International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Load combination of aftershocks and tsunami for tsunami-resistant design Choi, Byunghyun; Nishida, Akemi; Itoi, Tatsuya; Takada, Tsuyoshi Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  1 Load Combination of Aftershocks and Tsunami for Tsunami-resistant Design Byunghyun Choi Center for Computational Science and e-Systems, Japan Atomic Energy Agency, Kashiwa, Japan Akemi Nishida Center for Computational Science and e-Systems, Japan Atomic Energy Agency, Kashiwa, Japan Tatsuya Itoi Associate Professor, Graduate School of Engineering, the University of Tokyo, Tokyo, Japan Tsuyoshi Takada Professor, Graduate School of Engineering, the University of Tokyo, Tokyo, Japan ABSTRACT: Occurrence of huge tsunami and numerous aftershocks are expected after a gigantic subduction earthquake occurs. Therefore, the important coastal structures (tsunami refuge buildings, seawalls and nuclear power plants etc.) must be designed against tsunami as well as ground shaking. In tsunami-resistant design, it is needed to consider that tsunami may arrive at the structure in a short time after the mainshock from the experience of 2011 Tohoku earthquake. When the action effects both from aftershocks and tsunami to the structure occur simultaneously, practically reasonable assessment of load combination from aftershocks and tsunami is needed. In order to treat the load combination problem reasonably, stochastic load combination technique can be used, which requires stochastic modeling of action effects from aftershocks and tsunami. Once the combined action effect is estimated reasonably, the reliability analysis follows, where load and resistance factors can be obtained under the condition that the conditional target reliability for a limit state function is given. Load combination method of aftershocks and tsunami on the tsunami-resistant design is demonstrated at some sites in Japan. Finally, load and resistance factor design format for the tsunami-resistant design is proposed.  1. INTRODUCTION After a gigantic subduction earthquake (e.g., 2011 Tohoku earthquake) occurs, the occurrence of tsunami is expected along with many aftershocks that follow. If an important structure is located at seashore, the structure must be designed against tsunami as well as ground motion. And even if seismic design and tsunami-resistant design have been designed respectively, if the aftershock and tsunami occur at the same time, how should it be designed? In tsunami-resistant design, it is needed to consider that tsunami may arrive at the structure in a short time after the mainshock (from a few minutes to a few hours) from the experience of 2011 Tohoku earthquake. Therefore, both aftershocks and tsunami should be considered simultaneously for designing facilities located at seashore such as tsunami refuge buildings, seawalls and nuclear power plants etc. When the action effects both from aftershocks and tsunami to the structure occur simultaneously, practically reasonable assessment of load combination from aftershocks and tsunami is needed. In order to treat the load combination problem reasonably, stochastic load combination technique can be used, which requires stochastic modeling of action effects from aftershocks and tsunami. To do so, the authors developed the probabilistic aftershock hazard analysis method which calculates the relationship between the ground motion intensity due to the aftershocks 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  2 and their exceedance probability under the condition of a specified mainshock. Wave height of tsunami due to the mainshock depends on the distance from