JP5008084B2 - Quantitative seismic performance evaluation program for structures - Google Patents

Description

  The present invention relates to a quantitative seismic performance evaluation program for a structure, and more particularly to a program for quantitatively evaluating the seismic performance of a structure using a response value to a ground motion of a civil engineering / building structure (hereinafter simply referred to as a structure). .

  Recent seismic design of structures is a performance-definition type that can adopt various members and facilities as long as they meet the specified performance from the conventional specification-based design that employs members and facilities prescribed by related laws and regulations. We are moving to design. In performance-based seismic design, the designer presents multiple seismic design plans to the owner in advance, agrees with the architect about the seismic performance that should be targeted, and the actually designed structure meets the target performance. It is necessary to evaluate whether or not you are satisfied. The possibility of earthquake damage to a structure is not determined only by the attributes of the structure itself, but also depends on the strength of the earthquake motion (seismic activity and ground amplification at the site where the structure is installed), so the seismic performance is It is required to present and evaluate in consideration of the seismic activity at the installation site and the effects of ground amplification. In addition, it is desirable to present the seismic performance as quantitatively as possible in order to select the optimal plan by comparing multiple seismic design plans.

Conventionally, as an index for quantitatively presented and evaluated seismic performance of the multi-layer structure such as reinforced concrete buildings, known structural seismic index I _S based on the amount of energy structure can absorb during an earthquake (Non-Patent Document 1). Seismic Index of Structure I _S is mainly based on the skeleton information of the structure, is calculated for each floor as the product of the holdings performance summary measure E _O and shape index S _D and aging index T as shown in equation (1) . The possessed performance basic index E _O is a basic index for evaluating the seismic performance possessed by the structure. The strength index C, the toughness index F, and the correction coefficient (n + 1 / n + i) of the strength distribution in the height direction of the target floor i. ) And the product. The shape index _SD is calculated by engineering quantification of the influence of the shape of the vertical member on the earthquake resistance (complexity of shape, unbalanced distribution of rigidity, etc.), and the secular index T indicates that structural defects are earthquake resistant. Calculated based on the effect (cracking, deformation, aging, etc. of the structure). The calculated structure seismic index I _S, by determining the magnitude relationship between structure seismic determination index I _SO, including information about the local index Z and ground index G (2) expression, taking into account the influence of the installation site of the structure Determine the seismic performance of the finished structure.

Structural seismic index I _S = E _O · S _D · T ………………………………………………… (1)
E _O : possessed performance basic index (= (n + 1 / n + i) C · F), i: floor number of target floor, C: strength index, F: toughness index, S _D : shape index, T: secular index determination index _{I SO = E S · Z ·} G · U ............................................. (2)
E _S: seismic determination basic indicators, Z: Region index, G: ground index, U: application index

In the field of earthquake risk management such as real estate evaluation and earthquake insurance, as other indexes for quantitatively evaluating the seismic performance of structures, earthquake LCC (Life Cycle Cost) and earthquake PML (Probable Maximum Loss); Economic indicators such as the maximum expected loss) are used. The earthquake LCC is defined as the sum of the initial investment amount and the amount of damage caused by a future earthquake as shown in, for example, the equation (3), and occurs in structural components (structural members, non-structural members, building equipment) at the time of the earthquake. The amount of damage caused by an earthquake is calculated as the total amount of loss (Non-Patent Document 2). Specifically, summarized in loss rate curve as shown in FIG. 13 (A) the relationship between loss rate during an earthquake L _j and ground motion intensity of each component of the structure (fragility curve) (Non-Patent Document 3 reference ) _Obtain the expected value (L _j · p _j ) of the loss rate L _j of each component using the loss rate curve for each seismic intensity with the occurrence probability p _j assumed at the site where the structure is installed. Multiply the element's replacement price by the expected loss rate to calculate the amount of loss, and add them to calculate the amount of damage caused by the earthquake.

Earthquake LCC = initial cost + Σ (L _j · p _j ) x replacement cost ………………………… (3)
L _j : Loss rate with respect to seismic intensity, p _j : Occurrence probability of seismic intensity

  The definition of earthquake PML is not necessarily unified. For example, when an earthquake that causes the greatest loss to a structure occurs (an earthquake equivalent to a 475 year recurrence period or an earthquake with a 50-year excess probability of 10%) It is defined as the ratio of the physical loss amount corresponding to the 90% non-excess probability to the replacement cost (Non-patent Document 3). Specifically, the loss rate of each component (structural member, non-structural member, building facility) is obtained using the loss rate curve of FIG. 13A for each seismic intensity estimated at the installation site of the structure. Calculate the expected loss amount by multiplying the loss rate by the replacement cost of each component, and calculate the expected loss amount for the entire structure by summing the expected loss amounts for each component as shown in equation (4) To do. Next, a plurality of predicted loss amounts of the entire structure calculated for a large number of earthquake motions are rearranged in descending order, and the cumulative probability (annual excess probability) of the occurrence probability of the earthquake motion is calculated in order from the top of the loss amount as shown in FIG. ) And an event curve (90th percentile value) of the event curve (average value) and its 90% non-exceed probability (excess probability 10%) as shown in Fig.), And 50-year excess probability 10% (annual excess) from those event curves Estimate the estimated loss at the time of earthquake with probability = 0.0021). Thereafter, earthquake PML (= 100 × expected loss / replacement price (%)) is calculated as a ratio of the predicted loss amount to the replacement cost of the entire structure (corresponding to the price when newly constructed).

Expected loss of structure = Σ (loss rate of component x replacement cost of component) ……… (4)

Supervised by Ministry of Land, Infrastructure, Transport and Tourism, Housing Bureau Building Guidance Division "2001 revised edition-Seismic diagnostic criteria for existing reinforced concrete buildings-Commentary", Japan Architecture Disaster Prevention Association, October 25, 2001 Yuji Takahashi “Earthquake risk analysis of buildings by simple simulation” 50th Symposium on Structural Engineering, Architectural Institute of Japan, Vol. 50B, pages 453-463, March 2004 Non-life insurance rate calculation mechanism “Research on earthquake risk index-present state and future of earthquake PML”, December 2002, Internet <URL: http: // www. niliro. or. jp / disclosure / q_kenkyu /> Hiroshi Ishida et al. “Earthquake Risk Assessment Method for Building Structures Based on Uniform Hazard Spectrum Considering Ground Amplification”, Architectural Institute of Japan, 583, 23-30, September 2004 Hiroaki Yamanaka et al. "Science of Earthquake Shaking-The Form of Strong Vibrations Seen" The University of Tokyo Press, July 27, 2006, first edition, pages 131-182 (Chapter 5, predicting strong vibrations) Satoshi Ohno et al. “Distance attenuation formula of horizontal and vertical motion based on California strong motion record and application to inland earthquake in Japan” Architectural Institute of Japan, 544, 39-46, June 2001

However, the structural seismic index I _S described above is a value obtained by evaluating an acceptable final state of the structure, there is a problem that can not be properly presented and evaluated damage before structure to the final state. For example, can be determined to be safe structural seismic index I _S is to assume ground motion as long structure seismic determination index I _SO or more, if the structure even structure seismic determination index I _SO or subjected to any damage is there. Moreover, even if the structural seismic index _IS is the same seismic design, the degree of damage during an earthquake may vary greatly. Furthermore, structural seismic index I _S is a value calculated from the attribute of the structure, although in consideration of the influence of the installation site by comparison with the structure seismic determination index I _SO, regional indicators in structure seismic determination index I _SO In Z and the ground index G, there is a problem that the influence of the installation site cannot be accurately evaluated from the viewpoint of the degree of damage of the structure. The seismic design performance specified type, not only to assess whether safe or not with respect to assumed ground motion as structural seismic index I _S, including influence of damage or installation site of the previous structure to the final state A seismic performance index that can evaluate seismic performance is necessary.

