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2026 Vol.28, Issue 2 Preview Page

Research Paper

Multi-objective optimal design of buffers for the KRS+ using a surrogate model and numerical analysis framework

수치해석 및 대리모델 통합 프레임워크를 활용한 한국형 처분시스템 완충재의 다목적 최적 설계

Minseop Kim1*
,
Jinwoo Kim2
,
Jin-Seop Kim3
김 민섭1*
,
김 진우2
,
김 진섭3
1Senior Researcher, Disposal Performance Demonstration Research Division, Korea Atomic Energy Research Institute
2Post-Doctoral Researcher, Disposal Performance Demonstration Research Division, Korea Atomic Energy Research Institute
3Principal Researcher, Disposal Performance Demonstration Research Division, Korea Atomic Energy Research Institute
1비회원, 한국원자력연구원 처분성능실증연구부 선임연구원
2비회원, 한국원자력연구원 처분성능실증연구부 박사후연구원
3정회원, 한국원자력연구원 처분성능실증연구부 책임연구원
*Corresponding Author
31 March 2026. pp. 165-184
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Abstract

This study proposes an integrated framework combining numerical analysis and surrogate model to optimize the initial design conditions of bentonite buffers in a high-level radioactive waste repository. The bentonite exhibits complex thermo-hydro-mechanical (THM) behavior, which is non-linearly determined by various design factors, including initial dry density and saturation. Conventional finite element analysis faces limitations in extensive optimization due to high computational costs. To address this, surrogate models based on Gaussian Process Regression were constructed using numerical data for four types of bentonites (Bentonil-WRK, KJ-Ⅱ, MX80, and FEBEX) within the KRS+ system. The developed models rapidly predict key performance indicators, such as maximum temperature, saturation time, and time to reach swelling pressure, with high statistical reliability. Multi-objective optimization using the NSGA-II algorithm revealed that KJ-Ⅱ and MX80 offer superior performance and mechanical stability. The proposed methodology provides a systematic guide for assessing the long-term integrity of engineered barrier systems.

Keywords
Bentonite buffer
THM
Multi-objective optimization
Surrogate model
Korean reference disposal system

본 연구는 고준위 방사성 폐기물 처분장의 핵심 구성 요소인 벤토나이트 완충재의 초기 설계 조건을 최적화하기 위해 수치해석과 대리 모델을 결합한 통합 프레임워크를 제안한다. 벤토나이트 완충재는 복잡한 열-수리-역학적 복합 거동을 보이며, 이는 초기 건조밀도와 함수비 등 다수의 설계 인자에 의해 비선형적으로 결정된다. 기존의 유한요소 해석은 방대한 계산 비용으로 인해 광범위한 최적화 수행에 한계가 있었다. 이를 해결하기 위해 본 연구는 KRS+ 시스템을 대상으로 Bentonil-WRK, KJ-Ⅱ, MX80, FEBEX 4종의 벤토나이트에 대한 수치해석 결과를 바탕으로 가우시안 프로세스 회귀 기반 대리 모델을 구축하였다. 구축된 모델은 최고 온도, 포화 시간, 팽윤압 도달 시간을 신속하게 예측하며 높은 신뢰성을 확보하였다. NSGA-II 알고리즘을 통한 다목적 최적화 결과, KJ-Ⅱ와 MX80이 우수한 성능과 안정성을 제공함을 확인하였다. 특히 KJ-Ⅱ는 설계 목적에 따른 유연한 최적해 그룹을 제공하여 공학적 의사결정에 유리한 특성을 보였다. 본 연구의 방법론은 처분 시스템의 장기 건전성 평가를 위한 정량적 가이드를 제공할 것으로 기대된다.

키워드
벤토나이트 완충재
THM
다목적 최적화
대리모델
한국형 기준 처분시스템
References
1

Abed, A.A., Laitinen, M., Lamsa, J., Harjupatana, T., Solowski, W.T., Kataja, M. (2016), “Hydro-mechanical modelling of MX-80 bentonite: One dimensional study”, E3S Web of Conferences, Vol. 9, 18005.

10.1051/e3sconf/20160918005
2

Alonso, E.E., Gens, A., Josa, A. (1990), “A constitutive model for partially saturated soils”, Géotechnique, Vol. 40, No. 3, pp. 405-430.

10.1680/geot.1990.40.3.405
3

Börgesson, L., Hernelind, J. (1999), Coupled thermo-hydro-mechanical calculations of the water saturation phase of a KBS-3 deposition hole. Influence of hydraulic rock properties on the water saturation phase, SKB Technical Report No. TR-99-41, Swedish Nuclear Fuel and Waste Management Co., pp. 1-105.

