Foundation vibration estimation system

Abstract

To estimate foundation vibration occurring when ground vibration is transmitted to a top face of a foundation, in a short time with high accuracy.SOLUTION: A foundation vibration estimation system for estimating foundation vibration occurring when ground vibration is transmitted to a top face of a foundation, comprises: a provisional vibration transmission coefficient estimation unit 2 that provisionally estimates a vibration transmission coefficient as a provisional vibration transmission coefficient by formulating, as a function of frequency, the vibration transmission coefficient that is a ratio of the foundation vibration to the ground vibration on the basis of input information including the shape of the foundation and characteristics of the ground; a vibration transmission coefficient calculation unit 3 that calculates vibration transmissivity when the ground vibration is transmitted to the top face of the foundation by using a wave impedance of each of the ground and the foundation, the wave impedance being a resistance physical quantity when a vibration wave propagates; a vibration transmissivity settlement unit 4 that compares the provisional vibration transmission coefficient with a value based on the vibration transmissivity for each frequency, and settles a larger value as the vibration transmissivity; and a foundation vibration estimation unit 5 that estimates and outputs the foundation vibration by multiplying an amplitude of the ground vibration to be estimated by the settled vibration transmissivity corresponding to the frequency of the ground vibration to be estimated.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a base vibration estimation system that estimates base vibration that occurs when ground vibration is transmitted to the upper surface of a foundation. [Background technology]

[0002] For example, in urban areas, the ground often vibrates due to traffic vibrations, etc. In buildings constructed on such ground, ground vibrations outside the building can cause vibrations inside the building. For this reason, for example, when constructing a new foundation using the spread foundation method, it is common to study in advance how ground vibrations will be transmitted to the foundation, and to design the foundation so that the foundation vibrations on the top surface of the foundation are below a target value.

[0003] For example, Patent Document 1 describes a method for predicting vertical vibration of a building that predicts a response value of vertical vibration on a floor of a building due to environmental vibration caused by external vibration. In this vertical vibration prediction method, the relationship between the vertical deflection of floor beams supporting a floor in a building having the same framework system as the planned building and the amplification of vertical vibration on the floor with respect to the environmental vibration is obtained in advance, the vertical deflection of the floor beams of the planned building is applied to the relationship to obtain the amplification of vertical vibration on the floor with respect to the environmental vibration, and the vertical environmental vibration measured on the foundation of the building or on the ground near the building is added to the amplification to predict the response value of vertical vibration on the floor. Furthermore, Patent Document 2 discloses a method for predicting vibration levels of a building, which is configured to calculate the natural frequency of a building, calculate the amplification amount of the input vibration level of the building from the relationship between the previously obtained natural frequency of the building and the amplification amount of the input vibration level of the building, measure the micro-vibration level of the ground due to traffic vibrations, etc., and add the micro-vibration level of the ground to the amplification amount of the input vibration level of the building, thereby predicting the vibration level of the building in accordance with the location conditions, thereby designing a building that ensures comfortable livability.

[0004] In Patent Document 1, the amplification amount of vertical vibration on the floor is calculated based on the relationship, determined in advance as described above, between the vertical deflection amount of the floor beams supporting the floor in a building having the same structural system as the planned building, and the amplification amount of vertical vibration on the floor relative to the amount of environmental vibration. Furthermore, in Patent Document 2, the amount of amplification of the input vibration level of the building is calculated from the relationship between the natural frequency of the building obtained in advance and the amount of amplification of the input vibration level of the building, as described above. Thus, Patent Documents 1 and 2 do not evaluate the vibration performance of a floor based on the size of a room in a building or the like. In response to this, Patent Document 3 describes a method for evaluating the vibration performance of a floor, which is characterized by evaluating the vibration performance of a building floor using a floor deflection coefficient obtained by multiplying the size of a room in a building by the deflection value of the floor structure of the room when a predetermined vertical load is applied to the floor structure.

[0005] When examining how ground vibration is transmitted to a foundation as described above, the specific performance of the foundation may be evaluated by calculating the vibration transmissibility as an index. Vibration transmissibility is the ratio of the foundation vibration generated when the ground vibration is transmitted to the top surface of the foundation to the ground vibration, and if the vibration transmissibility can be accurately evaluated, it is possible to estimate the foundation vibration based on the ground vibration. Vibration transmissibility is also called the input loss of the foundation from the viewpoint of expressing the degree to which the vibration is attenuated and lost by the foundation when the ground vibration is input to the foundation and output as the foundation vibration from the top surface of the foundation. When deriving such vibration transmissibility, two methods are mainly used: a method that estimates it using a simplified prediction formula for rigid foundations (hereinafter referred to as the method using the simplified formula), and a method that estimates it through detailed analysis (hereinafter referred to as the detailed analysis method).

