient (C i ) is defined as the product of the regional coefficient (Z), the vibration characteristic coefficient (R t ), the standard shear force coefficient (C0), and the coefficient (A i ) representing the distribution of the floor shear force in the height direction. Note that in the primary design assuming medium and small earthquakes, C0 = 0.2, and in the secondary design for large earthquakes, it is determined to use C0 = 1.0.

[0049]

Number

[0050] Note that for the first floor,

[0051]

Number

[0052] From the above, A​i This normalizes the story shear force to the shear force a of the first story (see column a in Table 3). The value b (see column b in Table 3), and the amount obtained by normalizing the weight of the layers above that layer by the total weight (total weight) W from the first layer upwards, and α i It can be derived that this is the ratio.

[0053] [Table 3]

[0054]

number

[0055] Using the relationship in the above equation, assuming that the absolute acceleration energy transfer coefficient a (see column a in Table 4) in the k-direction of the i-th layer obtained from the microtremor diagnosis is also conserved during the elastic response due to seismic motion input, we multiply this by the maximum acceleration at the reference point to calculate the expected value b (see column b in Table 4) of the maximum absolute acceleration, and multiply this by the mass m of each layer of the structure. j From this, we can determine the expected value c of the maximum story shear force (see column c in Table 4), and the expected value E[A] of the coefficient representing the height distribution of the story shear force in the k direction of the i-th story. ik ] of This can be obtained (Equation 9). However, the maximum acceleration at the reference point is omitted as it is omitted from the numerator and denominator of the rightmost side of Equation 9. Furthermore, the absolute acceleration energy transfer coefficient a (see column a in Table 4) is defined in paragraph "0067" of this specification as the absolute acceleration time history of the microtremor time history of interest, that is, the ratio of the RMS of the absolute acceleration time history in the k direction of the i-th layer to the RMS of the absolute acceleration time history in the k direction of the first layer. Also, the second equality sign from the right in Equation 9 is derived from the equations of motion for the dynamic model of the structure in Figure 6(b) (see paragraphs "0032" to "0034"). Furthermore, the final equality sign in equation 9 is based on the assumption described in paragraph "0021," namely, that the absolute acceleration time histories of each layer (the i-th layer) obtained from ambient microtremor observations can be mathematically treated as part of a steady-state stochastic process. Based on the finding that the expected value of the maximum value within a certain duration can be calculated by multiplying the RMS by the peak factor, the peak factors of the absolute acceleration time histories of each layer are assumed to be equal. As shown above, the method of the present invention estimates the design index of the current standard, which is defined using the maximum value of the force acting inside the structure during an earthquake, using the RMS of the absolute acceleration time histories of each layer obtained from microtremor observations, based on the above assumption. Compared to the method that uses the actual measured maximum value, this method obtains an estimated value of the maximum value with less variation (stable), i.e., an estimated value of the design index.

[0056] [Table 4]

[0057]

number

[0058] Incidentally, in seismic standards, based on various analyses and studies, the α that appears in the two equations above is as follows: i (Normalized weight) and the building's primary natural period T are used as parameters for A i It stipulates that...

[0059]

number

[0060]

number

[0061] However, T[sec] is calculated assuming that λ is the majority of the columns and beams in the building are made of wood or steel. The ratio to the total height of the floors (excluding the basement) h[m] shall be calculated using the following formula. It is being done.

[0062]

number

[0063] The above regulations are designed to express the maximum response shear force distribution for each floor from low-rise to super-high-rise in a tower-like structure using a single formula. Furthermore, in the seismic standards, the above formula is used for A i Instead of calculating A, we directly create the model shown in Figure 6(b) for each individual building and calculate the maximum value of the story shear force using methods such as time history response analysis. i It is also permissible to request it.

[0064] 3. Expected values ​​of average transmission coefficient and response magnification (Vibration characteristic index, part 3) In the model shown in Figure 6(b), when considering the effects of an earthquake on the i-th layer, it is convenient to use the following indices that give the RMS or maximum value of the average acceleration, average velocity, etc. of the portion b (from the i-th layer to the n-th layer) supported by that layer.

[0065]

number

[0066]

number

[0067] Here, mj is the mass of the j-th layer, a (see column a in Table 5) and b (see column b in Table 5) are the energy transfer coefficients of acceleration and velocity in the k-direction of the j-th layer, respectively, and B aik Let B be the average acceleration energy transfer coefficient. vik This is called the average velocity energy transfer coefficient. However, the energy transfer coefficient is the ratio of the RMS of the microtremor time history of interest to the microtremor time history of the reference point, and in microtremor diagnosis, it is assumed that this is preserved at the time of the maximum elastic response due to seismic motion input, and the peak factor is appropriate. Assuming otherwise, the maximum response in the time history of interest is calculated by multiplying the maximum input value at the reference point by the energy transfer coefficient.

[0068] [Table 5]

[0069] For example, using the average acceleration energy transfer coefficient described above, the absolute acceleration time history a of each point (mass dM) of a portion b supported by a certain layer i within a structure k k-direction component A of the spatial mean of (t) k The expected value of the RMS of (t) E[σ Ak ] can be calculated as follows, depending on the acceleration time history of the reference point, a (see Table 6).

[0070] [Table 6]

[0071]

number

[0072]

number

[0073] The expected value A of the coefficient representing the height distribution of story shear force in Equation 9. imk And defined in equation 13 The average acceleration energy transfer coefficient B aik The following relationship exists between them.

[0074]

number

[0075] That is, A imk This is the average acceleration of the part supported by the part of interest i and the part supported by the first layer. It can be said that this is the ratio of the average acceleration of the entire structure. In equation 13, the average acceleration transfer coefficient B is calculated by setting j=1. aik This is the ratio of the mean absolute acceleration of the structure, a (see column a in Table 7), to the absolute acceleration of the reference point, b (see column b in Table 7), i.e., the acceleration response magnification R when the entire structure is reduced to a single-degree-of-freedom system as shown in Figure 7. amk This is the expected value.

[0076] [Table 7]

[0077]

number

[0078] Similarly, B when j=1 in equation 14 v1k This can be said to be the expected value of the velocity response multiplier when the entire structure is reduced to a single-degree-of-freedom system.

[0079]

number

[0080] The current standard uses the standard shear force coefficient in Equation 6, where C0=0 in the primary design assuming a small to medium earthquake. 2. In the secondary design for major earthquakes, the reason for using C0=1.0 is that the assumed ground conditions This is because the maximum acceleration of vibration was assumed to be 0.07G to 0.08G for small to medium earthquakes and 0.33 to 0.4G for large earthquakes, and the acceleration response ratio of short-period buildings was assumed to be 2.5 to 3.

[0081] 4. Expected value of the lateral load-bearing capacity (Seismic performance index, part 1) According to seismic standards, each floor of the building's structural model must be A i The distributed shear force is gradually increased when loading is applied, and the story shear force a (see column a in Table 8) acting on the i-th story when the i-th story yields is defined as the ultimate horizontal bearing capacity b (see column b in Table 8). The relationship between the story shear force generated in a structure due to micro-tremors in the ground and the acceleration at a reference point is defined in paragraphs "0064" to "0080" of this specification as the average acceleration transmission coefficient (B aik ) by This can be expressed. Furthermore, the relationship between interstory displacement and the acceleration at the reference point can be expressed using the transfer coefficient defined in paragraph "0067" of this specification. Using these, the expected value of the story shear force can be calculated when the maximum interstory displacement of the i-th story reaches the yield displacement, assuming that the structure responds linearly. This can be considered as the expected value c of the horizontal bearing capacity (see column c in Table 8), assuming that all stories except the i-th story do not yield. Interlayer displacement in the k-direction of the i-th layer (e) with respect to the acceleration d in the k-direction of the reference point (see column d in Table 8) ik The energy transfer coefficient e of (t) (see column e in Table 8) is defined as the ratio of their respective RMS values ​​as follows:

[0082] [Table 8]

[0083]

number

[0084] Maximum interstory displacement e ikmax The yield displacement e ikY The maximum value of the acceleration at the reference point when it reaches a ikY If you leave it as is,

[0085]

number

[0086] The expected value a of the maximum layer shear force at this time (see column a in Table 9) is calculated by multiplying the mass b of the part b supported by the i-th layer (see column b in Table 9) by the expected value A of the maximum average acceleration of this part. bkmax It can be calculated by multiplying by .

[0087] [Table 9]

[0088]

number

[0089] The expected value of the maximum acceleration at the reference point and the maximum value of the average acceleration in the above section b is the average acceleration energy transfer coefficient B. aik They are related using [this method].

[0090]

number

[0091] From the above,

[0092]

number

[0093] From equations 21 and 24,

[0094]

number

[0095] Expected value C of the story shear force coefficient when the ultimate horizontal load-bearing capacity is reached uikmThis is the relationship in equation 5 Using this, the above formula is obtained by dividing it by the weight supported by the layer.

[0096]

number

[0097] However, the floor height in the k direction of the i-th layer is H 0ik [m], yield deformation angle R Yik [rad], g[m / sec 2 Let ] be the acceleration due to gravity. Also, the expected value of the story shear force coefficient of the first story when the horizontal load-bearing capacity is reached, i.e., the expected value of the base shear coefficient C ui1km This is due to the relationship in equation 8. , the above equation is A i This can be calculated by dividing by R. This is obtained using equations 9, 17, and 19, which give the acceleration response magnification R. amk It can be seen that this can be expressed by the energy transfer coefficient a of the inter-story displacement with respect to the acceleration at the reference point (see Table 10).

[0098] [Table 10]

[0099]

number

[0100] The ratio of the seismic resistance to horizontal load is calculated by dividing the expected value of the seismic resistance obtained above by the required seismic resistance to horizontal load as stipulated by the seismic standards.

