Multi-slicing strategy for the three-dimensional discontinuity layout optimization (3D DLO)

Abstract

SummaryDiscontinuity layout optimization (DLO) is a recently presented topology optimization method for determining the critical layout of discontinuities and the associated upper bound limit load for plane two‐dimensional and three‐dimensional (3D) problems. The modelling process (pre‐processing) for DLO includes defining the discontinuities inside a specified domain and building the target function and the global constraint matrix for the optimization solver, which has great influence on the the efficiency of the computation processes and the reliability of the final results. This paper focuses on efficient and reliable pre‐processing of the discontinuities within the 3D DLO and presents a multi‐slicing strategy, which naturally avoids the overlapping and crossing of different discontinuities. Furthermore, the formulation of the 3D discontinuity considering a shape of an arbitrary convex polygon is introduced, permitting the efficient assembly of the global constraint matrix. The proposed method eliminates unnecessary discontinuities in 3D DLO, making it possible to apply 3D DLO for solving large‐scale engineering problems such as those involving landslides. Numerical examples including a footing test, a 3D landslide and a punch indentation are considered, illustrating the effectiveness of the presented method. © 2016 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.

Stability analysis of a fire‐loaded shallow tunnel by means of a thermo‐hydro‐chemo‐mechanical model and discontinuity layout optimization

“…I s and I n are the sets of indices of discontinuities restrained along the shear and normal direction, respectively. More details are given in previous works . Equation is an LP problem, which nowadays can be efficiently solved on personal computers, even with over a million of unknowns …”

“…A more recently proposed numerical approach, termed discontinuity layout optimization (DLO), is utilized for assessing the stability of fire‐loaded tunnels. It was previously adopted by the authors for solving other types of geotechnical problems in Zhang and Zhang et al In comparison to continuous and discontinuous nonlinear analysis methods, the DLO is a limit analysis procedure for solving convex optimization problems (linear programming in 2D and second‐order cone programming in 3D). It is characterized by great efficiency and robustness.…”

Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization

“…As pointed in Smith and Gilbert and Zhang, the spacing of the grid d p (fineness of the grid) has an influence on the final results, with a finer grid providing better results. Hence, the proper value of d p shall be determined firstly.…”

“…Recently, an innovative type of topology optimization method coined “discontinuity layout optimization (DLO)” was presented in Smith and Gilbert, which determines the critical layout of discontinuities and associated upper‐bound limit load for the plane (2D) and 3‐dimensional (3D) plasticity problems. By introducing a great amount of potential discontinuities, the layout of activated discontinuity will be automatically obtained by solving the corresponding linear programming (LP) and second‐order cone programming problems.…”

Transient Analysis of Grout Penetration With Time-Dependent Viscosity Inside 3D Fractured Rock Mass by Unified Pipe-Network Method

“…For predicting the grouting regions in fracture rock masses, numerical methods are much more flexible and are commonly implemented under the frameworks of extended [18][19][20][21][22]/embedded [23][24][25][26][27][28][29][30][31][32]/phase-field [33][34][35][36][37][38][39][40][41][42] finite element methods; rigid body based methods [43][44][45][46][47][48][49]; and even some sophisticated particle methods and peridynamic-based methods [50][51][52][53][54][55]. Nevertheless, most of these methods are developed for continuous media such as plain concrete [56][57][58], which are not suitable for highly fractured rock masses when the significant geological features of the fractures are not considered explicitly.…”