The last entrance plane method for contact indeterminacy between convex polyhedral blocks

Abstract This study proposes the last entrance plane (LEP) principle to identify the physical contact plane, which is applicable to resolve contact indeterminacy between convex polyhedral blocks. Based on contact theory, the LEP principle reveals that the physical contact point lies on the last entrance plane. The LEP method is developed to identify the physical contact plane before penetration considering the geometrical and kinematical information. It offers a unified solution to contact indeterminacy between 2D convex polygonal and 3D convex polyhedral blocks. Using discontinuous deformation analysis, several numerical tests are evaluated to validate the accuracy and robustness of the LEP method.

[1]  Guangqi Chen,et al.  Evaluation of impact force of rock landslides acting on structures using discontinuous deformation analysis , 2019, Computers and Geotechnics.

[2]  Wei Wang,et al.  A new algorithm to identify contact types between arbitrarily shaped polyhedral blocks for three-dimensional discontinuous deformation analysis , 2016 .

[3]  Guangqi Chen,et al.  Applying modified discontinuous deformation analysis to assess the dynamic response of sites containing discontinuities , 2018, Engineering Geology.

[4]  A. Munjiza,et al.  NBS contact detection algorithm for bodies of similar size , 1998 .

[5]  Mingyao Xia,et al.  CPU-accelerated explicit discontinuous deformation analysis and its application to landslide analysis , 2020 .

[6]  Nicholas Sitar,et al.  Generalized contact model for polyhedra in three‐dimensional discontinuous deformation analysis , 2018, International Journal for Numerical and Analytical Methods in Geomechanics.

[7]  Jae-Joon Song,et al.  NEW CONTACT-DEFINITION ALGORITHM USING INSCRIBED SPHERES FOR 3D DISCONTINUOUS DEFORMATION ANALYSIS , 2011 .

[8]  Hehua Zhu,et al.  A multi-shell cover algorithm for contact detection in the three dimensional discontinuous deformation analysis , 2014 .

[9]  José V. Lemos,et al.  Procedure for contact detection in discrete element analysis , 2001 .

[10]  Guy T. Houlsby,et al.  A new algorithm for contact detection between convex polygonal and polyhedral particles in the discrete element method , 2012 .

[11]  Guangqi Chen,et al.  Distributed-Spring Edge-to-Edge Contact Model for Two-Dimensional Discontinuous Deformation Analysis , 2019, Rock Mechanics and Rock Engineering.

[12]  Hehua Zhu,et al.  Integration of three dimensional discontinuous deformation analysis (DDA) with binocular photogrammetry for stability analysis of tunnels in blocky rockmass , 2016 .

[13]  Hong Zhang,et al.  Contact detection between polygonal blocks based on a novel multi-cover system for discontinuous deformation analysis , 2019, Computers and Geotechnics.

[14]  A. Munjiza.  The Combined Finite-Discrete Element Method , 2004 .

[15]  Hong Zhang,et al.  A 3-D DDA damage analysis of brick masonry buildings under the impact of boulders in mountainous areas , 2018, Journal of Mountain Science.

[16]  Mark A. Hopkins,et al.  Polyhedra faster than spheres , 2014 .

[17]  S. Amir Reza Beyabanaki,et al.  New point-to-face contact algorithm for 3-D contact problems using the augmented Lagrangian method in 3-D DDA , 2009 .

[18]  Guangqi Chen,et al.  Extension and application of Discontinuous Deformation Analysis with a damped contact spring model , 2019, International Journal of Rock Mechanics and Mining Sciences.

[19]  Qian Sheng,et al.  Time-Frequency Analysis of Seismic Wave Propagation across a Rock Mass Using the Discontinuous Deformation Analysis Method , 2017 .

[20]  Youssef M A Hashash,et al.  Shortest link method for contact detection in discrete element method , 2006 .

[21]  P. Cundall.  A computer model for simulating progressive, large-scale movements in blocky rock systems , 1971 .