[0006] The former method uses a simplified formula determined by the plan dimensions of the rigid foundation and the wavelength of the ground vibration. More specifically, when a rigid foundation is placed on homogeneous ground, L is the plan dimensions of the foundation and λ is the wavelength, and the vibration transmissibility η is expressed as follows using ξ (= L / λ) expressed by the plan dimensions L and the wavelength λ. η=|sin(πξ) / (πξ)| Figure 10 is a graph that expresses the above formula. In this graph, the vibration transmissibility is expressed in decibels (dB) as the magnitude based on the case where ground vibration is transmitted without attenuation (i.e., the value on the vertical axis in Figure 10 is 0). The above formula is a simple expression and is suitable for estimating vibration transmissibility. However, the above formula requires that the foundation be rigid, and if the foundation is a flat plate foundation such as a raft foundation, this condition of rigidity is not met. In this case, the vibration transmissibility may be greater than the value obtained from the above formula due to the foundation being subjected to bending effects, and vibration may not attenuate as expected. Therefore, if the foundation is designed based on the value obtained from the above formula, there is a possibility that ground vibrations may actually be transmitted to the inside of the building as greater vibrations than expected.

[0007] In the latter detailed analysis method, the transmission of ground vibration is calculated and analyzed using the finite element method and thin layer element method for each of the modeled foundation and ground. Therefore, the foundation vibration can be calculated with high accuracy. However, the larger the scale of the building, the larger the foundation model will be, and the longer the analysis time will be. It is desirable to estimate the base vibration that occurs when ground vibration is transmitted to the top surface of the foundation in a short time with high accuracy. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] JP 2009-42224 A [Patent Document 2] Japanese Patent Application Publication No. 11-140967 [Patent Document 3] JP 2014-218846 A Summary of the Invention [Problem to be solved by the invention]

[0009] The problem to be solved by the present invention is to provide a base vibration estimation system that can estimate base vibration generated when ground vibration is transmitted to the upper surface of the foundation in a short period of time and with high accuracy. [Means for solving the problem]

[0010] In order to solve the above problems, the present invention employs the following means. That is, the present invention provides a foundation vibration estimation system for estimating foundation vibration caused by ground vibration being transmitted to an upper surface of a foundation, comprising: a provisional vibration transmissibility estimating unit that provisionally estimates a vibration transmissibility, which is a ratio of the foundation vibration to the ground vibration, as a provisional vibration transmissibility by formulating the vibration transmissibility as a function of frequency based on input information including the shape of the foundation and characteristics of the ground, a vibration transmissibility calculating unit that calculates a vibration transmittance when the ground vibration is transmitted to the upper surface of the foundation by using a wave impedance, which is a resistance physical quantity when a vibration wave propagates, of each of the ground and the foundation, a vibration transmissibility determining unit that compares the provisional vibration transmissibility with a value based on the vibration transmissibility for each frequency and determines the larger value as the vibration transmissibility, and a foundation vibration estimation unit that estimates and outputs the foundation vibration by multiplying the amplitude of the ground vibration to be estimated by the determined vibration transmissibility corresponding to the frequency of the ground vibration to be estimated. According to the above configuration, the provisional vibration transmissibility estimating unit provisionally estimates the vibration transmissibility, which is the ratio of the foundation vibration caused by the ground vibration being transmitted to the top surface of the foundation to the ground vibration, as a function of frequency based on input information including the shape of the foundation and the characteristics of the ground. The vibration transmittance calculating unit calculates the vibration transmittance when the ground vibration is transmitted to the top surface of the foundation using the wave impedance, which is the resistance physical quantity when the vibration wave propagates, of each of the ground and the foundation. Then, the vibration transmissibility determining unit compares the provisional vibration transmissibility with a value based on the vibration transmittance for each frequency, and determines the larger value as the vibration transmissibility. That is, the vibration transmissibility estimated in the provisional vibration transmissibility estimating unit based on the shape of the foundation and the characteristics of the ground is treated as provisional, and the provisional vibration transmissibility is compared with a value based on a vibration transmittance calculated separately, and the larger value is used as the actual vibration transmissibility. In this way, even if the provisional vibration transmissibility is estimated as an excessively small value, if the value based on the vibration transmittance calculated separately is larger than the provisional vibration transmissibility, the provisional vibration transmissibility is not actually used as the vibration transmissibility, and the value based on the vibration transmittance is used instead as the vibration transmissibility. In this way, the value based on the vibration transmittance is used as the lower limit of the vibration transmissibility. Therefore, it is possible to prevent the vibration transmissibility from being underestimated and the foundation being designed and constructed based on this, which results in the ground vibration being transmitted to the inside of the building as a vibration larger than actually expected. In addition, the vibration transmittance when ground vibration is transmitted to the top surface of the foundation is calculated using wave impedance, which is the physical quantity of resistance when vibration waves propagate. Therefore, the value based on the vibration transmittance calculated as above, which is used as the lower limit, is an appropriate value to be used as the lower limit. Furthermore, the series of processes required to estimate the fundamental vibration as described above is basically simple and can be performed with a small amount of calculations, and the fundamental vibration can be calculated in a short time compared to when, for example, the finite element method or the thin layer element method is used. In this way, it is possible to provide a base vibration estimation system that can estimate base vibration caused when ground vibration is transmitted to the upper surface of the foundation in a short period of time with high accuracy.

