A Three-Dimensional Numerical Model for Simulating Deformation and Failure of Blocky Rock Structures

2006 ◽  
Vol 306-308 ◽  
pp. 1391-1396 ◽  
Author(s):  
Yu Yong Jiao ◽  
Quan Sheng Liu ◽  
Shu Cai Li
Keyword(s):  
Numerical Model ◽  
Stiffness Matrix ◽  
Three Dimensional ◽  
Small Displacement ◽  
Equilibrium Equations ◽  
Deformation And Failure ◽  
Static Relaxation ◽  
Global Equilibrium ◽  
C Program ◽  
Global Stiffness Matrix

This paper presents a three-dimensional numerical model for simulation of blocky rock structures based on static relaxation approach. The proposed method utilizes static equilibrium equations to calculate the displacements of blocks, compared to Newton’s second law applied by the traditional DEM. In order to obtain displacements simultaneously, the technique of global stiffness matrix is introduced in to form the global equilibrium equations. Because large displacements come from the accumulation of small displacement increments, an iteration procedure is adopted in the calculation. A C++ program is developed based on the proposed algorithm, and an illustrative example is computed for verification.

scholarly journals A rigorous method for three-dimensional asymmetrical slope stability analysis

2018 ◽  
Vol 55 (4) ◽  
pp. 495-513 ◽  
Author(s):  
Qinghui Jiang ◽  
Chuangbing Zhou
Keyword(s):  
Slope Stability ◽  
Slip Surface ◽  
Three Dimensional ◽  
Equilibrium Equations ◽  
Equilibrium Conditions ◽  
Fast Convergence Rate ◽  
Potential Failure ◽  
Global Equilibrium ◽  
Solution Accuracy ◽  
Rigorous Method

Most slope failures exhibit remarkable asymmetrical variation in the transverse direction. A rigorous method satisfying all six equilibrium conditions is proposed for evaluating three-dimensional (3-D) asymmetrical slope stability. As there is no need to predefine a symmetrical plane in this analysis, the method is applicable to slopes with complex geometries, geologies, and loading conditions. The proposed method can not only calculate the factor of safety, but also predict the direction of sliding of the potential failure mass. Global equilibrium equations are formulated in light of the safety factor, sliding direction, and an assumed distribution of normal stress on the slip surface. The Newton method is then used to solve these equations, which has been proven to enjoy both a large range of convergence and a fast convergence rate. Thereafter, physical admissibility conditions of the solutions, and the effects of the size of discretized columns on solution accuracy, are discussed in the present 3-D analysis. The method is validated by using five typical examples documented in the literature. The failure of the Kettleman, California, waste landfill slope is also re-evaluated using the proposed method. The calculated stability and direction of sliding match field observations.

Analytical Evaluation of the Double Stewart Platform Tensile Truss Stiffness Matrix

2013 ◽  
Vol 6 (1) ◽  
Author(s):  
Adam H. Hesselroth ◽  
Michael P. Hennessey
Keyword(s):  
Stiffness Matrix ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Stewart Platform ◽  
Physical Models ◽  
Measuring System ◽  
Small Displacement ◽  
Mobile Platforms ◽  
Specific System ◽  
External Forces

The 6 × 6 stiffness matrix for a single Stewart platform tensile truss is well known. This work extends the methodology used to determine the stiffness matrix of a double Stewart platform system, in which one Stewart platform is stacked on top of another, in serial fashion. A double Stewart platform may offer advantages for some applications in terms of increased stiffness in certain directions. Using principles of statics and considering small displacement perturbations in three-dimensional space of both mobile platforms (middle and bottom) from their weighted equilibrium locations, displacements can be related in a linear manner to application loading, implying a stiffness matrix. Scripts are then developed and executed in matlabtm to determine the stiffness matrix of a specific system. The matlabtm result is validated using single and double Stewart platform physical models and measuring system compliance responses to external forces and moments.

NEW CONTACT-DEFINITION ALGORITHM USING INSCRIBED SPHERES FOR 3D DISCONTINUOUS DEFORMATION ANALYSIS

2011 ◽  
Vol 08 (02) ◽  
pp. 171-191 ◽  
Author(s):  
TAE-YOUNG AHN ◽  
JAE-JOON SONG
Keyword(s):  
Three Dimensional ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Small Displacement ◽  
Contact Detection ◽  
Equilibrium Equations ◽  
Suggested Algorithm ◽  
Sphere Size ◽  
Discontinuous Deformation ◽  
Definition Of

The speed and stability of three-dimensional (3D) discontinuous deformation analysis (DDA) are strongly dependent on the efficiency and correctness of contact detection and the definition algorithm, which affects the simultaneous equilibrium equations solved in every open–close iteration (OCI) retry. In particular, the definition of vertex-to-vertex contacts in a tangled zone may abruptly change the entrance planes, even in the case of very small displacement of the objects. This study proposes a new contact-definition algorithm using an inscribed sphere virtually installed in every contacting vertex. The suggested algorithm generates virtual entrance planes in the case of a vertex-to-vertex contact, and controls the accuracy of the contact definition process by adjusting the sphere size. Verification tests of the proposed algorithm indicate an increase in the efficiency and stability of 3D DDA.

A THREE-DIMENSIONAL NUMERICAL MODEL FOR SELECTIVE WITHDRAWAL IN COASTAL AREA

2018 ◽  
Vol 74 (5) ◽  
pp. I_571-I_576
Author(s):  
Yasuo NIIDA ◽  
Norikazu NAKASHIKI ◽  
Takaki TSUBONO ◽  
Shin’ichi SAKAI ◽  
Teruhisa OKADA
Keyword(s):  
Numerical Model ◽  
Coastal Area ◽  
Three Dimensional ◽  
Selective Withdrawal

scholarly journals Blowing and drifting snow in Alpine terrain: numerical simulation and related field measurements

1998 ◽  
Vol 26 ◽  
pp. 174-178 ◽  
Author(s):  
Peter Gauer
Keyword(s):  
Numerical Simulation ◽  
Numerical Model ◽  
Three Dimensional ◽  
Field Measurements ◽  
Blowing Snow ◽  
Related Field ◽  
Drifting Snow ◽  
Physically Based ◽  
Snow Transport

A physically based numerical model of drifting and blowing snow in three-dimensional terrain is developed. The model includes snow transport by saltation and suspension. As an example, a numerical simulation for an Alpine ridge is presented and compared with field measurements.

Three-dimensional numerical model of short-circuiting transfer in GMAW

2020 ◽  
Vol 64 (12) ◽  
pp. 2011-2017
Author(s):  
K. Hashimoto ◽  
Y. Hirata ◽  
K. Kadota ◽  
Y. Ogino
Keyword(s):  
Numerical Model ◽  
Three Dimensional
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