Journal of Applied Mathematics and Physics, 2014, 2, 359-364
Published Online May 2014 in SciRes. http://www.scirp.org/journal/jamp
How to cite this paper: Yang, Q.Q., Su, Z.M. and Cai, F. (2014) DDA Simulations of Large Flume Tests and Large Landslides
Triggered by the Wenchuan Earthquake. Journal of Applied Mathematics and Physics, 2, 359-364.
DDA Simulations of Large Flume Tests and
Large Landslides Triggered by the
Qingqing Yang1, Zhiman Su2, Fei Cai3
1Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu, China
2Institute of Mountain Hazards and Environment, Chengdu, China
3Department of Environmental and Engineering Science, Gunma University, Kiryu, Japan
Email: yangq email@example.com m
Received March 2014
This paper presents some numerical simulations using Discontinuous Deformation Analysis
(DDA). First, DDA was applied to reproduce a series of granular flows released in a large flume.
The comparison between simulated velocity and that measured in the tests demonstrates the ef-
fectiveness of DDA on description of kinematic behavior of blocky assembly. Simulated results
were highly sensitive to the shape and angularity of blocky elements. Employing unrealistic block
might result in different behavior from real situation. Second, three large landslides triggered by
the Wenchuan earthquake were si mu lated. A well agreement with field data was obtained if ap-
parent friction coefficient determined by post-an al ysis was adopted.
Discontinuous Deformation Analysis, Flume Test, Lansdslide
Discontinuous Deformation Analysis (DDA) is one of most popular discrete element methods for discontinuous
rock mass. DDA, which was originally formulated by Shi , forms a system of algebraic equations based on
the principle of minimum potential energy and uses displacements as variables in an implicit formulation.
Though DDA was developed during the late 1980s, and is thus a relatively new numerical simulation tool, it has
been applied to a wide range of problems, and researchers in the DDA community have dedicated a great deal of
effort to document the accuracy of this method by performing validation studies.
2. DDA Simulations of Large Flume Tests
A detailed description about the large flume tests was presented in Yang et al. . The large flume consists of
an upper slope 5.5 m long and inclined at 45˚ connected to a lower slope 10.0 m long and inclined at 10˚. Table
1 shows the varied test conditions.
Q. Q. Yang et al.
Table 1. Summary of large flume tests.
Case No. Test conditions Initial
Cubes [kg] Cobbles [kg] Gravel
La r g e Small La r g e Small
2 Matting Triangle 200 200 0 0 0 400
3 Matting Triangle 0 0 0 0 400 400
4 Matting Triangle 200 200 0 0 400 800
10 Matting Tria ngle 0 0 200 200 0 400
14 Matting Tria ngle 0 0 200 200 400 800
The geometry and initial configuration of the numerical model were based on a 2D reproduction of the expe-
rimental conditions. The effect of the flume’s sidewalls was not taken into account because their roughness was
sufficiently small to ensure the flow in 2D conditions. The shear strength of the materials was measured by the
large-scale direct shear tests . The joints were assumed with zero tensile strength. The numerical control pa-
rameters were as follows: the time step size = 0.001 s, the maximum allowed displacement ratio = 0.00085, the
contact spring stiffness = 1 × 106 kN/m.
2.1. Mono-Mat e rials
Figure 1 illustrates the initial arrangement of granular elements for DDA simulations for case 2 (400 kg cubes),
case 3 (400 kg gravel), and case 10 (400 kg cobbles).
Figure 2(a) shows that the trend of the simulated velocities corresponded well with that of the measured ve-
locities in case 2. Both the simulated and measured velocities fluctuated due to the propulsion of subsequent
particles to the slowed front by impact. This confirmed the conclusion that continuous collisions among particles
are partly responsible for the high mobility and long run-out of rock avalanches . DDA accurately reflected
this important phenomenon of continuous collisions.
A total of 178 irregular quadrangles were generated randomly to simulate the gravel in case 3. The simulated
velocity agreed with the measured one (Figure 2(b)).
