Direct Calculation Method for the Analysis of Non-linear Behavior of Ground-Support Interaction of a Circular Tunnel Usi
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ORIGINAL PAPER
Direct Calculation Method for the Analysis of Non-linear Behavior of Ground-Support Interaction of a Circular Tunnel Using Convergence Confinement Approach Yu-Lin Lee
. Wen-Kuei Hsu . Chi-Min Lee . Yi-Xian Xin . Bo-Yu Zhou
Received: 13 May 2019 / Accepted: 26 August 2020 Springer Nature Switzerland AG 2020
Abstract The convergence-confinement method is widely used in conventional tunneling at a preliminary stage of the support design. A circular tunnel through the ground in an initially isotropic stress state and the behavior of ground-support interaction simplified utilizing a two-dimensional plane-strain are postulated. From a point of view of practical application, the direct algorithm process so-called the direct calculation method (DCM) is proposed in this paper to deal with solving the solution of stresses/displacements between the ground reaction curve (GRC) and the support confining curve (SCC) in the final equilibrium state by applying the simultaneous equations in the elastic region and using the numerical analysis known as the Newton recursion method for finding roots of the non-linear equations in the plastic region. This explicit procedure also can realize the analytical solution to an executable computation that can be Y.-L. Lee (&) Y.-X. Xin B.-Y. Zhou Department of Civil Engineering, Chung Hua University, No. 707, Sec.2, Wufu Rd., Hsinchu 30012, Taiwan, ROC e-mail: [email protected] W.-K. Hsu Department of Civil and Disaster Prevention Engineering, National United University, No. 1, Lienda, Miaoli 36003, Taiwan, ROC C.-M. Lee Department of Civil Engineering, Chung Yuan Christian University, No. 200, Zhongbei Rd., Taoyuan City 32023, Taiwan, ROC
stepwise estimated by using a simple calculation spreadsheet. The validity of the developed method for the analytical solution was examined by the finite element analysis (FEM) to investigate the influence of mechanical properties of the ground and the timedependent effects of the shotcrete lining-support on the GRC, SCC and stress path at the intrados of the tunnel. The agreement of results between DCM and FEM was found to be excellent in the elastic and elastic-perfectly plastic media. Keywords Direct calculation method Groundsupport interaction Newton recursion Convergenceconfinement method List of symbols CCM Convergence-confinement method CLC Confinement loss curve c Cohesion of the ground DCM Direct calculation method E Elastic modulus of the ground Eshot Elastic modulus of the shotcrete lining G Shear modulus of the ground GRC Ground reaction curve Ko In-situ initial stress ratio ks Stiffness of the support Kp Coefficient Kp ¼ tan2 45 þ u2 Kw Coefficient K ¼ tan2 45 þ w w
LDP
2
Longitudinal displacement profile
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Geotech Geol Eng
N ps r R Rp Rdp Rsp SCC tshot uR udR usR uzR u1 R Z / g kd kz ke ks m mshot h rc rR rdR rsR rh rdh rsh rv w
rc Stability number N ¼ 2r v Support pressure Distance in the polar coordinate Radius of tunnel excavation Plastic rad
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