[0011] In one aspect of the present invention, the vibration transmittance calculation unit calculates the wave impedance by multiplying the density of the constituent material of each of the ground and the foundation by the vibration propagation velocity, and calculates the wave impedance Z 1 and the wave impedance Z of the foundation 2 Using the above, the vibration transmittance calculation formula is given below.

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[0012] In another aspect of the present invention, the shape of the foundation includes the length of the foundation, and further includes a database in which a correspondence between the length of the foundation and a vibration damping constant is recorded, and the provisional vibration transmissibility estimation unit obtains the length of the foundation to be estimated from the input information, obtains the damping constant corresponding to the length of the foundation from the database, and estimates the provisional vibration transmissibility based on the damping constant. According to the above configuration, the damping constant corresponding to the length of the foundation included in the input information is obtained from a database in which the correspondence relationship between the length of the foundation and the damping constant of vibration is recorded, and the provisional vibration transmissibility is estimated based on the damping constant, so that the length of the foundation is reflected in the estimation of the provisional vibration transmissibility, thereby making it possible to further improve the estimation accuracy of the foundation vibration. Effect of the Invention

[0013] According to the present invention, it is possible to provide a base vibration estimation system that can estimate base vibration generated when ground vibration is transmitted to the upper surface of the foundation in a short period of time with high accuracy. [Brief description of the drawings]

[0014] [Figure 1] 1 is a block diagram of a fundamental vibration estimation system according to an embodiment of the present invention. [Diagram 2] 13 is a graph showing a variable Bz used in the above embodiment. [Diagram 3] 1 is a graph showing the relationship between the dimensions of a foundation and the damping constant. [Figure 4] FIG. 11 is an explanatory diagram of a foundation model used when examining a provisional vibration transmissibility in the above embodiment. [Diagram 5] FIG. 5 is a graph showing a calculation result of the vibration transmissibility by the method using a simplified formula in the case where the ground transmission velocity is set to 170 m / s in the model of FIG. 4. (a) is a graph showing a calculation result of the vibration transmissibility by the provisional vibration transmissibility in the above embodiment, (b) is a graph showing a calculation result of the vibration transmissibility by the detailed analysis method, and (c) is a graph showing a calculation result of the vibration transmissibility by the method using a simplified formula. [Figure 6] FIG. 5 is a graph showing a calculation result of the vibration transmissibility by the method using a simplified formula in the case where the ground transmission velocity is set to 260 m / s in the model of FIG. 4. (a) is a graph showing a calculation result of the vibration transmissibility by the provisional vibration transmissibility in the above embodiment, (b) is a graph showing a calculation result of the vibration transmissibility by the detailed analysis method, and (c) is a graph showing a calculation result of the vibration transmissibility by the method using a simplified formula. [Figure 7] FIG. 5 is a graph showing a calculation result of the vibration transmissibility by the method using a simplified formula in the case where the ground transmission velocity is set to 330 m / s in the model of FIG. 4. (a) is a graph showing a calculation result of the vibration transmissibility by the provisional vibration transmissibility in the above embodiment, (b) is a graph showing a calculation result of the vibration transmissibility by the detailed analysis method, and (c) is a graph showing a calculation result of the vibration transmissibility by the method using a simplified formula. [Figure 8] 5 is a graph showing vibration transmissibility determined in the above embodiment when the ground transmission speed in the model of FIG. 4 is set to 170 m / s, 260 m / s, and 330 m / s. [Figure 9] 4 is a flowchart of a fundamental vibration estimation method in the embodiment. [Figure 10]1 is a graph showing vibration transmissibility in a conventional method using a simplified formula. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] The present invention is a base vibration estimation system for estimating base vibration occurring on the top surface of a foundation, which compares, for each frequency, a provisional vibration transmissibility based on the foundation shape and ground characteristics with a value based on the vibration transmittance when ground vibration is transmitted to the top surface of the foundation using wave impedance, which is a physical quantity of resistance when vibration waves propagate, and determines the larger value as the vibration transmissibility, and estimates the base vibration by multiplying the vibration transmissibility by the amplitude of the ground vibration. In the present invention, the vibration transmissibility is defined as an index indicating the efficiency with which vibration of a specific frequency passes through a material or medium. On the other hand, the vibration transmittance using the wave impedance is defined as an index indicating how much energy is transmitted when a wave passes through a boundary surface, and base vibration is estimated. Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings. FIG. 1 is a block diagram of a fundamental vibration estimating system according to this embodiment. The base vibration estimation system 1 of this embodiment estimates base vibration that occurs when ground vibration outside a building is transmitted to the top surface of the foundation. The base vibration estimation system 1 can be used when a new building is constructed, to study in advance how ground vibration is transmitted to the foundation, and to design the foundation so that the base vibration on the top surface of the foundation is equal to or less than a target value. The fundamental vibration estimation system 1 includes a provisional vibration transmissibility estimating section 2 , a vibration transmittance calculating section 3 , a vibration transmissibility determining section 4 , a fundamental vibration estimating section 5 , and a database 6 .