  On the other hand, if the earthquake LCC or earthquake PML described above is used, it is possible to determine the damage before reaching the final state in consideration of the influence of the installation site. It may be possible to present and evaluate the design. However, since seismic design of ordinary structures often has to be planned before the specifications and costs of components (non-structural members and building equipment) are finalized, seismic LCC and seismic PML are designed as is. Currently, it is difficult to use as a performance index. In addition, regarding the loss rate curve (fragility curve) of the component, statistical data cannot be said to be abundant at this stage, and the loss rate curve of every component used in seismic design should be accurately modeled. Is currently difficult. A seismic performance index that can accurately determine seismic performance, including damage to structures before the final state, such as seismic LCC and seismic PML, and the effects of installation sites, even when component specifications and costs are not determined Development is desired.

  Accordingly, an object of the present invention is to provide a quantitative seismic performance evaluation program for a structure that can accurately determine damage during an earthquake even at a stage where the specifications and costs of the structural components of the structure are not determined.

  The inventor has paid attention to the seismic response value Ds of the structure calculated using as input the seismic motions of various epicenters assumed at the installation site of the structure. Conventionally, as a method for evaluating and managing seismic risk, as shown in FIG. 3, probability theory in the installation position of structure B from a plurality of seismic sources E (seismic model) and ground characteristics U (ground model) near structure B Seismic ground motion Vs (earthquake ground motion Vs with occurrence probability Vp) is obtained, and from the ground motion Vs and the response characteristic C (structure model) of the structure B, the probabilistic seismic response value Ds (the probability of occurrence) The earthquake risk curve (excess probability curve) P is calculated by calculating the earthquake response value Ds) with Dp and rearranging the earthquake response values Ds in descending order to obtain the cumulative probability (annual probability of excess) De. A method for evaluating the earthquake risk of the structure B in consideration of the seismic environment E, the ground amplification U, and the structure characteristics C by the curve P is known (see Non-Patent Document 4). Such an earthquake response value Ds can be calculated if the response characteristic C (structural member) is determined even if the specifications and costs of the structural components (non-structural members and building equipment) are not determined.

The earthquake risk curve P shown in FIG. 3 shows the relationship between the earthquake response value Ds and the excess probability De (occurrence probability Dp), and shows the relationship between the expected loss amount and the excess probability as shown in FIG. It is different from the event curve. However, since there is a correspondence between the earthquake response value Ds and the expected loss amount, there is a possibility that the seismic performance can be evaluated using the earthquake response value Ds in the same manner as the earthquake PML. Further, when the earthquake response value Ds of the earthquake risk curve P shown in FIG. 3 is integrated with respect to the excess probability ΔDe, an expected value (= Σ (Ds · ΔDe)) of the earthquake response value Ds in the service period of the structure B is obtained. Although the expected value of the seismic response value Ds is different from the expected value of the loss rate of the earthquake LCC (L _j · p _j ) described above, there is a corresponding relationship between them, so the expected value of the seismic response value Ds May be used to evaluate seismic performance in the same way as earthquake LCC.

  In general, structural components include deformation-type elements (such as structural members) that are easily damaged by deformation response values (interlayer deformation angles, etc.) during an earthquake, and acceleration-type elements that are easily damaged by acceleration response values during an earthquake. It is known that there is (building equipment). The above-mentioned earthquake LCC and earthquake PML are calculated by adding the loss amounts calculated considering the fragility curve and cost for both the deformation type element and the acceleration type element that are affected by the earthquake response value. It can be considered as an index that equally evaluates the influence of the deformation response value. If an index that evaluates the effects of acceleration response values and deformation response values to the same extent can be created without converting to loss amounts through fragility curves and costs, the earthquake resistance is highly correlated with earthquake LCC and earthquake PML. It can be expected to perform performance evaluation. Based on this idea, the present invention has been completed as a result of research and development of a seismic performance index using the seismic response value Ds of the target structure B.

  Referring to the block diagram of FIG. 1 and the flowchart of FIG. 2, the quantitative earthquake-proof performance evaluation program for a structure according to the present invention installs the computer 1 to evaluate the earthquake-proof performance of the target structure B, and installs the target structure B. Storage means 7 for storing the position L, the service period t, and the response characteristic C to the ground motion Vs (see step S103 in FIG. 2), a plurality of occurrence probabilities assumed within the service period t at the installation position L of the target structure B Response value calculation means 10 for inputting the earthquake motion Vs with Vp and calculating the maximum response values Da and Dd with the occurrence probability Dp of the acceleration a and deformation d generated in the target structure B according to the response characteristic C (see step S105), The expected earthquake response value Aa (= Σ (Da · Dp) of the acceleration a and deformation d generated in the target structure B within the service period t from the maximum response values Da and Dd of the acceleration a and deformation d and the occurrence probability Dp. , Ad (= Σ (Dd · Dp)), the expected value calculation means 30 (see step S106), and the product (= Aa · Ad) of the earthquake response expected values Aa and Ad of acceleration a and deformation d (= Aa · Ad) or their reciprocals. Using (= 1 / Aa · Ad) as the seismic performance index G, it functions as the performance evaluation means 40 (see step S107) for evaluating the seismic performance of the target structure B. The product of the earthquake response expected values Aa and Ad or the reciprocal thereof may be the sum of the logarithmic values of the earthquake response expected values Aa and Ad (= lnAa + lnAd) or a negative value thereof (= − (lnAa + InAd)) (described later (11)) See formula).

  Preferably, the storage unit 7 stores a ratio ratio α (= αa / αd) divided into an acceleration type αa that easily damages the components of the target structure B by acceleration and a deformation type αd that is easily damaged by deformation. The evaluation means 40 weights the expected earthquake response values Aa and Ad of the acceleration a and deformation d exponentially or coefficient according to the ratio α, and the predicted earthquake response values Aa and Ad of the weighted acceleration a and deformation d. A seismic performance index G is obtained (see equation (13) below).

  When the target structure B is a multilayer (n-layer) structure, the response value calculation means 10 calculates the maximum response values Dai and Ddi with the probability D of occurrence of acceleration a and deformation d for each layer i (1 ≦ i ≦ n). The expected value calculation means 30 calculates the expected earthquake response values Aai (= Σ (Dai · Dp)) and Adi (= Σ (Ddi · Dp)) of the acceleration a and deformation d for each layer i, and the performance evaluation means The seismic performance index Gi for each layer i can be obtained by 40, and the seismic performance of the target structure B can be evaluated by the average value (= Σ (1 / n) Gi) of the seismic performance index Gi for each layer i ( (See equation (12) below).

  More preferably, the storage means 7 stores the cost ratio ri (Σri = 1) for the entire layer i (n layers) of the target structure B, and the performance evaluation means 40 calculates the seismic performance index Gi for each layer i by the cost ratio. Coefficient weighting or exponential weighting is performed according to ri, and the seismic performance of the target structure B is evaluated based on the sum of the weighted seismic performance indices Gi for each layer i (= Σri · Gi) (formula (13) described later) reference).

