JP6239255B2 - Evaluation method of expected damage due to liquefaction in liquefaction countermeasure method - Google Patents

Description

  The present invention is a method for deriving the expected loss for each liquefaction countermeasure construction method for ground reinforcement and liquefaction countermeasure methods for examining the cost effectiveness of the liquefaction countermeasure construction method, and the expected damage amount during a certain service period It is related with the evaluation method of the expected damage due to liquefaction for each ground reinforcement and liquefaction countermeasure construction method.

  Conventionally, methods for evaluating the risk of liquefaction based on seismic intensity and ground conditions and methods for evaluating the probability of occurrence of earthquakes have been proposed. For example, there are a plurality of methods for evaluating the liquefaction risk such as the FL method and the PL method.

JP 2011-0747414 A JP 2002-024481 A

Seismic hazard station J-SHIS HP: http://www.j-shis.bosai.go.jp/ Public data

  As mentioned above, liquefaction risk assessment methods and earthquake occurrence probability assessment methods have been proposed individually, but methods for deriving expected losses in liquefaction, especially ground reinforcement and liquefaction countermeasures. A method for deriving the expected loss of liquefaction for each method has not been proposed. In order to appropriately examine the cost effectiveness of the liquefaction countermeasure method, it is necessary to accurately determine the expected loss of liquefaction for each ground reinforcement and liquefaction countermeasure method.

  As described above, there are multiple methods for evaluating the risk of liquefaction, but there is no method for evaluating the probability of occurrence of liquefaction on the target ground considering the probability of earthquake occurrence. There is no known way to calculate the expected damage due to.

An object of the present invention is to propose a method for evaluating the expected liquefaction loss of a liquefaction countermeasure method, which can accurately determine the expected loss when liquefaction occurs for each ground reinforcement or liquefaction countermeasure method.
Another object of the present invention is to provide a method for evaluating the expected damage due to liquefaction in the liquefaction countermeasure method, which can accurately determine the expected damage due to liquefaction for t years for each ground reinforcement or liquefaction countermeasure method. It is to propose.

The method for evaluating the expected damage due to liquefaction of the liquefaction countermeasure method of this invention is as follows:
Calculate the average and standard deviation of the maximum slope angle of the site at the time of past liquefaction for each ground reinforcement and liquefaction countermeasure construction method, and lognormal distribution etc. so that the probability of occurrence of the maximum slope angle due to liquefaction becomes 1 (S1) for modeling the building damage probability in the case of liquefaction for each area reinforcement and liquefaction countermeasure construction method with the probability density function of
A process (S2) of modeling a building repair cost according to the degree of damage to the building per building area by using past recovery cost data at the time of liquefaction, etc.
For each ground reinforcement and liquefaction countermeasure construction method, integrate the product of the "building damage probability when liquefied" obtained by each modeling and the "building repair costs according to the degree of building damage", And a step (S3) of setting the calculated integrated value to an expected loss when liquefaction occurs in the ground reinforcement or liquefaction countermeasure method.
In the process of modeling the building damage probability (S1), a plurality of types of construction methods, which are different construction methods for ground reinforcement or liquefaction countermeasures, and a case without reinforcement are modeled by a common method, Curves showing the relationship between the maximum inclination angle and the building damage probability modeled for each method and the case without reinforcement are also shown on the same graph.
In the process of obtaining the expected loss amount, the expected loss amount is calculated for each of the plurality of methods and the case without reinforcement, and the calculation result of the expected loss amount for each method and without reinforcement is the same graph. It is written together.

  According to this method, the “building damage probability when liquefied” is determined for each ground reinforcement and liquefaction countermeasure method, and this “building damage probability when liquefied” and “building repair costs according to the degree of damage” Therefore, the expected loss amount at the time of liquefaction occurrence can be obtained for each ground reinforcement or liquefaction countermeasure construction method. In addition, since the building damage probability and the building repair cost are both obtained from liquefaction damage data due to earthquakes that have actually occurred in the past, they are highly reliable values. In both cases, the expected loss at the time of liquefaction is obtained using highly reliable values, so the calculated expected liquefaction loss is highly reliable, and liquefaction occurs in the liquefaction countermeasure method. The expected loss amount can be accurately evaluated.

