5 Migration of Mining Pit and Multi-Scale Characterization of Migration Speed
5.3 Analysis for Shape-II, Shape-III and Shape-IV
5.3.1 Physical characteristics of mining pit migration
Morphological changes were tracked by using the URS and shifting of upstream edge was recorded at every 30 minutes. Longitudinal displacement of upstream boundary till the filled up of the pit with respect to time has been plotted for each shape of mining pit for V1 and V5 as shown in Figure 5.1. It shows similar trend for each set and the slope of the line increases from Shape-II to Shape-IV, that is, migration speed of upstream edge increases with increase in bank value. Experimental results from Neyshabouri et al. (2002) showed increase in pit migration with increase in length by width ratio of mining pit. By comparing the trapezoidal pit (Shape-II and Shape-III) with length by width ratio 0.82 and 1.025 respectively, we have observed the similar trend as that of Neyshabouri et al. (2002). Mining pit with irregular geometry has variable width as shown in Figure 2.16 and we observed maximum migration speed in this case. While comparing the migration speed with volume of extraction, it is observed that migration speed is more sensitive to the pit geometry than the volume of extraction.
0 2 4 6 8
0.0 0.2 0.4 0.6 0.8
0 1 2 3 4 5 6 7
0.0 0.2 0.4 0.6 0.8
0 2 4 6 8
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Distance (m)
Time (hr) Shape-II Slope= 0.105
Distance (m)
Time (hr) Shape-III Slope= 0.1321
Distance (m)
Time (hr) Shape-IV Slope= 0.17373
A)
0 2 4 6 8 0.0
0.2 0.4 0.6 0.8
0 1 2 3 4 5 6 7
0.0 0.2 0.4 0.6 0.8
0 2 4 6 8
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Distance (m)
Time (hr) Shape-II 0.125
Distance (m)
Time (hr) Shape-III 0.1603
Distance (m)
Time (hr) Shape-IV 0.217
Figure 5.1 Longitudinal displacement of upstream boundary with respect to time for A) V1 and B) V5
Shape-II is having highest volume of extraction and the lowest migration speed as compare to the other two sets. While comparing Shape-III and Shape-IV, higher migration speed is observed in Shape-IV with higher value of volume of extraction. This higher value of migration speed in Shape-IV may be due to the irregular pit geometry with length by width ratio almost 2.44 times of the L/B ratio of Shape-III. Mining pit also leads to the erosion of the bank and the greater bank value for Shape-IV allows the bank particle to get deposited in the pit, thus filing up the pit in a faster rate. The average migration speed of upstream edge at various discharges is plotted for three Shapes as shown in Figure 5.2. An increase in migration speed with increase in length by width ratio is observed for each discharge.It indicates the influence of length by width ratio of mining pit on the migration speed. The empirical formulation developed by Neyshabouri et al.
(2002) for migration of mining pit was based on only the length and width of the pit since they B)
had conducted the experiment for a constant discharge. However, migration of mining pit also depends on the flow characteristics.
0.044 0.046 0.048 0.050 0.052 0.054 0.056 0.058 100
150 200 250 300 350 400
450 Shape-II
Shape-III Shape-IV
Migration Speed (mm/hr)
Discharge (m3/s)
Figure 5.2 Average migration speed of upstream edge of the pit at each discharge for all three
shapes
An empirical formulation has been developed to determine the migration speed of the upstream edge till the downstream. The functional form of the pit migration speed Up can be assumed as follows:
pit properties, flow properties, fluid properties, sediment properties
Up f (5.12)
where pit properties includes length ( )L , maximum width ( )B and depth of the mining pit ( )y ; flow properties includes the average cross-sectional flow velocity V q
h , q is the discharge per unit width of the channel and h is the depth of flow; fluid and sediment characteristics are the density of water ( ) , density of bed material (s), kinematic viscosity of water (), median
grain diameter(d50), geometric standard deviation of bed material (g). The grain parameter is combined in terms of critical shear velocity (u*c) for representative grain diameter d50 of the bed material by neglecting the standard deviation g(Mohtar et al., 2016). , s, are kept constant during the experiment; hence these parameters can be neglected. In present work we have considered different geometric shaped pit with constant depth of pit for various discharge and flow depth. Therefore, the depth of pit can be omitted from the equation. By using dimensionless analysis Equation 5.12 can be written as
* *
p ,
c c
U V L
u f u B
(5.13)
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.001
0.002 0.003 0.004 0.005 0.006 0.007 0.008
Predicted dimensionless migration speed
Observed dimensionless migration speed R2=0.89
Figure 5.3 Predicted non-dimensional migration speed of mining pit
The final consolidated form of empirical formulation for the migration speed of mining pit is as follows:
6.89 0.414 12
* *
0.22 10
p
c c
U V L
u u B
(5.14)
Predicted dimensionless migration speed and corresponding experimental values are plotted in Figure 5.3. This empirical formulation can be used to determine the migration of upstream edge of the pit and simultaneously to calculate the time required for complete filling up of the pit.
Figure 5.4 Sensitivity of pit migration with two independent parameters
From Equation 5.14, it is observed that flow properties (V/u*c) and pit geometry (L/B) are two independent properties. The sensitivity of pit migration speed with respect to these two properties has been checked and presented in Figure 5.4. It is observed form the sensitivity analysis that pit migration speed is highly sensitive to the flow properties and less sensitive to the pit geometry.
The newly derived formula incorporates flow properties and pit geometry. Therefore, it can be applied for varying discharges as well as pit geometries. It also uses the pit geometry for the irregular-shaped pit by considering the maximum extents of the longitudinal and lateral disturbances, which gives a better justification for the application of the currently derived equation for a real problem, where finding the actual shape of the pit may not be possible. The transported sediment gets deposited along the upstream edge of the pit and causes filling of the original pit with time. Once the migration rate is calculated, the time required for filling of the pit can be determined using L U/ p with an assumption of a uniform infilling rate throughout the pit length. The knowledge of the infilling rate also will help in determining the potential mining site and the mining interval. However, more experimental and field observations are necessary for real field application of the equation.