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Eurock2015-poster

Adrien Haxaire
Adrien Haxaire

1) The document describes a study that implemented a fully-coupled thermo-hydro-mechanical (THM) model in PLAXIS 2D finite element software and applied it to simulate radioactive waste storage. 2) The case study modeled two underground galleries excavated in clay for waste storage, applying heat fluxes from the waste. Results showed maximum displacements of 12.9 cm during excavation and temperatures up to 360K after 444 years of heating. 3) Pore pressures increased initially due to heating but then returned to hydrostatic conditions as the tunnels closed and recharged with water. The THM model successfully simulated expected phenomena and can be used for further repository studies.

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Implementing a fully-coupled thermo-hydro-mechanical model: lessons learned from the application to radioactive waste storage Adrien Haxaire 1), Philip J. Vardon 2), Vahid Galavi 3), Ronald B.J. Brinkgreve 1,2) 1) Plaxis, Delft, The Netherlands 2) Department of Geoscience and Engineering, Delft University of Technology, Delft, The Netherlands 3) Deltares, Delft, The Netherlands Summary The fully-coupled thermo-hydro-mechanical (THM) model presented in Haxaire et al. (2013) has been implemented in the finite element code PLAXIS 2D. An application to radioactive waste storage is conducted and analysed. It is inspired by the OPERA research programme, in the Netherlands (Verhoef and Schr旦der, 2011). The formulation and the implementation is stable and provides qualitative results in accordance with expectation. Case study The case study is inspired by Arnold et al. (2015). Figure 1 presents the geometry, mesh and the boundary conditions and Table 1 the parameters used. The analysis is plane strain. It consists of a set of two 1.6 m radius galleries excavated at a 500 m depth in a Boom clay layer, with a spacing of 50 m (centre to centre). The mesh contains 2298 fifteen-noded elements, with 18729 nodes. The boundary conditions are applied to both galleries. A heat flux of 11 W/m2 is applied to both tunnel outer circumferences to model the heat emitted by the radioactive waste canisters once in place. First phase: excavation The largest total displacement on Figure 2.a. is 12.91 cm, or 8% of the radius of the gallery. This value was confirmed by a three dimensional calculation performed using PLAXIS 3D. Non zero values of the displacement field extend to 21 m below the galleries. The total deviatoric strain on Figure 2.b. exhibits the behaviour observed for the total displacement field: high displacements at the edge of the gallery, combined with an extended shear zone below the gallery. The maximum value obtained, 8.6 %, is close to the total displacement ratio, confirming thus that the displacements are mainly caused by shearing. Second phase: heating Figure 3 presents the temperature and the heat flux in the model at steady state, reached after approximatively 1.4.1010 seconds, i.e. 444 years. The maximum temperature, obtained at the boundary of the gallery, at point A, reaches 360 K. Figure 3 (a) exhibits the interaction between the two canisters. The temperature at the middle of the model, at point E (25.08 m, 51.30 m), reaches 328.4 K. Figure 3 (b) shows that the heat flux, as expected, is null at the centre of the model, confirming the interaction between the two canisters at steady state. Figure 4 presents the evolution of the pore pressure close to the Boom clay-canister interface, after the start of the heating. We can see on Figure 4 (a) that, as expected, the heating increases the pore pressure: as the permeability is low, the water expands but cannot flow. The pore pressure initially increases rapidly due to the rapid temperature increase and then is subsequently controlled by the recharge effects of closing and backfilling the tunnel, returning to hydrostatic conditions. Figure 4 (b) confirms this result over the three points A, C and E. Conclusion The current implementation of PLAXIS 2D's fully-coupled THM model has been shown to be able to simulate the THM effects of a radioactive waste repository. It can simulate a number of expected phenomena, leading to confidence in its ability to be used in further studies. From this positive experience, more refined studies can be conducted, such as considering the excavation damaged zone, or the impact of vapour fluxes on the THM processes, as well as full validations based on in situ experiments. References Arnold, P., Vardon, P.J., Hicks, M.A., Fokkens, J. and Fokker, P.A. 2015. A numerical and reliability-based investigation into the technical feasibility of a Dutch radioactive waste repository in Boom Clay. OPERA-PU-TUD311, COVRA, The Netherlands. Haxaire, A., Galavi, V. and Brinkgreve, R.B.J. 2013. Definition and implementation of a fully coupled THM model, Rock Mechanics for Resources, Energy and Environment - Kwaniewski & yd甜ba (eds), Taylor & Francis Group, London, ISBN 978-1-138-00080-3. Verhoef, E. and Schroder, T. 2011. Research Plan. OPERA-PG-COV004, COVRA, The Netherlands. Figure 1. Mesh and boundary conditions of the case study. Figure 2. Excavation: total displacements (a) and total deviatoric strain (b). Table 1. THM parameters used for the case study. Mechanical Unit Value Hydraulic Unit Value E50 ref [kN/m2] 145300 Sres [-] 0.01629 Eoed ref [kN/m2] 145300 Ssat [-] 1 Eur ref [kN/m2] 435800 gn [-] 1.103 Power (m) [-] 0.7 ga [1/m] 2.650 einit [-] 0.166 gl [-] 2.5 cref [kN/m2] 300 kx [m/s] 10-12 [属] 12.5 ky [m/s] 10-12 率 [属] 0 Thermal Unit Value 僚ur [-] 0.3 cs [J/kg.K] 1400 pref [kN/m2] 100 了s [W/m.K] 1.4 K0 nc [-] 0.7836 s [kg/m3] 2000 Model Hardening Soil 留s [-] 5. 10-5 Figure 3. Temperature distribution (a) and heat flux (b) at steady state. Figure 4. Pore pressure after 282 days of heating (a) and from the left canister to the centre of the model until 95 years (b).