In the evaluation method of the present invention, the ground reinforcement is calculated based on a product of “probability of liquefaction of the target ground in t years (t: arbitrarily set target period)” and the “expected loss when liquefaction occurs”. In addition, a process (S4) of making an expected damage amount due to liquefaction for t years in the liquefaction countermeasure method may be included.
The “probability of liquefaction of the target ground” is obtained, for example, by obtaining an earthquake hazard curve from a hazard map or the like released by J-SHIS.
Thus, in order to obtain the expected damage due to liquefaction for t years using the probability that the target ground will be liquefied and the expected loss at the time of liquefaction, the earthquake risk of the area and the liquefaction risk of the ground will be calculated. The liquefaction countermeasure method can be selected based on this.
For this reason, the liquefaction countermeasure method can be selected more accurately.

According to the method for evaluating the expected damage due to liquefaction of the liquefaction countermeasure method of this invention, for each of the ground reinforcement and liquefaction countermeasure method, the building repair probability according to the building damage probability and the degree of building damage in the case of liquefaction To calculate the expected loss at the time of liquefaction for each ground reinforcement or liquefaction countermeasure method. it can. In addition, the building damage probability and building repair cost are both highly reliable because they are obtained from liquefaction damage data due to earthquakes that have actually occurred in the past, so the expected loss amount obtained using these values. Is reliable and accurate. Therefore, the cost-effectiveness of the liquefaction countermeasure method can be obtained appropriately.
When the expected damage due to liquefaction for t years is calculated from the probability that the target ground will liquefy in t years and the expected loss when the liquefaction occurs, the earthquake risk of the area and the risk of liquefaction of the ground The liquefaction countermeasure method can be selected based on the degree.

It is a flowchart which shows the evaluation method of the expected damage amount by liquefaction of the liquefaction countermeasure construction method which concerns on one Embodiment of this invention. It is a graph which shows the distribution of the maximum inclination angle at the time of liquefaction generation | occurrence | production for every ground reinforcement and liquefaction countermeasure construction method calculated | required in the process of the same evaluation method. It is a graph which shows the probability distribution of the maximum inclination angle at the time of liquefaction generation calculated | required in the process of the same evaluation method. It is a graph which shows the building repair cost according to the damage degree calculated | required in the process of the evaluation method. It is a graph which shows the expected loss amount for every ground reinforcement and liquefaction countermeasure construction method at the time of liquefaction calculated | required in the process of the same evaluation method. It is a graph which shows the expected damage amount by liquefaction of t years calculated | required in the process of the evaluation method. It is a flowchart which shows the example of the method of calculating | requiring the probability that a target ground will liquefy in t years used in the process of the evaluation method. It is a graph which shows the example of the curve used as PL value information which is a liquefaction determination parameter | index used for the method of calculating | requiring the liquefaction probability. It is a graph which shows the example of the liquefaction risk degree curve calculated | required in the middle process in the method of calculating | requiring the liquefaction probability. It is a graph which shows the example of the earthquake hazard curve used for the method of calculating | requiring the same liquefaction probability. It is a graph which shows the example of generation | occurrence | production probability of the ground motion of the object period calculated | required in the middle process in the method of calculating | requiring the liquefaction probability. It is a graph which shows the example of the liquefaction generation | occurrence | production probability of the object period calculated | required with the method of calculating | requiring the liquefaction probability. It is a graph which shows the relationship between the damage probability curve at the time of liquefaction, and building repair expense.

  An embodiment of the present invention will be described with reference to the drawings. The method of evaluating the expected damage due to liquefaction in this liquefaction countermeasure construction method can be summarized as follows: For each type of ground reinforcement, the expected loss at the time of liquefaction is expressed as “building damage probability when liquefied” Calculated as the integrated value (area in Fig. 5) of the product with "building repair costs according to the degree of damage to the building", and the expected loss amount and the probability of earthquake occurrence (probability that the target ground will liquefy in t years) ) And the expected damage due to liquefaction for t years.

