Elsevier

Computers and Geotechnics

Volume 81, January 2017, Pages 87-97
Computers and Geotechnics

Technical Communication
A new approach for modeling landslide movement over 3D topography using 3D discontinuous deformation analysis

https://doi.org/10.1016/j.compgeo.2016.07.015Get rights and content

Abstract

Landslide movement analysis over three-dimensional (3D) topography is crucial for hazard evaluation and prevention. This paper presents a new approach to simulate landslide movement considering the 3D spatial effects of both the landslide mass and topography using discontinuous deformation analysis (DDA). The approach involves two aspects: the ordered blocky topography (OBT) treatment for the base slope and an algorithm for fast contact detection between the landslide block (LB) and the OBT. By introducing the OBT treatment, the LB-OBT contact detection can be simplified from the global range to the local sub-topography using the current algorithm, which enhances the computation efficiency. The approach has been implemented in the 3D-DDA program. Finally, the capability and performance of the proposed approach for landslide movement modeling were well demonstrated by two numerical examples.

Introduction

Landslides are considered among the most notable natural hazards around the world because of their frequent occurrence and catastrophic consequences. There have been many reports about landside-induced fatalities and economic losses, particularly along mountainous areas. For instance, more than 20,000 landslides were triggered by the 1999 Chi-Chi earthquake in Taiwan, causing more than 8000 causalities and nearly 10 billion US$ in economic losses [1], [2], [3]. Only a decade later, the 2008 Wenchuan earthquake shocked southwestern China and induced as many as 60,104 landslides, which consequently caused approximately 69,227 fatalities and destroyed innumerable infrastructures and houses [4], [5], [6]. The severe threats of landslides to people, property and environment depend largely on landslide velocity and travel distance, which are the main components of landslide movement [7]. Hence, the analysis of the post-failure behavior of a landside is of great importance to mitigation design and hazard evaluation and has drawn the attention of scholars worldwide.

Over the past few years, many methods have been proposed to analyze the post-failure movement of landslides based on the continuum mechanics. For example, Iverson et al. [7] employed a shock-capturing finite-volume method (FVM) and adaptive mesh refinement (AMR) to perform numerical simulation of a high-mobility landslide in Oso, Washington, USA. Similar simulation methods were also presented in previous studies [8], [9], [10], [11], [12]. In their simulation, the landslide mass was more likely treated as a continuous flow consisting of grain-fluid mixtures. Thus, they are very suitable for investigating the movement of rainfall-induced landslides with flow type. However, for landslides dominated by discontinuity, the continuous-based methods disregard the contact between individual rock masses, which causes difficulty in tracing the position or trajectory of the discrete rock mass during the landslide movement. In addition, with respect to the vertical information of the landslides in those simulations, only the landslide depth variation is presented while neglecting the vertical velocity information. Therefore, those simulations are not very useful for investigating landslide movement in three dimensions.

Regarding discrete numerical methods, the distinct element method (DEM) [13], [14], [15], [16], [17] and discontinuous deformation analysis (DDA) [18], [19], [20], [21], [22], [23], [24], [25] are the most popular ones for modeling landslide movement and analyzing the deformation of mass bodies. Both DEM and DDA adopt the equations of dynamic motion, which are solved at finite points in a series of time steps, but there are some significant differences in their formulations of the solution scheme and contact mechanics [3]. In the solution scheme, the governing equations in DDA are derived by the principle of minimization of the total potential energy of the block system, similar to the finite element method (FEM), whereas the equations in DEM are obtained from the force balance. This implementation in DEM will result in unbalanced force after a certain computation step, so artificial damping is required to dissipate energy [26]. In the contact mechanics, DDA uses a penalty method in which the contact is assumed to be rigid. No overlapping or interpenetration is allowed, so the block system behaves like a real physical case. However, the soft contact approach used in DEM requires joint stiffness determined by laboratory test or field investigation, which may be difficult to obtain in many cases [3]. In summary, the DDA method has the advantages of both the DEM and FEM methods [27] and thus is very capable of analyzing landslide movement with large deformation and large displacement in a discontinuous blocky system.

