ANALYSIS OF ORE BLOCKAGES IN THE VERTICAL SHAFT AT OPEN PIT MINE BY
DISCRETE ELEMENT METHOD
*A. Sato and Y. Obara
Graduate School of Science and Technology
Kumamoto University
Kurokami 2-39-1, Chuo-ku, Kumamoto, 860-8555, Japan.
(* Corresponding author: E-mail: asato@kumamoto-u.ac.jp)
ANALYSIS OF ORE BLOCKAGES IN THE VERTICAL SHAFT AT OPEN PIT MINE BY
DISCRETE ELEMENT METHOD
ABSTRACT
Limestone is one of the most important mineral resources, and in Japan it is only one mineral which can be
fully supplied by the domestic product. Generally limestone mines in Japan located at mountainous regions,
and the combination between bench-cut method and the carry-out system using vertical shaft is widely
used in the domestic mines. During mining operations, the occurrence of the blockage in the vertical shafts
is very serious problem. Once the blockage in the shafts is occurred, a lot of works and dangerous
procedures are necessary to solve the problems. It is thought that blockage is influenced by the cohesion
and friction coefficient due to clay minerals thrown into the vertical shafts, however, the quantitative and
precise reason is not revealed yet.
In this study, the process of blockage occurrence was simulated by 2-Dimensional Discrete Element
Method (DEM). In the 2D-DEM analysis, discontinuous circular particles are generated, and the individual
movement of each particle is calculated by forward difference method. In the analysis, several typical ore
distributions are applied, and the DEM analysis was conducted under the various combinations of cohesion
and friction coefficient. From analytical results, it was found that the friction coefficient strongly
influences to the occurrence of blockage and there were a threshold values which blockage does not occur.
Several kinds of shaft shape were also simulated towards different ore size distributions, and those
influences to the blockage occurrence were also discussed.
KEYWORDS
Blockage, Vertical shaft, Limestone, Cohesion, Friction coefficient Carry-out system of ores
INTRODUCTION
Limestone is one of the most important mineral resources, and in Japan it is only one mineral
which can be fully supplied by the domestic product. Now in Japan, more than 300 limestone mines are
under operations, and approximately 150 million tons of limestone are produced every year (Limestone
Associate of Japan, 2013). In the case of Japan, most of limestone mines are located at mountainous
regions, and the combination between bench-cut method and the carry-out system using vertical shafts
(Figure 1) is widely used. However, the blockage in the vertical shafts sometimes occurred and some
examples are recently reported (Hadjigeorgiou, 2007). Once the blockage in the shafts is occurred, it will
cause serious problems towards total mine operations, and a lot of works, such as the injection of huge
amount of water into the shafts, and dangerous procedures, such as the blasting in/near the shafts, are
necessary to solve the problems. Therefore, the blockage is one of the important issues which should be
avoided during mining operations. It is thought that blockage is influenced by the cohesion due to clay
minerals thrown into the vertical shafts, however, the quantitative and precise reason is not revealed yet.
In this study, the process of blockage occurrence is simulated by 2-Dimensional Discrete Element
Method (DEM). In the 2D-DEM analysis, discontinuous circular particles are generated, and the individual
movement of each particle is calculated by forward difference method (Cundall, 1971&1979). Since the
movement of each ore is similar to the procedure, it is suitable method to simulate the movement of ores
and the blockage process in the vertical shaft. For example, this method was applied to the analysis of the
hang-up phenomena (Hadjigeorgiou and Lessard, 2007). The blockage condition in the vertical shafts was
also simulated (Sato and Obara, 2014). In the case of Japanese limestone mines, vertical shafts which
diameter is 8m are widely used and this size was set as a standard analytical model. Ore size distributions
are also measured at many mines. In many cases, ore size distributions obey Gaussian distribution, and the
mean value and standard deviations of ore diameter have been obtained. In the analysis, several typical ore
distributions are applied in the DEM analysis. As is stated before, cohesion and friction coefficient
between ores are thought to be main factors which cause the blockage in the shafts. In this study, these
parameters are given to the analysis, and those influences to the blockage occurrence are discussed.
Moreover, the influence of shaft size and ore size distributions are also simulated, and those influences to
the blockage occurrence are discussed.
Vertical shaft
Ore storage
Carry-out tunnel
Figure 1 – Schematic of open pit limestone mine.
NUMERICAL ANALYSIS AND MODDELING OF VERTICAL SHAFTS
DEM Analysis
PFC2D which is produced by Itasca Consulting Group Inc., is used as a DEM analysis software. In
the 2D-DEM analysis, discontinuous circular particles are generated, and the individual movement of each
particle is calculated by forward difference method. Since the movement of each ore is similar to the
procedure, it is suitable method to simulate the movement of ores in the vertical shaft.