the epicenter of the mainshock and its magnitude can be given by the tsunami height attenuation law proposed elsewhere. Once the combined action effect is estimated reasonably, the reliability analysis follows, where load and resistance factors can be obtained under the condition that the conditional target reliability for a limit state function is given. Load combination method of aftershocks and tsunami on the tsunami-resistant design is demonstrated at some sites in Japan. Finally, load and resistance factor design format for the tsunami-resistant design is proposed. 2. METHODOLOGY 2.1. Proposed framework for load combination The concept of aftershocks and tsunami load combination is shown in Figure 1. First, the maximum tsunami arrival time in the evaluation site is expressed as elapsed time ta from the mainshock occurrence, tsunami completion time is expressed as te from the mainshock occurrence. Thus, tsunami duration can be represented by te-ta. According to the analysis result of the 2011 Tohoku earthquake, tsunami arrival time (ta) was a short time after the mainshock (from a few minutes to a few hours), and tsunami duration (te-ta) was a few minutes. On the other hand, load effects of the aftershocks exist immediately after the mainshock, simultaneous effects of aftershocks and tsunami in structure are considered to the tsunami duration (te-ta). In this study, the aftershocks and tsunami load combination in tsunami duration will be considered in the statistical method, we propose a load and resistance combination factors for tsunami-resistant design. In other words, the maximum high of the tsunami will arrive the site ta from the mainshock, and the maximum value is assumed to continue within tsunami duration, it will be combined with the maximum value of the aftershock loads during tsunami duration. 2.2. Analysis condition In this study, to evaluate load combination factors of aftershocks and tsunami in Tohoku region, the mainshocks are assumed to be the 2011 Tohoku earthquake (Mm=9.0) and the 1933 Sanriku earthquake (Mm=8.1), and the evaluation sites are assumed to be K-NET locations of Hachinohe, Tateichi, Kuji, Hudai, Miyako and  Kamaishi. The aftershock area is assumed to be an expanded fault plane that is enlarged from the relationship between the mainshock magnitude and aftershock area on the basis of the fault plane of the mainshock. The evaluation sites and aftershock area is shown in Figure 2. A target structure is assumed to be a tsunami evacuation building of 10-story RC structure. And its size is assumed width =40m, depth =20m, height =40m. From the experience of the 2011 Tohoku earthquake, the tsunami arrival time (ta) is set 0, 30, 60 minutes after the mainshock, the tsunami duration is set 30 minutes, inundation   Figure 1: Concept of aftershocks and tsunami load combination  Figure 2: Evaluation sites and aftershock area 138 140 142 144 1463334353637383940414243KamaishiMiyakoHudaiKujiTaneichiHachinoheAftershock Area (2011 Tohoku Earthquake)Mainshock Fault Plane (2011 Tohoku Earthquake)Mainshock Fault Plane (1933 Sanriku Earthquake)Aftershock Area (1933 Sanriku Earthquake)Mainshock Fault Plane (1896 Sanriku Earthquake)Aftershock Area (1896 Sanriku Earthquake)12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  3 height is assumed to be constant during tsunami duration. The limit state is set as a state that horizontal load of aftershocks and tsunami exceeds the lateral resistance of the structure. 