This method includes the following steps (S1) to (S4).
A process of modeling the building damage probability when liquefied (S1).
A process of modeling building repair costs according to the degree of building damage (S2).
-The process of obtaining the "expected loss when liquefaction occurs" from "building damage probability when liquefied" and "building repair costs according to the degree of building damage" obtained by each modeling (S3) .
A process of obtaining the expected damage due to liquefaction for t years (S4).
The processes in the steps (S1) to (S4) are performed using a computer.

  In the process of modeling the building damage probability in the case of liquefaction (S1), the average and standard deviation of the maximum inclination angle of the site at the time of past liquefaction is calculated for each ground reinforcement and liquefaction countermeasure method, and liquefaction The probability of building damage in the case of liquefaction is modeled by a probability density function such as lognormal distribution so that the occurrence probability of the maximum inclination angle by 1 is liquefied for each local reinforcement or liquefaction countermeasure method.

That is, in the process of modeling the building damage probability in the case of liquefaction (S1), the degree of building damage due to liquefaction is considered as the maximum inclination angle of the ground (= maximum inclination angle of the building), and actual liquefaction damage Model using data.
Specifically, first, as shown in FIG. 2, the distribution of the maximum inclination angle by the ground reinforcement and the liquefaction countermeasure method at the time of the past large earthquake is examined. The ground reinforcement and liquefaction countermeasure methods are, for example, each type (A method, B method) when there is no ground reinforcement and when there is ground reinforcement.

For each ground reinforcement or liquefaction countermeasure method, the average μ of the maximum inclination angle of the site at the time of past liquefaction and the standard deviation σ are calculated.
For example, in order to model with a logarithmic normal distribution probability density function, it is converted into a logarithmic mean λ and a logarithmic standard deviation ζ by the following equations.
λ = ln (μ) −0.5 × ζ ²
ζ = √ (ln (1+ (σ ² / μ ² ))

Then, for each ground reinforcement and liquefaction countermeasure method, the probability of occurrence of the maximum inclination angle x due to liquefaction is modeled with a probability density function such as a logarithmic normal distribution represented by the following equation (1) so that the area becomes 1 Turn into.
P _f (x) = Φ [{ln (x) −ln (λ)} / ζ] (1)

In the process of modeling the building repair cost according to the degree of damage (S2), the repair cost data according to the degree of building damage per building area is modeled using the restoration cost data at the time of past liquefaction. .
Specifically, as shown in FIG. 4, the repair cost for the maximum inclination angle is modeled by actually using data necessary for recovery from liquefaction damage.
Since the recovery cost is considered to depend on the building area, it is assumed to be a cost per unit of building area, for example, 1 m ² .
An approximate expression is created from the distribution diagram (FIG. 4) of the relationship between the maximum inclination angle and the restoration cost for the building area, and this approximate expression is used as a model for building repair costs according to the degree of damage.

  In the process of obtaining the “expected damage amount at the time of liquefaction” (S3), the “building damage probability in the case of liquefaction” obtained by the above modeling for each ground reinforcement or liquefaction countermeasure construction method and the above Integrate the product with “building repair costs according to the degree of building damage”, and use the calculated integrated value (the area enclosed by each curve and the horizontal axis in FIG. 5) for the liquid in the ground reinforcement and liquefaction countermeasure methods. The expected damage amount at the time of occurrence

That is, the expected loss amount corresponding to the type of ground reinforcement is obtained by “the probability of building damage in the case of liquefaction” × “building repair cost according to the degree of building damage”.
For example, assuming that “building damage probability when liquefied” is Pf (x) and “building repair cost according to the degree of damage” is Cl (x), the expected loss Cliq when liquefied is expressed by the following formula ( 2) Find from.
Cliq = ∫ (Pf (x) × Cl (x)) dx Equation (2)
The integral value Cliq in the above equation (2) indicates an area surrounded by each curve and the horizontal axis in FIG.

