The Concept of Validation Strategy about Fault Displacement Fragility Evaluation Methodology and its Application to Actual Damaged Structure

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1 The Conept of Validation Strategy about Fault Displaement Fragility Evaluation Methodology and its Appliation to Atual Damaged Struture Hideaki TSUTSUMI a, Yuji NIKAIDO b, Yoshinori MIHARA b, Ryusuke HARAGUCHI, Katsumi EBISAWA a a Central Researh Institute of Eletri Power Industry, Tokyo, Japan b Kajima Corporation, Tokyo, Japan Mitsubishi Heavy Industries, Ltd, Kobe, Japan Abstrat: The authors have onduted examination of fault displaement (FD) PRA methodology framework and identifiation of tehnial issues. As a part of the development, the authors are onfirming the validity of the Fault Displaement Fragility Evaluation Methodology (FDFEM) based on the atual damaged ase beause the unertainty to evaluate realisti response have alternatively been determined with referene to the values in seismi fragility evaluation methodology (SFEM) and have not been validated so far. Contrary to the fat that validation of SFEM is based on a number of shaking table test data and damage ases, the development of FDFEM should depend on a few damage ases and unprepared test data. In order to onfirm the feasibility of the omposition and proedures of the tentative FDFEM verifiation framework, the authors applied them to damage of Shin-Kang Dam in Chi-Chi Earthquake (Taiwan, 1999). Throughout this study, we got a prospet of the feasibility of the omposition and proedures of the tentative FDFEM validation framework. Keywords: Fault displaement PRA methodology, Fault displaement fragility evaluation methodology, Verifiation of evaluation methodology, Tentative verifiation proedure, Damage of hydroeletri power dam by Taiwan Chi-Chi earthquake. 1. Introdution The Chi-Chi Earthquake, a magnitude of 7.6, ourred in Taiwan in Sept During the event, dam and buildings have ollapsed by fault displaement (FD), and the influene of FD on strutures has attrated attention. Reently in Japan, interest on the impat of prinipal and seondary FDs on nulear failities has inreased, and it is urrently reognized as an urgent issue for investigation. The urrent status regarding FD PRA methodology in Japan is as follows. The Atomi Energy Soiety of Japan (AESJ) is onduting two ativities [1], [2]. Japan Soiety of Civil Engineers published researh report of FD evaluation that inluded investigation of Fault and FD, FD evaluation based on numerial analysis and experiment et. [3]. Also, the international onferene related to the trend of FD hazard inluding nulear power industry field were held in the United States[4]. The authors were onduting analysis and examination for developing fault displaement PRA methodology [5]. Under this ontext, the authors have onduted examination of FD PRA methodology framework and identified tehnial issues. As a part of the development, the authors are onfirming the validity of the Fault Displaement Fragility Evaluation Methodology (FDFEM) based on the atual damaged ase beause the unertainty to evaluate realisti response have alternatively been determined with referene to the values in seismi fragility evaluation methodology (SFEM) and have not been validated so far. Contrary to the fat that validation of SFEM is based on a number of shaking table test data and damage ases, the development of FDFEM should depend on a few damage ases and unprepared test data. In order to onfirm the feasibility of the omposition and proedures of the tentative FDFEM verifiation framework, the authors applied them to damage of Shin-Kang Dam in Chi-Chi Earthquake (Taiwan, 1999). Throughout this study, we got a prospet of the feasibility of the omposition and proedures of the tentative FDFEM validation framework. In this report, the basi poliy of development and validation strategy of FDFEM is desribed firstly and the appliation of the proedure to the ase of Shin-Kang Dam in Chi-Chi Earthquake (Taiwan, 1999) Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

