Estimation of Mineable Mineral Reserves: The Significance of Bench-wise Computation in Cross-Sectional Method

 

The extraction of any mineral requires the preparation of a mining plan. In the case of minor minerals, the mining plan must adhere to the guidelines outlined in the Kerala Minor Mineral Concession Rules of 2015. Additionally, mines employing explosives fall under the Mines Act of 1952, necessitating compliance with the Metalliferous Mines Regulation of 1961.

According to the Metalliferous Mines Regulation of 1961, mining activities should maintain a distance of 7.5 meters from the boundary. The regulation also stipulates that mining should be conducted in benches, with each bench having a height and width of 6 meters.

In Kerala, the requirement for a mining plan predates the Kerala Minor Mineral Concession Rules of 2015, as such plans were already mandatory for obtaining environmental clearance. Notably, the landscape of minor mineral mining across the country underwent a significant transformation following the Hon’ble Supreme Court’s judgment in the Deepak Kumar case (2012). This ruling mandates prior environmental clearance for the mining of minor minerals from any area, overturning the previous threshold of 5 hectares for environmental clearance. Since a mining plan is a prerequisite for obtaining environmental clearance, mine owners are obligated to submit it for the approval process.

According to the Mines and Minerals (Development and Regulation) Act, 1957, the submission of a mining plan is a prerequisite for the grant of a mining lease. Initially, the Indian Bureau of Mines (IBM) recognized specific individuals as Recognized Qualified Persons (RQP) for the preparation of mining plans, covering both major minerals. These individuals' services were employed for the formulation of mining plans for minor minerals as well.

However, a significant shift occurred in 2015 when the Government of Kerala introduced the Kerala Minor Mineral Concession Rules 2015. Under these new rules, a dedicated chapter was introduced for mining plans, specifically empowering the Director of Mining and Geology to recognize individuals for the preparation of mining plans exclusively for minor minerals occurring in the State.

Concurrently, the Indian Bureau of Mines ceased the recognition of individuals as RQP and instead permitted individuals with specific qualifications to undertake the preparation of mining plans, focusing primarily on major minerals.

Mineable reserve estimation- Conventional Method

In this paper, mining plan pertaining to granite (building stone) is discussed. The conventional method used for computation of mineable reserve is by using cross sectional area method. For a pit, the cross sectional area of the pit multiplied by influence give the volume of the mineral.

Following drawing gives a better idea about using cross sectional area method.

Consider a pit having length 10 m, depth, 2.3 m and width 2 m. The cross section of the pit is colored red and its area is 2x2.3 m which is 4.6 square meters. It has an influence of 10 meter which means up to a length of 10 m, the area of cross section remains same. So the total volume is 4.6 m² x 10 m = 46 m^{3 .} If the cross has different shape, the maximum possible distance the cross section has same shape is considered as its influence. Hence for an irregular shaped trench, different cross sections are taken and influence of each cross section is taken.

Following example gives you an idea regarding taking multiple sections for an irregular shaped trench. Each section has different shape and for each cross section influence is taken as L. Adding up of volumes arrived for each cross sections will give the total volume.

When it comes to granite building stone mining, we know we have to consider mining in benches and mineable reserve is computed taking into consideration of bench mining. So depending on the topography and shape of the land, different cross sections have to be taken to find out the mineral reserve.

In the above diagram, there are 4 cross sections and each have influence L. The total volume would be (area of AA’x L) + (Area of BB’x L) + (Area of CC’ x L) + (Area of DD’) x L. Now, the question is regarding how to decide how many sections are required and what is the influence of each section. The thumb rule is that more sections have to be drawn if the area is more irregular in shape and if the area is regular in shape (say rectangle), then only one cross section would be sufficient (as in figure 1). Hence, generally, the number of sections are decided based on the shape of the area and the spacing between each section (which is considered as influence) is kept constant. This method would average out the volume computation and the end result would be more accurate.

In mining plans also, RQPs use cross sectional area method to compute volume. In the following diagram which represents a mine with benches and no mining area (7.5 m), the volume can be computed by multiplying the area of cross section AA’ x Influence.

In bench mining operations, the cross-sectional shape of the pit varies depending on whether we draw the cross-section at the sides of the pit, owing to the benching technique. It is crucial to account for this difference in cross-sectional area when computing the actual volume. To achieve a higher level of accuracy, we can consider the cross-sectional area of each bench multiplied by the bench-wise influence.

In the provided illustration, there are three benches labeled 1, 2, and 3. The influence in each bench differs, with benches advancing towards the center from all sides. To obtain more precise volume values, the volume can be computed bench-wise. This involves multiplying the AA’ cross-sectional area of Bench 1 by the influence of Bench 1, doing the same for Bench 2, and repeating the process for Bench 3. By summing up these three volumes, the total volume can be calculated in accurate manner.

In real-life scenarios, it is occasionally observed that when volume is computed bench-wise compared to the conventional method, the difference in volume may not be very pronounced. As a result, some geologists may not prioritize bench-wise computations, as the variances in volume might not be conspicuous enough to warrant the additional complexity of such calculations.

Initially, when mining plans were introduced in the State for minor minerals, certain Recognized Qualified Persons (RQPs) would calculate mineable reserves by combining volumes obtained from both longitudinal and transverse sections. This often led to an overestimation of reserves, effectively doubling the calculated volume. Some RQPs opted for drawing sections through the widest areas of the land, exaggerating the volume intentionally. In other instances, the sum of influences from all cross sections would exceed the total length of the mine. Sometimes, some RQPs gives more weight to the influences of the widest cross sections.

