원자로건물 지진해석을 위한 모드 순응형 집중질량모델

Abstract

원자로건물은 지진발생시 기능을 유지하기 위해 구조물의 심각한 손상이 없어야 하며, 이를 위해서는 원자로건물뿐만 아니라 내부의 주증기계통과 차폐벽 및 파이핑 시스템과 같은 비구조요소들(Non-Structural Components: NSCs) 또한 각자의 기능을 유지하여야 한다. 따라서 원자로건물의 내진성능을 검증하기 위해서 비구조요소를 포함한 원자로 격납건물에 대한 모델링이 반드시 병행되어야 한다. 그러나 기존의 원자로건물에 대한 지진해석에서는 원자로 격납건물 자체에 중점을 두어 연구가 주로 수행되었으며 비구조요소들을 포함하는 해석 및 모델링 기술은 아직 미비한 상황이다. 한편 원자로건물의 지진해석에는 유한요소모델 또는 집중질량모델을 필요에 따라 선택적으로 사용하고 있다. 유한요소모델은 구조물을 3차원 평면요소(solid elements)로 모델링하면서 질량을 일정하게 분포시키는 모델링 기법이며 가장 정확한 해석을 할 수 있는 방법으로 알려져 있다. 반면에 집중질량모델은 구조물을 기둥요소(stick elements)로 간략하게 모델링하면서 질량을 요소의 양끝단에 집중시키는 모델링 기법으로, 다수의 지진데이터를 고려하는 지진해석에 있어서 구조물 모델링과 해석 시간을 상당히 단축시킬 수 있다는 장점을 가지고 있다. 따라서 구조물의 지진해석, 민감도 해석, 지진취약도 분석과 같이 많은 지진데이터를 사용하는 해석에는 집중질량모델이 선호되고 있다. 그러나 일반적으로 집중질량모델의 경우 유한요소모델에 비해 정확도가 다소 떨어지므로 본 논문에서는 이를 개선하기 위해 새로운 집중질량모델을 제안하였다. 제안된 집중질량모델은 유한요소모델을 이용하여 고유치해석으로 통해 구조물 동적해석에 필요한 모드들을 선택한 후, 이 선택된 모드에 해당하는 고유치(이하 목표고유치)들을 일치시키는 새로운 방법이다. 따라서 이 모델은 구조물의 기하학적 형상만을 고려하는 기존의 집중질량모델과는 차이가 있다. 본 논문에서는 이 새로운 집중질량모델을 모드 순응형 집중질량모델로 명명하였으며, 제안된 모드 순응형 집중질량모델의 동적성능을 검증하기 위하여 균일한 단면으로 이뤄진 구조물에 적용하여 구체적인 모델링 절차를 설명하고 화이트 노이즈를 이용한 시간이력해석을 수행하여 결과를 검증하였다. 이 해석결과를 바탕으로 유한요소모델과 기존방법의 집중질량모델, 제안된 모드 순응형 집중질량모델의 동적성능을 비교하였으며, 제안된 집중질량모델의 효율성을 검증하였다. 또한 제안된 집중질량모델을 OPR1000원자로 격납건물(울진 5, 6호기)에 적용하였다. 입력 지진데이터는 미국 원자력규제위원회(US NRC)에서 제시하는 표준지반응답스펙트럼에 해당하는 인공지진파를 이용하였으며 유한요소모델과 기존 집중질량모델, 제안 모델의 동적응답을 비교하였다. 추가적으로 한국형 표준원전(APR1400)의 원자로 격납건물 및 주증기계통과 차폐벽등의 비구조요소들을 고려한 유한요소모델과 제안된 모드 순응형 집중질량모델을 작성하여 지진해석을 수행하고 동적 변위 및 가속도 응답을 검증하였다. 해석 결과 원자로건물의 각 층별에서의 변위와 가속도 응답의 최대값(peak responses)들 모두 유사하게 나타났으며, 변위와 가속도의 응답 또한 매우 유사하게 나타났다. 특히, 변위 응답은 공학적으로 무시할 수 있는 매우 작은 수준의 차이가 나타났으며 가속도 응답의 경우에는 각 비구조요소들 모두 유사하게 나타났다. 본 연구는 모드 순응형 집중질량모델이 타당한 동적응답을 제공하는 것을 보여 주고 있으며, 이 모델링 기법은 구조물의 지진해석에 있어서 새로운 대안으로 고려될 수 있을 것으로 사료된다.|Nuclear reactor buildings, which consist of containment building and non-structural components such as reactor vessel, steam generator, walls, and piping, should be not collapsed to maintain their functions during earthquake events. Therefore, the seismic performance evaluation of the nuclear reactor buildings requires modeling both main structure and non-structural components. However, the most seismic analysis of the nuclear reactor building has focused on the nuclear containment building itself. Also, the researches related to the modeling techniques including such non-structural components are rare and insufficient. Two approaches are normally accepted for the seismic analysis or capacity evaluation of nuclear reactor buildings: finite element method and lumped mass model. The finite element model considers the structures with three dimensional plane elements (solid element) and distributed mass. The model is used if high accurate results are required. On the other hands, the lumped mass model simplifies the structures with series of the column elements (stick element) and the masses are lumped at the ends of each element. The modeling technique reduces the complexity of structural modeling details and computational time. Due to such advantages, the modeling technique is accepted for the seismic, sensitivity, and fragility analyses which use several seismic ground motions. Modeling technique of the conventional lumped mass model calculates the mass amount lumped at the nodes considering geometric configuration of the structures, like a tributary area. However, the analysis results are usually not the same as those of the finite element model. In order to overcome such deficiency, the present study develops a new lumped mass model. The developed lumped mass model uses the effective modes selected from the eigenvalue analysis of the finite element model and controls the mass distribution to be equal or adaptive to the selected or target eigenvalues. Such concept is distinguished from the conventional lumped mass model. In the present study, the new model is named the “frequency adaptive lumped mass model” and detailed development procedures are explained applying the prismatic column structure. To investigate the numerical performance of the new model, a time history analysis using white noise is carried out and the results are compared with the dynamic results obtained from the finite element and