2.3. Analysis model The design equation corresponding to the limit state function using aftershocks and tsunami load combination for a tsunami refuge building is represented by   n A An T TnA Mn T Tn M Mn T TnR Q QrQ Q Q Q          (1) where QAn is the conditional representative value of aftershocks load during tsunami duration under the specified mainshock occurrence, we assume it is a mean value based on aftershock hazard analysis, QTn is the conditional representative value of tsunami load under the specified mainshock occurrence, we assume it is a mean value estimated from Abe law (1989), QMn is the conditional representative value of mainshock load under the specified mainshock occurrence, we assume it is a median value estimated from the attenuation relationship (Si and Midorikawa, 1999), Rn is the nominal value of lateral resistance, γA is the load factor for aftershocks, γT is the load factor for tsunami, γM is the load factor for aftershocks by the mainshock of aftershocks,   is the resistance factor, and r(=QAn/QMn) is the ratio of the nominal value of the load effect due to aftershocks during the tsunami duration to the nominal value of the load effect due to the mainshock.  In this study, first, load effect of the aftershocks is modeled. In this study, the horizontal base shear force of n story structures is focused on. According to the Recommendations for Loads on Buildings (2004), the seismic base shear force (QA) is given as  12 nA kkPGAQ wg   (2) where wk is the weight of the floor k [kN], g is the gravity acceleration [m/s2], n is the number of stories of target building, and PGA is Peak Ground Acceleration due to aftershocks [m/s2].  The PGA is a random variable that is determined by the probabilistic aftershock hazard analysis method proposed by authors. (e.g., approximately 2 times of the ground seismic response). To model the error among earthquakes, σ is used as the variation among the earthquakes. Mean value and mean + σ of aftershock PGA in each evaluation site are summarized in Table 1. Also, the distribution type of PGA is assumed to be lognormal. Median of PGA due to the mainshock in each evaluation site is calculated using the attenuation relationships (Si and Midorikawa, 1999).   Next, according to the tsunami-resistant design (2004), the tsunami force (QT) is given as       212 22 2 1 1316 62zT zQ gB h z dzgB hz z hz z      (3) where B is the width of target structure [m], ρ is the mass per unit volume of water [t/m3], z1 is the minimum height of the tsunami pressure receiving surface (1 20 z z  ) [m], z2 is the maximum height of the tsunami pressure receiving surface (1 2 3z z h  ) [m], and h is the design tsunami inundation depth [m]. According to Abe (1989), the mean value of the design tsunami inundation depth is calculated. And the distribution type of h is assumed to be lognormal. According to Aida (1978), its natural logarithm standard deviation is 0.42. The mean value of load bearing capacity (R) is decided by the target reliability index. Its COV (Coefficient of Variation) is assumed 0.2, and the distribution type is assumed to be lognormal. The Advanced First Order Second Moment (AFOSM) is used as an analysis method (Hoshiya et al., 1986). In this study, βT is the conditional target reliability index under the specified mainshock occurrence. Therefore, it is necessary to determine βT by considering the occurrence frequency of the mainshock. According to the Headquarters for Earthquake Research Promotion (2014), a return period of Tohoku earthquake is   12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  4 Table 1: Summary of input values for reliability analysis Sites Variable 2011 Tohoku Eq 1896 Sanriku Eq 1933 Sanriku Eq Type Note Mean COV Mean COV Mean COV Hachinohe PGA0-30 [cm/s2] 83 1.61 68.2 1.37 11.7 1.13 Lognormal Mean 185 1.35 140 1.25 22.2 1.05 Lognormal Mean +σ PGA30-60 [cm/s2] 62 1.73 53.5 