[0101] 5. Expected value of the product of the ultimate cumulative strength index and the shape index, and the structural seismic resistance index (Seismic performance index, part 2) According to the seismic diagnosis standards, for each floor (each level) of a low-to-medium-rise reinforced concrete building, the structural seismic index is I. s The basic performance index E0 and the shape index S D It is expressed as the product of , and the longitudinal index T.

[0102]

number

[0103] Regarding the basic performance index E0 in the above formula, a detailed formula is defined for calculating it by summing the products of the strength index (C) and ductility index (F) in each direction for individual columns, walls, and beams of each layer. However, in principle, the basic performance index E0 is the product of the strength index and ductility index of that layer (E0 = It is explained as C × F). The toughness index of a layer is the toughness index corresponding to the interlaminar deformation unit at which the layer reaches its ultimate limit, so this is F U This is expressed as follows, and accordingly, a coefficient equivalent to the base shear coefficient at the interlayer drift angle where the layer reaches its ultimate limit (ultimate cumulative strength index) is set to C TU This is how it is expressed.

[0104]

number

[0105] From the above relationship,

[0106]

number

[0107] Equation 29 is derived by assuming that the story shear force a (see column a in Table 11) is bilinear with respect to the interstory displacement e, as shown by the line segment OYU in Figure 8. In this case, the story shear forces (cumulative strength index) at the yield point Y and the ultimate point U are equal (C TY =C TU ), yield correlation displacement (e Y This becomes a cumulative strength index for ). However, Figure 8 shows the distribution coefficient A in the height direction of the story shear force a (see column a in Table 11) and the weight Σw that the story supports. i Divide by the cumulative intensity index C T The inter-story displacement e is divided by the floor height H0 to obtain the inter-story drift angle R, which is then plotted. The subscript i is omitted.

[0108] [Table 11]

[0109] The inter-story displacement-story shear force relationship obtained from the microtremor diagnosis is assumed to represent the relationship shown in Figure 8, although it is near the origin of the relationship shown in Figure 8. The seismic diagnosis standards specify the age index T and the ductility index F. U When set to 1.0, the I of that layer, when it reaches its ultimate state for the seismic motion assumed by the standard (design basis ground motion: G0), S The value is specified to be 0.6. Therefore, the correlation displacement energy transfer coefficient h obtained from microtremor diagnosis is... egi Multiplying this by the reference point displacement corresponding to the design basis earthquake motion (G0), we obtain the expected value of the correlated displacement (E[e G0 When calculating ]), this is exactly , yield displacement (e Y =R Y If H0, then the value is 0.6. Therefore, equation 3 0 is F U If we set =1 and T=1,

[0110]

number

[0111] Assuming that the cumulative strength index and the inter-story drift angle (inter-story displacement) are proportional, the quantity obtained by multiplying the ultimate cumulative strength index in the k-direction of the i-th layer by the shape index ((C TU S D ) ik The expected value of ) is slightly Correlated displacement energy transfer coefficient h obtained from dynamic diagnosis egik It corresponds to the design basis earthquake motion (G0). Reference point displacement x G0

[1978] Multiply by to obtain the correlation displacement (e G0ik ) is calculated, and this gives the yield displacement (e Yik This is the value obtained by dividing by ) and multiplying the result by 0.6.

[0112]

number

[0113] Now, according to the seismic diagnosis standards, I s The value = 0.6 represents the number of buildings that suffered moderate to severe damage from the 1968 Tokachi-oki earthquake and the 1978 Miyagi-oki earthquake. s Estimated values ​​of the distribution of values ​​and information on buildings that have not experienced earthquake damage. s The validity of the criteria was verified through a comparison of the value distributions. In addition, studies on the 1978 Izu Oshima offshore earthquake, the 1987 Chiba Prefecture offshore earthquake, and the 2011 Great East Japan Earthquake are included. However, the maximum acceleration, velocity, duration, etc., of the observed seismic motion up to the 1978 Miyagi Prefecture offshore earthquake are orders of magnitude different from those of the 21st century, exemplified by the 2011 Great East Japan Earthquake. Therefore, it is reasonable to assume that the seismic motion assumed by the diagnostic criteria is that of the seismic motion up to 1978, when the criteria were first established.

[0114] The U.S. National Oceanic and Atmospheric Administration (NOAA) has compiled and published a database of strong earthquake records observed in Japan up to 1978. Based on statistical analysis of this data, it is reasonable to assume that the expected maximum displacement of the seismic motion at that time was approximately 2.5 cm in both horizontal directions, and this value is substituted into Equation 32. Furthermore, the yield displacement e in the k-direction of the i-th layer in the same equation is also calculated. Y [m] is the floor height H0[m] and yield deformation angle R Y Expressed in [rad], we obtain an equation to calculate the expected value of the product of the ultimate cumulative intensity index and the shape index from the energy transfer coefficient.

[0115]

number

[0116] From equation 30 and the above equation, the structural seismic index I s This can be calculated from microtremor diagnosis.

[0117]

number

[0118] However, I sm is the structural seismic resistance index obtained from the microtremor diagnosis, F U , and T are the ultimate ductility index and the aging index, respectively.

[0119] 6. History Absorbed Energy (Seismic Performance Index Part 1) Calculating the non-linear response, that is, how the structure deforms and moves under the action of an earthquake from the information described or planned to be described in the design drawings after a certain layer of the structure reaches the yield strength, that is, after exhibiting non-linearity with respect to stress, is not easy even if the seismic motion is specified and the structure and the ground are simplified as shown in Fig. 6(b) or Fig. 7.

[0120] There are various models (constitutive laws) regarding the stress and strain acting between each layer of the structure after yielding. Concrete and soil exhibit non-linearity even at very small strains. Also, as variables explaining non-linearity, not only the interlayer displacement as shown in Fig. 8 but also its relative velocity, absolute acceleration, and furthermore, stress and strain in other directions such as axial force are considered. The members constituting the layer, the materials constituting them, and the connection status of each member are diverse, and there are also diverse methods of reducing them to a single constitutive law. It cannot be said which one is correct.

[0121] In seismic design, there are several typical non-linear models, which are used for analyzing experimental results at the member level or on a full-scale model. However, even if they are compatible in terms of the loading method of the experimental apparatus and the measurement methods such as displacement, their effectiveness in the actual action of an earthquake in a three-dimensional space cannot be verified.

[0122] Fig. 9 shows the relationship between the friction-type interlayer shear force and the support part acceleration, Fig. 10 shows the relationship between the friction-type interlayer shear force and the interlayer velocity, and Fig. 11 shows the relationship between the friction-type interlayer shear force and the interlayer displacement, respectively. Microtremor Through diagnosis, the vibration of the representative points of each layer of the actual structure can be measured, and the response characteristics of each layer with respect to the structural model in Fig. 6(b) can be quantified. From the results, the expected value of the hysteretic energy absorption using the friction model as shown in Figs. 9 to 11 can be calculated.

[0123] This model is a stress model of a structure like stacked stones. As shown in Figs. 9 and 10, when the absolute acceleration of the part supporting the layer exceeds the limit acceleration and a relative velocity occurs between the layers, a certain shear force acts in the opposite direction to the velocity.

[0124] Starting from zero interlayer displacement, as the interlayer displacement increases in a certain direction and reaches a certain magnitude, the structure deforms such that the interlayer displacement continues to decrease. When it decreases to a certain magnitude and then the structure deforms to increase, the relationship with the interlayer displacement is as shown in Fig. 11. In the bilinear shear force-interlayer displacement relationship shown in Fig. 8, when plotting the relationship between the interlayer shear force and the support part acceleration, it is as shown in Fig. 9. Therefore, for the part where the shear force is constant (the line segment YU in Fig. 8) in the bilinear shear force-interlayer displacement relationship, the above friction model can be applied.

[0125] The hysteretic energy absorption W of the i-th layer calculated from the k-direction component ik is, as shown in the following formula, the work W done by the restoring force (layer shear force) a (refer to column a in Table 12) with respect to the relative motion (interlayer displacement e ik ) occurring between the upper surface and the lower surface of the i-th layer of the structure, and the increment (refer to column b in Table 12) is obtained by integrating with respect to the vibration duration t0. ik

[0126]

Table 12

[0127]

Number

[0128] Let the spatial average absolute acceleration and mass of the portion supported by the i-th layer in the k direction be A ik (t) and (Σm) respectively. Then, the equation of motion in the k direction of the portion supported by the portion of interest is as follows.

[0129]

Equation

[0130] Since the restoring force is assumed to have a yield limit strength a (see Table 13), from Equation 36, it can be seen that A ik (t) also has a limit value, which is denoted as the limit acceleration A cik .

[0131]

Table 13

[0132]

Equation

[0133] From the micro motion observation, when the structure responds elastically, that is, when the restoring force does not have a limit value, the spatial average acceleration of the portion supported by the i-th layer can be predicted, and this is denoted as a (see Table 14).

[0134]

Table 14

[0135] When the restoring force is friction-type and the lower surface of the layer vibrates with an acceleration a (see Table 14), and a (see Table 14) is a part of a stationary Gaussian process with a duration of s0, the expected value of the history absorption energy W ik per unit mass is obtained from the parameters obtained from the power spectral density function of a (see Table 14) and the limit acceleration A ci and the theoretical formula represented by them is obtained from the irregular vibration theory.

[0136] [Number]

[0137] Here, E[*]: Expectation value of * [Operator]

[0138] Also, for the k direction of the i-th layer a (see Table 15): Restoring force [N] e ik (t): Relative displacement between the upper and lower surfaces [m] A cik : Limiting acceleration [m / sec 2 Σw: Supported weight [N]

[0139]

Table 15

[0140] Also, for the spatially averaged elastic response acceleration time history a (see Table 14) of the part supported by the i-th layer during an earthquake, and the k-direction component of the velocity time history obtained by integrating this: s0: Duration of strong ground motion [sec] T vik : Central period of the velocity time history [sec] σ aik : RMS of the acceleration time history [m / sec 2 α vik : Bandwidth index of the velocity time history [dimensionless] σ vik : RMS of the velocity time history [m / sec]

[0141] However, the duration of strong ground motion s0 is the duration for treating the time history (x(t)) of the duration t0 with non-stationarity like ground motion as the part of the duration s0 of a stationary Gaussian process (G(t)) having the same power spectral density function, such that the maximum value of x(t) appears as the maximum value with an average of once during the duration s0 of G(t).