Since the theory and numerical code of DDA were presented, many extensions and improvements to the original code have been proposed for a wide range of applications—for example, DDA simulation for seismic landslide movement [3], [23], [28], [29] and rockfall analysis [18], [30], [31], [32]. However, practical applications for landslides using DDA have concentrated thus far on the 2D problem. To extend to a more realistic practical problem, the 3D-DDA simulations are necessary for two reasons. First, the 3D spatial effects due to the rock fragment shape and topography are very important for the landslide movement in lateral directions. Second, the trees and barriers distributed in the 3D spatial could also affect the landslide movement.

Regarding the 3D-DDA method, only in recent years has a series of developments been achieved, having been first proposed in 2001 by Shi [20]. However, the development of 3D-DDA is still at an early stage, and most of the studies concentrate on the basic theory, especially the contact theory, because the contact mechanism between 3D blocks is rather complicated. To date, a set of contact models have been proposed to address the contact mechanism [24], [27], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42]. Particularly, Zhang et al. [24] presented a novel algorithm that can detect contacts between arbitrarily shaped 3D polyhedral blocks (both convex and concave blocks). Owing to these contributions, many test models employing simple geometries have been conducted to validate the performance and accuracy of 3D-DDA [43], [44], [45]. Nevertheless, the application for realistic landslide movement simulation is still very rare owing to the difficulties in topography implementation.

The purpose of this paper is to present a new approach for modeling landslide movement over complicated 3D topography using the 3D-DDA method. For this purpose, three problems should be addressed. The first is how to consider the topography in the computation. A proper method should then be developed to easily generate a complicated topography that can be incorporated in the block system for DDA simulation. The last point will be how to ensure the computational efficiency because more complicated topography indicates many more faces and vertices for contact detection. The details of the problems and their solutions could be found in the following sections.

Section snippets

Theory of 3D-DDA

In the DDA method, the formulation of blocks is very similar to that of finite element meshes. A problem is solved in which all elements are physically isolated blocks defined by preexisting discontinuities. The global equilibrium equations are derived by the principle of minimization of potential energy contributed by the noncontact and contact loadings. The large displacements are the accumulation of incremental displacements and deformations at each time step. Within each small time step,

Treatment of the topography

For the simulation of landslide movement over 3D topography, a very large base area is required, which should include the source area, slope and potential run-out area. In the original 2D-DDA, the base of the slope or named topography is treated as a single block. By this treatment, the original 2D-DDA can be extended for more practical engineering problems.

Regarding the treatment of topography in 3D-DDA, very few works on this problem have been published. A possible solution for the problem is

Overview

The main feature of the OBT is that the upper surface consists of a series of regular triangular faces that are arranged orderly. Fig. 4 shows a simple OBT model. In this model, the upper surface of the OBT is made up of 30 vertices ranging from 8 to 37, and 40 faces numbered from 6 to 45.

To present the features of the OBT in detail, the projection view of the upper surface in the xy plane is presented in Fig. 5. Apparently, the surface is first decomposed into 5 rows and 4 columns, totaling 20

Numerical examples

To validate the capability and performance of the proposed approach for modeling the landslide movement over 3D topography, two numerical examples were carried out. The first one employs a simple model introduced in Section 4.3, and the second example shows the landslide movements over complicated 3D topography.

Conclusions

Three-dimensional simulation of landslide movement over complicated topography is very important for hazard evaluation and mitigation design in practical engineering. For this purpose, we proposed a new approach involving the OBT treatment and contact detection algorithm between the OBT and LB.

By introducing the OBT, LB-OBT contact detection can be simplified from the global topography to the local sub-topography, which enhances the computation efficiency. The generation method of the OBT was

Acknowledgement

The authors extend their gratitude to three anonymous reviewers for their insightful comments. In addition, the authors appreciate the financial support from National Science & Technology Pillar Program of the Ministry of Science and Technology of China (Grant No. 2014BAL05B01).

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