1.46 9.5 1.20 Lognormal Mean 135 1.50 107 1.35 17.8 1.11 Lognormal Mean +σ PGA60-90 [cm/s2] 53 1.81 46.3 1.52 8.4 1.25 Lognormal Mean 113 1.59 91.8 1.41 15.5 1.16 Lognormal Mean +σ PGAmain [cm/s2] 176 - 238 - 93 - - Median h[m] 9.6 0.42 3.7 0.42 1.2 0.42 Lognormal  R[kN] - 0.2 - 0.2 - 0.2 Lognormal  Taneichi PGA0-30 [cm/s2] 106 1.58 81.3 1.36 14.8 1.12 Lognormal Mean 234 1.28 166 1.22 28.2 1.05 Lognormal Mean +σ PGA30-60 [cm/s2] 79 1.71 63.8 1.45 12.1 1.19 Lognormal Mean 171 1.43 128 1.31 22.5 1.11 Lognormal Mean +σ PGA60-90 [cm/s2] 67 1.79 55.1 1.51 10.6 1.25 Lognormal Mean 143 1.52 109 1.38 19.7 1.16 Lognormal Mean +σ PGAmain [cm/s2] 215 - 283 - 118 - - Median h[m] 10.3 0.42 4.1 0.42 1.3 0.42 Lognormal  R[kN] - 0.2 - 0.2 - 0.2 Lognormal  Kuji PGA0-30 [cm/s2] 125 1.52 76.7 1.34 16.6 1.11 Lognormal Mean 274 1.21 157 1.21 31.6 1.03 Lognormal Mean +σ PGA30-60 [cm/s2] 94 1.65 60.2 1.42 13.5 1.18 Lognormal Mean 201 1.35 120 1.31 25.3 1.10 Lognormal Mean +σ PGA60-90 [cm/s2] 79 1.73 52.1 1.48 11.9 1.23 Lognormal Mean 168 1.44 103 1.37 22 1.14 Lognormal Mean +σ PGAmain [cm/s2] 270 - 262 - 126 - - Median h[m] 11.3 0.42 4.3 0.42 1.4 0.42 Lognormal  R[kN] - 0.2 - 0.2 - 0.2 Lognormal  Hudai PGA0-30 [cm/s2] 146 1.52 78.8 1.33 19.3 1.09 Lognormal Mean 322 1.20 161 1.21 36.6 1.02 Lognormal Mean +σ PGA30-60 [cm/s2] 108 1.65 61.9 1.42 15.7 1.16 Lognormal Mean 235 1.35 123 1.30 29.3 1.08 Lognormal Mean +σ PGA60-90 [cm/s2] 92 1.74 53.5 1.48 13.8 1.21 Lognormal Mean 197 1.44 106 1.36 25.6 1.13 Lognormal Mean +σ PGAmain [cm/s2] 336 - 268 - 141 - - Median h[m] 12.4 0.42 4.7 0.42 1.5 0.42 Lognormal  R[kN] - 0.2 - 0.2 - 0.2 Lognormal  Miyako PGA0-30 [cm/s2] 167 1.38 69.8 1.31 21.5 1.07 Lognormal Mean 358 1.07 142.2 1.21 40.7 0.99 Lognormal Mean +σ PGA30-60 [cm/s2] 125 1.51 54.9 1.40 17.5 1.14 Lognormal Mean 265 1.21 109.3 1.30 32.6 1.06 Lognormal Mean +σ PGA60-90 [cm/s2] 106 1.59 47.5 1.46 15.4 1.19 Lognormal Mean 223 1.30 93.7 1.36 28.5 1.11 Lognormal Mean +σ PGAmain [cm/s2] 469 - 234 - 148 - - Median h[m] 15.0 0.42 5.0 0.42 1.6 0.42 Lognormal  R[kN] - 0.2 - 0.2 - 0.2 Lognormal  12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  5 Table 1: Summary of input values for reliability analysis (continue) Sites Variable 2011 Tohoku Eq 1896 Sanriku Eq 1933 Sanriku Eq Type Note Mean COV Mean COV Mean COV Kamaishi PGA0-30 [cm/s2] 174 1.35 52.7 1.27 20 1.06 Lognormal Mean 373 1.05 107 1.20 37.9 0.99 Lognormal Mean +σ PGA30-60 [cm/s2] 130 1.49 41.5 1.36 16.3 1.13 Lognormal Mean 276 1.18 82.5 1.29 30.4 1.05 Lognormal Mean +σ PGA60-90 [cm/s2] 111 1.54 35.9 1.42 14.3 1.18 Lognormal Mean 232 1.27 70.8 1.35 26.5 1.10 Lognormal Mean +σ PGAmain [cm/s2] 533 - 179 - 134 - - Median h[m] 18.1 0.42 4.8 0.42 1.5 0.42 Lognormal  R[kN] - 0.2 - 0.2 - 0.2 Lognormal   600 years, and that of Sanriku earthquake is 97 years. So we set the conditional target reliability index (βT) from 0 to 1.0, the design value of aftershocks and tsunami load combination is calculated. Then, the load combination factor is calculated from the ratio of the representative value and the design value. 3. RESULT 3.1. Analysis result The aftershocks and tsunami load combination factor from reliability analysis result is shown in Figures 3 and 4. First, the result at Kamaishi is shown in Figure 3, and the results at all evaluation sites are shown in Figure 4.  