[0142] The above T vikThe following parameters are calculated from the time history obtained by microtremor observation, the energy transfer rate, and the predicted value of the maximum value of the vibration time history of the reference point due to the assumed earthquake. First, assuming that the structure vibrates in the vibration mode obtained by microtremor observation even during an earthquake and in the elastic response state, the vibration period T of a (see column a in Table 16) vik , the bandwidth exponent α vik is calculated using the microtremor acceleration time history b of the lower surface of the portion supported by the i-th layer, that is, the upper surface of the i-th layer (see column b in Table 16). Further, for the RMS σ of c (see column c in Table 16) vik and the RMS σ of this velocity time history vik , they are calculated using the average transfer rate of each layer (j = i…n) (refer to paragraphs "0059" to "0075" of this specification) and the RMS of the reference point during an earthquake.

[0143]

Table 16

[0144]

Number

[0145]

Number

[0146] The RMS of the acceleration and velocity of the reference point during an earthquake can be rewritten in relation to the expected value V maxk of the maximum velocity and the expected value A maxk of the maximum acceleration of the reference point during an earthquake using the peak factor.

[0147]

Number

[0148]

Number

[0149] Furthermore, the critical acceleration in the k-direction of the i-th layer is calculated using the fact that the horizontal load-bearing capacity a (see column a in Table 17), obtained in paragraphs "0081" to "0100" of this specification, is equal to the yield layer shear force (a (see column b in Table 17)). From equations 37 and 25,

[0150] [Table 17]

[0151]

number

[0152] Based on the above, the expected value W of the hysteretic absorption energy in layer i due to a major earthquake, calculated from the k-direction component, is mik [Nm] can be calculated as follows:

[0153]

number

[0154] However, yield displacement e ikY This is expressed as the product of the yield deformation angle and the floor height. Also, the i-th layer k-th Regarding direction, R Yik : Yield deformation angle [dimensionless] H 0ik :Standard floor height [m] a (See Table 18): Inter-story displacement energy transfer coefficient with respect to reference point acceleration [dimensionless]

[0155] [Table 18]

[0156] Furthermore, regarding the k-direction component of the micro-motion time history of the upper surface of the area of ​​interest, T vik :Central period of the time history of micro-motion [sec] α vik : Bandwidth index of the time history of microtremor velocity [dimensionless] However, the bandwidth index is obtained by dividing the central frequency of the time history by the central frequency of the differential time history, and the bandwidth index of the microkinetic time history is the ratio of the central frequency of the microkinetic time history to the central frequency of the microacceleration time history.

[0157] Furthermore, regarding the parts supported by the layers, Σm: Mass [kg] B aik : Average acceleration transfer coefficient (see Equation 13) [dimensionless] B vik : Average velocity transfer coefficient (see Equation 14) [dimensionless]

[0158] Furthermore, regarding the k-direction component of the large earthquake motion at the reference point, the following parameters are given by the designer's judgment or by criteria, as they determine the magnitude and properties of the input. s0: Duration of strong earthquake [sec] V maxk :Maximum speed [m / sec] A maxk :Maximum acceleration [m / sec 2 ] γ v : Peak factor of velocity time history [dimensionless] γ a : Peak factor of acceleration time history [dimensionless]

[0159] Furthermore, by dividing both sides of the above equation by Σm / 2, we obtain the velocity-converted value V of the expected value of the hysteretic absorption energy per unit mass supported. mik Obtain [m / sec]

[0160]

number

[0161] 7. Damage level (Seismic damping performance index, part 2) Assuming that the degree of damage to a certain layer of a structure due to earthquake action is proportional to the hysteretic energy absorbed, the ratio of this to the limit value is defined as the degree of damage (I d ) can be used as a design indicator.

[0162]

number

[0163] Now, regarding the k-direction of the i-th layer: I dik :Damage degree [dimensionless] W mik Expected value of hysteretic absorption energy [Nm 2 / sec 2 ] W lik : Limit value of hysteretic absorption energy [Nm 2 / sec 2 ]

[0164] Limit value of hysteretic absorption energy W lik This can be calculated by assuming that the restoring force of individual members or groups of members is bilinear, as shown in Figure 8, and accumulating their respective limit values.

[0165]

number

[0166] However, the limit value is defined as the energy absorbed in one repetition by doubling the area of ​​the projection of line segment OYU onto the horizontal axis in Figure 8, and this n kj The calculation assumes it is doubled. Here, with respect to the individual members j, or member group j, in the k direction of the i-th layer: n kj : Maximum number of repetitions [dimensionless] q kj :Strength [N] F jk :Toughness index [dimensionless] e Yj Yield displacement [m] R Yik Yield deformation angle [rad] H 0ik :Floor height [m]

[0167] The expected value of the yield shear force (ultimate horizontal load-bearing capacity) in the k-direction of the i-th layer is calculated in paragraphs "0081" to "0100" of this specification, so if the ductility index of the layer and the critical number of cycles are given, The limit value of the hysteretic absorption energy can be calculated. Using equation 47, the entire layer is treated as one group, and equation 25 is used.

[0168]

number

[0169] However, regarding the k-direction of the i-th layer N ik : Maximum number of repetitions [dimensionless] a (See column a in Table 17): Expected value of yield shear force (horizontal bearing capacity) [N] F uik :Toughness index [dimensionless] Σm: Mass of the supporting part [kg]

[0170] The degree of damage is calculated as the quotient of the expected value of the hysteretic absorption energy in Equation 44 and the limit value in Equation 48, as follows:

[0171]

number

[0172] Damage degree I dik The vibration characteristics obtained from microtremor observations of the surrounding ground system of the structure, with respect to the k-direction of the i-th layer, are represented by the average acceleration transmission coefficient B of the portion supporting it. aik , average velocity transmission rate T vik , and the interlayer displacement energy transfer coefficient a in the k-direction of the i-th layer with respect to the acceleration at the reference point (see Table 20), and the central period T of the velocity time history. vik , and bandwidth index α vik The characteristics of the input ground motion are expressed as follows: strong motion duration s0, maximum velocity V maxk and maximum acceleration A maxk and their respective peak factors γ v gamma a It is represented as follows. Furthermore, as a structural specification, the yield deformation angle R in the k-direction of the i-th layer is given.Yik , and standard floor height H 0ik It uses the toughness index F, and its recovery performance is uik and the limit number of repetitions N ik It is represented as follows.

[0173] 8. Seismic Diagnosis Standards, Current Standards, and Seismic Motion Levels Reflecting Recent Earthquake Conditions Microtremor Diagnosis (MTD2017) quantifies the vibration amplification characteristics of a structure as a sample average of the energy transfer coefficient from the observed microtremor time history. It also visualizes the vibration modes and measures the natural period and bandwidth. For seismic performance evaluation, it uses vibrations from a major earthquake at reference points on the first floor, basement, etc., of the structure as input, estimates the maximum elastic response from the energy transfer coefficient, and calculates the expected value of the structural seismic index. Furthermore, it estimates the hysteretic absorbed energy from the predicted average acceleration and velocity of the parts supported by the floor or section of interest, and calculates the degree of damage. While the setting of the necessary seismic motion levels is at the discretion of each designer, it is effective to convert and display the assumed levels of current standards, etc., into microtremor diagnosis input values.

[0174] Table 19 shows the diagnostic criteria, the standard seismic motion level assumed by the current criteria (expected values ​​of maximum acceleration, velocity, displacement (Amax, Vmax, Dmax), and duration of strong motion). The expected value (S0) is shown. In addition, the seismic motion level based on recent observed seismic motion is shown as a reference at the bottom. The diagnostic criteria are estimated from seismic motion observed in Japan up to 1978, as mentioned above. The current criteria are estimated from the statements of those involved in the establishment of the criteria and the shape of the notification spectrum (pp. 488-490 of the 2015 edition of the Commentary on Technical Standards for Structural Buildings, published by the National Official Gazette Sales Cooperative Association). Recent observed seismic motion is estimated from strong motion observation records of the 2011 Tohoku earthquake and the 2016 Kumamoto earthquake, but no statistical processing has been performed. Furthermore, the seismic motion levels in recent earthquake environments are an order of magnitude higher than the current standards, making it meaningless to use the current framework of maximum elastic response and the microtremor diagnostic framework as input ground motion. Seismic design for ground motion at this level needs to be carried out using a fundamentally different method than that currently in place.

[0175] [Table 19]

[0176] The role of microtremor diagnosis In rational seismic design, microtremor diagnosis plays the following roles.

[0177] (1) Post-completion inspection and additional countermeasures After the structure is completed, a microtremor diagnosis is performed to determine the vibration mode and vibration period (T c ), story shear force distribution coefficient (A im ), response magnification (R amk , R vmk ), cumulative strength index a (see Table 20), damage degree (I dm The following parameters are measured and compared with the design calculations to confirm the validity of the calculations and construction, and additional countermeasures are implemented as needed. In addition, each of the above indicators is calculated for the entire structure, and the vibration characteristics of each section are also determined by vertical array measurements installed in that section.

[0178] [Table 20]

[0179] (2) Regular health checks and repairs Regular microtremor assessments will be conducted, measuring the indicators mentioned above. If deterioration of the structure is found, repairs will be carried out. Furthermore, a microtremor assessment will be conducted again after the repairs to confirm their effectiveness.

[0180] (3) Diagnosis and seismic reinforcement of existing structures Microtremor assessments will be conducted on existing structures built under current or old seismic standards, and countermeasures will be designed and implemented as needed. Furthermore, measurements and assessments will be performed before and after reinforcement to quantitatively confirm the effectiveness of the reinforcement.

