Effects of time integration schemes on discontinuous deformation simulations using the numerical manifold method

Abstract

Summary Numerical stability by using certain time integration scheme is a critical issue for accurate simulation of discontinuous deformations of solids. To investigate the effects of the time integration schemes on the numerical stability of the numerical manifold method, the implicit time integration schemes, ie, the Newmark, the HHT‐α, and the WBZ‐α methods, and the explicit time integration algorithms, ie, the central difference, the Zhai's, and Chung‐Lee methods, are implemented. Their performance is examined by conducting transient response analysis of an elastic strip subjected to constant loading, impact analysis of an elastic rod with an initial velocity, and excavation analysis of jointed rock masses, respectively. Parametric studies using different time steps are conducted for different time integration algorithms, and the convergence efficiency of the open‐close iterations for the contact problems is also investigated. It is proved that the Hilber‐Hughes‐Taylor‐α (HHT‐α), Wood‐Bossak‐Zienkiewicz‐α (WBZ‐α), Zhai's, and Chung‐Lee methods are more attractive in solving discontinuous deformation problems involving nonlinear contacts. It is also found that the examined explicit algorithms showed higher computational efficiency compared to those implicit algorithms within acceptable computational accuracy.

Dynamic Stability Analysis of Rockmass: A Review

“…Zhao et al [95,96] extended NMM to study wave propagation across rockmasses and developed a continuum-discontinuum-coupled model to simulate rock failure under dynamic loads. Qu et al [97,98] used the improved NMM to evaluate the dynamic stability of fractured rockmass slopes under seismic action. Wu and Wong [99] studied the collapse instability caused by joints or mining fissures in underground adits or tunnels using the numerical method.…”

Modified predictor‐corrector solution approach for efficient discontinuous deformation analysis of jointed rock masses

“…The CA approach has been incorporated in the original DDA approach, where the OCI is applied to ensure that the no‐tension and no‐penetration requirements are satisfied . The no‐penetration requirement is represented by where δ p is the computed penetration value in OCI, δ c is the contact search tolerance, and δ represents a user‐defined ratio, usually set to be around 10 −4 to 10 −6 . The convergence of open‐to‐open, closed‐to‐closed (or locked‐to‐locked, sliding‐to‐sliding) contact modes is achieved through iterations, where the contact terms in the equilibrium equation may be added or removed according to the status of individual contacts.…”