  Desirably, the storage means 7 stores the position E1, the scale E2, the occurrence probability E3, and the distance attenuation equation E4 of one or more seismic sources E (step S101 in FIG. 2), and the installation position L of the target structure B and each seismic source. Earthquake motion calculation that calculates response spectrum Vs with occurrence probability Vp of a plurality of earthquake motions assumed in service period t at installation position L from position E1, magnitude E2, occurrence probability E3, and distance attenuation equation E4 of E for each seismic source E Means 20 is provided (step S104), and the response spectrum Vs with the occurrence probability Vp for each epicenter E is input to the response value calculation means 10, and the maximum response value Da with the occurrence probability Dp of the acceleration a and deformation d generated in the target structure B is provided. , Dd is calculated (step S105). More preferably, the ground characteristic U of the installation position L of the target structure B is stored in the storage means 7 (step S102), and the seismic motion calculation means 20 calculates the response spectrum Vs with the occurrence probability Vp for each epicenter E and the ground characteristics U. A response spectrum Vs with a probability Vp of earthquake motion assumed on the ground surface at the installation position L is calculated (steps S104 to S105).

  Alternatively, in the storage means 7, the fault model E5 of one or more seismic centers E around the installation position L of the target structure B and the past small / medium earthquake recorded waveform or statistically processed artificial earthquake waveform E6 and empirical or statistical The time history waveform calculation formula E7 by the dynamic Green function method is stored (step S101), and the earthquake motion calculation means 20 is used at the installation position L from the fault model E5, the earthquake waveform E6, and the time history waveform calculation formula E7 of each epicenter E. A time history waveform Vs with occurrence probability Vp of a plurality of ground motions assumed within a period t is calculated for each epicenter E (step S104), and a time history waveform Vs with occurrence probability Vp for each epicenter E is sent to the response value calculation means 10. The maximum response values Da and Dd with the occurrence probability Dp of the acceleration a and the deformation d generated in the target structure B may be calculated (step S105). Also in this case, more preferably, the ground characteristic U of the installation position L of the target structure B is stored in the storage means 7 (step S102), and the time history waveform Vs with the occurrence probability Vp for each epicenter E is obtained by the earthquake motion calculation means 20. The response spectrum Vs with the occurrence probability Vp of the ground motion assumed on the ground surface at the installation position L can be calculated from the ground characteristics U (steps S104 to S105).

  The quantitative seismic performance evaluation program for a structure according to the present invention is assumed at the installation position L within the service period t after storing the installation position L of the target structure B, the service period t, and the response characteristic C to the ground motion Vs. Input a plurality of earthquake motions Vs with occurrence probability Vp, and calculate maximum response values Da and Dd with occurrence probability Dp of acceleration a and deformation d generated in target structure B according to response characteristic C, and calculate acceleration a and deformation d. The earthquake response expected values Aa and Ad of the acceleration a and deformation d generated in the target structure B within the service period t are calculated from the maximum response values Da and Dd and the occurrence probability Dp, and the earthquake response expected values Aa and Ad are calculated. Since the seismic performance of the target structure B is evaluated using the product or its inverse as the seismic performance index G, the following advantageous effects can be obtained.

(A) Acceleration and deformation response similar to earthquake LCC and earthquake PML by using the product (or its inverse) of the expected earthquake response values Aa and Ad of the acceleration and deformation generated in the target structure B as the seismic performance index G The seismic performance of the structure B can be quantitatively evaluated in consideration of the effect of the value.
(B) The acceleration response expectation value Aa and the deformation response expectation value Ad are responses by the structural member even if the non-structural member of the target structure B and the detailed specifications (fragility curve) and cost of the building equipment are unknown. Since the characteristic C can be calculated, the seismic performance can be evaluated even in the design stage before the detailed specifications and costs of the components are finally determined. In addition, it is possible to evaluate the seismic performance of the existing structure B without being influenced by the repurchasing price (cost) of the component that varies depending on the time.
(C) Depending on the application of the target structure B (normal office building, school, factory, etc.), the component member αa that is susceptible to the acceleration response value and the component member αd that is susceptible to the deformation response value By changing the weighting of the expected earthquake response values Aa and Ad according to the ratio ratio α, it can be expected that the correlation between the seismic performance index G based on both expected response values Aa and Ad and the earthquake LCC or earthquake PML is enhanced.

(D) Even when the target structure B is a multi-layer structure, the seismic performance index Gi for each layer i is obtained from the expected earthquake response values Aai and Adi for each layer i, and the average value Σ (1 / n) G i is calculated. By using the seismic performance index G, it is possible to evaluate seismic performance highly correlated with the earthquake LCC and the earthquake PML. Further, by changing the weighting of the seismic performance index Gi for each layer i according to the cost ratio ri (Σri = 1) to the whole of each layer i, the correlation between the sum Σri · Gi and the earthquake LCC or earthquake PML is further increased. It can be expected to increase.
(E) Presenting and evaluating appropriate seismic performance considering the influence of the installation site by inputting the seismic motion Vs with the occurrence probability Vp taking into account the seismic environment and ground amplification at the installation position L of the target structure B be able to.
(F) By repeatedly calculating the seismic performance index G while changing the installation position L, the service period t, and the response characteristics C of the target structure B, various design plans for seismic performance that are optimal for the owner can be presented for comparison. At the same time, it can be a means for the designer to quantitatively judge and evaluate the seismic performance of the structure designed.

  FIG. 1 shows an example of a block diagram of a computer 1 incorporating a program of the present invention. The computer 1 shown in FIG. 1 is connected to an input device 2 such as a keyboard / mouse and an output device 3 such as a display / printer, and has an epicenter data (seismic model) E, ground property data (ground model) U, structure data ( Structure model) It has storage means 7 for storing C, L, t, and the like. Data stored in the storage unit 7 is input from the input device 2 through the input unit 5. The computer 1 in the illustrated example has a response value calculation means 10, an earthquake motion calculation means 20, an expected value calculation means 30, an earthquake resistance evaluation means 40, an input means 5 and an output means 6 as built-in programs. ing. The output unit 6 is a program for outputting the evaluation result (seismic performance index G) by the seismic performance evaluation unit 40 to the output device 3.

  FIG. 2 shows a flowchart of a method for evaluating the seismic performance of the target structure B (see FIG. 5) by each program of FIG. Hereinafter, each program of FIG. 1 will be described with reference to the flowchart of FIG. First, in step S101, the epicenter data (seismic source model) E is stored in the storage means 7. In the present invention, the epicenter E that includes uncertainty in any of the occurrence scale, the occurrence location, and the occurrence timing can be set by, for example, the epicenter position E1, the magnitude (magnitude) E2, and the occurrence probability E3. The occurrence probability E3 is calculated according to the service period t of the target structure B. In addition, an appropriate distance attenuation equation E4 is set based on statistical analysis of past earthquake records, and the target structure B is obtained by an empirical method from the epicenter distance from the epicenter position E1, the magnitude E2 of the epicenter E, and the distance attenuation equation E4. A response spectrum Vs of earthquake motion (response spectrum Vs with occurrence probability Vp) in which the occurrence probability Vp at the installation position L is defined is predicted (see response spectrum calculation means 21 in FIG. 1). For example, in step S101, the storage means 7 stores the position E1, the scale E2, the occurrence probability E3, and the distance attenuation equation E4 of one or more epicenters E in the evaluation target area (for example, the whole of Japan or the Kanto region). In response to the input of the installation position L of the structure B (step S103), the epicenter E around the installation position is selected.

  Alternatively, in step S101, instead of the distance attenuation equation E4, the fault model E5 of one or more epicenters E around the installation position L of the target structure B and the past small / medium earthquake recording waveform or the artificially processed artificially The earthquake waveform E6 and the time history waveform calculation formula E7 by the empirical or statistical Green function method are stored in the storage means 7, and the fault model E5, the earthquake waveform E6 and the time history waveform calculation formula E7 of each epicenter E are half An empirical method may be used to predict the time history waveform Vs of the earthquake motion with the occurrence probability Vp at the installation position L (time history waveform Vs with the occurrence probability Vp) (see the time history waveform calculation means 22 in FIG. 1). .