[0181] (4) Analysis of the relationship between earthquake damage and the vibration characteristics of the ground and structures Using the case of a building that underwent microtremor diagnosis and subsequently suffered damage from an earthquake as an example, we will analyze the relationship between the degree of damage and the diagnostic indicators, and use this analysis to revise future design methods, diagnostic methods, and standard values ​​for each indicator. [Examples]

[0182] 1) Target facilities and measurement methods Completed in 1972 (Showa 47), this building has one basement floor, four above-ground floors, and a total floor area of ​​838m². 2 Figures 12 to 15 show the structure of the first floor 12 to the fourth floor 15 of the reinforced concrete (RC) hospital building 11 (with one span in the X direction and three spans in the Y direction, and the fourth floor being steel-framed; tentatively named Y Hospital). The results of a microtremor diagnosis conducted on this RC hospital building 11 are presented below. A seismic diagnosis was conducted in April 2014, and a reinforcement plan was formulated with a value exceeding 0.6. However, it was determined that construction could not be carried out while the hospital was operational, and in order to prevent collapse, "axial load-bearing reinforcement" was implemented by reinforcing the main columns using the SRF method (a method of wrapping with polyester fiber belts; see paragraph "0194" of this specification).

[0183] Microtremor observations were performed using four microtremometers 21 in four different configurations as shown in Figures 12 to 15. In the first (measurement 1) and second (measurement 2) measurements, one microtremometer was installed in a vertical array at each of the A2 and A4 streets on each floor from the first to the fourth floor. In measurement 3, the microtremometers were installed at a point on the A4 street on the first floor and at points A2, A4, and B1 on the second floor. In measurement 4, the microtremometers were installed at a point on the A4 street on the first floor and at points A2, A4, and B1 on the third floor.

[0184] The measurements took approximately two hours and involved sequentially setting up instruments, taking five minutes of continuous measurement, and rearranging the instrument positions, performing measurements and removal using four different instrument configurations. Before the reinforcement work, the measurements were taken while the hospital was operational, from 3 PM to 6 PM on August 8, 2017. After the reinforcement work, the measurements were taken from 2 PM to 4 PM on September 22, 2017. The construction period for the reinforcement work was from July 20 to September 30, 2017, but as of August 8, only preliminary preparations had been made and no construction had been carried out. Also, as of September 22, the structural work was completed with only a few finishing touches remaining.

[0185] For microtremor diagnosis, the total time history of the 5-minute recording observed at each point was divided into 5 to 7 overlapping segments of approximately 1 minute each. Each index was calculated for each segment, and the average value and standard deviation were calculated for each measurement. The tables shown from Table 21 onwards show these average values. The above measurements were performed both before (pre-reinforcement) and after (post-reinforcement) the reinforcement work using the SRF method to examine the effect of the reinforcement.

[0186] The microtremor meter was used to observe the acceleration time history, and after applying a 10Hz high-cut filter and a 0.2Hz low-cut filter (4th-order Butterworth), velocity and displacement were determined by numerical integration using the linear acceleration method. Figures 16 to 22 show the floor plan and structural frame diagram of the target building. An expansion joint is installed on the 4' side. The seismic diagnosis was conducted separately for sides 1 to 4' and the rest of the building. The diagnosis results cited in this specification are for sides 1 to 4'.

[0187] 2) Performance indicators Table 21 shows the expected value of the cumulative intensity index shown in formula 32 (C T S D ) mik The values ​​before and after reinforcement were obtained from seismic diagnosis calculations. TU S D This is shown in comparison. Measurement 1 refers to a vertical array of A2 type, and Measurement 2 refers to a vertical array of A4 type. Table 22 also shows a comparison of the rate of change before and after reinforcement with the calculated value. Tables 23 and 24 show the value W obtained from microtremor diagnosis before and after reinforcement for the normalized input energy.Komik The value W obtained by calculation Koik This shows the rate of change before and after reinforcement, and a comparison with the calculation. Tables 25 and 26 also show the expected value of the degree of damage (I d0m Values ​​before and after reinforcement and calculated value (I d ) and a comparison with the calculations before and after reinforcement are shown. Note that in Table 21 The values ​​in parentheses are those that take into account the second type of structural element. Furthermore, the damage level is calculated by using Equation 47 to determine the limit value of hysteretic energy absorption from the strength and ductility of the member group obtained in the seismic diagnosis calculation, and then calculating the hysteretic energy absorption using a simplified formula (see paragraph "0199" of this specification). In addition, in the calculation of this example, in determining the limit acceleration used in the calculation of hysteretic energy absorption (see paragraph "0149" of this specification), the product of the cumulative strength index and the shape index (see Equation 32) is used instead of the ultimate horizontal load-bearing capacity.

[0188] [Table 21]

[0189] [Table 22]

[0190] [Table 23]

[0191] [Table 24]

[0192] [Table 25]

[0193] [Table 26]

[0194] The reinforcement work was carried out using a method (SRF method) that ensures shear strength and axial load capacity by wrapping high-ductility polyester fiber material (belts) around the main columns of each floor from the first to the third floor. The reinforcement design ensures that the verification ratio of all columns exceeds 1.0. The maximum verification ratio of the axial force during an earthquake on each floor is used to determine the collapse risk value (I f This value is used as a design index for reinforcement aimed at preventing collapse. The right two columns of Table 25 show the I value before and after reinforcement. f The values ​​are listed. In the calculation, the axial load-bearing capacity of the column is the remaining axial load-bearing capacity under large deformation (F>3.0), so for RC columns, it is zero before reinforcement. Collapse risk level I f It is infinite.

[0195] Looking at the diagnostic calculations before and after reinforcement on the right side of Table 21, the cumulative strength index C was increased by the reinforcement work, except in the X direction of the first floor. TU S D The C has decreased, but this is because slits were cut into the column-type wall or the column with a wing wall and the column was wrapped around it. However, after reinforcement TU S D This is the diagnosis before reinforcement. This is an approximate value calculated by reflecting the increase or decrease in strength and toughness of the reinforced member in the cross-section results, and then grouping and summarizing the results again. Note that the shape index S is affected by the cutting of the slit. D Changes in the strength index due to reinforcement work are not considered. In this reinforcement design, it was assumed that there was sufficient strength in the Y direction, and the goal was to secure axial strength and prevent collapse even if the strength was slightly reduced. Also, as shown in Tables 25 and 26, the reinforcement reduces the damage level to I d The level of damage decreased significantly to about 20-30% before reinforcement, and after reinforcement, it fell below the standard value of 1.0 in all floors and directions, indicating that the reinforcement work brought the damage within the acceptable limits.

[0196] The cumulative intensity index C calculated using diagnostic methods shown in Tables 21 and 22. TU S D and the expected value of the cumulative intensity index obtained from microtremor diagnosis (C T S D ) mikLet's compare the values ​​before reinforcement. For Measurement 2, although the microtremor diagnostic value on the 3rd floor is about 40% lower, it can be seen that the values ​​are almost the same as on the other floors and in the same direction. On the other hand, in Measurement 1, the 1st floor is almost the same, but the microtremor diagnostic results on the 2nd and 3rd floors are significantly smaller, about 20% of the diagnostic calculation. This is thought to reflect the structural characteristics around the measurement location, as follows. As shown in the frame diagram in Figure 17, the X direction of Measurement 1 (2-way) is a frame with almost no walls. Also, the opening in the wall of the adjacent 1-way is large, and there are no walls in the 3-way. On the other hand, the X direction of Measurement 2 (4-way) is a frame with almost no walls, and the adjacent 4' frame is similar. The Y direction of Measurement 1 (2-way, A-way) has no walls or large openings. On the other hand, the Y direction of Measurement 2 (4-way, A-way) has openings but is attached to walls. This is also reflected in the seismic diagnosis shape index. That is, the shape index S shown on the right side of Table 21. D The value is small at 0.63 on the 2nd and 3rd floors in the X direction. As a result of the uneven distribution of walls in the X direction, the inter-story displacement is large in both the X and Y directions near the 2nd floor.

[0197] Looking at the rate of change before and after reinforcement in Table 22, in measurement 1 (around 2), (C T S D ) mik The performance improved by approximately 20% across the board. This can be attributed to the effect of the column reinforcement using the SRF method shown in Figures 16 to 22, which improved the vibration characteristics of the X-direction frames (1 to 3) and the Y-direction A-frames (2) around the center of the column, thereby reducing the inter-story displacement for the design basis earthquake. On the other hand, in measurement 2, there was almost no change before and after reinforcement, or (C T S D ) mik The values ​​have decreased. However, looking at the absolute values ​​in Table 21, in Measurement 2, after reinforcement, the values ​​were consistent in both the X and Y directions, with the 1st and 2nd floors at around 0.5 to 0.6 and the 3rd floor at around 0.2. Similarly, in Measurement 1, the values ​​were consistent, with the 1st floor at around 0.6 and the 2nd and 3rd floors at around 0.2. We believe that the above is the result of reinforcing the main columns with the SRF method, which has stabilized the vibration characteristics.

[0198] Table 22 shows a comparison of the magnitudes of the diagnostic calculations and the values ​​obtained from microtremor measurements. On the first floor, where eccentricity is minimal, both Measurement 1 and Measurement 2 yield almost identical calculated and measured values. This indicates that the setting of the expected value of the maximum ground surface displacement for seismic motion assumed by the microtremor diagnostic method and seismic diagnosis (see paragraphs "0113" to "0114" of this specification) was appropriate in this example. Furthermore, on the second and third floors, where eccentricity is present, significantly different values ​​were measured between Measurement 1 and Measurement 2, demonstrating that detailed structural characteristics can be grasped through vertical array observation.

