# Frontiers of Structural and Civil Engineering

 Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (6) : 1495-1509     https://doi.org/10.1007/s11709-019-0574-y
 RESEARCH ARTICLE
Application of coupled XFEM-BCQO in the structural optimization of a circular tunnel lining subjected to a ground motion
1. Department of Civil Engineering, Tishk International University-Sulaimani, Sulaimaniya 46001, Iraq
2. Mathematics Department-College of Science, Sulaimani University, Sulaimaniya 46001, Iraq
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 Abstract A new structural optimization method of coupled extended finite element method and bound constrained quadratic optimization method (XFEM-BCQO) is adopted to quantify the optimum values of four design parameters for a circular tunnel lining when it is subjected to earthquakes. The parameters are: tunnel lining thickness, tunnel diameter, tunnel lining concrete modulus of elasticity and tunnel lining concrete density. Monte-Carlo sampling method is dedicated to construct the meta models so that to be used for the BCQO method using matlab codes. Numerical simulations of the tensile damage in the tunnel lining due to a real earthquake in the literature are created for three design cases. XFEM approach is used to show the cracks for the mentioned design cases. The results of the BCQO method for the maximum design case for the tunnel tensile damage was matching the results obtained from XFEM approach to a fair extent. The new coupled approach manifested a significant capability to predict the cracks and spalling of the tunnel lining concrete under the effects of dynamic earthquakes. Corresponding Author(s): Nazim Abdul NARIMAN Just Accepted Date: 30 August 2019   Online First Date: 17 October 2019    Issue Date: 21 November 2019
 Cite this article: Nazim Abdul NARIMAN,Ayad Mohammad RAMADAN,Ilham Ibrahim MOHAMMAD. Application of coupled XFEM-BCQO in the structural optimization of a circular tunnel lining subjected to a ground motion[J]. Front. Struct. Civ. Eng., 2019, 13(6): 1495-1509. URL: http://journal.hep.com.cn/fsce/EN/10.1007/s11709-019-0574-y http://journal.hep.com.cn/fsce/EN/Y2019/V13/I6/1495
 Fig.1  Free-field shear strain (ovaling deformation style). Fig.2  Horizontal component time history of the ground motion. Fig.3  Vertical component time history of the ground motion. Fig.4  Finite element model. (a) Soil and tunnel lining models; (b) tunnel lining model; (c) boundary conditions. Tab.1  Ranges of tunnel lining parameters Fig.5  Coefficient of regression-maximum principal stress of the tunnel. Tab.2  Design cases Fig.6  Compressive damage of the tunnel-minimum case. Fig.7  Compressive damage of the tunnel-medium case. Fig.8  Compressive damage of the tunnel-maximum case. Fig.9  Tensile damage of the tunnel-minimum case. Fig.10  Tensile damage of the tunnel-medium case. Fig.11  Tensile damage of the tunnel-maximum case. Fig.12  Minimum case (time= 3.607 s). Fig.13  Minimum case (time= 6.138 s). Fig.14  Medium case (time= 2.454 s). Fig.15  Medium case (time= 5.565 s). Fig.16  Maximum case (time= 1.981 s). Fig.17  Maximum case (time= 4.937 s). Fig.18  Maximum case (time= 4.941 s).