Development of a Composite Implicit Time Integration Scheme for Three-Dimensional Discontinuous Deformation Analysis

Guoyang Liu (), Junjie Liu, Shouyi Luo, Wu Bo, Jiashuo Kang and Jianbin Miao
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Guoyang Liu: School of Architecture and Civil Engineering, Shenyang University of Technology, Shenyang 110870, China
Junjie Liu: School of Architecture and Civil Engineering, Shenyang University of Technology, Shenyang 110870, China
Shouyi Luo: School of Architecture and Civil Engineering, Shenyang University of Technology, Shenyang 110870, China
Wu Bo: School of Engineering, Tibet University, Lhasa 850011, China
Jiashuo Kang: School of Architecture and Civil Engineering, Shenyang University of Technology, Shenyang 110870, China
Jianbin Miao: School of Architecture and Civil Engineering, Shenyang University of Technology, Shenyang 110870, China

Mathematics, 2023, vol. 11, issue 18, 1-19

Abstract: Discontinuous deformation analysis (DDA) is a discontinuum-based and implicit method for investigating the deformational behavior of block systems. The constant acceleration integration (CAI) scheme characterized by unconditional stability is employed in the traditional DDA. In this study, the problems of the CAI scheme regarding the time step in DDA are pointed out. A too large or too small time step size adopted in the CAI scheme will have adverse effects on the DDA computation. To overcome the weaknesses, an alternative composite implicit time integration (CITI) scheme, which is a combination of the trapezoidal rule and the three-point backward Euler method, is implemented in the three-dimensional (3D) DDA method. Verification examples and slope numerical simulations are presented to illustrate the accuracy and effectiveness of the proposed methodology. The results showed that the CITI scheme can overcome the numerical error caused by the large time step size, and the algorithm damping is closely related to the time step size and the selected splitting parameter.

Keywords: 3D DDA; CAI scheme; CITI scheme; time step size; algorithm damping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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