[0199] Table 23 shows the normalized input energy W. K0ik and the permissible limit value W l0ik Looking at this, the standardized hysteretic absorption energy (hereinafter referred to as standardized input energy) W is shown on page 112 of the SRF Construction Method Design and Construction Guidelines and Commentary, 2015 edition, published by the Structural Quality Assurance Institute. E In the simplified formula, the influence of seismic motion and structures on input energy is a uniform coefficient m E Since it is assumed that = 5.0, the calculation assumes that the input energy does not change before and after reinforcement. On the other hand, as shown in Equation 49 of this specification, the formula reflects the effects of the structural strength, response magnification, and vibration bandwidth, so it changes before and after reinforcement. However, in Table 23, the W of the green book E A i It is multiplied by and displayed as a value normalized only by the supporting mass.

[0200] In terms of the absolute value of the normalized input energy, the measurement in the X direction of measurement 1 before reinforcement, which is greatly affected by eccentricity, is about 4 to 7 times larger than the calculated value, but other values ​​are almost the same. It can be said that this is the value. Therefore, this example can be said to demonstrate that the setting values ​​for the seismic motion level equivalent to the current standards shown in Table 19 are also appropriate for the degree of damage, as indicated by the microtremor diagnostic method.

[0201] Tables 23 and 24 show the rate of change in the normalized input energy before and after reinforcement. Measurement 1, which is greatly affected by eccentricity, shows a uniform decrease of about 60%. On the other hand, in Measurement 2, there is a large decrease in the X direction on the 1st and 2nd floors, but an increase in both directions on the 3rd floor. In particular, the increase rate in the Y direction of Measurement 2 is large, about 7 times. These directly relate to the strength (C) before and after reinforcement, which is shown in Table 22. T S D ) mik This reflects the changes in the standardized input energy. In other words, in this example, a cumulative intensity index is used in the calculation of the limit acceleration of the standardized input energy, so the increase or decrease in this intensity is reflected in the result. However, although the rate of increase in the Y direction is large, the absolute value itself is not large compared to the allowable value.

[0202] Let's examine the degree of damage shown in Tables 44 and 45. Calculations show that before reinforcement, the X-direction exceeds the standard value of 1.0, but after reinforcement, both the X and Y directions fall below the standard (damage is below the permissible value). Microtremor diagnosis shows that, except for the X-direction of Measurement 1 which is affected by eccentricity, the values ​​are below the standard. The Y-direction of the third floor in Measurement 2 is 1.16, which can be considered close to the standard value.

[0203] Based on the above, it can be said that if this building were to experience a major earthquake as assumed by current standards, there is a possibility that the vibrations in the X direction near the two directions may exceed the permissible limit, but the damage in other parts is likely to remain within the permissible limit. Although it cannot be determined by microtremor diagnosis, the collapse risk value I shown in Table 44 is considered to be the highest possible. f Since the reinforced section is below the standard value of 1.0, it is believed that the building will avoid collapse even if subjected to seismic motion significantly exceeding the current standard.

[0204] 3) Coefficient A representing the distribution of story shear force in the height direction i Table 27 shows the coefficient A representing the distribution of story shear force in the height direction. i Expected value of (A imk The values ​​before and after reinforcement are obtained using Equation 9, and the absolute acceleration energy transfer coefficient a (see Table 4) obtained by microtremor observation and the mass m of each layer of the structure are used. jThe values ​​calculated from the above are shown in comparison to the values ​​obtained from the current standard calculation formula (Equation 10), and Table 29 shows the rate of change before and after reinforcement, as well as the ratio of calculated to measured values.

[0205] [Table 46]

[0206] [Table 47]

[0207] [Table 48]

[0208] Let's look at the measured values ​​before and after reinforcement. In Measurement 1, the change was only about 2% at most on each floor and in each direction. In Measurement 2, there was an increase of 10% to 20% on the 3rd floor, but the change on the 2nd floor was less than 5%. Looking at the ratio of calculation to measurement, on the 2nd floor, they were in almost agreement regardless of the measurement point or whether reinforcement was present. On the other hand, on the 3rd floor, before reinforcement, in both Measurement 1 and 2, the measurement was about 10% smaller than the calculation, and after reinforcement, in Measurement 2, the measurement and calculation matched, or the value was about 10% larger in the Y direction.

[0209] Looking at the absolute values ​​of each of the above figures, the measured values ​​and calculations are in almost perfect agreement. This indicates that the uniform seismic intensity distribution, which is considered to be the maximum response story shear force distribution for low-rise buildings under current standards, was measured using a microtremor measurement method for the coefficient representing the distribution of story shear force in the height direction. Furthermore, the change before and after reinforcement of the 3rd floor, compared with the calculations, suggests that the reinforcement work corrected the particularly high strength of the 3rd floor by cutting slits, bringing it closer to that of the 2nd floor and below.

[0210] For measurement 2, the 3rd floor Y direction is measured as A i (A imkThe fact that the value is considerably larger than calculated indicates that cutting the slit has resulted in a structure that increases the vibration in this part. This is the measured value of the intensity index shown in Table 21 (C T S D ) mik The decrease in (0.60 → 0.20), the normalized input energy W shown in Table 23 K0ik An increase (5.4 → 37.9), and the damage level I shown in Table 25. d0ik This is reflected in the increase (0.80 → 1.16). However, because the columns were wrapped with the SRF method after the slits were cut, the collapse risk is below 1.0 on each floor in the same table. Furthermore, microtremor observations in the same table confirm that the degree of damage around measurement 2 is also below the standard value (1.0) on each floor. Also, around measurement 1, the Y direction is below 1.0. Regarding the fact that some damage in the X direction of measurement 1 is predicted, seismic coating was applied to one wall using the SRF method. It is effective to absorb vibrational energy by doing so. The reinforcement this time was carried out for the purpose of preventing collapse, and from the standpoint of damage control, we would like to implement the above measures in future construction work.

[0211] 4) Average acceleration, average velocity transmission coefficient B aik B vik From the microtremor observation results, the average acceleration and average velocity transfer coefficient were calculated using equations 13 and 14, and the values ​​before and after reinforcement are compared and shown in Tables 30 and 31. These represent the spatial average acceleration, or velocity, of the part supported by the i-th floor of the structure, and the ratio of this to the acceleration, or velocity, of the reference point. Therefore, the value for the first floor represents the average response ratio of the entire structure. Also, A i The average acceleration energy transfer coefficient B aik These are values ​​where the values ​​of each floor are normalized by the values ​​of the first floor (see formula 17).

[0212] [Table 30]

[0213] [Table 31]

[0214] This building is located on Type 2 ground, and the natural period of the ground is T c =0.6 sec, building height h=14.3m, of which the height of the steel frame portion is 2.95m, the ratio of the height h[m] of the steel frame floors (excluding the basement) to λ=0.206, therefore, according to the current standard formula (see formula 12), the building's natural period is calculated as T=h(0.02+0.01λ)=0.32 sec. Therefore, T <T c Therefore, the vibration characteristic coefficient R t The calculation yields 1.0, and it is concluded that the acceleration response magnification is 2.5 to 3.0, which is the standard value at the time the current standards were established.

[0215] Based on the above, let's look at the measured response magnification, which is the first-order value. Both acceleration and velocity are almost the same value. In Measurement 1, it was 2.5 to 4.0 before reinforcement and 2.0 to 3.7 after reinforcement. In Measurement 2, it was 2.0 to 2.4 before reinforcement and 1.6 to 2.2 after reinforcement. The absolute values ​​are roughly equal to the assumed range of 2.5 to 3.0 in the current standards. This demonstrates the validity of the microtremor diagnostic method.

[0216] Next, let's look at the rate of change before and after reinforcement. As shown in Table 31, regarding the acceleration response magnification of the parts supported by each floor, only the Y direction of measurement 2 after reinforcement increased slightly (7%), while at the other measurement points, it decreased to about 70% to 90% in all directions. Furthermore, regarding the velocity response magnification, it increased slightly in the Y direction of measurement 2, but decreased in all other directions. These values ​​quantitatively represent that the structural system has changed to be less susceptible to earthquake effects due to the reinforcement work. These values ​​are used in the calculation of the degree of damage, and the above characteristics are reflected in each index value described in the previous section.

[0217] 5) Micro-vibration characteristics Table 32 shows the RMS of microtremor acceleration before and after reinforcement, as well as the energy transfer coefficient and its rate of change before and after reinforcement. Table 52 shows the central period and bandwidth index of microtremor acceleration before and after reinforcement. Tables 34 to 37 show the characteristics regarding microkinetic velocity and displacement. Microkinetic acceleration was measured using an accelerometer, and velocity and displacement were obtained by integrating this data using the linear acceleration method after applying 10 Hz high-cut and 0.2 Hz low-cut filters. In each table, "floor" refers to the floor surface of that floor.

[0218] [Table 32]

[0219] [Table 33]

[0220] [Table 34]

[0221] [Table 35]

[0222] [Table 36]

[0223] [Table 37]

[0224] The energy transfer coefficient is the ratio of the RMS of the reference point defined in paragraph "0067" of this specification to the RMS of each floor, that is, the vibration amplification factor, and is the basis for calculating each of the diagnostic indicators shown in the preceding sections.

[0225] The central period is given by Equation 1, and the bandwidth index is calculated using the method described in paragraph "0156" of this specification. The central period is the expected value of the zero-crossing period for a steady-state Gaussian process, and the bandwidth index is 1.0 for a sine wave and 0 for white noise. The larger the bandwidth, the closer it approaches zero. Looking at the changes before and after reinforcement, the acceleration is approximately the same or slightly larger before and after. As for velocity, the central period is slightly larger at measurement 1 and slightly smaller at measurement 2. The bandwidth index is increasing at both observation points, meaning the bandwidth has narrowed. Looking at the micro-displacement, the central period clearly decreases and the bandwidth increases after reinforcement. This indicates that the vibration approached a sine wave due to reinforcement, and the rigidity of the structural system improved.