  Conventionally, a method for predicting a time history waveform of a large ground motion of the epicenter E at the installation position L by regarding the past small / medium ground motion records (waveforms) at the installation position L as an empirical Green function, When there is no small / medium ground motion record (waveform), there is a method to predict the time history waveform of the large ground motion of the epicenter E at the installation position L by the statistical Green function created considering the statistical properties of general ground motion. It has been developed (see non-patent document 5, for example). According to such a semi-empirical method using the time history waveform calculation formula E7 based on the empirical or statistical Green's function method, the path characteristics of the seismic wave are considered in comparison with the empirical method based on the distance attenuation formula E4. The detailed seismic motion Vs can be predicted. In order to predict a more detailed seismic motion Vs, in step S101, a theoretical method (difference method, finite element method, etc.) for calculating the time history waveform of the seismic motion of the epicenter E is stored, for example, according to the frequency band. It is also possible to predict the time history waveform Vs of seismic motion by complementarily adding the waveform by the time history waveform calculation formula E7 by the empirical or statistical Green function method and the waveform by the theoretical method (broadband hybrid method). .

  Preferably, in step S102, the ground characteristic data (amplification characteristic) U at the installation position L of the target structure B is stored in the storage means 7. The distance attenuation formula E4 and the time history waveform calculation formula E7 described above are for an engineering basis, and the response spectrum Vs or the time history waveform Vs on the ground surface at the installation position L can be amplified by the influence of the ground. If the ground characteristic data U of the installation position of the target structure B is stored, the response spectrum Vs or the time history waveform Vs of the ground motion assumed on the ground surface at the installation position L is predicted in consideration of amplification by the ground. (Refer to the ground amplification calculation means 23 in FIG. 1). Note that the influence of amplification by the ground is taken into account when calculating the response spectrum Vs or the time history waveform Vs in step S104 described later. However, the influence of the interaction between the ground and the target structure B is described in step S105 described later. This is taken into account when calculating the response values Da and Dd of the structure B.

  In step S103, the storage unit 7 stores the installation position L, the service period t, and the response characteristics C with respect to the ground motion Vs as the structure data (structure model) of the target structure B. The installation position L of the target structure B is used, for example, to calculate the epicenter distance from the epicenter position E1 (step S104). The service period t of the target structure B can be, for example, a normal service life (about 10 to 50 years) of the structure B, and is used to calculate the occurrence probability E3 of the epicenter E. The response characteristic C is used to calculate the response values Da and Dd of the target structure B from the response spectrum or the time history waveform Vs (step S105). For example, the mass / rigidity / height of the multilayer structure B is represented by a mass system model C1 as shown in FIG. 5 (A), and the restoring force characteristics C2 of each member element of the structure B as shown in FIG. 5 (B). Appropriately modeled, the response characteristic C of the structure B according to its strength and toughness is expressed as a load-deformation relationship (capacity curve) C3 of each layer of the mass point model C1 as shown in FIGS. Can be represented.

  Steps S104 to S105 in FIG. 2 are based on the acceleration a and deformation d generated in the target structure B from the hypocenter data E, the ground characteristic data U and the response characteristic C of the target structure B around the installation position L of the target structure B. The process of calculating the maximum response values Da and Dd with the occurrence probability Dp is shown. Specifically, as shown in FIG. 3, the occurrence probability Vp assumed within the service period t at the installation position L of the target structure B by the seismic motion calculation means 20 from the one or more source data E and the ground characteristic data U. The attached seismic motion Vs is calculated for each seismic source E (step S104), and the response value calculation means 10 generates a plurality of seismic motions Vs generated in the target structure B from the stochastic ground motion Vs, the ground property data U, and the response characteristics C of the target structure B An acceleration maximum response value Da with occurrence probability Dp and a deformation maximum response value Dd with occurrence probability Dp are calculated (step S105).

As an example of step S104 of FIG. 2, FIG. 4 calculates the earthquake motion Vs with the occurrence probability Vp expressed by the response spectrum by the earthquake motion calculation means 20 (particularly the response spectrum calculation means 21) based on Non-Patent Document 6, for example. An example of the flowchart of a process is shown. First, according to the distance attenuation equation E4 in step S301 in FIG. 4, the magnitude E2 (moment magnitude Mw) of each epicenter E and the equivalent epicenter distance Xeq (km) from the position E1 of each epicenter E to the installation position L of the structure B From this, the acceleration response spectrum Sa (cm / s ² , the median value of a probability distribution described later) in the engineering base at the installation position L of the structure B is calculated for each epicenter E. In the distance attenuation equation E4 in step S301, δ _E and δ _P are stratification factors for each earthquake and stratification factors for the Pleistocene, a and c are coefficients for correcting distance and Pleistocene amplification, b is a distance coefficient, dP is the Pleistocene amplification factor for pre-Tertiary ground. Next, in step S302, the probability distribution of the acceleration response spectrum Sa is discretized based on the occurrence probability E3 of each epicenter E, and a plurality (N) of acceleration response spectra Sa1 to San (uniform hazard spectra) are created for each epicenter E. To do. For example, assuming that the probability distribution of the acceleration response spectrum value Sa in each cycle is a lognormal distribution and they are completely correlated, the acceleration response spectrum Sa calculated in step S301 is converted into a plurality of accelerations as shown in step S302. The response spectrums Sa1 to San can be decomposed (discretized).

  In step S303 of FIG. 4, acceleration response spectra S′a1 to S′an on the ground surface are calculated from the acceleration response spectra Sa1 to San of the engineering base and the ground characteristic data U. In step S304, displacement response spectra S′d1 to S′dn on the ground surface are calculated from the acceleration response spectra S′a1 to S′an on the ground surface. In step S305, the occurrence probabilities Vp1 to Vpn of a plurality (N) of acceleration response spectra Sa1 to San are calculated based on the occurrence probability E3 (for example, due to the steady Poisson process) of the earthquake source E. According to the flowchart of FIG. 4, a set of N (ground acceleration response spectrum S′a, ground displacement response spectrum S′d, occurrence probability Vp) is set as the response spectrum Vs with the occurrence probability Vp expressed in the response spectrum. It can be calculated for each epicenter E (step S306).

  In step S104 in FIG. 2, the earthquake motion Vs with the occurrence probability Vp expressed by the time history waveform can be calculated by the earthquake motion calculation means 20 (particularly the time history waveform calculation means 22). In that case, the fault model E5 of each epicenter E around the installation position L of the target structure B, the past small / medium earthquake recorded waveform around the installation position L, or the statistically processed artificial earthquake waveform E6, experience Generation of a plurality of time history waveforms Vs on the ground surface of the installation position L of the structure B and each of the time history waveforms Vs from the time history waveform calculation formula E7 by the statistical or statistical Green function method and the ground characteristic data U The probability Vp is calculated for each epicenter E. The fault model E5 of each epicenter E is a model including the epicenter distance from the position E1 of each epicenter E to the installation position L of the structure B, the magnitude E2 of each epicenter E, and the occurrence probability E3 of the epicenter E. be able to. 2 is not indispensable for the present invention, for example, the occurrence probability Vp assumed in the vicinity of the installation position L of the target structure B. When the attached earthquake motion Vs (response spectrum or time history waveform) is obtained in advance, the earthquake motion Vs with the occurrence probability Vp may be used.