[0016] First, input information including the shape of the foundation and the characteristics of the ground is input to the foundation vibration estimation system 1. The input information regarding the shape of the foundation includes the dimensions (length) of the foundation, 2b×2c×d. That is, the shape of the foundation includes the length of the long side of the foundation when viewed in a plane, the length of the short side, and the thickness (depth). In the following description, either b or c may be the length of the long side. The input information on the properties of the soil includes various constants of the surface soil, which is the supporting soil for the direct soil. The constants include the propagation velocity V, density ρ, and Poisson's ratio ν of the soil. These pieces of input information may be input directly to the foundation vibration estimation system 1 when estimating foundation vibration using the foundation vibration estimation system 1, or may be input in advance to the database 6, and the database 6 may be referenced when using the foundation vibration estimation system 1.

[0017] The provisional vibration transmissibility estimating unit 2 formulates the vibration transmissibility as a function of frequency based on the above input information. Vibration transmissibility is the ratio of the base vibration caused by the transmission of ground vibration to the top surface of the foundation to the ground vibration. If the vibration transmissibility can be accurately evaluated, it is possible to estimate the base vibration based on the ground vibration. Vibration transmissibility is also called the input loss of the foundation from the viewpoint of expressing the degree to which the vibration is attenuated and lost by the foundation when the ground vibration is input to the foundation and output as base vibration from the top surface of the foundation. In other words, vibration transmissibility and input loss are the same thing, and in the following explanation, the term vibration transmissibility is basically used, but even when the term input loss is used, it means vibration transmissibility. The provisional vibration transmissibility estimation unit 2 formulates and estimates the vibration transmissibility as described above, using a method for predicting vibration when the mass part of a spring-mass-damping model of a one-mass system is excited, which is conceptually a method for predicting the foundation response when a foundation supported by a spring in the ground is excited.

[0018] First, the provisional vibration transmissibility estimation unit 2 calculates the spring constant K of the ground spring based on the planar dimensions (length) b and c of the foundation, the propagation velocity V of the ground, density ρ, and Poisson's ratio ν, using the following equation (1).

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[0019] Next, the provisional vibration transmissibility estimating unit 2 calculates the mass of the foundation based on the thickness d of the foundation, and further calculates the mass of the entire building including the foundation as mass m. The provisional vibration transmissibility estimation unit 2 calculates the natural frequency f of the foundation based on the spring constant K of the ground spring and the mass m by the following equation (2): 0 Calculate.

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[0020] In addition, the provisional vibration transmissibility estimator 2 calculates the damping constant h. In this embodiment, the results of analysis of various cases of each of the modeled foundation and ground using a detailed analysis method that analyzes the mode of ground vibration transmission by the finite element method and the thin layer element method are recorded in the database 6. FIG. 3 is a graph showing the relationship between the dimensions of the foundation and the damping constant. The damping constant h tends to vary somewhat depending on the ground characteristics and the width dimension of the foundation. However, the depth dimension of the foundation tends to have a greater effect on the damping constant h than the ground characteristics and the width dimension of the foundation. Therefore, in this embodiment, a relational expression (represented by a straight line L in FIG. 3, for example) is recorded in the database 6 as a result of identifying a function that expresses the relationship between the depth dimension of the foundation and the damping constant h in the results of analysis in various cases using the detailed analysis method. In this way, the database 6 stores the correspondence between the dimension (length) of the foundation and the damping constant h of vibration. As shown in FIG. 3, the above relational expression has a relationship such that the damping constant h becomes smaller as the dimension of the foundation becomes larger, and the damping constant h becomes larger as the dimension of the foundation becomes smaller. The provisional vibration transmissibility estimating unit 2 applies the dimensions of the foundation to the above-mentioned relational expression to calculate the damping constant h.

[0021] The provisional vibration transmissibility estimation unit 2 estimates the natural frequency f of the foundation calculated as described above. 0 By applying the damping constant h to the following equation (3), the vibration transmissibility ΔL is formulated as a function of frequency f.

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[0022] The provisional vibration transmissibility estimation unit 2 formulates the vibration transmissibility using a vibration prediction method when the mass part of a spring-mass-damping model of a one-mass system is excited, which is a prediction method of the foundation response when a foundation supported by a spring in the ground is excited, such as the response prediction of a machine foundation during mechanical operation as described above, which is not usually used for predicting the vibration transmissibility to the foundation of a building or the like when ground vibration is applied. The foundation vibration estimation system 1 of this embodiment estimates the foundation vibration using the vibration transmissibility. However, as will be described later, the value of the vibration transmissibility ΔL formulated as the above formula (3) is not necessarily used as the vibration transmissibility when actually estimating the foundation vibration, and in some cases, the value of the vibration transmissibility ΔL formulated as the above formula (3) is adjusted and used as the vibration transmissibility when actually estimating the foundation vibration. From this point of view, the above vibration transmissibility ΔL is merely a provisional estimate. For this reason, the above vibration transmissibility ΔL is hereinafter referred to as a provisional vibration transmissibility. In this way, the provisional vibration transmissibility estimating unit 2 provisionally estimates the vibration transmissibility as a provisional vibration transmissibility by formulating the vibration transmissibility as a function of frequency as shown in Equation (3). The provisional vibration transmissibility estimating unit 2 obtains the length of the foundation to be estimated from the input information, obtains the damping constant h corresponding to the foundation length from the database, and estimates the provisional vibration transmissibility based on the damping constant h.