Vertical Shaft’s Models
The fundamental geometry of the vertical shaft which is widely used in Japan is shown in Figure
2 (a). In the case of Japanese limestone mines, vertical shafts which diameter is 8m are widely used and
this size is set as a basic analytical model. In order to consider the effect the exit size, other two models,
which exit size are 5m and 7m respectively as shown in Figure 2 (b) and (c), are applied to the analysis.
Ore Size Distribution
Size of ores or diameter distribution of ores after blasting is mainly influenced by the diameter of
drilling holes to set explosives and its intervals. In Japan, 120 of drilling hole are widely used. An
example of ore size distribution observed at a limestone mine is shown on Table 1. Here, ore size
distribution is represented by mean diameter dm and standard deviation . In the following analysis, this
distribution is taken as particle distribution 1(PD1). Here we also assume other two distributions. These
values are also shown on Table 1 as particle distribution 1 and 2, respectively.
Table 1 – Particle size distributions
Mean diameter dm
Standard deviation σ
Particle
Distribution 1
0.378m
0.113m
Particle
Distribution 2
0.3m
0.1m
Particle
Distribution 3
0.25m
0.1m
Table 2 – Parameters for DEM analysis
Case1
Case2
Case3
Case4
Case5
Shaft model (See Figure 1)
(a)
(a)
(a)
(b)
(c)
Inner diameter (m)
3
3
3
5
7
Type of particle distribution
1
2
3
1
1
Mean diameter dp(m)
0.378
0.3
0.25
0.378
0.378
Standard deviation σ
0.113
0.1
0.1
0.113
0.113
Coefficient of friction
between particles
0.02～0.1
0.05～0.5
0.1～0.3
0.3～0.6
0.7~1.4
Coefficient of friction
between particles and walls
0.02～0.1
0.05～0.5
0.1～0.3
0.3～0.6
0.7~1.4
Cohesion(N/m)
0～1.0×104
0～1.0×104
0～1.0×104
0～1.0×104
0～1.0×104
8m
8m
500m
8m
500m
500m
5m
7m
3m
(a) Exit diameter: 3m (b) Exit diameter: 5m (c) Exit diameter: 7m
Figure 2 – Vertical shaft models
Procedures of Analysis
The DEM analysis starts from the generation of particles in a vertical shaft. Here, it is assumed
that the diameter of particles obeys Gaussian distribution. The mean values dm and standard deviations 
have already been shown on Table 1. Then, other parameters such as cohesions and friction coefficients
between particles and between particles and shaft walls are necessary. The parameter used in the analysis is
summarized as Table 2. Particles are randomly generated in the analytical region (Figure 3 (a)), and they
are fallen to the bottom of the vertical shafts (Figure 3 (b)). This process is continued until the all forces
acting between particles are balanced. The balanced condition is set to be an initial condition. Then the
carry-out exit is opened (Figure 3 (b)), flow out analysis of particles starts. If all particles flow out from the
shaft, it is determined as no blockage condition. If blockage occurs during flow out process, it is
determined as blockage condition.
Experimentally it is thought that cohesions and friction coefficients are the crucial factors towards
the blockage of ores in the shaft. Therefore, the analyses are conducted under the variety of combination of
cohesions and friction coefficients. Because of the characteristics of limestone mine, rock type of the shaft
wall and ores are same. Other parameters necessary for the DEM analysis are given as follows; gravity
acceleration g = 9.81 m/s2, density of particles p = 2700 kg/m3and number of particles n = 2,000.
Carry out exit
(a) Generation of particles
(b) Initial condition
Figure 3 – Generation of particles in the analytical region and initial condition of flow out analysis
RESULTS
Effect of Particle Size
The effect of the particle size towards the shaft blockage is discussed by using basic shaft model
as shown in Figure 2 (a). As for Case1 ~ Case3 (In each case, same shaft model is used, and the particle
size are different to each other), the occurrence of blockage is confirmed under the various combinations of
cohesions and friction coefficients. An example of blockage occurrence is shown in Figure 4. Moreover,
the relation between the condition of cohesions and friction coefficients are shown as the blockage – flow
out map as shown in Figure 5, 6 and 7. In this blockage – flow out map, vertical axis and horizontal axis
represent friction coefficient and cohesion, respectively. The combination of the friction coefficient and the
cohesion at witch blockage occurs is expressed by , and the combination at witch blockage does not
occur expressed by  . From the distribution of occurrence and not occurrence of blockage, the conditions
of friction coefficients and cohesions are obtained. Each case of Case1~3, it is necessary to give relatively
large friction coefficient in order to cause blockage when the value of cohesion is almost zero. However, as
the value of cohesion is increased, blockage occurs everywhere when the friction coefficient takes larger
values than a certain value. That is, the friction coefficient is thought to be a main factor which causes
blockage in Case1 ~ Case3. Moreover, the minimum value of friction coefficient can be confirmed for each
case. From the results, the minimum value of friction coefficient becomes larger when the particle size
becomes smaller. It means that smaller particles in the shaft are better in order to void from blockages.