  As an example of step S105 in FIG. 2, FIG. 6 shows earthquake motion Vs with an occurrence probability Vp calculated for each epicenter E (for example, N (acceleration response spectra S′a1 to S ′ calculated in step S306 in FIG. 4). an, a set of displacement response spectra S′d1 to S′dn, occurrence probabilities Vp1 to Vpn) and response characteristics C of the target structure B (multi-mass point system model C1, restoring force characteristics C2 set in step S103, capacity From the city curve C3), the response value calculation means 10 (especially the response value calculation means 11 using the response spectrum) calculates the maximum response values Da and Dd with the occurrence probability Dp of the acceleration a and deformation d of the target structure B. The flowchart of the process to calculate is shown.

  In step S401 of FIG. 6, for example, the target structure B is a multi-mass point system model C1 (n = 3 in the illustrated example) and a restoring force characteristic C2 (three broken line model in the illustrated example) of FIG. As a response characteristic C of the structure B according to its strength and toughness, a capacity curve C3 (load-deformation relationship) of each layer as shown in FIGS. The maximum response acceleration Dai and the maximum interlayer deformation angle Ddi are calculated for each layer i of the target structure B using C and the earthquake motion Vs with the occurrence probability Vp (acceleration response spectrum S′a, displacement response spectrum S′d). If necessary, when modeling the target structure B and creating the response characteristic C, the response characteristic C may be created by modeling in consideration of the influence of the interaction with the ground at the installation position L. .

  In step S401 of FIG. 6, by sequentially inputting a plurality of earthquake motions Vs with occurrence probability Vp (acceleration response spectrum S′a, displacement response spectrum S′d) calculated for each epicenter E, in each layer i in step S402. A set of the maximum response acceleration Dai with the occurrence probability Dp and the maximum interlayer deformation angle Ddi can be calculated. The maximum response values Dai and Ddi can be calculated for each occurrence probability Vp regardless of the number of seismic centers E, and the occurrence probability Dp can use the occurrence probability Vp of the ground motion Vs as it is (Dp = Vp). The response value calculation means 12 using the time history waveform of FIG. 1 uses the maximum response value Dai with the occurrence probability Dp of the acceleration a and deformation d of the target structure B from the time history waveform Vs with the occurrence probability Vp for each epicenter E. , Ddi for each layer i. In the flowchart of FIG. 6, instead of the response value calculation unit 11, the response value calculation unit 12 may be used to calculate the maximum response acceleration Dai with the occurrence probability Dp and the maximum interlayer deformation angle Ddi for each layer i.

  Steps S106 to S107 in FIG. 2 are processes for calculating the seismic performance index G of the target structure B from the maximum response acceleration Dai with the occurrence probability Dp calculated for each layer i for the target structure B and the maximum interlayer deformation angle Ddi. Show. Specifically, in step S106, the expected value calculation means 30 calculates the expected earthquake response value Aai (= Σ (Dai · Dp)) of the acceleration a within the service period t from the maximum response acceleration Dai and its occurrence probability Dp. In addition, the expected earthquake response value Adi (= Σ (Ddi · Dp)) of the deformation d within the service period t is calculated from the maximum interlayer deformation angle Ddi and its occurrence probability Dp. Next, in step S107, the seismic performance evaluation means 40 multiplies the expected seismic response values Aai and Adi of the acceleration a and deformation d by the seismic performance evaluation means 40, and the seismic performance index Gi for each layer i of the target structure B is shown in FIG. And the average seismic performance index Gi of each layer i is calculated as shown in equation (12) to calculate the total seismic performance index G of the target structure B.

Gi =-((1/2) lnAai + (1/2) lnAdi)
= (1/2) Gai + (1/2) Gdi …………………………………… (11)
G = Σ (1 / n) Gi …………………………………………………………………… (12)

  In order to consider the effects of the acceleration response value and the deformation response value equally in the seismic performance index G as in the case of the earthquake LCC and earthquake PML, the acceleration response expected value Aai and the deformation response expected value Adi as in the equation (11) Multiplication with is effective. In earthquake LCC, etc., the effects of acceleration response values and deformation response values with different properties (units) are converted into loss amounts through fragility curves and costs, respectively. If the acceleration response value and deformation response value with different properties (units) are simply added together, the effect of the response value having a large absolute value will increase, and the effects of the acceleration response value and the deformation response value will be equalized. It is difficult to make an index that takes into account. By using the product of the acceleration response expectation value Aai and the deformation response expectation value Adi as in equation (11), the influence of the acceleration response value and the deformation response value can be considered equally.

  In equation (11), the earthquake response expected values Aai and Adi are assumed to be natural logarithmic values so that the weighting described later can be handled easily. The smaller the product of the earthquake response expected values Aai and Adi, the larger the seismic performance index G becomes. As described above, the seismic performance index G has a negative value (negative sign), but it is not an essential condition for the present invention to use a logarithmic value or a negative value. The seismic performance index G is multiplied by the expected earthquake response values Aa and Ad. If it is, it is enough. For example, the product (= Aa · Ad) of the earthquake response expected values Aa and Ad or the reciprocal (= 1 / Aa · Ad) may be used as the earthquake performance index G as it is. In addition, in equation (11), a coefficient (1/2) is added to uniformly consider the effects of the acceleration response value and the deformation response value, and the geometric mean of the earthquake response expected values Aa and Ad is used as the earthquake performance index G. The coefficient (1/2) is not an essential condition for the present invention, and the coefficient may be 1. In equation (11), Gai represents an earthquake resistance performance index based on the expected acceleration response value Aai in the layer i, and Gdi represents an earthquake resistance performance index based on the expected deformation response value Adi in the layer i.

  Preferably, the storage means 7 has a ratio ratio αi (= αai / αdi) obtained by dividing the component of each layer i of the target structure B into an acceleration type αai that is easily damaged by acceleration and a deformation type αdi that is easily damaged by deformation. As shown in the equation (13), after the earthquake response expected values Aai and Adi are exponentially weighted or coefficient weighted according to the ratio αi, the weighted acceleration response expected value Aai and deformation response expected Multiply the value Adi to calculate the seismic performance index Gi for each layer i. As described above, there are a deformation type αa (structural member or the like) that is easily damaged by deformation and an acceleration type αd (building equipment or the like) that is easily damaged by acceleration. The ratio ratio α (αa / αd) generally varies depending on the application of the structure B. Therefore, the correlation between seismic performance index G and seismic LCC or seismic PML can be achieved by changing the weighting of expected seismic response values Aa and Ad according to the purpose of target structure B (normal office building, school, factory, etc.) It can be expected to further enhance the sex.

Gi =-(αai · lnAai + αdi · lnAdi)
= Αai ・ Gai + αdi ・ Gdi …………………………………………… (13)
G = Σri ・ Gi ………………………………………………………………………… (14)

  The ratio ratio αi (= αai / αdi) used in the seismic performance index G of the present invention corresponds to the fragility curve and cost used in the earthquake LCC and the like, and the repurchasing price of the component of each layer i of the target structure B And the loss rate can be determined. For example, for the existing structure B, the seismic performance index G of the present invention and the earthquake LCC are calculated and compared, and the ratio α (= αa / αd) of both elements corresponding to the use of the structure B is obtained and stored in advance. If memorized in the means 7, even in the design stage before the detailed specifications and costs of the components of the structure B are determined, the earthquake resistance performance in consideration of the ratio α according to the use of the structure B The index G can be calculated.