  In the process of obtaining the expected damage amount at the time of occurrence of liquefaction for t years (S4), “probability that the target ground will liquefy in t years (t: target period set arbitrarily (for example, service period))”, Based on the product of the “expected loss at the time of liquefaction”, the expected damage amount due to liquefaction for t years in the ground reinforcement or liquefaction countermeasure construction method is used.

The expected damage due to liquefaction for t years according to the ground reinforcement and liquefaction countermeasure construction method is obtained by “probability of liquefaction in t years” × “expected loss when liquefaction occurs”.
For example, if “probability of liquefaction in t years” is Pliq (t) and “expected loss when liquefied” is Cliq, the expected damage Eliq (t) due to liquefaction is calculated by the following equation (3). Desired.
Eliq (t) = Pliq (t) × Cliq Equation (3)

FIG. 6 is a graph showing an example of the expected damage amount due to liquefaction for t years for a certain ground reinforcement type A and no countermeasures obtained in this way.
In addition, the probability that the target ground is liquefied is obtained, for example, by obtaining an earthquake hazard curve from a hazard map or the like released by J-SHIS.

According to this method, the “building damage probability when liquefied” is determined for each ground reinforcement and liquefaction countermeasure method, and this “building damage probability when liquefied” and “building repair costs according to the degree of damage” Therefore, the expected loss amount at the time of liquefaction occurrence can be obtained for each ground reinforcement or liquefaction countermeasure construction method.
Since the building damage probability and the building repair cost are both obtained from liquefaction damage data caused by earthquakes that have actually occurred in the past, the building damage probability and the building repair cost are highly reliable values. In both cases, the expected loss at the time of liquefaction is calculated using highly reliable values, so the calculated expected liquefaction loss is highly reliable, and the expected liquefaction loss of the liquefaction countermeasure method is calculated. Evaluation can be performed with high accuracy.
In addition, in order to obtain the expected damage due to liquefaction for t years using the probability that the target ground will liquefy and the expected loss at the time of liquefaction occurrence, the earthquake risk of the area and the liquefaction risk of the ground were taken into account. The liquefaction countermeasure method can be selected.

In this way, it is possible to select a liquefaction countermeasure method based on the seismic risk of the area and the possibility of liquefaction of the ground, as well as the probability of damage to the building based on the data of liquefaction damage caused by the actual earthquake. Since repair costs are sought, it becomes a reliable evaluation method.
Conventionally, there is no known method for evaluating the probability of occurrence of liquefaction in the target ground taking into account the probability of occurrence of an earthquake, and a method for calculating the amount of damage. A countermeasure method can be selected.

  Next, an example of a method for obtaining the probability that the target ground liquefies during the target period (t years) will be described with reference to FIG. This method is a method proposed in the previous application (Japanese Patent Application No. 2013-029739). For example, an earthquake hazard curve is obtained from a hazard map or the like published by J-SHIS, and obtained as follows.

An outline of a method for obtaining the probability that the target ground liquefies during the target period (t years) is as follows.
A liquefaction determination value information acquisition process (R1) for acquiring liquefaction determination value information indicating a liquefaction determination index indicating the risk of liquefaction of the target ground with respect to the seismic intensity index S;
A liquefaction risk curve conversion step (R2) for converting the liquefaction determination value information into a probability of occurrence of a liquefaction risk;
An earthquake hazard curve acquisition process (R3) for acquiring an earthquake hazard curve indicating the relationship of the excess probability to the seismic intensity index S of the target ground;
The seismic motion occurrence probability conversion process (R4) for obtaining the seismic motion occurrence probability during the target period t from the acquired earthquake hazard curve,
The liquefaction occurrence probability calculation process during the target period (R5) for obtaining the liquefaction occurrence probability during the target period t by multiplying the obtained liquefaction risk and the earthquake occurrence probability and integrating with the seismic intensity index S. ), And.
In FIG. 1, the process consisting of the above process (R1) and the process (R2) and the process consisting of the process (R3) and the process (R4) are reversed in parallel with each other. You can go.