[0226] Tables 38 to 40 show the central period measurements for microkinetic acceleration, velocity, and displacement, as well as the current standard for primary fixed period. The calculated values ​​for periodic vibrations are shown for comparison. Structures subjected to microtremors or seismic motion undergo irregular vibrations, so the central periods of displacement, velocity, and acceleration increase with bandwidth (see paragraph "0156" in this specification). In this example, the central periods of acceleration, velocity, and displacement are found around the value of the primary natural period calculated using the current standard formula. Furthermore, since approximately the same central period values ​​are obtained for acceleration, velocity, and displacement at each point, each floor, and each direction, it can be considered that the entire building is vibrating in its own unique mode.

[0227] [Table 38]

[0228] [Table 39]

[0229] [Table 40] [Examples]

[0230] 1) Target facilities and measurement methods The measurement target is an 11-story reinforced concrete (SRC) apartment building completed in 1994 (two spans in the X direction, one span in the Y direction, with a piloti-style parking area on the first floor (see Figure 24)). However, there are stairwells etc. in the X direction. From the end of August to September 2017, two independent columns on the first floor (A2, A3) were reinforced using the SRF method (see lines 1 to 3 of paragraph "0194" in this specification). Floors 2 to 11 are residential units, and the two sides from floors 2 to 10 are seismic walls. The measurements were taken using two vertical arrays with instruments placed near columns B2 and B3 on each floor, and three-point planar observations with three instruments each placed near B1, A2 (see Figure 25), and B3 on the first floor and rooftop. Before reinforcement, measurements were taken on August 25, 2017, with four instruments, and after reinforcement, measurements were taken on December 19, 2017, with twelve instruments. Note that access to the second floor was not possible near B2. Figure 26, a first-floor plan view, shows the locations of the reinforced columns and the instrument placement.

[0231] 2) Measurement results Figure 27 shows the horizontal trajectories of the micro-displacement of the reinforced B3 vertical array, divided into three 2-minute sections based on 6-minute measurements for each floor. It can be seen that the displacement is amplified from the first floor upwards, and that each point is moving in a nearly circular motion.

[0232] Table 41 shows the energy transfer coefficient (ratio of micro-motion displacement RMS between the first floor and the floor above) and the rate of change before and after reinforcement for the B2 vertical array and the rooftop surface, and Table 42 shows the same for the B3 vertical array. In Table 41, the column labeled "surface" represents the energy transfer coefficient related to rotation around the coordinate axes of the rooftop surface. After reinforcement, the coefficient around the X axis decreases to about 1 / 10 and around the Y axis to about 1 / 30. The columns below RF in Tables 41 and 42 show the energy transfer coefficient for translational motion and the ratio before and after reinforcement, but for B2 and B3 In both cases, the decrease is more significant on the upper floors. This indicates that the vibration modes have been stabilized by using the SRF method, which involves wrapping around two independent columns (A2 and A3) in the piloti area of ​​the first floor, especially column A2 which is exposed through the lower floor wall.

[0233] Furthermore, Figure 27 shows the motion of the rooftop surface before reinforcement, and Figure 28 shows the motion after reinforcement. These motions were obtained by inputting displacement data (XYZ 3 components) from microtremometers installed at three locations on the rooftop surface into the structural analysis result visualization software AVS, and visualizing (animating) the data at a single moment. The animation shows that before reinforcement, the rooftop surface vibrates significantly up, down, left, and right, but after reinforcement, it vibrates in a circular motion within a roughly horizontal plane. This clearly demonstrates that the energy transfer coefficients around the X and Y axes, which are labeled as surfaces in Table 1.3.9.1, have decreased to 11% and 3%, respectively, before and after reinforcement.

[0234] [Table 41]

[0235] [Table 42]

[0236] Tables 43 and 44 show the measured values ​​of the story shear force distribution coefficient (Ai) and the central period of micro-motion displacement (Tc) after reinforcement, as well as the calculated value of the primary natural period (T) based on seismic standards (as described in paragraphs "0038" to "0058" of this specification). The measured value of A1 is in close agreement up to around the 5th floor, but is clearly smaller than the calculated value on the upper floors, indicating less amplification of seismic motion, i.e., it is a vibration mode unique to piloti structures. The central period varies slightly between the lower floors and the rooftop, but on the upper floors, both B2 and B3 are almost constant and close to the calculated value.

[0237] [Table 43]

[0238] [Table 44]

[0239] Table 45 shows the story shear force coefficient of the first story when the horizontal load-bearing capacity is reached near B3 (C ui1km) is the measured value (Equation 27). For floors 2 to 10, the Y direction is compared to the X direction. The high values ​​reflect that the partition walls between the 2nd to 10th floors are seismic walls in two different configurations. Also, the values ​​are lower on the 4th and 5th floors compared to the other floors. It is said that the building was hit by heavy rain while concrete pouring was underway on the 4th and 5th floors, causing the work to be interrupted, and the workers to withdraw and resume work about a week later. It is thought that this heavy rain and the interruption degraded the quality of the concrete, leading to a decrease in its horizontal load-bearing capacity (strength).

[0240] [Table 45]

[0241] Tables 46 and 47 show the contents described in paragraphs "0119" to "0172" of this specification, and the velocity-converted values ​​(V) of the expected hysteretic absorption energy derived therefrom. mik ) and degree of damage (I dik This shows the input ground motion. The properties of the input ground motion are assumed to be the current seismic standards, with a strong motion duration s0 = 7 sec and a maximum velocity V max =0.8m / sect, maximum acceleration V max = 4.0 m / sec 2 Furthermore, considering that it is a building conforming to the new seismic standards, the ductility index F is set for each floor and direction. uik =3.0 is used. Regarding the limit of repetitions, N is used considering that the columns on the second floor and above are made of steel-reinforced concrete. ik Assuming = 15, the first floor was determined from an experiment that confirmed the effect of reinforcement by the SRF method. ik I set it to =45.

[0242] Tables 46 and 47 show the input ground motion as representative values ​​of recent seismic conditions, with strong motion duration s0 = sec and maximum velocity V. max =1.2m / sec, maximum acceleration A max = 10 m / sec 2 (See Table 19). The toughness index and limit cycle count were as described above.

[0243] Table 46 shows the calculation results for hysteretic absorption energy, which indicates that for the seismic motion assumed by the current standards, almost no energy is absorbed in the Y direction (it does not reach the yield displacement). Regarding the X-direction, the results indicate that yielding occurred on the 4th, 5th, and top floors, where concrete construction defects are suspected. Furthermore, for the seismic motions representative of recent seismic environments shown in Table 48, the results indicate that significant absorbed energy was generated except for the intermediate floors in the Y-direction near B3.

[0244] Tables 47 and 49 show the degree of damage, indicating whether the energy absorbed by each floor falls within the damage limit. For the seismic motion assumed by the current standards, the results show that both the X and Y directions near B2 and B3 are below the limit value (1.0). In this sense, it can be said that the building conforms to the current standards (new seismic standards). However, the 4th and 5th floors and the top floor, where concrete construction defects are suspected, are close to the limit. On the other hand, for the seismic motion representative of recent seismic environments shown in Table 49, the Y direction near B3 is within the limit except for the 4th and 5th floors, but significant damage occurs in the X direction. This building has a piloti structure, and Table 48 calculates that a large amount of hysteretic spherical energy is generated on the 1st floor. Nevertheless, the 1st floor and the 2nd floor directly above it, where the columns were reinforced with the SRF method, remained almost within the limit value. For other floors as well, the results suggest that measures such as the reinforcement method should be considered to reduce damage.

[0245] Although the above example uses hypothetical values, the limit cycle count and toughness index of each member can be determined by observing the load-displacement history and degree of damage obtained from repeated loading experiments on similar members. Furthermore, the maximum acceleration, velocity, displacement, and duration of strong ground motion can be determined by comprehensively analyzing the results of ground motion observations.

[0246] [Table 46]

[0247] [Table 47]

[0248] [Table 48]

[0249] [Table 49]

[0250] As described above, the damage level of the present invention can quantitatively indicate the degree of structural damage according to the level of seismic motion and the effectiveness of countermeasures against it, using various transmission rates measured by micro-motion observation of the structure, along with the limit cycle count and ductility index. This contributes to the rationalization of seismic design.

[0251] The following describes an example of applying the method of the present invention to a concrete block wall.

[0252] 1. Installation Figure 29 is a schematic diagram showing the arrangement of the block wall, foundation, ground, and microtremor meter. The microtremor meter 1 is installed horizontally on the top 17 of the block wall 16, the foundation 18, or the ground surface 20 near the foundation 18. When installing the microtremor meter 1 on the top 17 of the block wall 16, the feet 1a of the microtremor meter 1 should be on the center line of the top 17 of the block wall 16. When installing on the top 17 and the surrounding ground 21, and when there is significant flicker on the foundation 18, a steel plate is used.

[0253] 2. Measurement Simultaneous measurements will be taken for approximately 6 minutes on the top 17 and the foundation 18. The data will be analyzed using free kick and microtremor diagnostic Excel, similar to the building diagnosis. At this time, the floor height will be the height of the block wall 16 (the difference in the z coordinates of the microtremor meter 1 on the top 17 and the microtremor meter 1 on the foundation 18 or surrounding ground 21) H, and the weight supported by the floor will be assumed to be zero. The calculations involve calculating the velocity, displacement, RMS, central period, and transmission coefficient for each time history. The interstory displacement or the absolute displacement at the top is taken as the time history d(t), and the measurement point of the foundation 17 or the surrounding ground 21 (see No. 1 in Figure 29) is used as the reference point, with the transmission coefficient (h) relative to it. dk ) calculate.

[0254] 3. Diagnosis Reference point displacement x for a major earthquake assumed by the diagnostic criteria Gkmax The relative or absolute displacement of the top 23, assuming a value of 2.5 cm, is predicted using the following formula (yellow book, formula 1.4.8).