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Eurock2015-poster

  • 1. Implementing a fully-coupled thermo-hydro-mechanical model: lessons learned from the application to radioactive waste storage Adrien Haxaire 1), Philip J. Vardon 2), Vahid Galavi 3), Ronald B.J. Brinkgreve 1,2) 1) Plaxis, Delft, The Netherlands 2) Department of Geoscience and Engineering, Delft University of Technology, Delft, The Netherlands 3) Deltares, Delft, The Netherlands Summary The fully-coupled thermo-hydro-mechanical (THM) model presented in Haxaire et al. (2013) has been implemented in the finite element code PLAXIS 2D. An application to radioactive waste storage is conducted and analysed. It is inspired by the OPERA research programme, in the Netherlands (Verhoef and Schr旦der, 2011). The formulation and the implementation is stable and provides qualitative results in accordance with expectation. Case study The case study is inspired by Arnold et al. (2015). Figure 1 presents the geometry, mesh and the boundary conditions and Table 1 the parameters used. The analysis is plane strain. It consists of a set of two 1.6 m radius galleries excavated at a 500 m depth in a Boom clay layer, with a spacing of 50 m (centre to centre). The mesh contains 2298 fifteen-noded elements, with 18729 nodes. The boundary conditions are applied to both galleries. A heat flux of 11 W/m2 is applied to both tunnel outer circumferences to model the heat emitted by the radioactive waste canisters once in place. First phase: excavation The largest total displacement on Figure 2.a. is 12.91 cm, or 8% of the radius of the gallery. This value was confirmed by a three dimensional calculation performed using PLAXIS 3D. Non zero values of the displacement field extend to 21 m below the galleries. The total deviatoric strain on Figure 2.b. exhibits the behaviour observed for the total displacement field: high displacements at the edge of the gallery, combined with an extended shear zone below the gallery. The maximum value obtained, 8.6 %, is close to the total displacement ratio, confirming thus that the displacements are mainly caused by shearing. Second phase: heating Figure 3 presents the temperature and the heat flux in the model at steady state, reached after approximatively 1.4.1010 seconds, i.e. 444 years. The maximum temperature, obtained at the boundary of the gallery, at point A, reaches 360 K. Figure 3 (a) exhibits the interaction between the two canisters. The temperature at the middle of the model, at point E (25.08 m, 51.30 m), reaches 328.4 K. Figure 3 (b) shows that the heat flux, as expected, is null at the centre of the model, confirming the interaction between the two canisters at steady state. Figure 4 presents the evolution of the pore pressure close to the Boom clay-canister interface, after the start of the heating. We can see on Figure 4 (a) that, as expected, the heating increases the pore pressure: as the permeability is low, the water expands but cannot flow. The pore pressure initially increases rapidly due to the rapid temperature increase and then is subsequently controlled by the recharge effects of closing and backfilling the tunnel, returning to hydrostatic conditions. Figure 4 (b) confirms this result over the three points A, C and E. Conclusion The current implementation of PLAXIS 2D's fully-coupled THM model has been shown to be able to simulate the THM effects of a radioactive waste repository. It can simulate a number of expected phenomena, leading to confidence in its ability to be used in further studies. From this positive experience, more refined studies can be conducted, such as considering the excavation damaged zone, or the impact of vapour fluxes on the THM processes, as well as full validations based on in situ experiments. References Arnold, P., Vardon, P.J., Hicks, M.A., Fokkens, J. and Fokker, P.A. 2015. A numerical and reliability-based investigation into the technical feasibility of a Dutch radioactive waste repository in Boom Clay. OPERA-PU-TUD311, COVRA, The Netherlands. Haxaire, A., Galavi, V. and Brinkgreve, R.B.J. 2013. Definition and implementation of a fully coupled THM model, Rock Mechanics for Resources, Energy and Environment - Kwaniewski & yd甜ba (eds), Taylor & Francis Group, London, ISBN 978-1-138-00080-3. Verhoef, E. and Schroder, T. 2011. Research Plan. OPERA-PG-COV004, COVRA, The Netherlands. Figure 1. Mesh and boundary conditions of the case study. Figure 2. Excavation: total displacements (a) and total deviatoric strain (b). Table 1. THM parameters used for the case study. Mechanical Unit Value Hydraulic Unit Value E50 ref [kN/m2] 145300 Sres [-] 0.01629 Eoed ref [kN/m2] 145300 Ssat [-] 1 Eur ref [kN/m2] 435800 gn [-] 1.103 Power (m) [-] 0.7 ga [1/m] 2.650 einit [-] 0.166 gl [-] 2.5 cref [kN/m2] 300 kx [m/s] 10-12 [属] 12.5 ky [m/s] 10-12 率 [属] 0 Thermal Unit Value 僚ur [-] 0.3 cs [J/kg.K] 1400 pref [kN/m2] 100 了s [W/m.K] 1.4 K0 nc [-] 0.7836 s [kg/m3] 2000 Model Hardening Soil 留s [-] 5. 10-5 Figure 3. Temperature distribution (a) and heat flux (b) at steady state. Figure 4. Pore pressure after 282 days of heating (a) and from the left canister to the centre of the model until 95 years (b).