Kriging-based reliability analysis of the long-term stability of a deep driftconstructed in the Callovo-Oxfordian claystone

Callovo-Oxfordian(COx)claystone has been considered as a potential host rock for geological radioactive waste disposal in France(Cigéo project).During the exploitation phase(100 years),the stability of drifts(e.g.galleries/alveoli)within the disposal is assured by the liner,which includes two layers:concrete arch segment and compressible material.The latter exhibits a significant deformation capacity(about 50%)under low stress(<3 MPa).Although the response of these underground structures can be governed by complex thermo-hydro-mechanical coupling,the creep behavior of COx claystone has been considered as the main factor controlling the increase of stress state in the concrete liner and hence the long-term stability of drifts.Therefore,by focusing only on the purely mechanical behavior,this study aims at investigating the uncertainty effect of the COx claystone time-dependent properties on the stability of an alveolus of Cigéo during the exploitation period.To describe the creep behavior of COx claystone,we use Lemaitre’s viscoplastic model with three parameters whose uncertainties are identified from laboratory creep tests.For the reliability analysis,an extension of a well-known Kriging metamodeling technique is proposed to assess the exceedance probability of acceptable stress in the concrete liner of the alveolus.The open-source code Code_Aster is chosen for the direct numerical evaluations of the performance function.The Kriging-based reliability analysis elucidates the effect of the uncertainty of COx claystone on the long-term stability of the concrete liner.Moreover,the role of the compressible material layer between the concrete liner and the host rock is also highlighted.

Soft Tissue Deformation Modeling in the Procedure of Needle Insertion:A Kriging‑Based Method

The simulation and planning system(SPS)requires accurate and real-time feedback regarding the deformation of soft tissues during the needle insertion procedure.Traditional mechanical-based models such as the finite element method(FEM)are widely used to compute the deformations of soft tissue.However,it is difficult for the FEM or other methods to find a balance between an acceptable image fidelity and real-time deformation feedback due to their complex material properties,geometries and interaction mechanisms.In this paper,a Kriging-based method is applied to model the soft tissue deformation to strike a balance between the accuracy and efficiency of deformation feedback.Four combinations of regression and correlation functions are compared regarding their ability to predict the maximum deformations of ten characteristic markers at a fixed insertion depth.The results suggest that a first order regression function with Gaussian correlation functions can best fit the results of the ground truth.The functional response of the Kriging-based method is utilized to model the dynamic deformations of markers at a series of needle insertion depths.The feasibility of the method is verified by investigating the adaptation to step variations.Compared with the ground truth of the finite element(FE)results,the maximum residual is less than 0.92 mm in the Y direction and 0.31 mm in the X direction.The results suggest that the Kriging metamodel provides real-time deformation feedback for a target and an obstacle to a SPS.