[0255]

number

[0256] However, in the above equation, d(t) = y2(t) - y1(t), h dk The relative displacement can be predicted by using =RMS[d(t)] / RMS[y1(t)].

[0257] Also, d(t)=y2(t), h dk The absolute displacement can be predicted by using =RMS[d(t)] / RMS[y1(t)].

[0258] Here, d(t), y2(t), and y1(t) are the relative displacement between the top 23 and the reference point, the absolute displacement of the top 23, and the y-direction (orthogonal to the block wall 22) component of the absolute displacement of the reference point, respectively.

[0259] The relative displacement between the top 16 and the foundation 17 during an earthquake, calculated using formula 50, or the expected value of the absolute displacement of the top 16, determines the risk of the block wall 15 toppling over (I tbw ) calculate.

[0260] If D / H is the average value of the tipping limit slope, then the following equation holds.

[0261]

number

[0262] However, D[cm] is the width of the block wall 15 (see Figure 29), E[d Gkmax ] is the expected value of the absolute or relative displacement of the top 16 of the block wall 15 in the event of a major earthquake as assumed by the seismic diagnosis standards, and a (see Table 50) is the top displacement at the overturning limit when the overturning limit tilt is D / H.

[0263] [Table 50] [Examples]

[0264] Next, a specific example of microtremor measurement using the method of the present invention applied to a concrete block wall will be described below.

[0265] The specifications are as follows: Location: Block wall of a certain apartment building in Hirakata City, Osaka Prefecture Structure: CB construction Thickness: 150 [mm] Extension: ~15000[mm] Height: 1870 [mm] (The height from the reference measuring device to the top is 1790 [ mm] Block size: (thickness x length x height) 150 [mm] x 390 [mm] x 200 [mm] Retaining wall: None Four micro-motion measuring devices were used.

[0266] Figures 30(a) to (c) show the actual measurement conditions at each measurement point, with (a) showing the conditions at measurement point 1, (b) showing the conditions at measurement point 2, and (c) showing the conditions at measurement point 3. Figure 31 is a schematic explanatory diagram showing the arrangement of the measurement devices (microtremometers) when viewed from above on the block wall, corresponding to Figure 30.

[0267] The risk of the concrete block wall collapsing was calculated using formula 51. The results are shown in Table 51.

[0268] [Table 51]

[0269] According to Table 51, the risk of overturning was below 1.0 in all cases, and it was determined that the risk of overturning was not significant under the seismic motion assumed by the seismic diagnosis standards (maximum displacement of 2.5 cm). However, there is a risk of overturning under seismic motion exceeding this (for example, recent seismic motion).

[0270] About the role of microtremor diagnosis The method of assuming that the effects of earthquakes are inertial forces proportional to ground acceleration (inertial force approximation) has become the fundamental principle of current seismic design, regardless of whether it is an old or new seismic design standard, or whether it is a dynamic or static calculation. This, coupled with numerical calculation methods such as the finite element method and the development of digital computers, has been the driving force behind the construction of structures of unprecedented scale, shape, and material in earthquake-prone regions around the world, including Japan, from the late 1960s to the present day. The new seismic standards, which mandate the numerical tracking of structural collapse processes, have made seismic calculations so complex that structural design is impossible without specialized software. Even experts cannot physically grasp the details of structural seismic indices, ultimate horizontal load-bearing capacity, or the calculation process of dynamic analysis. Currently, we have no choice but to trust the numbers produced by computers. On the other hand, seismic activity has increased from the end of the 20th century to the present century, and both the magnitude and duration of observed seismic motion are several times to an order of magnitude higher than the assumptions of the current standards, which were established based on seismic observations up to the 1970s.

[0271] At recent seismic levels where ground acceleration exceeds 1G, the inertial force approximation is no longer valid. The irrationality of designing structures and ground systems that attempt to move in three dimensions by separating them into x and y directions becomes apparent. Fundamentally, the spatiotemporal scale of a major earthquake is incomparable to the scale of individual structures. If one tries to capture the seismic motion of a major earthquake at the scale of a structure, it becomes extremely random. The phenomena caused by major earthquakes change drastically and discontinuously with even slight changes in conditions. This is what is called a statistical phenomenon. Constructing structures of unprecedented scales and forms based on calculations using current standards is not rational, both in terms of input seismic motion and in terms of calculation assumptions and models.

[0272] The research into modern earthquake-resistant structures, which began in Japan following the 1891 Nobi Earthquake, combined with the development and improvement of reinforced concrete material design and construction techniques, allowed these structures to withstand the 1923 Great Kanto Earthquake and, by the 1960s, created a stately landscape in major cities such as Tokyo, characterized by low- and medium-rise reinforced concrete buildings. However, with the removal of height restrictions in 1963, the 1964 Tokyo Olympics, high economic growth policies, and the rapid spread of concrete pump construction methods, older buildings are being demolished, leading to rapid overcrowding and the construction of high-rise buildings.

[0273] In the area affected by the magnitude 7 earthquake of the 1995 Great Hanshin-Awaji Earthquake, even with seismic motion more than three times greater than the current standards, approximately half of the low- and mid-rise reinforced concrete (RC) buildings remained undamaged, excluding pilotis, even under the old standards, and only a few percent collapsed. Civil engineering structures such as Shinkansen elevated bridges and expressways While roads and other structures collapsed, it is said that the earthquake motion was several times stronger than anticipated in the design, and the damage was concentrated in areas heavily influenced by the ground, such as former riverbeds, making the collapse inevitable. The same was true in the 2011 Great East Japan Earthquake. Even under the old standards, only a few buildings collapsed due to earthquake motion. Of the 98 low- and medium-rise reinforced concrete public buildings with an Is value of 0.3 or less that experienced earthquakes of magnitude 5 or higher, none collapsed, and 97 buildings continued to be used with almost no damage. On the other hand, school buildings and condominiums that had undergone seismic reinforcement became unusable and had to be demolished or undergo large-scale repairs. In addition, although the Tohoku Shinkansen had already undergone seismic reinforcement using steel plates on its bridge piers, after the earthquake, the destruction of beams and damage to the superstructure such as overhead lines caused it to become inoperable, and it took more than 50 days to restore service.

[0274] The need for a fundamental revision of the current seismic standards is stated in the aforementioned diagnostic criteria. Here, we will describe the characteristics of microtremor diagnosis and the role it plays in rational seismic design, supervision, and reinforcement work.

[0275] (1) Response calculation The most important performance requirements for structures during an earthquake are minimal damage and the ability to continue using them. In recent earthquakes with ground acceleration exceeding 1G, tracking the nonlinear changes in structures using indicators such as horizontal load-bearing capacity is not only physically difficult, but from the perspective of ensuring continued use, structures that do not undergo nonlinear changes in the first place are desirable. That is, buildings with high strength (high hurdles to nonlinear changes), as stated in the diagnostic criteria. Response calculations reveal the vibration modes, maximum acceleration, velocity, displacement, and hysteretic absorbed energy when the structural ground system responds linearly to a specific or general seismic motion. Microtremor diagnosis allows for direct acquisition of information necessary for calculations within the elastic range. Furthermore, comparison between calculations and actual measurements is easily performed.

[0276] (2) Earthquake motion assumptions The action of an earthquake is a proximity action. It is rational to determine the assumed seismic motion (the seismic motion used in calculations) in accordance with the actual phenomenon of propagation from the epicenter to the surrounding ground, from the surrounding ground to the foundation, and from the base to the columns on the first floor, from bottom to top. The current building code method of predetermining the response acceleration or response spectrum of a structure is not only rational, but also risks generating excessive seismic force on the structure, causing it to collapse or suffer significant damage. Moreover, numerically synthesizing seismic motion to match the response spectrum and performing time history response analysis is putting the cart before the horse.

[0277] One method for defining assumed seismic motion is to use the engineering bedrock surface, which is used in limit state design calculations, etc. However, the seismic motion actually experienced by a structure is influenced not only by the seismic motion of the engineering bedrock directly below, but also by the bedrock surface extending in three dimensions over a wide area. Calculations that reflect actual phenomena, i.e., three-dimensional ground vibration analysis calculations, are almost impossible. If one-dimensional superimposed reflections are calculated instead, the difference between the seismic motion actually input to the structure and the calculated seismic motion will inevitably be extremely large.

[0278] Microtremor diagnosis involves applying input vibrations to the foundation of the structure. Furthermore, the properties of the assumed earthquake motion are based on maximum acceleration, maximum velocity, maximum displacement, and duration of strong motion. However, even if specific numerical values ​​are determined for the magnitude of the assumed earthquake motion, these are merely expected values ​​(average values). Actual earthquake motion will be a large variation of these values.

[0279] (3) Performance evaluation In recent earthquakes where ground acceleration exceeds 1G and lasts for several minutes or more, visible displacement is unavoidable in all structures, from wooden buildings to skyscrapers, and an evaluation index that clearly incorporates the occurrence of numerous repeated displacements is necessary. Furthermore, an index should be applied to each floor of the structure. Rather than simply aggregating data, performance evaluation should be conducted using a collection of indicators related to individual components and parts. In microtremor diagnosis, a definition of damage level is used as an indicator to directly evaluate the continued usability of a structure. This is called the seismic damping performance index.