Effect of Carry-out Exit Size
The effect of the carry-out exit size towards the shaft blockage is discussed by using models as
shown in Figure 2 (b) and (c). In these cases, particle distribution 1 is applied. Here also, flow out analysis
is conducted, and results are summarized as the blockage and flow-out maps as shown in Figure 8 and 9.
Same as before, it is found that the influence of coefficient is dominant. It is also found from Figures 5, 8
and 9, that the minimum friction coefficient becomes larger as the size of carry-out exit becomes larger.
The large enough size of carry-out exit towards particle size is very effective in order to avoid from
blockage. By considering the mining operations, setting the larger exit size at the initial shaft design is
easier than the control of ore size after each blasting. The initial design of the shaft is important to avoid
from blockage.
Blockage
Figure 4 – An example of blockage occurrence
0.5
0.5
Blockage
Without blockage
Blockage
Without blockage
0.4
Friction Coefficient
Friction Coefficient
0.4
0.3
0.2
]
Minimum friction
coeficient
0.1
0
0
2x10
3
4x10
3
6x10
3
8x10
3
1x10
4
0.3
Minimum friction
coeficient
0.2
0.1
1.2x10
0
4
0
2x10
3
4x10
Cohesion, N/m
6x10
3
8x10
3
1x10
4
1.2x10
4
Cohesion, N/m
Figure 6 – Blockage and flow out map for Case2
Figure 5 – Blockage and flow out map for Case1
0.5
Blockage
Without blockage
0.4
Friction Coefficient
3
0.3
Minimum friction
coeficient
0.2
0.1
0
0
2x10
3
4x10
3
6x10
3
8x10
3
1x10
4
1.2x10
4
Cohesion, N/m
Figure 7 – Blockage and flow out map for Case3
1.5
1.5
Blockage
Without blockage
1
0.75
Blockage
Without blockage
1.25
Friction Coefficient
Friction Coefficient
1.25
Minimum friction
coeficient
0.5
1
0.75
0.5
Minimum friction
coeficient
0.25
0.25
0
0
0
2x10
3
4x10
3
6x10
3
8x10
3
1x10
4
1.2x10
0
4
2x10
3
4x10
3
6x10
3
8x10
3
1x10
4
Cohesion, N/m
Cohesion, N/m
Figure 8 – Blockage and flow out map for Case4
Figure 9 – Blockage and flow out map for Case5
CONCLUSIONS
In this study, the process of blockage occurrence was simulated by 2-Dimensional Discrete
Element Method (DEM). Experimentally, it is thought that cohesions and friction coefficients will
strongly influence, and those effects to the blockage occurrence were discussed. Moreover, several kinds of
shaft size were also simulated towards different ore size distributions, and those influences to the blockage
occurrence were discussed.
It was confirmed that the blockage phenomena can be simulated by DEM analysis. In the case of
the blockage at the region of carry out exit, the blockage occurs when the friction coefficient takes larger
value than a certain value for each case. If the friction coefficient is small enough, there is a possibility that
blockage will not occur. From the results when the particle size was changed, it was found that the smaller
particles are better in order to avoid from blockage. In the case of the carry out exit size is larger, same
tendency was observed. By considering the mining operations, it can be though that setting the larger exit
size at the initial shaft design is better and effective to avoid from occurrence of blockage.
REFERENCES
Cundall, P.A. (1971), A Computer model for simulating progressive large scale movement in blocky rock
system, Proc. of the Symposium of the Int. Soc. of Rock Mech. (Nancy, France), 1, Paper No.II-8.
Cundall, P.A. and O.D.L.Strack (1979), A discrete numerical model for granular assembly, Geotechnique,
29 (1), pp.47-65.
Hadjigeorgiou, J. and Lessard, J.F. (2007), Numerical investigations of ore pass hang-up phenomena, Int. J.
Rock Mech. & Mining Sci., 44, pp.820-834.
Limestone Associate of Japan, Retrieved from Association of Geologists website:
http://www.limestone.gr.jp/analysis/index.htm
Sato, A. and Obara, Y. (2014), Blockage Simulation of Vertical Shaft for Ore Carry-out by Discrete
Element Method, Journal of MMIJ, 130, pp.421-427.