[0023] Next, the calculation result of the vibration transmissibility (provisional vibration transmissibility) calculated as described above will be verified. FIG. 4 is an explanatory diagram of the foundation model used when examining the provisional vibration transmissibility. As shown in Figure 4, the plan dimensions of the spread foundation are assumed to be 14m x 30m, and it is assumed to be embedded in uniform ground. The foundation thickness (depth) was set to three values: 0.5m, 1m, and 2m. In addition, the propagation velocity of the ground was set to three values: 170m / s, which assumes a loam layer, 330m / s, which assumes a hard ground, and 260m / s, which is a value between the loam layer and hard ground. The damping constant h of the ground was calculated as 1.0 in all cases.

[0024] The calculation results of the provisional vibration transmissibility, the detailed analysis method, and the simplified formula method when the ground transmission velocity is 170 m / s in the model of Figure 4 are shown in Figures 5(a), 5(b), and 5(c), respectively. The calculation results of the provisional vibration transmissibility, the detailed analysis method, and the simplified formula method when the ground transmission velocity is 260 m / s in the model of Figure 4 are shown in Figures 6(a), 6(b), and 6(c), respectively. The calculation results of the provisional vibration transmissibility, the detailed analysis method, and the simplified formula method when the ground transmission velocity is 330 m / s in the model of Figure 4 are shown in Figures 7(a), 7(b), and 7(c), respectively. Figures 5(a), 6(a), and 7(a) are graphs showing the results of formulating the vibration transmissibility as a provisional vibration transmissibility as in the above embodiment (Example 1). Figures 5(b), 6(b), and 7(b) are graphs showing the results of analysis using the three-dimensional finite element method and thin layer element method, respectively, assuming that the vibration source is located 30 m from the foundation (Comparative Example 1). Figures 5(c), 6(c), and 7(c) are graphs showing the results of analysis using a known simplified prediction formula for a rigid foundation (Comparative Example 2).

[0025] In the results of Example 1 calculated as the provisional vibration transmissibility by the provisional vibration transmissibility estimator 2 in the above embodiment in each of the above figures, the vibration transmissibility increases once as the frequency increases, becomes a positive value, and the ground vibration is amplified and transmitted to the upper surface of the foundation, and then gradually decreases, and the effect of attenuating the ground vibration by the foundation appears. The value in the frequency band where the vibration transmissibility becomes a positive value, the gradient of the line showing the subsequent decrease in vibration transmissibility, and the ratio of the difference between the results of each of the results of the foundation thickness in Example 1 are very close to those of Comparative Example 1, which provides detailed and accurate values. Therefore, it is considered that the formula result of the vibration transmissibility (provisional vibration transmissibility) in the above embodiment is highly accurate.

[0026] Here, in Example 1 showing the provisional vibration transmissibility of this embodiment and Comparative Example 1 corresponding to the detailed analysis method, as the frequency continues to increase, the vibration transmissibility decreases endlessly, and the effect of the vibration input loss due to the foundation continues to increase endlessly. This is due to the assumption that the ground is a simple one with only one layer. In the actual measured value of the actual foundation, the ground layer is not only one layer but multiple layers, and the state is complicated, so the vibration transmissibility does not decrease endlessly even if the frequency increases, but shows a characteristic of reaching a plateau with a certain value as the lower limit. In such a situation, if the foundation vibration is estimated using the provisional vibration transmissibility obtained in Example 1 as is, for example, the vibration transmissibility is calculated as a value smaller than the actual value, and as a result, the foundation vibration may be estimated as a vibration smaller than the actual value. In this case, if the foundation is designed based on this provisional vibration transmissibility, the actual vibration transmissibility will be larger than the provisional vibration transmissibility used at the time of design, and therefore the ground vibration may be transmitted to the foundation as a vibration larger than that assumed at the time of design.

[0027] In order to prevent the above-mentioned situation from occurring, it is necessary to reflect the above-mentioned characteristics in the vibration transmissibility as accurately as possible. For this reason, in the foundation vibration estimation system 1 of this embodiment, a lower limit is set for the provisional vibration transmissibility, and when the provisional vibration transmissibility is smaller than the lower limit, the provisional vibration transmissibility value is not used as the vibration transmissibility, but the lower limit value is used, thereby determining and confirming the vibration transmissibility to be used when finally estimating the foundation vibration. In this embodiment, this lower limit is determined as an equation for determining the value of the transmission characteristics of vibration when vibration passes between two different materials, based on the wave impedance of the two different materials.