  More preferably, the cost ratio ri (Σri = 1) of each layer i with respect to the entire n layers of the target structure B is determined and stored in the storage means 7, and the seismic performance index of each layer i as shown in the equation (14). The overall seismic performance index G of the target structure B is calculated by calculating the sum of the weighted seismic performance index Gi of each layer i after Gi is weighted with a coefficient or index weighted by the cost ratio ri. In formula (12), it is assumed that the structural elements (structural members, non-structural members, building equipment) of the structure B are evenly distributed to each layer i, but the cost of the structural elements of each layer i is not uniform. Can be expected to further increase the correlation between the seismic performance index G of the present invention and the earthquake LCC or earthquake PML by changing the weighting of the seismic performance index Gi of each layer i as shown in equation (14).

[Verification experiment]
In order to confirm the effectiveness of the seismic performance index G shown in equations (11) to (14), verification to confirm the correlation with earthquake LCC and earthquake PML by a parametric study using an earthquake-ground-structure model Went. As an earthquake model, the installation position L of the target structure B is determined assuming a specific city in the Kanto region, the service period t of the structure B is set to 50 years, Twenty acceleration response spectra Sa1 to San (uniform hazard spectra) in which the occurrence probability Vp on the engineering basis was defined were created (see Table 1). In some cases, the seismic performance index G was calculated using a spectrum value multiplied by 1.5 (cases 13 to 15 in Table 2). In addition, as ground models, 3 of ground characteristic data U1 (first type ground with engineering base only), U2 (second type ground with elastic cycle 0.36 sec), U3 (third type ground with elastic cycle 1.21 sec). The type was used. FIG. 7 shows acceleration response spectra on the engineering foundation, on the second kind ground U2, and on the third kind ground U3.

The structure model assumes an RC frame structure of three layers (n = 3), and a structure model (three-layer mass of each mass model C1 and restoring force characteristic C2 as shown in FIGS. 5A and 5B). 1 t, each layer height 3.5 m) was used. The structure seismic index _{I S} are two different types of structures _(I S = 0.4, 0.6) assumes the further structural seismic index _{I S} is the strength index C and toughness index F in the same structure In consideration of the case where the combinations are different, five types of response characteristics C having different load-deformation relationships (capacity curves) C3 of the respective layers are used as shown in FIGS. 29 cases shown in Table 2 are created by changing the combination of the strength of the spectra Sa1 to San and the formation model U and the response characteristic C of the structure B in the engineering base, and for each case, the equations (11) and (12) The seismic performance index G was calculated using the formula.

  Moreover, in order to compare with the seismic performance index G using Formula (11) and Formula (12), the loss rate curve (fragility curve) shown in FIG. The earthquake LCC was calculated by the formula 3). FIG. 13C shows the standard fragility curve (High) of each component and the fragility curve (Low) of a component that is more easily lost for the four types of fracture modes of the low-rise RC rigid frame structure. For case 21, the earthquake LCC was calculated using the fragility curve (Low), and for the other cases, the earthquake LCC was calculated using the fragility curve (High). Further, by combining the response value of the excess probability of 10% (non-excess probability of 90%) on the fragility curve of FIG. 13C and the loss rate in each failure mode, the non-excess probability of 90% shown in FIG. A damage degree curve (varnarability curve) was created, and the earthquake PML was calculated from the loss rate corresponding to the maximum response value on the Varnarability curve.

  In calculating the earthquake LCC and the earthquake PML, in order to examine the difference in the usage of the structure, the acceleration type αai and the deformation type αdi of the constituent members and the ratio αi (= αai: αdi) are used for the cases 19 and 24-26. Is set to 3: 1 for factory use, and for cases 20 and 27 to 29, the acceleration type αai and deformation type αdi of the constituent members and the ratio αi (= αai: αdi) are set to 1: 3 for school use. It was. In addition, in order to examine the uneven distribution of the components in each layer in the multi-layered structure, the repurchasing price ratio of each floor of the three-layer structure is assumed to be unequal in cases 22 and 23, and The procurement price was assumed to be distributed evenly.

  FIG. 10A shows the relationship between the seismic performance index Gi calculated using the equation (11) for each layer i of the structure and the earthquake LCC for 29 cases in Table 2, and FIG. The relationship between the seismic performance index G calculated using equation (12) and the earthquake LCC for the entire object is shown. Both (A) and (B) of the figure show that the seismic performance index G tends to decrease as the seismic performance index G increases, and there is a correlation between the seismic performance index G according to the present invention and the seismic LCC. Was confirmed. In FIG. 10, the case 21 deviates from the tendency of the other cases, but this is considered to be due to the use of a different fragility curve (Low).

  FIG. 11A shows the relationship between the seismic performance index Gi calculated using the equation (11) for each layer i of the structure and the earthquake PML for 29 cases in Table 2, and FIG. The relationship between the seismic performance index G calculated using equation (12) and the earthquake PML for the entire structure is shown. FIGS. 6A and 6B also show that the seismic performance index G tends to decrease as the seismic performance index G increases, and it is confirmed that there is a correlation between the seismic performance index G and the earthquake PML according to the present invention. did it. However, the variation is larger than the correlation between the seismic performance index Gi and the earthquake LCC in FIG. The reason is that the earthquake LCC takes the expected value (average value) of the loss rate, while the earthquake PML takes one point on the Varnarability curve, so the slope of the response value risk curve changes suddenly. This is thought to be due to the large variation at each location. Also in FIG. 11, the case 21 deviates from the tendency of the other cases, which is considered to be due to the use of a different fragility curve (Low).

  FIG. 12A shows the seismic performance index Gai based on the expected acceleration response value Aai in equation (11) and the earthquake LCC (earthquake LCC calculated only for the acceleration type component) for each layer i in 29 cases of Table 2. (B) shows the relationship between the seismic performance index Gdi based on the deformation response expectation value Adi of equation (11) and the earthquake LCC (earthquake LCC calculated only for the deformation type component). From the figure, it can be seen that the relationship between the seismic LCC of each floor and each component and the seismic performance indexes Gai, Gdi is almost constant if the fragility curve and the replacement price ratio are the same. However, the range that the seismic performance index Gai of each layer i can take in the figure (A) is about -1.6 to -0.5, whereas the seismic performance index Gdi of each layer i in FIG. The possible range is about 4.2 to 6.6, and the seismic performance index Gdi occupies the seismic performance index G rather than the seismic performance index Gai because the absolute values of the values that can be realistically taken are different. It can be seen that the ratio is high.

  In FIG. 12, the cases 19 and 24 to 26 in which the proportion ratio αi of the constituent members is set to the factory use (acceleration type αai> deformation type αdi) are out of the tendency of the other cases. It can be seen that the cases 20 and 27 to 29 that are used (acceleration type αai <deformation type αdi) are also out of the tendency of other cases. Therefore, when the seismic performance index Gi was calculated using the equation (13) in which the earthquake response expected values Aai and Adi were exponentially weighted according to the ratio αi, the factory use cases 19 and 24 to 26 were changed to the other cases. The cases 20 and 27 to 29 for school use can be substantially matched with the tendency of the other cases. From this, by changing the weighting of the expected earthquake response values Aai and Adi according to the ratio ratio αi between the acceleration type αai and the deformation type αdi in each layer i of the structure B as shown in the equation (13), It was confirmed that the correlation between the seismic performance index G and the earthquake LCC can be enhanced.

  10 (B) and 11 (B), the seismic performance index G of the entire structure calculated using the equation (12) for cases 22 and 23 in which the repurchasing price ratio of each layer i is unequal. However, it can be seen that it is slightly different from the tendency of other cases. Therefore, when the seismic performance index G of the entire structure is calculated using the equation (14) in which the seismic performance index Gi of each layer i is exponentially weighted according to the cost ratio ri, the cases 22 and 23 tend to be the trends of the other cases. And almost matched. From this, by changing the weighting of the seismic performance index Gi of each layer i according to the cost ratio ri of each layer i of the structure B as shown in equation (14), the seismic performance index G of the present invention, the earthquake LCC, etc. It was confirmed that the correlation of the can be further improved.

