Grade Distribution Modeling within the Bauxite Seams of the Wachangping Mine, China, Using a Multi-Step Interpolation Algorithm
Abstract
:1. Introduction
2. Methodology
3. Scattered Grade Data
4. Grade Distribution Model
5. Results and Discussion
5.1. Comparison of Interpolation Methods
5.2. Confirmation by Exploratory Boreholes
5.3. Optimum Model
6. Conclusions
- (1)
- A multi-step interpolation algorithm was proposed to establish the grade distribution model of the mineralized seams in three dimensions. For a longwall mining panel with a U-shaped layout, where the tail and head roadways at both sides of the panel will be excavated beforehand, a five-step interpolation procedure was established. Firstly, the sample data with large variations and irregular distributions measured in the tail roadway were mapped into the nodes of a regular rectangular mesh grid and then used to estimate the over-sampled node data by conventional interpolation methods. Secondly, using a biharmonic spline method, the interpolated curve of the floor altitude of the tail roadway was established to recover interpolation data into the original frame. Thirdly, similar to the first step, the grade distribution data on the head roadway wall were interpolated. Fourthly, similar to the second step, the interpolation data were recovered by interpolated floor altitudes of the head roadway. Finally, the 3D distribution data between roadways were interpolated by a linear method.
- (2)
- During the first and the third steps, the nearest neighbor, linear, natural neighbor, cubic, biharmonic spline, IDW, SK, and OK interpolations were used to select which one is optimal for smooth and exact interpolations of the mineralized seams. A comparison of the differences between interpolated and sampled data—and between the field data from exploratory boreholes and corresponding interpolated data—showed that the stabilities of the interpolation curves decrease sequentially from natural neighbor, OK, SK, IDW, linear, cubic, and biharmonic spline, to the nearest neighbor methods. The multi-step interpolation using the natural neighbor method has an optimal stability and a minimal difference with the grade distribution in three dimensions. It seems that the natural neighbor interpolation has some predominant characteristics to be more physically realistic in the data interpolation.
- (3)
- Using the multi-step interpolation in which the natural neighbor method was selected to estimate the grade data distributed on the roadway wall, the ore reserve was estimated at 97,576 m3 with a mass fraction of Al2O3, marked as Wa, of 61.68% and a mass ratio of Al2O3 to SiO2, marked as Wa/s, of 27.72. Subsequently, compared with the field data measured by the six exploratory boreholes, mean absolute errors, the root mean squared errors, and relative standard deviations of errors between interpolated and measured grade data are 2.544, 2.674, and 32.37% of Wa; and 1.761, 1.974, and 67.37% of Wa/s, respectively. On the whole, these differences are small relative to other methods.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Method | Bauxite Seam Volume/m3 | Ore Reserve/m3 | In-Situ Average Grade of Bauxite Seam | Average Grade of Bauxite Orebody Applying Industrial Constrains | Assessment of Difference Ratio Between Interpolation Data and Sample Data Dis/% | Time Consuming/s | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Wa/% (SD) | Wa/s (SD) | Wa/% (SD) | Wa/s (SD) | Mean | Max | Min | |||||||
Wa | Wa/s | Wa | Wa/s | Wa | Wa/s | ||||||||