[0028] For this purpose, first, the vibration transmittance calculation unit 3 calculates the vibration transmittance when ground vibration is transmitted to the upper surface of the foundation using the wave impedance, which is the physical quantity of resistance when vibration waves propagate through the ground and foundation. More specifically, the vibration transmittance calculation unit 3 multiplies the density of the constituent material of the ground and the foundation by the vibration propagation velocity, and calculates the wave impedance according to the following equation (4).

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[0029] The vibration transmittance calculation unit 3 calculates the ground wave impedance Z 1 and the wave impedance of the foundation Z 2 Using the above, the vibration transmittance is calculated by the following vibration transmittance calculation formula (5): 2 Calculate.

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[0030] The vibration transmissibility determination unit 4 determines, for each frequency, a provisional vibration transmissibility ΔL and a value based on the vibration transmittance, i.e., a lower limit value ΔL of the vibration transmissibility. min The vibration transmissibility thus determined is the provisional vibration transmissibility ΔL, and the lower limit value ΔL min is set, and the lower limit ΔL min If the provisional vibration transmissibility ΔL is smaller than the lower limit ΔL, the provisional vibration transmissibility ΔL is not used as the vibration transmissibility. min The value is set to use.

[0031] FIG. 8(a) shows a graph indicating the vibration transmissibility determined by vibration transmissibility determination unit 4 when the transmission velocity of the ground in the model of FIG. 4 is set to 170 m / s. Similarly, FIG. 8(b) shows a graph indicating the vibration transmissibility determined by vibration transmissibility determination unit 4 when the transmission velocity is set to 260 m / s. Similarly, FIG. 8(c) shows a graph indicating the vibration transmissibility determined by vibration transmissibility determination unit 4 when the transmission velocity is set to 330 m / s. In Example 2 shown in each of these figures, the calculation results of the vibration transmissibility by the detailed analysis method (Comparative Example 1) shown in FIG. 5(b), FIG. 6(b), and FIG. 7(b) are also shown.

[0032] In each diagram in Figure 8, the graphs shown as Example 2 are in a state in which a lower limit value is set for each of Example 1 shown in Figures 5(a), 6(a), and 7(a). It can be seen that as the frequency increases, the vibration transmissibility decreases and, when it reaches the value set as the lower limit value, even if the frequency becomes higher, the vibration transmissibility is maintained at the value set as the lower limit value. In this way, even if the provisional vibration transmissibility is calculated in a manner different from the actual properties, the vibration transmissibility is prevented from falling below the value set as the lower limit. This prevents the vibration transmissibility from deviating from the actual properties and being underestimated, which leads to the foundation being designed and constructed based on this, resulting in the transmission of ground vibration to the foundation as vibration larger than that assumed at the time of design. Moreover, the error of Example 2 with respect to Comparative Example 1, which is considered to be an accurate evaluation result, is about 2 dB or less at most, and it can be confirmed that highly practical results are obtained.

[0033] The base vibration estimation unit 5 acquires the frequency of the ground vibration to be estimated, and acquires the vibration transmissibility determined by the vibration transmissibility determination unit 4, which corresponds to the frequency of the ground vibration to be estimated. The determined vibration transmissibility is a provisional vibration transmissibility corresponding to the frequency of the ground vibration to be estimated that is a value based on the vibration transmittance, i.e., a lower limit value ΔL min If it is greater than , it is the provisional vibration transmissibility value, and the provisional vibration transmissibility corresponding to the frequency of the ground vibration to be estimated is the value based on the vibration transmittance, that is, the lower limit value ΔL min If it is smaller than the lower limit of vibration transmissibility ΔL min It is as follows. The base vibration estimation unit 5 further estimates the base vibration by multiplying the amplitude of the ground vibration to be estimated by the determined vibration transmissibility corresponding to the frequency of the ground vibration to be estimated, obtained as described above. The fundamental vibration estimation unit 5 outputs the fundamental vibration estimated in this manner to an output device (not shown) such as a display or a printer.

[0034] Next, a fundamental vibration estimation method using the fundamental vibration estimation system 1 will be described with reference to Figures 1 to 8 and 9. Figure 9 is a flowchart of the fundamental vibration estimation method. First, the provisional vibration transmissibility estimating unit 2 formulates the vibration transmissibility as a function of frequency based on the above input information. Specifically, the provisional vibration transmissibility estimation unit 2 calculates the spring constant K of the ground spring using equation (1) based on the planar dimensions (length) b and c of the foundation, the propagation velocity V of the ground, density ρ, and Poisson's ratio ν. Next, the provisional vibration transmissibility estimating unit 2 calculates the mass of the foundation based on the thickness d of the foundation, and further calculates the mass of the entire building including the foundation as mass m. Then, the provisional vibration transmissibility estimation unit 2 calculates the natural frequency f of the foundation by the formula (2) based on the spring constant K of the ground spring and the mass m. 0 Calculate. Furthermore, the provisional vibration transmissibility estimation unit 2 calculates the damping constant h and the natural frequency f of the foundation 0 By applying the damping constant h to equation (3), the vibration transmissibility ΔL is formulated as a function of frequency f. In this manner, the provisional vibration transmissibility estimating unit 2 provisionally estimates the vibration transmissibility as a provisional vibration transmissibility by formulating the vibration transmissibility as a function of frequency as shown in Equation (3) (step S1).