Figure 2(c) also shows that DDA accurately predicted the velocity of the cobbles in case 10. Furthermore, the
cobbles were also simulated by regular octagons. The simulated velocity of the regular octagon was much higher
than that of the hexagon, and also much higher than the velocity measured in the tests. A majority of the octa-
gonal blocks moved beyond the flume and stopped on the horizon; this was significantly different from the situ-
ation occurred in the tests. Thus, the velocity and run-out were highly sensitive to the shape and angularity of the
granular elements in the numerical analysis. This conclusion corresponded with that drawn by other researchers
, who found that the DDA simulation results are extremely sensitive to computed meshes. Therefore, the
shape and angularity of the blocks had to be determined carefully in the numerical model because the use of un-
realistic granular elements may cause the grain behavior to be modeled inaccurately.
Figure 3 shows that two composites were initially arranged as alternating layers of blocks and gravel (a compo-
site of 400 kg cubes and 400 kg gravel in case 4, and a composite of 400 kg cobbles and 400 kg gravel in case
14). A total of 68 cubes in case 4 and 105 cobbles in case 14 were arranged at the positions as close as possible
to those in the tests.
DDA accurately predicted low velocities of the composite of cubes and gravel in case 4 (Figure 4(a)), com-
paring with the cube and gravel mono-materials with small volumes (cases 2 and 3). The agreement between the
simulation and experiment indicates that the energy dissipation caused by friction between the gravel and cubes
was modeled accurately by DDA.
DDA also accurately predicted an unexpectedly high velocity of the composite of cobbles and gravel in case
14 (Figure 4(b)), almost the same as those for the cobble and gravel mono-materials. However, the simulated
Q. Q. Yang et al.
(a) (b) (c)
Figure 1. Initial geometry of the blocks in Cases 2, 3, and 10. (a) Case 2; (b) Case 3; (c) Case 10.
(a) (b) (c)
Figure 2. Simulated and measured velocities of mono-materials in Cases 2, 3, and 10. (a) Case 2; (b) Case 3; (c) Case 10.
Figure 3. Initial geometry of the blocks in Cases 4
and 14. (a) Case 4; (b) Case 14.
Fig ure 4. Simulated and measured velocities of composites in Cases 4 and 14. (a) Case 4; (b) Case 14.
Q. Q. Yang et al.
velocity fluctuated more because the DDA in this study did not take the energy loss caused by the collision
among particles and the collision between particles and the flume into account. Thus, the velocity of the frontal
particles increased more significantly when subsequent high-velocity particles provided propulsion to allow
them to accelerate. Collisions frequently occurred and considerably dissipated the energy. A restitution coeffi-
cient should be introduced to consider the energy loss caused by the collisions. Ma et al.  proposed a mod-
ified DDA method by introducing a restitution coefficient to account for the energy loss caused by the collisions
when simulating rock-fall. They found that the velocity of rock-falls is most accurately simulated using a resti-
tution coefficient of 0.7. Unfortunately, the restitution coefficient was not introduced in DDA program used in
3. DDA Simulat ions of Large Landslides
3.1. The Donghekou Landslide
The Donghekou landslide-debris flow is a typical rapid, long run-out, compound landslide with the height dif-
ference between the toe and main scarp of 540 m, a sliding distance of 2270 m, and a volume of 15 million m3
. This landslide buried seven villages and and killed 780 people, and it dammed two confluent rivers forming
a massive lake. It is composed of sandstone, shale, and schist of Cambrian age and is located about 4 km from
the active fault-rupture trace.
The main numerical control parameters of DDA simulation are as follows: the time step size = 0.01 s, the
maximum allowed displacement ratio = 0.0015, the contact spring stiffness = 5 × 108 kN/m, and the factor of
over-relaxation = 1.3.