2 2. The basi onept of validation strategy of fault displaement fragility evaluation methodology (FDFEM) in FD PRA and omposition and proedure of tentative FDFEM verifiation framework 2.1 The urrent status of fault displaement PRA and fragility evaluation methodology Sine the effet extent on the risk of nulear failities (e.g. Core Damage Frequeny) has not been obvious, priority is given to the development of reasonable framework. One the effet to the risk is signifiant, it will be refined. The FD PRA proedure onsists of aident senario identifiation, hazard evaluation, fragility evaluation and aident sequene evaluation as shown in Fig. 1. The evaluation proedure is basially the same as the framework of the earthquake and tsunami PRA proedure. Contrary to the fat that validation of SFEM is based on a number of shaking table test data and damage ases, the development of FDFEM should depend on a few damage ases and unprepared test data. Therefore, validation of FDFEM is onduted using atual damage ases of general industries around the world. Fig. 1 Proedure of Fault Displaement PRA 2.2 Basi onept of the validation strategy of fault displaement fragility evaluation methodology The authors propose the following basi onept of the validation strategy of FDFEM; (1) Sine the effet extent on the risk of nulear failities (e.g. Core Damage Frequeny) has not been obvious, priority is given to the development of reasonable framework. One the effet to the risk is signifiant, it will be refined (2) Validation of FDFEM is onduted using atual damage ases of general industries around the world. (3) Sine the design standards of nulear failities and general industrial failities may be different, the differene is onsidered as one of the epistemi unertainty fators. (4) Quantitative handling of epistemi unertainty fators in (3) is as follows. First, rough variation band is given as an initial value, and then repeats iteration several times based on the judgment of expert engineers, finally find the rational variation band. (5) The development of the FDFEM validation framework onsists of the following three stages. Stage1: Develop the tentative FDFEM validation framework Stage2: Apply the tentative framework to the atual damage ase and improve the framework Stage3: Apply the improved framework to the atual damage ase again and develop the final FDFEM validation framework Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

3 2.3 Struture and proedure of tentative FDFEM verifiation framework The tentative FDFEM validation framework is established based on the building fragility evaluation in the earthquake/tsunami PRA proedure briefly shown in the upper side of Fig.2 and the development of the validation framework onsists of the five steps and relationship of eah steps is shown on the lower side of Fig.2. Contrary to the flow down of the proedure of the SFEM, the framework itself, damage mode/part, a median image model, and the rational range of various influential parameters are set through the iteration proess with peer review. Additionally, FDFEM validation framework will be finalized by adjustment for nulear industry speified fault displaement fragility evaluation methodology desribed as Step5 in the Figure. (Proedure of Seismi/Tsunami Fragility Evaluation Methodology) (Struture and Proedure of FDFEM Verifiation Framework) Fig.2 Struture and Proedure of FDFEM Verifiation Framework ompared with Seismi/Tsunami Fragility Evaluation Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

4 The omponents of the steps as follows and details are desribed in the next hapter with the appliation example. Step1: Collet and analyze the findings of fault displaement damage Step1 onsists of following 3 items; Step1-1: Collet Damage Information/Data Step1-2: Strutural Damage Status Step1-3: Collet and Analyze of Observed Wave Step2: Set parameters to evaluate strength Step2 onsists of following 2 items; Step2-1: Identifiation of damaged part/mode Step2-2: Set tentative variation range of strength parameter for eah damaged part/mode Step3: Set parameters to evaluate response Step3 onsists of following 3 items; Step3-1: Set tentative response analysis model and input displaement 1) Set tentative response analysis model based on damaged part/mode identified in Step2-1 2) Set tentative input displaement based on Step1-3 3) Set variation of displaement onsidering unertainty of input displaement of 2) Step3-2: Set median image model in tentative displaement response analysis model 1) Set variation range of damage parameter based on damage mode identified in Step2-1 (from sketh data in survey report on damage ase et.) 2) Repeat iteration by sensitivity analysis so as to approximate the variety range set in 1) using the Step 3-1 tentative response analysis model 3) Set the median image model from the approximation result of 2), Step3-3: Identify important unertainty fators of the median image model and setting the range of tentative response parameter 1) Set the tentative range of response parameter for eah damaged part/mode after identifying important unertainty fators through the proedure in Step3-2 Step4: Set rational relationship between the parameters to evaluate the strength and response Step4 onsists of following 3 items; Step4-1: First analysis on overlap between the range of strength and response and setting unertainty fators whih have an impat on the overlap 1) As shown in Fig.3, the indiator of damage in struture is overlap of load strength apaity range and response range for eah damage mode. In other words, it is onsidered to be damaged when the response exeeds the strength. 2) Analyze the separation between the upper limit of the tentative range of response parameter for eah damage mode in Step3-3 and the lower limit of the tentative range of strength parameter for eah damage mode in Step2-2 (Fig.3) 3) Set the overlapping oeffiient. from the analysis of the unertainty fator onerning the separation in 2), the ratio of the upper limit value of the range of response and the lower limit value of the range of strength is set as Step4-2: Reestablish the overlap between the range of strength and response and setting unertainty fators whih have an impat on the overlap 1) Review Step2 and Step3-1 and re-exeute Step4-1as the overlapping oeffiient set in Step4-1-3) is not logial Step4-3: Set rules for the tentative framework 1) Set the method of finding the parameters neessary for evaluating the fragility of the struture. Assume that both the tentative range of response parameter for eah damage mode in Step3-3 and the lower limit of the tentative range of strength parameter for eah damage mode in Step2-2 follow a lognormal distribution. 2) The median and logarithm standard deviation of eah strength and response are obtained as follows. Eah median and logarithm standard deviation is obtained by two point estimation method using upper and lower limit values of the range of yield strength and response respetively. Divide Eah logarithm standard deviation into aleatory and epistemologial unertainty by SRSS method. Assume the overlapping oeffiient set in Step4-1-3) Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