[0035] Next, the vibration transmittance calculation unit 3 multiplies the density of the constituent material of the ground and the foundation by the vibration propagation velocity to calculate the wave impedance according to equation (4). The vibration transmittance calculation unit 3 calculates the ground wave impedance Z 1 and the wave impedance of the foundation Z 2 Using the vibration transmittance calculation formula (5), the vibration transmittance τ 2 is calculated (step S2). Furthermore, the vibration transmittance calculation unit 3 calculates the vibration transmittance τ 2 By expressing it in decibels as in equation (6), the lower limit of vibration transmissibility (value based on vibration transmittance) ΔL min Calculate.

[0036] The vibration transmissibility determination unit 4 determines, for each frequency, a provisional vibration transmissibility and a value based on the vibration transmittance, i.e., a lower limit value ΔL of the vibration transmissibility. min and the larger value is determined as the vibration transmissibility (step S3). The fundamental vibration estimation unit 5 acquires the frequency of the ground vibration to be estimated, and acquires the vibration transmissibility determined by the vibration transmissibility determination unit 4 corresponding to the frequency of the ground vibration to be estimated. The base vibration estimation unit 5 further estimates the base vibration by multiplying the amplitude of the ground vibration to be estimated by the determined vibration transmissibility corresponding to the frequency of the ground vibration to be estimated, obtained as described above (step S4).

[0037] The foundation vibration estimation system 1 as described above is a system that estimates foundation vibration caused when ground vibration is transmitted to the upper surface of the foundation, and includes a provisional vibration transmissibility estimation unit 2 that provisionally estimates a vibration transmissibility, which is the ratio of the foundation vibration to the ground vibration, as a provisional vibration transmissibility by formulating the vibration transmissibility as a function of frequency based on input information including the shape of the foundation and the characteristics of the ground; a vibration transmissibility calculation unit 3 that calculates the vibration transmittance when the ground vibration is transmitted to the upper surface of the foundation using wave impedance, which is the resistance physical quantity when vibration waves propagate, of each of the ground and foundation; a vibration transmissibility determination unit 4 that compares the provisional vibration transmissibility with a value based on the vibration transmissibility for each frequency and determines the larger value as the vibration transmissibility; and a foundation vibration estimation unit 5 that estimates and outputs the foundation vibration by multiplying the amplitude of the ground vibration to be estimated by the determined vibration transmissibility corresponding to the frequency of the ground vibration to be estimated. According to the above configuration, the provisional vibration transmissibility estimating unit 2 provisionally estimates the vibration transmissibility, which is the ratio of the foundation vibration caused by the ground vibration being transmitted to the top surface of the foundation, as a function of frequency based on input information including the shape of the foundation and the characteristics of the ground. The vibration transmittance calculating unit 3 calculates the vibration transmittance when the ground vibration is transmitted to the top surface of the foundation using the wave impedance, which is the resistance physical quantity when the vibration wave propagates, of each of the ground and the foundation. Then, the vibration transmissibility determining unit 4 compares the provisional vibration transmissibility with a value based on the vibration transmittance for each frequency, and determines the larger value as the vibration transmissibility. That is, the vibration transmissibility estimated by the provisional vibration transmissibility estimating unit 2 based on the shape of the foundation and the characteristics of the ground is treated as provisional, and the provisional vibration transmissibility is compared with a value based on a vibration transmittance calculated separately, and the larger value is used as the actual vibration transmissibility. In this way, even if the provisional vibration transmissibility is estimated as an excessively small value, if the value based on the vibration transmittance calculated separately is larger than the provisional vibration transmissibility, the provisional vibration transmissibility is not actually used as the vibration transmissibility, and the value based on the vibration transmittance is used instead as the vibration transmissibility. In this way, the value based on the vibration transmittance is used as the lower limit of the vibration transmissibility. Therefore, it is possible to prevent the vibration transmissibility from being underestimated and the foundation being designed and constructed based on this, which results in the ground vibration being transmitted to the inside of the building as a vibration larger than actually expected. In addition, the vibration transmittance when ground vibration is transmitted to the top surface of the foundation is calculated using wave impedance, which is the physical quantity of resistance when vibration waves propagate. Therefore, the value based on the vibration transmittance calculated as above, which is used as the lower limit, is an appropriate value to be used as the lower limit. Furthermore, the series of processes required to estimate the fundamental vibration as described above is basically simple and can be performed with a small amount of calculations, and the fundamental vibration can be calculated in a short time compared to when, for example, the finite element method or the thin layer element method is used. In this way, it is possible to provide a base vibration estimation system 1 that can estimate base vibrations that occur when ground vibrations are transmitted to the upper surface of the foundation in a short time and with high accuracy.