The seismic performance index G of the present invention can be calculated if the response characteristic C by the structural member is determined even if the detailed specification and cost of the non-structural member and building equipment of the target structure B are unknown. It can be used effectively for the evaluation of seismic performance at the design stage where element specifications and costs are not determined. Moreover, because of the high correlation between the seismic LCC and seismic PML, unlike the seismic conventional emphasizing safety structure seismic index I _S in a conventional final state, damage to the front of the structure to the final state The included seismic performance can be accurately evaluated from the economical viewpoint.

  Thus, the provision of a “quantitative seismic performance evaluation program for a structure capable of accurately determining damage during an earthquake even at a stage where the specifications and costs of structural components of the structure are not determined” can be achieved.

  In step S106 of FIG. 2, the acceleration response expectation value Aa and the deformation response expectation value Ad are calculated from the maximum response acceleration Da for each layer i of the target structure B, the maximum interlayer deformation angle Dd, and the occurrence probability Dp. Instead of the occurrence probability Dp, the acceleration response expected value Aa and the deformation response expected value Ad may be calculated using the maximum response acceleration Da and the excess probability De of the maximum interlayer deformation angle Dd. In that case, as shown in FIG. 1, the expected value calculating means 30 is provided with an excess probability curve creating means 31, and the excess probability curve creating means 31 rearranges the maximum response acceleration Da of the target structure B in descending order to each excess. The probability De is obtained and plotted on a plane determined by the response value axis and the excess probability axis to create an excess probability curve P of the maximum response acceleration Da. Similarly, the maximum interlayer deformation angle Dd of the target structure B is rearranged in descending order to obtain each excess probability De, plotted on a plane defined by the response value axis and the excess probability axis, and plotted with the maximum interlayer deformation angle Dd. An excess probability curve P is created.

  FIG. 8 is a flowchart of a process of creating an earthquake risk curve P for each layer i of the target structure B by the excess probability curve creating means 31 from the maximum response acceleration Da (or the maximum interlayer deformation angle Dd) with the occurrence probability Dp. Indicates. First, in step S501, a plurality of acceleration response values Da with occurrence probabilities Dp (or deformation response values Dd) in a specific hierarchy are input, and response values Da with occurrence probabilities Dp arranged at random in step S502 are in descending order of response values Da. Rearrangement, The cumulative probability (excess probability) De of each response value Da is calculated along the order rearranged in step S503. In step S504, by plotting a set (Da, De) of each response value Da and the corresponding excess probability De on the XY plane determined by the response value axis (X axis) and the excess probability axis (Y axis), respectively. The excess probability curve P can be created. This excess probability curve P is the same as the earthquake risk curve P in FIG. 3, and as described above with reference to FIG. 3, the acceleration response value Da (or deformation response value Dd) of the excess probability curve P is used as the excess probability ΔDe. Is integrated to obtain the expected earthquake response value Aa (or Ad) of the acceleration response value Da (or deformation response value Dd). In step S504, excess probability curves Pa and Pd are created for acceleration response value Da and deformation response value Dd, respectively, and earthquake response expectation values Aa and Ad are obtained, and both are substituted into equation (11) or (13). Then, the seismic performance index G is calculated.

  Alternatively, as shown in step S505 in FIG. 8, a pair (Da, De) of each response value Da and the corresponding excess probability De is set in the order of the excess probability De in descending order of the excess probability axis (X axis) and the response value axis. The excess probability curve P may be created by plotting on the XY plane determined by (Y axis). Also in this case, by integrating the acceleration response value Da (or deformation response value Dd) of the excess probability curve P with respect to the excess probability ΔDe, the earthquake response expected value Aa (or Ad of the acceleration response value Da (or deformation response value Dd) is obtained. ). The excess probability axis (X axis) of the excess probability curve P in step S505 represents the excess probability of the response value Da (or Dd), and corresponds to the period for reproducing the earthquake motion. The response value axis (Y axis) of the excess probability curve P represents the magnitude of the response value Da (or Dd) and corresponds to the magnitude of earthquake damage. Therefore, when the excess probability axis and the response value axis are converted into the reproduction period axis and the earthquake damage axis, the excess probability curve P in step S505 can be considered as the relationship between the earthquake reproduction period and the damage (FIG. 9D and (See (E)).

  Conventionally, as shown in FIG. 9 (A), for example, an earthquake resistance matrix is defined in which the earthquake resistance of a structure is defined as a stepwise change in earthquake damage (damage) with respect to seismic intensity with different occurrence probabilities ( For example, Non-Patent Document 3). The seismic performance matrix in the figure shows the importance of the structure by the stepwise change of the combination of the four levels of seismic motion level expressed by the frequency of reproduction on the vertical axis and the four levels of earthquake damage (damage) on the horizontal axis. Three types of seismic performance (performance grades) T1, T2, and T3 are defined depending on the application. Each seismic motion level boundary in the seismic performance matrix M corresponds to each earthquake motion strength reproduction period (for example, 50% occurrence probability over 80%, 10%, 5%), and each seismic damage (damage) level boundary. Corresponds to the response reference value S corresponding to the structure type / type of the structure (for example, damage limit value, safety limit value, or safety margin margin values S1 to S5 provided at an appropriate ratio therebetween). ing. Therefore, as shown in the figure (B), the coordinates of the intersections R1 to R6 between the boundary line of the earthquake motion level and the boundary line of the earthquake damage level are set to the earthquake occurrence excess probability (80%, 10%, 5%) and the structure. If it is determined by the combination of the response reference values (S1 to S5) of objects (excess probability, response reference value), the earthquake recurrence period (X axis) and damage (Y axis) as shown in (C) of the figure A fixed seismic performance evaluation plane (XY plane) can be generated, and the seismic performance T1, T2, T3 can be defined by the seismic performance evaluation plane.

  The inventors of the present invention have an excess probability curve (earthquake) of the response acceleration Da (or interlayer deformation angle Dd) of the target structure B created in step S505 of FIG. 8 on the seismic performance evaluation plane as shown in FIG. By plotting the risk curve (P), a program for evaluating the seismic performance of the target structure B was developed and disclosed in Japanese Patent Application No. 2007-174927. FIG. 9D shows earthquake risk curves Pa and Pb of acceleration response values Da (or deformation response values Dd) of different target structures A and B on the earthquake resistance performance evaluation plane. The area surrounded by Pa and Pb and the reproduction frequency axis (X axis) corresponds to the acceleration response expected value Aa (or the deformation response expected value Ad). In the figure, the expected response value Aa (or Ad) is smaller in the earthquake risk curve Pb than the earthquake risk curve Pa, and the seismic performance index Ga (or Gd), which is the reciprocal thereof, is an earthquake risk curve than the earthquake risk curve Pa. Since Pb is larger, it can be seen that the target structure B is larger than the target structure A in the seismic performance index G calculated by the equation (13). That is, if the seismic risk curves Pa and Pb shown on the seismic performance evaluation plane as shown in FIG. 9D are used, the difference in the seismic performance index G between the target structure A and the target structure B is represented by a large area. It can be expressed qualitatively and visually as a difference in height.