5 Capaity, Response orrespond to the stress/response oeffiients in the fragility assessment. 3) In order to make the rules of Step4-3-1) and Step4-3-2) speified for nulear industry, onsider the epistemologial unertainty fator in basi poliy (3). Step5: Set nulear failities speified evaluation methodology for fault displaement fragility Establish evaluation methodology of nulear industry speified fault displaement fragility based on Step4-3. Firstly in this establishment, roughly divide into the differene between the nulear power industry speified one and others in the ontents relating strength term and response term. Then, identify the important unertainty fators of eah term, larify whihever have an impat, and onsider the epistemologial unertainty fator. Failure mode B Failure mode C Failure mode A : Unertainty range of Capaity : Unertainty range of Response Input Fault Displaement Fig.3 Conept of Overlap between the Range of Strength and Response Unertainty 3. Appliation of tentative FDFEM verifiation framework to the damage ase 3.1 Target ase and the progress of appliation In order to onfirm the feasibility of the omposition and proedures of the tentative FDFEM verifiation framework, the authors applied the proedure mentioned in previous hapters to the atually fault indued damage struture of the Shin-Kang Dam in Chi-Chi Earthquake (Taiwan, 1999). Chelongpu Fault whih is the low angle reverse fault shown in Fig.4 The reasons for hoie of the ase are that many related information is maintained. For instane, the fault itself, the surrounding topography / geologial struture, the shape and harateristis of the struture, the damage situation, and so on, by field survey after the earthquake, and the restoration work, et.as for progress of appliation, Step1 through Step 4-1 in hapter2.3 is being onsidered inluding quantitative evaluation, and Step4-2 through STEP 5 is in qualitative examination phase. This paper mainly refer to the former part of the progress..3.2 Step1 (Collet and analyze the findings of fault displaement damage) (1) Step1-1: Colletion of Damage Information/Data Fig.5 (a) shows the topologial relationship between the Chelongpu Fault and Shin-Kang Dam. The end of Chelongpu Fault nearby Shin-Kang Dam is branhed into three lines stated A, B, and C fault in Fig.5. The dam is loated between A and B fault. C fault is observed near the dam right bank. (2) Step1-2: Strutural Damage Status The length and height of Shin-Kang Dam are about 290 meters and about 27 meters respetively (Fig. 5 (b)). As shown in Fig. 5 (), the vertial slip fault struk at the point about 20 meters from the right side of the dam and 8 meters differential ourred at the point. As a result, the embankment body was destroyed and reservoir funtion was lost[6] and also, the rak ourred over the 270 meters of left embankment body due to the shortening of dam length of 6 meters in the axial diretion and 2 meters in the downstream diretion., The port of the intake tunnel (height 4 m, width 4 m) peeled off the tunnel main body and shifted about 30 m[7] Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