conventional lumped mass models. For a practical application, nuclear reactor buildings (OPR1000 and APR1400) are considered and their lumped mass models are prepared following the new modeling procedures. The dynamic performance of the models is assessed through a seismic analysis using an artificial ground motion which is related to the design response spectrum proposed in the US NRC. In addition, non-structural components for the APR1400 nuclear reactor building are included into the model and the seismic analysis is performed. From the results, the peak responses of the structure such as displacement and acceleration are similar to those of the finite element model. This study shows that the frequency adaptive lumped mass model provides an acceptable dynamic response and the modeling technique is expected to be used as a new alternative approach for the seismic analysis of structures.; Nuclear reactor buildings, which consist of containment building and non-structural components such as reactor vessel, steam generator, walls, and piping, should be not collapsed to maintain their functions during earthquake events. Therefore, the seismic performance evaluation of the nuclear reactor buildings requires modeling both main structure and non-structural components. However, the most seismic analysis of the nuclear reactor building has focused on the nuclear containment building itself. Also, the researches related to the modeling techniques including such non-structural components are rare and insufficient. Two approaches are normally accepted for the seismic analysis or capacity evaluation of nuclear reactor buildings: finite element method and lumped mass model. The finite element model considers the structures with three dimensional plane elements (solid element) and distributed mass. The model is used if high accurate results are required. On the other hands, the lumped mass model simplifies the structures with series of the column elements (stick element) and the masses are lumped at the ends of each element. The modeling technique reduces the complexity of structural modeling details and computational time. Due to such advantages, the modeling technique is accepted for the seismic, sensitivity, and fragility analyses which use several seismic ground motions. Modeling technique of the conventional lumped mass model calculates the mass amount lumped at the nodes considering geometric configuration of the structures, like a tributary area. However, the analysis results are usually not the same as those of the finite element model. In order to overcome such deficiency, the present study develops a new lumped mass model. The developed lumped mass model uses the effective modes selected from the eigenvalue analysis of the finite element model and controls the mass distribution to be equal or adaptive to the selected or target eigenvalues. Such concept is distinguished from the conventional lumped mass model. In the present study, the new model is named the “frequency adaptive lumped mass model” and detailed development procedures are explained applying the prismatic column structure. To investigate the numerical performance of the new model, a time history analysis using white noise is carried out and the results are compared with the dynamic results obtained from the finite element and conventional lumped mass models. For a practical application, nuclear reactor buildings (OPR1000 and APR1400) are considered and their lumped mass models are prepared following the new modeling procedures. The dynamic performance of the models is assessed through a seismic analysis using an artificial ground motion which is related to the design response spectrum proposed in the US NRC. In addition, non-structural components for the APR1400 nuclear reactor building are included into the model and the seismic analysis is performed. From the results, the peak responses of the structure such as displacement and acceleration are similar to those of the finite element model. This study shows that the frequency adaptive lumped mass model provides an acceptable dynamic response and the modeling technique is expected to be used as a new alternative approach for the seismic analysis of structures.