[22]  Bin Zeng,et al.  GPU-based parallel computation for discontinuous deformation analysis (DDA) method and its application to modelling earthquake-induced landslide , 2017 .

[23]  G. Shi.  Contact theory , 2015 .

[24]  Zheng Han,et al.  Detection of contacts between three-dimensional polyhedral blocks for discontinuous deformation analysis , 2015 .

[25]  Dawei Zhao,et al.  A fast contact detection algorithm for 3-D discrete element method , 2004 .

[26]  Jian-Hong Wu,et al.  Compatible algorithm for integrations on a block domain of any shape for three-dimensional discontinuous deformation analysis , 2010 .

[27]  Nicholas Sitar,et al.  A fast direct search algorithm for contact detection of convex polygonal or polyhedral particles , 2017 .

[28]  Bin Gu,et al.  Advances in Two-Dimensional Discontinuous Deformation Analysis for Rock-Mass Dynamics , 2017 .

[29]  Eric Perkins,et al.  A fast contact detection algorithm insensitive to object sizes , 2001 .

[30]  P. A. Cundall,et al.  FORMULATION OF A THREE-DIMENSIONAL DISTINCT ELEMENT MODEL - PART I. A SCHEME TO DETECT AND REPRESENT CONTACTS IN A SYSTEM COMPOSED OF MANY POLYHEDRAL BLOCKS , 1988 .

[31]  Yu-Yong Jiao,et al.  Object-Oriented Contact Detection Approach for Three-Dimensional Discontinuous Deformation Analysis Based on Entrance Block Theory , 2017 .

[32]  Bernard Amadei,et al.  Extensions of discontinuous deformation analysis for jointed rock masses , 1996 .

[33]  Wei Wang,et al.  A new DDA model for kinematic analyses of rockslides on complex 3-D terrain , 2018, Bulletin of Engineering Geology and the Environment.

[34]  Guangqi Chen,et al.  Development of a Coupled DDA–SPH Method and its Application to Dynamic Simulation of Landslides Involving Solid–Fluid Interaction , 2019, Rock Mechanics and Rock Engineering.

[35]  Zheng Han,et al.  Extensions of edge-to-edge contact model in three-dimensional discontinuous deformation analysis for friction analysis , 2016 .

[36]  Zhiye Zhao,et al.  The vertex-to-vertex contact analysis in the two-dimensional discontinuous deformation analysis , 2012, Adv. Eng. Softw..

[37]  Jian-Hong Wu,et al.  A new algorithm to identify contact patterns between convex blocks for three-dimensional discontinuous deformation analysis , 2008 .

[38]  Eric Perkins,et al.  A contact algorithm for partitioning N arbitrary sized objects , 2004 .

[39]  Zhiye Zhao,et al.  An alternative scheme for the corner-corner contact in the two-dimensional Discontinuous Deformation Analysis , 2010, Adv. Eng. Softw..

[40]  Guangqi Chen,et al.  Parallel computing of three-dimensional discontinuous deformation analysis based on OpenMP , 2019, Computers and Geotechnics.

[41]  Hehua Zhu,et al.  Method for Estimating Normal Contact Parameters in Collision Modeling Using Discontinuous Deformation Analysis , 2017 .

[42]  Jian Chen,et al.  Investigation of highly efficient algorithms for solving linear equations in the discontinuous deformation analysis method , 2016 .

[43]  Wei Wu,et al.  Tunnel stability assessment by 3D DDA-key block analysis , 2018 .

[44]  Huo Fan,et al.  An Angle-Based Method Dealing with Vertex–Vertex Contact in the Two-Dimensional Discontinuous Deformation Analysis (DDA) , 2015, Rock Mechanics and Rock Engineering.

[45]  Lu Zheng,et al.  Method for Resolving Contact Indeterminacy in Three-Dimensional Discontinuous Deformation Analysis , 2018, International Journal of Geomechanics.

[46]  Guangqi Chen,et al.  Improvement of joint definition and determination in three-dimensional discontinuous deformation analysis , 2019 .