  In addition, the seismic risk curves Pa and Pb in FIG. 9 (E) represent the excess probability curves of the acceleration response values Da (or deformation response values Dd) of the different target structures A and B as in FIG. Although shown on the evaluation plane, the area (namely, the acceleration response expected value Aa or the deformation response expected value Ad) surrounded by the earthquake risk curves Pa and Pb and the reproduction frequency axis (X axis) is the same. Shows the case. Since the expected response value Aa (or Ad) is the same, the seismic performance index G calculated by the equation (13) is the same value for the target structure A and the target structure B. It is difficult to determine the difference in seismic performance between the object A and the target structure B. However, if the earthquake risk curves Pa and Pb as shown in the figure are used, the target structure A has better seismic performance than the target structure B against rare earthquakes (relatively small earthquakes). It can be seen that the target structure B exhibits better seismic performance than the target structure A against extremely rare earthquakes (relatively large earthquakes). That is, both the magnitude of the seismic performance index G and the shape of the seismic risk curve P are calculated by calculating the seismic performance index G described above using the seismic risk curve P represented on the seismic performance evaluation plane as shown in FIG. It is possible to present and evaluate the seismic performance of a structure. The seismic performance evaluation means 40 of FIG. 1 indicates that the seismic performance index G and the seismic risk curve P and both are output to the output means 6 for presentation and judgment of the seismic performance.

It is a functional block diagram of one Example of the quantitative seismic performance evaluation program by this invention. It is an example of the flowchart of the quantitative seismic performance evaluation program by this invention. It is explanatory drawing of the response value of a structure using a stochastic ground motion, and its excess probability curve (earthquake risk curve). It is an example of the flowchart of an earthquake motion calculation means (program). It is explanatory drawing of an example of the response characteristic of the structure used by this invention. It is an example of the flowchart of a response value calculation means (program). It is explanatory drawing of an example of the earthquake motion with an occurrence probability used by this invention. It is an example of the flowchart of the preparation method of the excess probability curve of the response value of an acceleration and a deformation | transformation. It is explanatory drawing of the earthquake evaluation method using the excess probability curve of FIG. It is a graph which shows the correlation with the earthquake-resistant performance parameter | index G by this invention, and earthquake LCC. It is a graph which shows the correlation with the earthquake-resistant performance parameter | index G by this invention, and earthquake PML. It is a graph which shows the correlation with the acceleration response expectation value by this invention, a deformation response expectation value, and earthquake PML. It is explanatory drawing of an example of the conventional loss rate curve (fragility curve) and an event curve.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Computer 2 ... Input device 3 ... Output device 5 ... Input means 6 ... Output means 7 ... Storage means 10 ... Response value calculation means 11 ... Spectral response value calculation means 12 ... Time history waveform response value calculation means 20 ... Earthquake motion calculation means DESCRIPTION OF SYMBOLS 21 ... Response spectrum calculation means 22 ... Time history waveform calculation means 23 ... Ground amplification calculation means 30 ... Expected value calculation means 31 ... Excess probability curve creation means 40 ... Earthquake resistance performance evaluation means 41 ... Earthquake resistance performance index calculation means a ... Acceleration d ... Deformation Aa ... Expected acceleration response value Ad ... Expected deformation response value B ... Target structure C ... Response characteristics (structure model)
C1 ... Multi-mass point model C2 ... Restoring force characteristics of each member C3 ... Load-deformation relationship (capacity curve) of each layer
Ds ... Earthquake response value Da ... Maximum response value of acceleration (maximum response acceleration)
Dd ... Maximum response value of deformation (maximum interlayer deformation angle)
De ... Seismic response value occurrence probability Dp ... Seismic response value occurrence probability E ... Earthquake source data (seismic model) G ... Seismic performance index L ... Installation position (structure model) P ... Excess probability curve (earthquake risk curve)
t ... Service period (structure model) U ... Ground property data (ground model)
Vs ... Earthquake motion (response spectrum, time history waveform)
Vp: Probability of earthquake motion

Claims (9)

In order to evaluate the seismic performance of the target structure, the storage means for storing the installation position of the target structure, the service period, and the response characteristics to the ground motion, with a plurality of occurrence probabilities assumed within the service period at the installation position Response value calculating means for inputting a seismic motion and calculating a maximum response value with an occurrence probability of acceleration and deformation generated in the target structure according to the response characteristics, and within a service period from the maximum response value and the occurrence probability of the acceleration and deformation The expected value calculation means for calculating the expected earthquake response value of the acceleration and deformation generated in the target structure, and the seismic performance of the target structure is evaluated using the product of the expected acceleration response value of the acceleration and deformation or the inverse thereof as the seismic performance index. Quantitative seismic performance evaluation program for structures that function as performance evaluation means. The program according to claim 1, wherein the product of the expected earthquake response value or its inverse is a sum of logarithmic values of the expected earthquake response value or a negative value thereof. In the program according to claim 1 or 2, the storage means stores a ratio of the components of the target structure divided into an acceleration type that is easily damaged by acceleration and a deformation type that is easily damaged by deformation, and the performance evaluation means Quantitative seismic performance evaluation program for structures obtained by exponentially weighting or coefficient weighting the expected seismic response values of acceleration and deformation according to the ratio, and obtaining the seismic performance index by the weighted expected response values of acceleration and deformation . 4. The program according to claim 1, wherein when the target structure is a multi-layer structure, the response value calculation means calculates a maximum response value with an occurrence probability of acceleration and deformation for each layer, and calculates the expected value. The expected earthquake response value of acceleration and deformation is calculated for each layer by means, the seismic performance index is obtained for each layer by the performance evaluation means, and the seismic performance of the target structure is evaluated by the average value of the seismic performance index for each layer. Quantitative seismic performance evaluation program for structures. 5. The program according to claim 4, wherein the storage means stores a cost ratio for the entire layer of the target structure, and the performance evaluation means weights the seismic performance index for each layer by coefficient weighting or index weighting according to the cost ratio; Quantitative seismic performance evaluation program for structures that evaluates seismic performance of target structures based on the sum of weighted seismic performance indices for each layer. 6. The program according to claim 1, wherein the storage means stores the position / scale, occurrence probability, and distance attenuation formula of one or more hypocenters, the installation position of the target structure, and the position / scale of each seismic source. Based on the probability of occurrence and distance attenuation formula, there is a ground motion calculation means for calculating the response spectrum with the probability of occurrence of multiple ground motions at the installation location within the service period, and responds with the response spectrum with the probability of occurrence for each seismic source. Quantitative seismic performance evaluation program for structures input to value calculation means. The program according to any one of claims 1 to 5, wherein one or more fault models and past small / medium earthquake recorded waveforms or statistically processed artificial earthquake waveforms around the installation position of the target structure are stored in the storage means. And an empirical or statistical Green's function time history waveform calculation formula, and a plurality of assumed fault models, seismic waveforms and time history waveform calculation formulas within the service period at the installation position A quantitative seismic performance evaluation program for a structure provided with a ground motion calculation means for calculating a time history waveform with a probability of occurrence of ground motion for each hypocenter and inputting the time history waveform with a probability of occurrence for each seismic source into a response value calculation means. The program according to claim 6 or 7, wherein the storage means stores ground characteristics of the installation position of the target structure, and the seismic motion calculation means calculates a response spectrum or time history waveform for each seismic source and the ground characteristics of the installation position surface. A quantitative seismic performance evaluation program for structures obtained by calculating response spectra or time history waveforms. The program according to any one of claims 1 to 8, wherein the maximum response values with the acceleration and deformation occurrence probability calculated by the response value calculating means are rearranged in descending order to obtain respective excess probabilities, and the response value axis and the excess probability axis A creation means for creating an excess probability curve by plotting on a plane determined by the following is provided, and the target structure is within the service period from the acceleration and deformation maximum response value of the excess probability curve and the excess probability by the expected value calculation means. Quantitative seismic performance evaluation program for structures by calculating expected earthquake response values for acceleration and deformation.