The deposit, calculated using the friction angle of about 35˚, measured in laboratory, was combined with the
actual final deposit observed in the field, as illustrated in Figure 5. The sliding mass remained in approximately
the same place at 200 s (20,000 time steps) after the inception of motion. The calculated run-out was much
shorter than the actual run-out. The trial calculations show that simulation results were significantly affected by
friction coefficient. The friction coefficient measured in the laboratory was difficult to reproduce the extremely
long run-out of the rock avalanche. This implies that the ‘size effect’ should be considered in the simulation of
For the Donghekou landslide, the apparent friction coefficient was 0.238 . When the apparent friction coef-
ficient was used, the calculated deposit corresponded well with the actual deposit (Figure 6). Whether the ap-
parent friction coefficient can be served as a reasonable parameter in reproducing the actual deposit of field rock
avalanches will be further confirmed by other two large landslides also triggered by the Wenchuan earthquake.
Figure 5. Calculated final deposit of the Donghekou landslide when the measured fric-
tion coefficient was used.
Figure 6. Calculated final deposit of the Donghekou landslide when the apparent fric-
tion coefficient was used.
Q. Q. Yang et al.
3.2. The Xinbei Middle School Landslide
The Xinbei Middle School landslide reactivated by the Wenchuan earthquake, its geologic components consist-
ing of thick limestone of upper Devonian and lower Carboniferous Periods. It has a length of 560 m, a width of
200 m, an average thickness of 20 m, a maximum thickness of 40 m, a height difference of 300 m, and a volume
of 2.4 million m3. Among the displaced sliding mass, there are huge blocks with maximum single-block vo-
lumes of 1000 m3. The huge blocks destroyed a three-story building and several adjacent houses. About 700
people were killed by this landslide. At the toe part of the landslide deposit, upheaval occurred at the ground
surface along the main street, which was thought to be related to the thrust scarp resulting from movement on
the earthquake fault.
The main numerical control parameters necessary for DDA were the same as those used for the simulation of
the Donghekou rock avalanche. The apparent friction coefficient of this landslide was 0.625. The calculated de-
posit was combined with the actual final deposit observed in the field, as illustrated in Figure 7. The calculated
deposit was consistent with the actual deposit for the Xinbei Middle School landslide.
3.3. The Shibangou Landslide
The Shibangou landslide was 815 m long, 790 m wide, an average thickness of 15 m, a maximum thickness of
50 m, a height difference of 240 m, and a volume of 4.5 million m3. More than 200 people were killed by this
landslide. It dammed the Qingzhujiang river forming a massive lake with a maximum reservoir capacity of 11
The main numerical control parameters of DDA were the same as those used for the simulation of the Dong-
hekou rock avalanche. The apparent friction coefficient of 0.268 was used for the Shibangou landslide.
Figure 8 shows that the calculated deposit agreed well with the actual deposit observed in the field for the
Figure 7. Calculated final deposit of the Xinbei Middle School landslide when ap-
parent friction coefficient was used.
Figure 8. Calculated final deposit of the Shibangou landslide when apparent fric-
tion coefficient was used.
Q. Q. Yang et al.
In this paper, the large flume tests and three large landslides triggered by the Wenchuan earthquake were repro-
duced by DDA, and the following conclusions to be obtained.
(1) DDA was capable of giving considerably satisfactory simulations of the large flume tests, and the differ-
ences between the simulations and measurements were limited to an acceptable range. This consistency de mo n-
strates that DDA effectively described the kinematic behavior, material characteristics, and topographic con-
straint of granular flows in the large flume tests.
(2) Both the simulated and measured velocities in the large flume tests fluctuated due to the propulsion of
subsequent particles to the slowed front by impact. DDA accurately reflected this important phenomenon of the
continuous collision among particles, which was partly responsible for the high mobility and long run-out of
(3) The simulated results were highly sensitive to the shape and angularity of granular elements; thus, em-
ploying realistic elements was important for predicting the behavior of granular flows in real situatio ns.
(4) DDA also accurately predicted low velocities of the composite of cubes and gravel, and the agreement
between the simulation and experiment indicates that DDA accurately modeled the energy dissipation caused by
the friction among particles.
(5) Simulation results show that friction coefficient strongly influenced final deposits of large events. The
calculated deposit was only similar to the actual deposit when the apparent friction coefficient, which was de-
termined by field investigation, was used rather than the friction coefficient measured in the laboratory.
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