4

Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J. (1984), Classification and Regression Trees, Wadsworth & Brooks/Cole, Monterey, pp. 1-358.

5

Cho, W.J., Kwon, S.K., Choi, J.W. (2008), “Thermal conductivity of granite from the KAERI underground research tunnel site”, Tunnel and Underground Space, Vol. 18, No. 3, pp. 219-225.

6

Deb, K. (2011), “Multi-objective optimisation using evolutionary algorithms: An introduction”, Multi-Objective Evolutionary Optimisation for Product Design and Manufacturing, Springer, London, pp. 3-34.

10.1007/978-0-85729-652-8_1
7

Forrester, A., Sobester, A., Keane, A. (2008), Engineering Design via Surrogate Modelling: A Practical Guide, John Wiley & Sons, Chichester, pp. 1-210.

10.1002/9780470770801
8

Gens, A. (1995), “Constitutive laws”, Modern Issues in Non-Saturated Soils, International Centre for Mechanical Sciences, Vol. 357, Springer, Vienna, pp. 129-158.

10.1007/978-3-7091-2692-9_2
9

Karnland, O. (2010b), Chemical and mineralogical characterization of the bentonite buffer for the acceptance control procedure in a KBS-3 repository, SKB Technical Report No. TR-10-60, Swedish Nuclear Fuel and Waste Management Co., pp. 1-84.

10

Kim, J., Kim, M., Yoon, S., Kim, J.S. (2026), “A unified van Genuchten-type water retention model for compacted bentonite”, Engineering Geology, 108590.

10.1016/j.enggeo.2026.108590
11

Kim, J., Kim, M., Yoon, S., Lee, D.H., Lee, M.H., Kim, J.S. (2024a), Comprehensive database of thermo-hydro-mechanical properties for Bentonil-WRK, KAERI/TR-10601/2024, Korea Atomic Energy Research Institute, pp. 1-120.

12

Kim, J.S., Lee, C., Yoon, S., Lee, M., Lee, Y.H., Kim, J.W., Lee, M., Cha, Y., Kim, J.T., Hong, C.H., Park, T., Kim, M., Kim, T., Ha, S.J., Kim, K.I., Kwon, S., Choi, S., Lee, Y., Kwon, J.S. (2025a), “Advancements in long-term safety evaluation technology for engineered barrier system (EBS): A comprehensive review of Korea’s high-level waste disposal R&D program”, Korean Journal of Chemical Engineering, Vol. 42, No. 6, pp. 1301-1316.

10.1007/s11814-025-00466-5
13

Kim, K.I., Lee, C., Cho, D., Rutqvist, J. (2024b), “Enhancement of disposal efficiency for deep geological repositories based on three design factors− Decay heat optimization, increased thermal limit of the buffer and double-layer concept”, Tunnelling and Underground Space Technology, Vol. 153, 106017.

10.1016/j.tust.2024.106017
14

Kim, M., Lee, S., Yoon, S., Jeon, M.K. (2022), “Identification of mechanical parameters of Kyeongju bentonite based on artificial neural network technique”, Journal of Nuclear Fuel Cycle and Waste Technology, Vol. 20, No. 3, pp. 269-278.

10.7733/jnfcwt.2022.022
15

Kim, M.J., Lee, S.R., Yoon, S., Jeon, J.S., Kim, M.S. (2018), “Optimal initial condition of a bentonite buffer with regard to thermal behavior in a high-level radioactive waste repository”, Computers and Geotechnics, Vol. 104, pp. 109-117.

10.1016/j.compgeo.2018.08.011
16

Kim, M.S., Jeon, J.S., Kim, M.J., Lee, J., Lee, S.R. (2019), “A multi-objective optimization of initial conditions in a radioactive waste repository by numerical thermo-hydro-mechanical modeling”, Computers and Geotechnics, Vol. 114, 103106.

10.1016/j.compgeo.2019.103106
17

Kim, M.S., Lee, C., Yutaka, S., Kim, J.S., Jeon, M.K. (2025b), “Comparative analysis of primary variables selection in modeling non-isothermal two-phase flow: Insights from EBS experiment at Horonobe URL”, Geomechanics for Energy and the Environment, Vol. 41, 100628.

10.1016/j.gete.2024.100628
18

Lee, C., Lee, J., Kim, G.Y. (2020a), “Numerical analysis of FEBEX at Grimsel Test Site in Switzerland”, Tunnel and Underground Space, Vol. 30, No. 4, pp. 359-381.

10.7474/TUS.2020.30.4.359
19

Lee, C., Lee, J., Kim, M., Kim, G.Y. (2020b), “Implementation of Barcelona Basic Model into TOUGH2-MP/FLAC3D”, Tunnel and Underground Space, Vol. 30, No. 1, pp. 39-62.