  In FIG. 7, in the liquefaction determination value information acquisition process (R1), the liquefaction determination index indicating the risk of liquefaction of the target ground with respect to the seismic intensity index S is set according to the degree of the seismic intensity index S. This is a process of obtaining the liquefaction judgment value information shown. For example, as shown in FIG. 8, the liquefaction determination value information is information including a graph in which the seismic intensity index S on the horizontal axis is the maximum ground motion acceleration PGA, and the PL value is the liquefaction determination index on the vertical axis. .

  The liquefaction determination index may be an index used in an evaluation method based on the PL method, which is a conventional liquefaction determination method. The PL method is an index for determining the risk of liquefaction of the target ground with respect to the assumed seismic intensity. The seismic intensity is the maximum ground acceleration PGA. The liquefaction determination index PL is, for example, a value determined by the following equation (1).

According to the PL method, it is possible to evaluate if the N value (an index indicating the strength of the ground, which is obtained by a standard penetration test) and the soil quality according to the depth of the groundwater level and the ground surface depth are known. Other parameters (such as fine particle content and density) required for the calculation by the PL method may be extracted from an appropriate database.
For the above reasons, it is also possible to use the results of SWS (Swedish Sounding Test). This is because the converted N value can be used.
The earthquake type (inland or trench type) required by the PL method is determined from the degree of influence of the earthquake category on the seismic hazard curve.

  In addition, as an evaluation example for evaluating the liquefaction occurrence probability using the liquefaction determination standard used in the PL method, there are examples shown in the following Tables 1 and 2. Table 1 shows the groundwater level, N value, and soil quality in the target ground. Table 2 shows liquefaction criteria for Saitama Prefecture.

  Note that the liquefaction determination index may be an FL method that is a past liquefaction determination method, a method based on landform classification, or the like.

  In FIG. 7, a liquefaction risk level curve conversion process (R2) is a process of converting the liquefaction determination value information into a liquefaction risk level indicated by an occurrence probability. For example, it converts into the liquefaction risk level curve shown in FIG. This liquefaction risk level curve is a curve representing the probability of liquefaction with respect to the maximum ground motion acceleration (PGA).

  The liquefaction determination curve (PL value information) based on the PL value with respect to the maximum ground acceleration (PGA) is as described above with reference to FIG. 8, but this is used as a liquefaction determination criterion in the liquefaction risk curve conversion process (R2). Based on this, the vertical axis is converted into occurrence probability. For example, the conversion process is performed by setting PL = 5 to 50% and PL = 15 to 100%. The conversion result may be replaced with a lognormal distribution, or the vertical axis may be converted into an occurrence probability with the shape shown in FIG.

For example, the conversion is performed by the following equation.
Plr = PL × 0.1 (PL ≦ 5)
Plr = 0.5 × (PL −5) × 0.1 +0.5 (5 <PL ≦ 15)
Plr = 1 (15 <PL)

  In FIG. 7, the seismic hazard curve acquisition process (R3) acquires an earthquake hazard curve indicating the relationship of the excess probability to the maximum ground motion speed PGV of the target ground, and the seismic intensity index corresponding to the maximum ground motion speed PGV and the liquefaction occurrence probability. This is a process of converting to S. FIG. 10 shows an example of an earthquake hazard curve. The “excess probability” is the probability of the earthquake, for example, the annual excess probability. The method of obtaining the earthquake hazard curve may be a method of obtaining an already created earthquake hazard curve by inputting it to a computer (not shown) used for processing of this evaluation method via a communication network or the like. Moreover, it is good also as a method of creating by calculating from appropriate input information with a computer.

The earthquake hazard curve may be obtained from, for example, a hazard map published by J-SHIS.
When creating an earthquake hazard curve, for example, the latitude, longitude, and ground amplification factor are obtained from the database from the information such as the address of the target point entered in the computer (prefecture, municipality, town chome data), and nearby Active fault information (predicted seismic intensity, estimated distance / depth / magnitude / probability of occurrence) is obtained from the database, analyzed, and created. For the database and analysis, for example, fault data and calculation methods published by the Ministry of Education, Culture, Sports, Science and Technology Earthquake Research Promotion Headquarters are used.