[0038] Generally, vibrations are transmitted relatively easily in the low frequency range, but tend to be difficult to transmit in the high frequency range. This is because the energy of the vibrations is more likely to be absorbed and scattered within the material. Particularly at high frequencies, the fine structure and interface effects within the material affect the vibration energy, causing more dissipation. Therefore, in the high frequency band, the vibration transmissibility is calculated to be lower than the vibration transmittance using the wave impedance. Specifically, when vibration passes through a material, some of the energy is reflected or absorbed, making it difficult to maintain complete transparency. Therefore, in this embodiment, the provisional vibration transmissibility and the vibration transmittance using the wave impedance are compared for each frequency, and the lower limit of the vibration transmissibility is set to a value based on the wave impedance so that the provisional vibration transmissibility does not fall below the vibration transmittance.

[0039] In addition, the vibration transmittance calculation unit 3 multiplies the density of the constituent material of the ground and the foundation by the vibration propagation speed to calculate the wave impedance, and calculates the wave impedance Z 1 and the wave impedance of the foundation Z 2 Using the vibration transmittance calculation formula (5), the vibration transmittance τ 2 Calculate. According to the above-described configuration, the vibration transmittance can be appropriately calculated, and therefore the value based on the vibration transmittance used as the lower limit of the vibration transmissibility can be appropriately calculated.

[0040] In addition, the shape of the foundation includes the length of the foundation, and further includes a database 6 in which the correspondence between the length of the foundation and the vibration damping constant is recorded. The provisional vibration transmissibility estimation unit 2 obtains the length of the foundation to be estimated from the input information, obtains the damping constant corresponding to the foundation length from the database, and estimates the provisional vibration transmissibility based on the damping constant. According to the above configuration, the damping constant corresponding to the length of the foundation included in the input information is obtained from a database in which the correspondence relationship between the length of the foundation and the damping constant of vibration is recorded, and the provisional vibration transmissibility is estimated based on the damping constant, so that the length of the foundation is reflected in the estimation of the provisional vibration transmissibility, thereby making it possible to further improve the estimation accuracy of the foundation vibration.

[0041] In particular, in this embodiment, the shape of the foundation includes the thickness (depth) of the foundation, and the provisional vibration transmissibility estimation unit 2 calculates the natural frequency of the foundation based on the mass based on the thickness of the foundation, and calculates the provisional vibration transmissibility based on the natural frequency of the foundation. In the conventional simplified formula, since the thickness of the foundation is not included as a variable, the evaluation result may not reflect the thickness of the foundation. In contrast, in this embodiment, the provisional vibration transmissibility estimating unit 2 calculates the natural frequency of the foundation based on the mass based on the thickness of the foundation, and calculates the provisional vibration transmissibility based on the natural frequency of the foundation, so that the thickness of the foundation can be reflected when estimating the foundation vibration. This makes it possible to estimate the foundation vibration more accurately than when the conventional simplified formula is used. [Explanation of symbols]

[0042] 1 Base vibration estimation system 4 Vibration transmissibility determination unit 2 Provisional vibration transmissibility estimation section 5 Fundamental vibration estimation section 3 Vibration transmittance calculation section 6 Database

Claims

1. A base vibration estimation system that estimates base vibration caused by ground vibration transmitted to an upper surface of a foundation, comprising: a provisional vibration transmissibility estimating unit that provisionally estimates a vibration transmissibility, which is a ratio of the foundation vibration to the ground vibration, as a provisional vibration transmissibility by formulating the vibration transmissibility as a function of frequency based on input information including the shape of the foundation and characteristics of the ground; A vibration transmittance calculation unit that calculates a vibration transmittance when the ground vibration is transmitted to the upper surface of the foundation by using a wave impedance, which is a resistance physical quantity when a vibration wave propagates, of each of the ground and the foundation; a vibration transmissibility determination unit that compares the provisional vibration transmissibility with a value based on the vibration transmittance for each frequency and determines a larger value as the vibration transmissibility; a fundamental vibration estimation unit that estimates and outputs the fundamental vibration by multiplying the amplitude of the ground vibration to be estimated by the determined vibration transmissibility corresponding to the frequency of the ground vibration to be estimated; A fundamental vibration estimation system comprising:

2. The vibration transmittance calculation unit Calculating the wave impedance by multiplying the density of the constituent material and the vibration propagation velocity in each of the ground and the foundation; The wave impedance Z of the ground １ and the wave impedance Z of the foundation ２ Using the above, the vibration transmittance calculation formula is given below. [0010] Thus, the vibration transmittance τ ２ Calculate 2. The fundamental vibration estimation system according to claim 1 .

3. the shape of the foundation includes a length of the foundation; The method further includes a database in which a correspondence relationship between the length of the foundation and a damping constant of vibration is recorded, The provisional vibration transmissibility estimation unit obtains the length of the foundation to be estimated from the input information, obtains the damping constant corresponding to the length of the foundation from the database, and estimates the provisional vibration transmissibility based on the damping constant.

3. The fundamental vibration estimation system according to claim 1 or 2.

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