10.7474/TUS.2020.30.1.039
20

Lee, J., Cho, D., Choi, H., Choi, J. (2007), “Concept of a Korean reference disposal system for spent fuels”, Journal of Nuclear Science and Technology, Vol. 44, No. 12, pp. 1565-1573.

10.1080/18811248.2007.9711407
21

Lee, J., Kim, H., Kim, I., Choi, H., Cho, D. (2020c), “Analyses on thermal stability and structural integrity of the improved disposal systems for spent nuclear fuels in Korea”, Journal of Nuclear Fuel Cycle and Waste Technology, Vol. 18, pp. 21-36.

10.7733/jnfcwt.2020.18.S.21
22

Lloret, A., Villar, M.V. (2007), “Advances on the knowledge of the thermo-hydro-mechanical behaviour of heavily compacted ‘FEBEX’ bentonite”, Physics and Chemistry of the Earth, Parts A/B/C, Vol. 32, No. 8-14, pp. 701-715.

10.1016/j.pce.2006.03.002
23

MacQueen, J. (1967), “Some methods for classification and analysis of multivariate observations”, Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, Vol. 1, No. 14, Berkeley, pp. 281-297.

24

Park, S., Yoon, S., Kwon, S., Lee, M.S., Kim, G.Y. (2021), “Temperature effect on the thermal and hydraulic conductivity of Korean bentonite buffer material”, Progress in Nuclear Energy, Vol. 137, 103759.

10.1016/j.pnucene.2021.103759
25

Raiko, H., Sandström, R., Rydén, H., Johansson, M. (2010a), Design analysis report for the canister, SKB Technical Report No. TR-10-28, Swedish Nuclear Fuel and Waste Management Co., pp. 1-150.

26

Rutqvist, J., Ijiri, Y., Yamamoto, H. (2011), “Implementation of the Barcelona Basic Model into TOUGH–FLAC for simulations of the geomechanical behavior of unsaturated soils”, Computers & Geosciences, Vol. 37, No. 6, pp. 751-762.

10.1016/j.cageo.2010.10.011
27

Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S. (2008), Global Sensitivity Analysis: The Primer, John Wiley & Sons, Chichester, pp. 1-504.

10.1002/9780470725184
28

Sellin, P., Leupin, O.X. (2013), “The use of clay as an engineered barrier in radioactive-waste management-a review”, Clays Clay Miner, Vol. 61, No. 6, pp. 477-498.

10.1346/CCMN.2013.0610601
29

Sobol, I.M. (1993), “Sensitivity estimates for nonlinear mathematical models”, Mathematical Modelling and Computational Experiments, Vol. 1, No. 4, pp. 407-414.

30

van Genuchten, M. (1980), “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils”, Soil Science Society of America Journal, Vol. 44, No. 5, pp. 892-898.

10.2136/sssaj1980.03615995004400050002x
31

Villar, M.V. (2005), MX-80 bentonite: Thermal-hydro-mechanical characterisation performed at CIEMAT in the context of the prototype project, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas (CIEMAT), pp. 1-100.

32

Villar, M.V., Gomez-Espina, R. (2009), Report on thermo-hydro-mechanical laboratory tests performed by CIEMAT on FEBEX bentonite 2004-2008, CIEMAT-1178, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas (CIEMAT), pp. 1-52.

33

Yoon, S., Kim, G.Y. (2017), Specific heat behavior model of compacted bentonite buffer, KAERI/TR-6994/2017, Korea Atomic Energy Research Institute, pp. 1-45.

34

Yoon, S., Kim, J.S., Kim, J.W., Lee, J.W. (2024), “Evaluation of thermal properties for the bentonil-WRK bentonite”, Journal of Nuclear Fuel Cycle and Waste Technology, Vol. 22, No. 1, pp. 9-16.

10.7733/jnfcwt.2024.008
35

Yoon, S., Kim, M.J., Park, S., Kim, G.Y. (2021), “Thermal conductivity prediction model for compacted bentonites considering temperature variations”, Nuclear Engineering and Technology, Vol. 53, No. 10, pp. 3359-3366.

10.1016/j.net.2021.05.001
Information
  • Publisher :Korean Tunneling and Underground Space Association
  • Publisher(Ko) :한국터널지하공간학회
  • Journal Title :Journal of Korean Tunnelling and Underground Space Association
  • Journal Title(Ko) :한국터널지하공간학회 논문집
  • Volume : 28
  • No :2
  • Pages :165-184
  • Received Date : 2026-03-10
  • Revised Date : 2026-03-26
  • Accepted Date : 2026-03-26
  • DOI :https://doi.org/10.9711/KTAJ.2026.28.2.165
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