  In FIG. 7, the seismic motion occurrence probability conversion process (R4) is performed by differentiating the excess probability with the seismic intensity indicator S in the equation showing the seismic hazard curve for the seismic intensity indicator S corresponding to the liquefaction occurrence probability. 11 is a process for obtaining the seismic motion occurrence probability during the target period t with respect to the maximum ground motion acceleration PGA as shown in FIG.

In FIG. 7, the liquefaction occurrence probability calculation process (R5) during the target period is obtained by multiplying the liquefaction risk obtained in each of the conversion processes (R2) and (R4) and the occurrence probability of earthquake motion. This is a process of obtaining the liquefaction occurrence probability during the target period t by integrating with the index S.
The liquefaction occurrence probability during the target period t is shown, for example, as a graph with the maximum ground motion acceleration PGA on the horizontal axis and the probability density on the vertical axis as shown in FIG. 12, and the area in the probability density curve is the target. It becomes the liquefaction occurrence probability during the period t.

The process of multiplying the liquefaction risk degree Plr and the earthquake motion occurrence probability Per and integrating with the earthquake motion intensity index S is performed by the following equation, for example.
Pliq = ∫ (Per × Plr) ds

  According to this liquefaction occurrence probability evaluation method, the liquefaction occurrence probability at the target point during the target period t based on the seismic motion occurrence probability can be evaluated in this way. Therefore, it can contribute to various construction and civil engineering projects.

S1: A process for modeling the probability of building damage when liquefied S2: A process for modeling building repair costs according to the degree of damage S3: A process for setting the expected loss when liquefaction occurs S4: Liquefaction for t years R1: Liquefaction judgment value information acquisition process R2: Liquefaction risk curve conversion process R3: Seismic hazard curve acquisition process R4: Earthquake motion occurrence probability conversion process R5: Liquefaction occurrence probability calculation process during the target period

Claims (2)

Calculate the average and standard deviation of the maximum slope angle of the site at the time of past liquefaction for each ground reinforcement and liquefaction countermeasure construction method, and lognormal distribution etc. so that the probability of occurrence of the maximum slope angle due to liquefaction becomes 1 In the probability density function, the process of modeling the building damage probability in the case of liquefaction, for each local reinforcement and liquefaction countermeasure method,
A process of modeling building repair costs according to the extent of building damage per building area, using past recovery costs data during liquefaction,
For each ground reinforcement and liquefaction countermeasure construction method, integrate the product of the "building damage probability when liquefied" obtained by each modeling and the "building repair costs according to the degree of building damage", The process of setting the calculated integral value as the expected loss when liquefaction occurs in the ground reinforcement or liquefaction countermeasure method,
Viewing including the door,
In the process of modeling the building damage probability, a plurality of types of construction methods, which are different methods for ground reinforcement or liquefaction countermeasures, and a case where there is no reinforcement are modeled by a common method, and each method is reinforced. A curve showing the relationship between the maximum inclination angle and the building damage probability, modeled with no case, is shown on the same graph.
In the process of obtaining the expected loss amount, the expected loss amount is calculated for each of the plurality of construction methods and the case without reinforcement, and the calculation result of the expected loss amount for each construction method and the case without reinforcement is shown in the same graph. Along with
Evaluation method of expected damage due to liquefaction by liquefaction countermeasure method. In the method for evaluating the expected damage due to liquefaction of the liquefaction countermeasure method according to claim 1,
Based on the product of “probability of liquefaction of target ground in t year (t: arbitrarily set target period)” and “expected damage amount when liquefaction occurs”, t in the ground reinforcement and liquefaction countermeasure construction method The expected damage due to annual liquefaction
Evaluation method of expected damage due to liquefaction by liquefaction countermeasure method.

Images