According to Figure 3, regardless of the mainshocks, when the target reliability index increases, the tsunami load factor increases, the aftershock load factor by the mainshock is almost constant, the resistance factor decreases. By the time elapsed from the mainshock, the aftershock load factor by the mainshock tend to become smaller. The difference between 30-60 [min] and 60-90 [min] was smaller than that between 0-30 [min] and 30-60 [min]. This is because the occurrence rate of aftershocks decreased as the time elapsed from the mainshock. But the influence of the time elapsed from the mainshock in the tsunami load factor and the resistance factor was small. To confirm the influence of variation (the error among the earthquakes) in the aftershock hazard, Figures 3(a), 3(c), 3(e) and Figures 3(b), 3(d), 3(f) are compared. As a result, the variation is significant in the aftershock load factor by the mainshock, the aftershock load factor was approximately 3 times in consideration of the error among the earthquakes. On the other hand, to confirm the influence of the magnitude of mainshock, result of the 2011 Tohoku earthquake (Mm=9.0) and the 1896 Sanriku earthquake (Mm=8.5) and the 1933 Sanriku earthquake (Mm=8.1) are compared. Because the shortest distance from the evaluation site to the fault plane is different site by site, it is difficult to compare directly. But the aftershock load factor and tsunami load factor of the 1933 Sanriku earthquake had a smaller tendency than the results of the 2011 Tohoku earthquake and the 1896 Sanriku earthquake. Also by the time elapsed from the mainshock, the decrease of aftershock load factor by mainshock and the increase of tsunami load factor are observed. Especially, changes in the tsunami load factor of the 1933 Sanriku earthquake is remarkable. This is because the mainshock magnitude of the 1933 Sanriku earthquake is smallest among the other earthquakes, is due to the load effect of the tsunami has accounted for a small portion compared with the load effect due to aftershocks. Next, summarized are the results of all evaluation sites, the relationship between the fault distance and the load combination factor for target reliability index is shown in Figure 4. In order to evaluate the load combination factor for safe side,  12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  6 (a) 2011 Tohoku Earthquake (Mean)  (b) 2011 Tohoku Earthquake (Mean+σ)  (c) 1896 Sanriku Earthquake (Mean)  (d) 1896 Sanriku Earthquake (Mean+σ)  (e) 1933 Sanriku Earthquake (Mean)  (f) 1933 Sanriku Earthquake (Mean+σ)  Figure 3: The aftershock and tsunami load combination factor (at Kamaishi) 0 0.2 0.4 0.6 0.8 100.20.40.60.811.21.41.61.82Target Reliability Index(βT)Load Combination Factor  Aftershock(γM0-30)Tsunami(γT0-30)Resistant(φ0-30)Aftershock(γM30-60)Tsunami(γT30-60)Resistant(φ30-60)Aftershock(γM60-90)Tsunami(γT60-90)Resistant(φ60-90)0 0.2 0.4 0.6 0.8 100.20.40.60.811.21.41.61.82Target Reliability Index(βT)Load Combination Factor  Aftershock(γM0-30)Tsunami(γT0-30)Resistant(φ0-30)Aftershock(γM30-60)Tsunami(γT30-60)Resistant(φ30-60)Aftershock(γM60-90)Tsunami(γT60-90)Resistant(φ60-90)0 0.2 0.4 0.6 0.8 100.20.40.60.811.21.41.61.82Target Relibility Index(βT)Load Combination factor  Aftershock(γM0-30)Tsunami(γT0-30)Resistant(φ0-30)Aftershock(γM30-60)Tsunami(γT30-60)Resistant(φ30-60)Aftershock(γM60-90)Tsunami(γT60-90)Resistant(φ60-90)0 0.2 0.4 0.6 0.8 100.20.40.60.811.21.41.61.82Target Reliablity Index(βT)Load Combination Factor  Aftershock(γM0-30)Tsunami(γT0-3Resistant(φ0-3)Aftershock(γM30-60)Tsunami(γT30-60)Resistant(φ30-60)Aftershock(γM60-90)Tsunami(γT60-90)Resistant(φ60-90)0 0.2 0.4 0.6 0.8 100.20.40.60.811.21.41.61.82Target Reliability Index(βT)Load Combination Factor  Aftershock(γM0-30)Tsunami(γT0-30)Resistant(φ0-30)Aftershock(γM30-60)Tsunami(γT30-60)Resistant(φ30-60)Aftershock(γM60-90)Tsunami(γT60-90)Resistant(φ60-90)0 0.2 0.4 0.6 0.8 100.20.40.60.811.21.4.61.82Target Reliability Index(βT)Load Combination Factor  