Nearest | 189,260 | 97,750 | 54.80 (15.53) | 17.89 (18.94) | 63.73 (7.54) | 29.20 (17.18) | 18.48 | 45.24 | 0 | 0 | 0 | 0 | 76.2 |
Linear | 189,260 | 96,192 | 54.84 (13.28) | 17.52 (14.98) | 61.78 (7.08) | 27.18 (11.84) | 18.58 | 42.19 | −0.12 | 0 | 0 | 0.09 | 80.4 |
Natural | 189,260 | 97,576 | 54.88 (13.11) | 18.02 (14.48) | 61.68 (6.85) | 27.72 (10.27) | 17.67 | 35.92 | −0.15 | 0 | 0 | 0.09 | 81.4 |
Cubic | 189,260 | 98,151 | 55.32 (13.82) | 17.57 (16.01) | 62.34 (7.59) | 27.30 (13.34) | 19.6 | 42.67 | 6.44 | 1.74 | −4.34 | −50.9 | 76.2 |
Biharmonic | 189,260 | 99,763 | 56.32 (13.94) | 17.38 (16.59) | 62.78 (7.97) | 26.97 (14.59) | 21.76 | 41.14 | 9.03 | 6.59 | −1.41 | −51.4 | 78.1 |
IDW | 189,260 | 93,348 | 53.15 (12.93) | 17.40 (14.31) | 60.74 (6.17) | 27.44 (10.79) | 14.92 | 41.27 | 0 | 0 | 0.05 | 0 | 153.3 |
SK | 189,260 | 100,750 | 55.34 (14.11) | 18.28 (15.87) | 62.88 (7.19) | 28.52 (11.77) | 19.65 | 48.37 | 2.21 | 0 | 0 | −58.3 | 2161.7 |
[E: 11.22] | [E: 11.71] | ||||||||||||
[EV: 2.04] | [EV: 0.97] | ||||||||||||
OK | 189,260 | 100,630 | 55.28 (14.12) | 18.24 (15.89) | 62.85 (7.16) | 28.52 (11.78) | 19.53 | 48.04 | 1.78 | 0 | 0 | −51.2 | 2601.5 |
[E: 11.23] | [E: 11.73] | ||||||||||||
[EV: 2.05] | [EV: 0.97] |
Position | I and F | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Nearest | Linear | Natural | Cubic | Biharmonic | IDW | SK | OK | Nearest | Linear | Natural | Cubic | Biharmonic | IDW | SK | OK | |
EB-1 (107, 72) | −10.88 | −7.78 | −6.24 | −7.03 | −1.37 | −9.43 | −4.81 | −5.01 | ||||||||
−42.00 | −33.35 | −19.11 | −36.21 | −40.46 | −23.00 | −15.59 | −15.98 | |||||||||
EB-2 (204, 32) | 5.08 | 3.65 | 3.36 | 5.22 | 6.38 | −0.28 | 4.01 | 3.89 | ||||||||
−18.48 | −9.39 | −12.29 | −5.80 | −23.49 | −22.21 | −18.14 | −18.33 | |||||||||
EB-3 (326, 72) | 6.22 | 6.72 | 5.03 | 8.32 | 7.94 | 0.58 | 6.73 | 6.66 | ||||||||
−10.13 | −5.38 | −5.71 | −6.88 | −5.94 | -12.09 | 1.36 | 1.27 | |||||||||
EB-4 (430, 54) | 3.16 | 5.31 | 5.92 | 5.76 | 8.81 | 1.49 | 7.01 | 6.93 | ||||||||
1.65 | 7.82 | 11.31 | 3.48 | 11.80 | 10.08 | 16.36 | 16.14 | |||||||||
EB-5 (518, 5) | 3.37 | 2.41 | 1.95 | 3.64 | 3.28 | 0.29 | 2.17 | 2.07 | ||||||||
2.97 | −3.56 | −1.90 | −4.91 | −13.78 | −2.86 | −4.86 | −5.28 | |||||||||
EB-6 (556, 99) | 6.23 | 8.46 | 6.21 | 10.61 | 11.29 | 2.81 | 7.18 | 7.08 | ||||||||
4.48 | 8.95 | 9.36 | 11.31 | 13.59 | 1.72 | 6.74 | 6.24 | |||||||||
All | Evaluation index | Nearest | Linear | Natural | Cubic | Biharmonic | IDW | SK | OK | |||||||
3.125 | 3.050 | 2.544 | 3.612 | 3.464 | 1.310 | 2.832 | 2.808 | |||||||||
2.412 | 1.993 | 1.761 | 2.005 | 3.193 | 2.218 | 1.826 | 1.832 | |||||||||
3.424 | 3.258 | 2.674 | 3.807 | 3.877 | 2.165 | 2.989 | 2.966 | |||||||||
3.377 | 2.579 | 1.974 | 2.733 | 3.710 | 2.716 | 2.157 | 2.171 | |||||||||
44.74% | 37.54% | 32.37% | 33.22% | 50.23% | 131.5% | 33.78% | 34.06% | |||||||||
102.4% | 97.74% | 67.37% | 122.47% | 59.81% | 138.3% | 83.58% | 54.15% |
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Wang, S.; Li, X. Grade Distribution Modeling within the Bauxite Seams of the Wachangping Mine, China, Using a Multi-Step Interpolation Algorithm. Minerals 2017, 7, 71. https://doi.org/10.3390/min7050071
Wang S, Li X. Grade Distribution Modeling within the Bauxite Seams of the Wachangping Mine, China, Using a Multi-Step Interpolation Algorithm. Minerals. 2017; 7(5):71. https://doi.org/10.3390/min7050071
Chicago/Turabian StyleWang, Shaofeng, and Xibing Li. 2017. "Grade Distribution Modeling within the Bauxite Seams of the Wachangping Mine, China, Using a Multi-Step Interpolation Algorithm" Minerals 7, no. 5: 71. https://doi.org/10.3390/min7050071