6 Chelungpu Fault Shin-Kang Dam Fig.4 Loation of Chelongpu Fault and Shin-Kang Dam in Chi-Chi Earthquake. Right Bank Fault C Fault Strike Zone Fault A Craked Zone Left Bank Fault B (a) Topologial Relationship of Chelongpu Fault and Shin-Kang Dam (b) Strutural Overview of Shin-Kang Dam () Damage Overview of Shin-Kang Dam Fig.5 Topologial Relationship of Chelongpu Fault and Shin-Kang Dam and Strutural and Damage Overview of Shin-Kang Dam Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

7 Veloity (m/s) Displaement (m) (3) Step1-3: Colletion and Analysis of Observed Wave As shown in Fig. 6 veloity and displaement waveforms are observed near Shin-Kang Dam. Time (s) Time (s) Fig.6 Observation Veloity and Displaement Waveforms 3.3 Step2: Set parameters to evaluate the strength (1) Step2-1: Identifiation of damaged part/mode Based on the damage situation of olleted Step1-2, severe damages of the dam body are mainly absorbed by the deformation of the ground and the dam body diretly above the C fault, and the dam body somewhat away from the C fault remains slightly raked and deformed. Therefore, as the damaged part/mode shown in Fig. 7, the following two ases were set separately for damage of the right bank ut-off dam body and rak of the left bank dam body. - Case A: Craking mode of the dam wall body with minor damage (deformation of about 1 m) - Case B: Funtional loss mode of the dam body and diretly above the fault Left Bank Case A CaseB Right Bank Fig.7 Identifiation of Damaged Part/Mode (2) Step2-2: Setting tentative variation range of strength parameter for eah damaged part/mode Assume that the onrete onstitutive law follows equation (1-1) to (1-4). In this report, we desribe only the average image of the median aording to the onstitutive law, the analysis of the range of parameters regarding strength is underway and will be reported next time. E 0 K (1-1) E p f 2 0 (1-2) peak K exp 1.25 peak peak p.86 peak 1 exp exp (1-3) peak 2 (1-4) Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

8 Comp. Stress (MPa) Tnsile Stress (MPa) Where, σ is ompressive stress (N/mm 2 ), ε is ompressive strain (mm/mm), ε peak is strain at ompressive strength(assumed to be 0.002), ε p is ompressive plasti strain (mm/mm), and K is the elasti stiffness residual rate. Fig. 8 (a) shows the ompressive stress - ompressive strain relationship, and Fig. 8 (b) shows the tensile - rak displaement relationship. As material properties of the ground, Young's modulus is 100 MPa at soft rok (shear wave veloity Vs 134 m/s), 8 GPa at hard rok (Vs 1200 m/s), Poisson's ratio 0.4, mass density is 2.0 ton / m 3, frition oeffiient Ground) is 0.4. Damage Fator Damage Fator Comp. Strain (a) Compressive Stress-Strain Curve (body) Crak Width (mm) (b) Tensile Stress-Crak Width Curve (body) Fig.8 Mehanial properties of onrete of dam body 3.4 Step3: Set parameters to evaluate response (1) Step3-1: Set tentative response analysis model and input displaement The response of the onrete struture is assumed to follow the onrete isotropi plastiity damage onstitutive law of Fig. 9. In this report, only the average image of the median aording to the onstitutive law is desribed and the analysis of the range of parameters regarding response is underway and will be reported next time. The numerial model is made by finite element method using isotropi plasti damage model shown in Fig. 10. Damage of onrete is aptured as a whole state by tensile, shear, and ompressive failure, and expressed as a diretion independent salar value. Derease in slope of unloading response is treated as redution rate of elasti rigidity (= damage value) of material and derease in elasti stiffness is expressed by two damage variables dt and d (0 to 1) on the tensile side and ompression side. These variables an be are funtions of plasti strain, strain speed and field variables. As an analysis method, time history response analysis method is hosen. Sine it involves large deformation, destrution and ontat-peel, an expliit method that an proeed stably and get solution even with a problem of strong nonlinearity is adopted. For the numerial analysis, the ommerial nonlinear finite element method ode Abaqus was used. The tentative input displaement was set based on STEP13. In this report, the variety of input displaement is not onsidered. Table 1 shows the details of the ut-off wall FEM model and the analysis ode. σt σt0 24 m E0 wt=1 w=0 (1-d)E0 (1-d)(1-dt)E0 w=0 E0 (1-dt)E0 ε w=1 E 0 :Initial Stiffness σ t0 :Tensile Strength σ u :Comp. Strength d t :Tensile Damage Fator d :Comp. Damage Fator w t :Stiff. Reovery Rate (Tension to Comp.) w :Stiff. Reovery Rate (Comp. to Tension) 14 m 36 m Fig.9 Cyli Constitutive Law of Conrete Fig.10 Outline of Dam Body FE Model Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