Aftershock(γM0-30)Tsunami(γT0-30)Resistant(φ0-30)Aftershock(γM30-60)Tsunami(γT30-60)Resistant(φ30-60)Aftershock(γM60-90)Tsunami(γT60-90)Resistant(φ60-90)12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  7 (a) Aftershock load factor γM (βT=0.0)  (b) Tsunami load factor γT (βT=0.0)  (c) Resistance factorφ (βT=0.0)  (d) Aftershock load factor γM (βT=0.5)  (e) Tsunami load factor γT (βT=0.5)  (f) Resistance factorφ (βT=0.5)  (g) Aftershock load factor γM (βT=1.0)  (h) Tsunami load factor γT (βT=1.0)  (i) Resistance factor φ (βT=1.0)  Figure 4: The relationship between the fault distance and the load combination factor  including the effects of elapsed time from the mainshock, the aftershock load factor by the mainshock and tsunami load factor in each target reliability index are selected large value, but resistance factor is selected small value. According to Figure 4, the load combination factor was almost constant regardless of the fault distance. However, the aftershock load factor by mainshock of the 1933 Sanriku earthquake was smallest among the other earthquakes. This is because the aftershock occurrence rate is related to mainshock magnitude. On the other hand, the 50 100 150 20000.20.40.60.811.21.41.61.82Fault Distantce[km]Aftershock Load Factor by Mainshock  2011 Tohoku Earthquake(Mean)2011 Tohoku Earthquake(Mean+σ)1933 Sanriku Earthquake(Mean)1933 Sanriku Earthquake(Mean+σ)1896 Sanriku Earthquake(Mean)1896 Sanriku Earthquake(Mean+σ)50 100 150 20000.20.40.60.811.21.41.61.82F ult Distance[km]Tsunami Load Factor  2011 To oku Earthquake(Mean)2011 To oku Earthquake(Mean+σ)1933 Sanriku Earthquake(Mean)1933 Sanriku Earthquake(Mean+σ)1896 Sanriku Earthquake(Mean)1896 Sanriku Earthquake(Mean+σ)50 100 150 20000.20.40.60.811.21.41.61.82Fault Distance[km]Resistance Factor  2011 Tohoku Earthquake(Mean)2011 Tohoku Earthquake(Mean+σ)1933 Sanriku Earthquake(Mean)1933 Sanriku Earthquake(Mean+σ)1896 Sanriku Earthquake(Mean)1896 Sanriku Earthquake(Mean+σ)50 100 150 20000.20.40.60.811.21.41.61.82Fault Distance[km]Aftershock Load Factor by Mainshock  2011 Tohok  rt k ( )2011 Tohok  rt k ( )1933 Sanriku Earthquake(Mean)1933 Sanriku Earthquake(Mean+σ)1896 Sanriku Earthquake(Mean)1896 Sanriku Earthquake(Mean+σ)50 100 150 20000.20.40.60.811.21.41.61.82Fault Distance[km]Tsunami Load Factor  2011 To o  rt ( )2011 To ok  rt k ( )1933 Sanriku Earthquake(Mean)1933 Sanriku Earthquake(Mean+σ)1896 Sanriku Earthquake(Mean)1896 Sanriku Earthquake(Mean+σ)50 100 150 20000.20.40.60.811.21.41.61.82Fault Distance[km]Resistance Factor  2011 To ok  rt k ( )2011 To ok  rt k ( )1933 Sanriku Earthquake(Mean)1933 Sanriku Earthquake(Mean+σ)1896 Sanriku Earthquake(Mean)1896 Sanriku Earthquake(Mean+σ)50 100 150 20000.20.40.60.811.21.41.61.82Fault Distance[km]Aftershock Load Factor by Mainshock  2011 Tohoku Earthquake( ean)2011 Tohoku Earthquake( ean+ )1933 Sanriku Earthquake(Mean)1933 Sanriku Earthquake(Mean+σ)1896 Sanriku Earthquake(Mean)1896 Sanriku Earthquake(Mean+σ)50 100 150 20000.2.40.60.811.21.41.61.82Fault Distance[km]Tsunami Load Factor  2011 Tohoku Earthquake(Mean)2011 Tohoku Earthquake(Mean+σ)1933 Sanriku Earthquake(Mean)1933 Sanriku Earthquake(Mean+σ)1896 Sanriku Earthquake(Mean)1896 Sanriku Earthquake(Mean+σ)50 100 150 20000.20.40.60.811.21.41.61.82Fault Distance[km]Resistance Factor  2011 To oku Earthquake(Mean)2011 To oku Earthquake(Mean+ )1933 Sanriku Earthquake(Mean)1933 Sanriku Earthquake(Mean+σ)1896 Sanriku Earthquake(Mean)1896 Sanriku Earthquake(Mean+σ)12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  8 resistance factor was almost constant regardless of the mainshock magnitude. In addition, when the aftershock hazard is increased by the error among the earthquakes, the aftershock load factor by the mainshock were increased in any cases. However, there was no change in the tsunami load factor due to the error among the earthquakes in the 2011 Tohoku earthquake, but the tsunami load factor became smaller by aftershock hazard increase in the 1896 Sanriku earthquake and the 1933 Sanriku earthquake. The reason for this is that the proportion of the tsunami load effects on the aftershock load effect in the 1896 Sanriku earthquake and the 1933 Sanriku earthquake are smaller than the 2011 Tohoku earthquake.  