[0280] (4) Rational earthquake-resistant structure Given the recent seismic intensity levels, structures that exhibit the overall collapse pattern assumed by current standards are, by calculation, inevitably destined to collapse, making continued use impossible. A rational design would involve pre-planning sections that allow for significant deformation and vibration to absorb seismic energy, as well as sections that keep deformation within damage limits. In a regular-shaped reinforced concrete (RC) structure, the top and base of each column act as bending hinges, resulting in overall deformation and movement. In eccentric structures, such as pilotis, the tops and bases of the columns in areas with fewer walls move, and the pilotis floor and the eccentrically swayed parts vibrate significantly, absorbing energy, thereby keeping the deformation of other floors and sections to a minimum. In reinforced concrete (RC) structures, unless the site is on bedrock, the rigidity of the structural frame is sufficiently greater than that of the surrounding ground. Therefore, in addition to the vibration of the frame as described above, it is desirable to plan for energy absorption at the boundary between the surrounding ground and the frame (foundation). Incorporating the relative motion between the foundation and the surrounding ground into the design is effective. In wooden structures, the deformation and energy absorption capacity of individual joints and nailing points is large, so joints and nailing points should be designed to have three-dimensional mobility and resilience. Furthermore, it is desirable to specifically reflect in the design the reduction of seismic effects by lifting the base from the foundation. By performing microtremor diagnosis to calculate the cumulative strength index and degree of damage of each part of the structure against the assumed seismic motion of current standards, and by visualizing the natural vibration modes, the antinodes and nodes of the vibration can be extracted, and by reinforcing key members and joints to provide energy absorption capacity, it is possible to create a structure with the motion capacity and energy absorption capacity to withstand a major earthquake. The SRF method is effective for the above reinforcement.

[0281] (5) Inspection of new construction and inspection of structural renovation work After the structure is completed or after renovation work is finished, a microtremor diagnosis is performed to determine the vibration mode and vibration period (T m ), story shear force distribution coefficient (A im ), response magnification (R amk, R vmk ), cumulative strength index (C T S D ) m , damage degree (I dm ) is measured and compared with the design calculations, This allows us to verify the validity of the calculations and construction work, and to use this information to decide whether to add countermeasures as needed. Furthermore, each of the above indicators is calculated for the entire structure, and the vibration characteristics of each section are also determined by vertical array measurements installed in that section. Currently, intermediate and final inspections of new constructions are limited to visual checks by inspectors to verify consistency with the drawings. The same applies to seismic retrofitting. Microtremor diagnosis can add objective numerical data to the inspectors' decision-making criteria.

[0282] (6) Regular health checkups Regular microtremor assessments will be conducted, and the indicators mentioned in the previous section will be measured. If deterioration of the structure is found, this information will be used to determine whether repairs should be carried out. Furthermore, after repairs, microtremor assessments can be conducted again to confirm the effectiveness of the repairs.

[0283] (7) Seismic diagnosis and seismic retrofitting design of existing structures This method involves conducting microtremor diagnoses on existing structures built under current or old seismic standards to evaluate their seismic performance and, if necessary, to provide data for designing and constructing countermeasures. It can also be used to quantitatively confirm the effectiveness of reinforcement by conducting measurements and diagnoses before and after reinforcement. Currently, seismic assessments are conducted over a period of several months and cost several million or even more than ten million yen. This is because the calculations are complex and require a high level of expertise. By simplifying the diagnostic calculations and integrating them with indicators obtained from microtremor assessments, the cost and time involved can be significantly reduced.

[0284] (8) Analysis of cases with and without damage In the future, as a large number of actual measurement examples are accumulated and correlation analyses are conducted between actual damage and no damage during actual earthquakes, it is expected that the ratio of calculations to the judgment of the diagnostician will be minimized, making it possible to perform seismic diagnosis and renovation design, such as identifying areas for repair, primarily based on microtremor diagnosis results. Furthermore, it will be possible to increase the role of microtremor diagnosis during new construction, after renovation, and during periodic inspections, and to narrow down calculations and judgments to the necessary scope.

[0285] Regarding the challenges of seismic standards and solutions using the SRF method (bandage reinforcement), a paper titled "Revolution in Seismic Design" was published in April 2017. Along with microtremor diagnosis, we hope this will help streamline seismic design and reduce the economic burden and risks associated with earthquakes.

[0286] As is clear from the detailed explanation above, according to the present invention, by defining the expected values ​​of the cumulative strength index and structural seismic index used in the diagnosis and seismic retrofitting design of existing structures, the expected value of the distribution coefficient of story shear force in the height direction used in the design of new construction, and the degree of damage for directly evaluating the continued usability of a structure, and directly obtaining these expected values ​​from micro-tremor measurements, it becomes possible to measure the vibration characteristics, strength, degree of damage, etc. of each floor zone by observing with vertical arrays set up in each part of the structure. As a result, it has become possible to directly, inexpensively, and quickly evaluate not only the soundness and safety of a structure in much more detail than conventional methods that directly apply external forces to the object, but also seismic performance evaluation, seismic design, and the continued usability of the structure (which is the most important target performance for implementing seismic reinforcement work), according to the individual vibration characteristics.

[0287] In other words, according to the present invention, by using the above indicators, seismic diagnoses can be performed much more cheaply and quickly than current seismic diagnoses after new construction, after renovation work, and during periodic inspections, thus enabling rational seismic reinforcement design and seismic design of new structures. [Explanation of Symbols]

[0288] 1 Microtremometer 1a Foot 2 Analyzer 10 Structures 10a,10b,10c layer boundary surface 11. Reinforced concrete hospital building 12 1st floor 13 2nd floor 14 3rd floor 15 4th floor 16 Block wall 17 Top 18 Basics 20 Ground surface 21. Surrounding ground

Claims

1. In a method for evaluating the performance of a structure through continuous microtremor observation, The seismic performance of the structure is evaluated based on the observations, using the root mean square (RMS) of these time histories to calculate an estimated value A of an index used in the seismic design of the structure, and using the ratio of this value A to the value B of the index used at the design stage, The aforementioned index is the product of the cumulative strength index and the shape index as defined in the current standards. The quantity obtained by multiplying the ultimate cumulative intensity index in the k-direction of the i-th layer by the shape index ((C ＴＵ S Ｄ ) ｉｋ ) The expected value is [Number 32] It is represented as, (Here, h ｅｇｉｋ is the correlation displacement energy transfer rate obtained by the micro-vibration diagnosis, the reference point displacement x Ｇ０ [1978] is the reference point displacement corresponding to the reference ground motion (G0), e Ｇ０ｉｋ is the correlation displacement, e Ｙｉｋ is the yield displacement. Also, C ＴＵ is the final cumulative strength index, S Ｄ is the shape index, (C ＴＵ S Ｄ )mik is the expected value of the product of the final cumulative strength index and the shape index.) The estimated value A of the index is the amount obtained by multiplying the ultimate cumulative intensity index in the k direction of the i-th layer by the shape index ((C ＴＵ S Ｄ ) ｉｋ The expected value of ) A diagnostic and evaluation method for structures based on their constant micro-vibrations.

2. In a method for evaluating the performance of a structure through continuous microtremor observation, The seismic performance of the structure is evaluated based on the observations, using the root mean square (RMS) of these time histories to calculate an estimated value A of an index used in the seismic design of the structure, and using the ratio of this value A to the value B of the index used at the design stage, The aforementioned indicator is the degree of damage, The degree of damage is [Number 49] (Here, I ｄｉｋ This is the degree of damage, B ａｉｋ This is the average acceleration transmission coefficient of the portion that supports the vibration characteristics obtained from microtremor observations of the ground system surrounding the structure, with respect to the k direction of the i-th layer, and B ｖｉｋ This is the average velocity energy transfer coefficient, and T ｖｉｋ This is the average velocity transmission coefficient of the part that supports the vibration characteristics obtained from microtremor observations of the ground system surrounding the structure, and in Table 18, a is the interstory displacement energy transmission coefficient in the k direction of the i-th layer with respect to the acceleration at the reference point, and T ｖｉｋ However, this is the central period of the velocity time history, and α ｖｉｋ However, it is a bandwidth index, and s ０ This is the duration of the strong earthquake, and V ｍａｘｋ This is the maximum speed, A ｍａｘｋ γ is the maximum acceleration, ｖ γ is the peak factor of the maximum velocity. ａ This is the peak factor of the maximum acceleration. Also, R Ｙｉｋ This is the yield deformation angle in the k direction of the i-th layer, and H ０ｉｋ This is the standard floor height, F ｕｉｋ This is a toughness index, N ｉｋ This is the limit of the number of repetitions. [Table 18] ） It is represented as, The estimated value A of the indicator is the degree of damage represented by the above formula 49. A diagnostic and evaluation method for structures based on their constant micro-vibrations.

3. In a method for evaluating the performance of a structure through continuous microtremor observation, The seismic performance of the structure is evaluated based on the observations, using the root mean square (RMS) of these time histories to calculate an estimated value A of an index used in the seismic design of the structure, and using the ratio of this value A to the value B of the index used at the design stage, The aforementioned indicator is the risk of falling, The risk of falling is [Number 51] (Here, I ｔｂｗ is the risk of falling, D [cm] is the width of the block wall, and E [d Ｇｋｍａｘ ] represents the expected absolute or relative displacement of the top of the block wall in the event of a major earthquake as assumed by the seismic diagnosis standards, and a (see Table 50) is the top displacement at the overturning limit when the overturning limit tilt is D / H. [Table 50] Also, H is the height of the block wall, and h ｄｋ This is the transmission rate. ） It is represented as, The estimated value A of the indicator is the risk of falling, as expressed by the above formula 51. A diagnostic and evaluation method for structures based on their constant micro-vibrations.

4. A method for diagnosing and evaluating a structure based on the ambient microtremors of a structure, according to any one of claims 1 to 3, comprising dividing the continuously measured ambient microtremor time history, extracting a plurality of partial time histories, calculating the expected value of the index for each partial time history, and using the sample average thereof as the estimated value of the index.

5. The method for diagnosing and evaluating a structure based on ambient microtremors of the structure according to claim 4, wherein the duration of the partial time history is 1 to 2 minutes.

6. A method for diagnosing and evaluating a structure based on ambient microtremors, according to any one of claims 1 to 3, wherein the aforementioned observations are performed after the construction of a new structure, before and after renovation work, and during periodic inspections, and the estimated values ​​at each observation point are compared with each other to diagnose and evaluate at least one of the changes over time among the seismic performance of the structure, the risk of collapse during a major earthquake, the continuity of use, and the changes before and after renovation work.

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