Exaggerating mineable reserves can have adverse consequences for quarry owners, as geologists typically demand royalties and mineral prices based on the quantities specified in the mining plan. Furthermore, it has been observed that in some bench-wise computations, the influence values appear to increase from top to bottom. Such practices are deemed unacceptable, as in bench mining, influence generally diminishes as mining progresses towards the bottom of the mine.

Some quarry owners, seeking to maximize perceived value, may request Recognized Qualified Persons (RQPs) to exaggerate the quantities in mining plans. However, this practice can lead to significant issues if the stated mineable quantities exceed the actual reserves in the mine. In instances where geologists harbor doubts about the computations, a common recourse is to apply a thumb rule of 3.2 lakhs tonnes per hectare, leading to demands for a mining plan that aligns with these quantities. Unfortunately, this approach often results in the underestimation of mineable reserves, translating into substantial revenue loss for the government.

In the given scenario, the most prudent solution would be to adopt bench-wise computation for mineable reserves. While the goal is to determine the precise quantity, the cross-sectional area method inherently falls short of achieving exact accuracy.

The subsequent analysis aims to assess the percentage increase in volume when computations are not conducted in benches. This comparison involves different areas of regular shapes but with varying length-to-breadth ratios. For a more comprehensive understanding, readers are encouraged to read the preceding three papers on mining plans published in this website.

The Mine Planner App has been utilized to calculate bench-wise volumes, and modifications have been made to this App to enable the computation of volumes using the conventional method. It is crucial to emphasize that the quarries under consideration for this analysis exhibit regular shapes and are situated in flat terrains, devoid of overburden. In real-life scenarios, granite building stone quarries are typically found in sloping areas, characterized by soil cover and irregular shapes.

The study focused on areas with length-to-breadth ratios of 1:1, 2:1, 3:1, and 4:1. The table below presents the mineable reserves obtained through both bench-wise computation and the conventional method.

Longitudinal Section and Transverse Sections of 1 ha land- comparison of bench-wise method and conventional method

Bench-wise Reserve Estimation-1 ha land having Length to Breadth ratio = 1:1 

Conventional Reserve Estimation-1 ha land having Length to Breadth ratio = 1:1 

Bench-wise Reserve Estimation-1 ha land having Length to Breadth ratio = 4:1 

Conventional Reserve Estimation-1 ha land having Length to Breadth ratio = 4:1 

The values derived from the analysis have been interpolated to provide results for various areas. The following graphs illustrate the computation results for different length-to-breadth ratios, considering areas ranging from 0.5 hectares to 16 hectares. This range encompasses the minimum and maximum areas typically found in granite building stone mines in Kerala.

Length to Breadth ratio= 1:1

Length-to-Breadth Ratio= 2:1

Length-to-Breadth Ratio= 3:1

Length-to-Breadth Ratio= 4:1

The key findings of the analysis are summarized below:

1.      For the purposes of this study, all quarries were assumed to be situated in a flat terrain with regular boundaries (square or rectangular shapes) and no overburden.

2.      There is an average increase of 45.2% in mineable reserve when using the conventional method for computation with a length-to-breadth ratio of 1:1.

3.      With a length-to-breadth ratio of 2:1, there is an average increase of 16.1% in mineable reserve when using the conventional method.

4.      For length-to-breadth ratios of 3:1 and 4:1, the increases are 9.1% and 6.6%, respectively.

5.      Given that most quarries have length-to-breadth ratios between 1:1 and 2:1, an increase in volume ranging from a minimum of 16.1% to 45.2% can be anticipated.

6.      In Kerala, where new quarries average around 3.5 hectares in area, the difference in volume (bench-wise vs. conventional) is approximately 10.56 lakh tonnes for a quarry with a 1:1 length-to-breadth ratio and about 3.29 lakh tonnes for a 2:1 ratio. The corresponding royalty amounts to Rs. 5.6 crores for 10.56 lakh tonnes and Rs. 1.9 crores for 3.29 lakh tonnes.

Conventional Method -Overestimation levels for various Length to Breadth ratios

In conclusion:

1.      Bench-wise mineable reserve calculation yields higher accuracy compared to the conventional method employed by Recognized Qualified Persons (RQPs).

2.      The disparity in mineable reserves is more significant when the length-to-breadth ratio is less than 2:1.

3.      The difference in mineable reserve is diminished for areas with a length-to-breadth ratio of 4:1, beyond which no lease is granted in the State as per regulations. A higher length-to-breadth ratio results in a shallower depth, leading to fewer benches. When the number of benches is limited, their influence on the mineable reserve is reduced. This is why 4:1 ratio quarries have a lesser impact on mineable reserves when computed using both methods.

4.      The mineable reserve of a granite building stone mine is influenced by various factors, including the topography of the terrain, the size of the mine, its shape, the length-to-breadth ratio, and the thickness of the overburden. Regardless of these variables, when computing mineable reserves using the cross-sectional area method, adopting a bench-wise calculation approach is advisable. This ensures that deviations from the actual quantity are minimized and provides a more accurate representation of the volume within the mine.

Author: Biju Sebastian

Caution:

The data provided in this paper is for regular shaped quarry and not for the usual irregular shaped quarry and hence these data should be used with utmost care. The information provided is only for making general awareness on assessment of mineable mineral reserve in the context of granite (building stone) mines in Kerala. As mentioned in this paper the mineable reserve depends on topography, size and shape of quarry and no two quarries have same topography or size or shape. 

Disclaimer:

The information on this website is provided "as is" and "without warranty." In terms of how this information is used or the results of its usage, the author disclaims all liability.