3.2. Load combination factor for tsunami-resistant design Summarizing the result of Figure 4, the load and resistance factor design format for the tsunami-resistant design of conditional target reliability index is as follows. Because we consider the very rare condition that the gigantic subduction earthquake (Tohoku and Sanriku earthquake) occurs, the conditional target reliability index is set to 0 and 0.5.  Mm=9.0, conditional target reliability index=0, Mean: 0.98 0.14 0.88n Mn TnR Q Q  (4) Mean+σ: 0.98 0.41 0.88n Mn TnR Q Q  (5) Mm=9.0, conditional target reliability index=0.5, Mean: 0.95 0.15 1.26n Mn TnR Q Q  (6) Mean+σ: 0.95 0.49 1.25n Mn TnR Q Q  (7) Mm=8.5, conditional target reliability index=0, Mean: 0.98 0.11 0.86n Mn TnR Q Q  (8) Mean+σ: 0.98 0.25 0.86n Mn TnR Q Q  (9) Mm=8.5, conditional target reliability index=0.5, Mean: 0.95 0.15 1.25n Mn TnR Q Q  (10) Mean+σ: 0.95 0.47 1.24n Mn TnR Q Q  (11) Mm=8.1, conditional target reliability index=0, Mean: 0.98 0.06 0.87n Mn TnR Q Q  (12) Mean+σ: 0.98 0.11 0.87n Mn TnR Q Q  (13) Mm=8.1, conditional target reliability index=0.5, Mean: 0.95 0.10 1.19n Mn TnR Q Q  (14) Mean+σ: 0.95 0.24 1.08n Mn TnR Q Q  (15) 4. CONCLUSIONS To evaluate the load combination of aftershocks and tsunami on the tsunami-resistant design, some case study are demonstrated at some sites in Japan. Finally, load and resistance factor design format for the tsunami-resistant design is proposed. 5. REFERENCES B. Choi, T. Itoi and T. Takada. (2013). “Probabilistic aftershock occurrence model and hazard assess-ment for post-earthquake restoration activity plan”. J. Struct. Constr. Eng. AIJ. Vol.78. No.690. pp.1377-1383. (in Japanese). Port and Airport Research Institute. (2011). Survey results. http://www.pari.go.jp/info/tohoku-eq/20110328mlit.html/ (accessed 2013-11-01). R. Sato. (1989). “Handbook of fault parameters for Japanese earthquakes”. Kajima Institute Publ-ishing. (in Japanese).  ISO. (1998). “General principles on reliability for structures”. ISO 2394. Architectural Institute of Japan. (2004). “Recommen-dations for Loads on Buildings”. H. Si and S. Midorikawa. (1999). “Attenuation Relations for Peak Ground Acceleration and Velocity Considering Effects of Fault Type and Site Condition”. J. Struct. Constr. Eng. AIJ. No. 523. 63-70. (in Japanese). T. Okada, T. Sugano, T. Ishikawa, T. Ogi, S. Takai and T. Hamabe. (2004b). “Structural Design Method of Building to Seismic Sea Wave, No.2 Design Method (a Draft)”. Building Letter. The Building Center of Japan.  pp.1-8. (in Japanese). K. Abe. (1989). “Estimation of Tsunami heights from Magnitudes of Earthquake and Tsunami”. Bull. Earthquake Res. Inst. Tokyo Univ. 64. pp.51-69. I  Aida. (1978). “Reliability of a tsunami source model derived from fault parameters”. Journal of Physics of the Earth. Vol.26. No.1. pp.57-73. M. Hoshiya and K. Ishii. (1986). “The reliability designing of structures”. Kajima Institute Publi-shing. (in Japanese).  The Headquarters for Earthquake Research Promotion. (2014).Long-termEvaluation. http://www.jishin.go.jp/main/choukihyoka/kaikou.htm/ (accessed 2014-12-18). 

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