9 Table 1 Speifiations of FE model and method Model Element Node Element Type Constitutive Low Method Code Ver. Case A Case B C3D8R (Redued Integration) Conrete Isotropi Plastiity Damage Model Stress Deformation Analysis (Expliit/Large Deformation) Abaqus/Expliit 3DEXPERIENCE R2017x (2) Step3-2: Set median image model in tentative displaement response analysis model As the ondition for the alulation of rak damage (Case A), fored displaement 1m obtained by damage survey was given to the bottom of the body part shown in Fig. 11 (a). We performed iteration by sensitivity analysis to approximate the sketh of the ut-off wall rak shown in Fig. 11 (b). The analysis result is shown in Fig. 11 (). A median image model for ase A was set based on the analysis result. Downstream 図 解析 Bモデル図 Axial Fore Axial Fore Upstream Fored Displaement on Bottom (a) Crak analysis model(case A) (b) Outline of Sketh of Craks on Dam Body () Example of result of numerial analysis Fig.11 Crak Analysis Model, Crak Sketh and FE Analysis Result Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

10 As the ondition for the alulation of fault rise damage (Case B), the fault slip rate is 7.6 meters for vertial upward, 6 meters toward the dam axial diretion (left bank to right bank), the 2 meters toward downstream diretion, and the slip speed of 1 m/s. We performed iteration by sensitivity analysis so as to approximate the sketh or pitures of the damage of the dam body setion shown in Fig. 12 (b). The analysis results are shown in Fig. 12 (). Fig. 12 (d) shows the relationship between the hardness of the foundation ground and soft roks (shear rate Vs 134 m / s) and hard roks (Vs 1200 m / s) for ontat and peeling of the ut-off wall body and foundation ground as one example of many attempts of sensitivity analysis. In the ase of hard rok, the ground surfae tends to be hardly deformed and showed different state from survey. Throughout many attempts, a median image model was set. (a) Strike Slip Analysis Model () Outline of Sketh of Dam Blok Damage Damage Moved 2m Moved 4m Moved 7.6m (d) Numerial Analysis Results of Dam Body (d) Analysis Result of Contat/Peel of Dam Body and Supporting Ground Fig.12 Strike Slip Analysis Model, Sketh and Photo, and FE Analysis Result Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

11 Axial Fore (kn) Comp. Stress/stiffness (3) Step3-3: Identifiation of important unertainty fators of the median image model and setting Through the aumulation of interim ontent by sensitivity analysis in the median model setting, important unertainty fators are identified and the range of response in ases A and B have been studied. 3.5 Step4:Set rational relationship between the parameters to evaluate the strength and response (1) Step4-1: First analysis on overlap between the range of strength and response and setting As a riterion for reinfored onrete (RC) is shown and eah failure mode in the displaement urve (a: raking ourrene, b: reinforing steel yield, : maximum yield strength, d: Peeling of onrete, e: ollapse) in Fig.13 (left figure). Though there is a differene between reinfored and lean onrete, Point orresponds to ase A, Point b and orresponds to ase B were targeted. The progress of ollapse of the dam body an also be expressed by the FD-Axial Fore relationship shown in Fig. 13 (right). The loss-of-funtion modes from a through d and FE analysis results are shown in Fig.14. It is lear from the figure that the ompressive failure field generate in thinner and ompressive side by bending moment our by vertial slip at (a) of 60 m FD, then brittle destrution our through (b) of 150 m FD, after that area of destrution spread on right side of dam body keeping residual axial fore from () through (d) of 500 m FD. Sine these trends are similar to the general behavior of ompressive test for onrete speimen, they are onsidered as the reasonable image of the tentative median of responses. We also investigate the response range by using this median image making use of the model. It is under onsideration whether the range of lower limit value overlaps the upper limit value of the response and the range of the strength set in Step2-2. An oeffiient indiating the overlapping situation is also under onsideration. Max. Strength a b Crak Rebar Yeild Conrete Flaking d Collapse Displaement/ Curveture e a b Displaement/ Strain Fig.13 Funtion Loss Diagram RC (left) and LC Under Uniaxial Compression (right) d A A Damage Rate (0-1.0) Stiffness Redution B C D B C Damage Progress D Fault Displaement(m) Fig.14 Diagram of the relation between fault slip and axial fore in eah damage mode Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA

12 3.6 Step4-2: Reestablishment of overlap between the range of strength and response and setting Step4-3: Set rules for the tentative framework Step5: Set rules for the tentative framework Step4-2 and Step4-3 are prepared for further study based on the result from Step4-1. For Step5, we are also preparing to onsider the following ontents: In the stress term and the response term in the speifiations for the nulear power industry desribed in 2.3 (3), although the latter does not make a big differene, the former has an effet, whih is expeted to reflet the reognition on the next report. 4. Summary and future plan The results of this researh are as follows; 1) In addition to establishing basi poliies for FDFEM verifiation, proposed the omposition and proedure of the tentative FDFEM verifiation framework. The onfiguration/proedure onsists of 5 Steps. 2) In order to onfirm the feasibility of the omposition and proedures of the tentative FDFEM verifiation framework, the authors applied the proedure mentioned in previous hapters to the atually fault indued damage struture of the Shin-Kang Dam in Chi-Chi Earthquake (Taiwan, 1999). Chelongpu Fault. The sope of its appliation in this paper is in the middle of Step4. 3) As important data of the Shin-Kang Dam, the surrounding topography / geologial struture, the shape and harateristis of the struture, and the damage situation were published. Thus we ould ondut various and valuable studies on the tentative FDFEM verifiation framework using these piees of information. 4) Through this appliation, the prospet of the feasibility of FDFEM was obtained. In the future, we will arry out the final Step5 and improve the omposition and proedures of the tentative FDFEM verifiation framework. Improvement onfiguration proedure will be applied to ondut FDFEM for nulear faility and promoted for pratial appliation. Aknowledgements This study was onduted as the preparation projet regarding nulear power plant risk assessment and study under the Ageny for Natural Resoures and Energy, Ministry of Eonomy, Trade and Industry. The authors hereby express gratitude to the organizations and all who supported the projet. The authors are also grateful to Emeritus Professor Tatsuo Ohmahi(Tokyo Institute of Tehnology) and Emeritus Professor Kazuo Konagai(University of Tokyo) for providing preious data and suggestive advies for this paper. Referenes [1] Atomi Energy Soiety of Japan (AESJ), Implementation standard for proedure of seismi probabilisti risk assessment for nulear power plants, (In Japanese), (2015) [2] AESJ, Report on development risk evaluation methods and measures for fault movement by engineering approah, (In Japanese), (to be published) [3] Japan Soiety of Civil Engineers, Researh report of fault displaement evaluation, (In Japanese), (2015) [4] Fault Displaement Hazards Analysis Workshop Organizing Committee, Fault Displaement Hazards Analysis Workshop, Menlo Park, CA, (2016). [5] Katsumi Ebisawa, et al., Analysis and examination for developing fault displaement PRA methodology, PSA2017, (2017). [6] Kazuo Konagai et al: About the damage of the Shin-Kang Dam in Chi-Chi Earthquake (preliminary report),dai-dam No.171,2000, (In Japanese) [7] Tatsuo Ohmahi: Damage of dam aused by Chi-Chi Earthquake,Dam Engineering Vol.10,1999, (In Japanese) Probabilisti Safety Assessment and Management PSAM 14, September 2018, Los Angeles, CA