On the Permissibility of Orientation Error Through a Single Vertical Mine Shaft
Abstract Generated abstract
This paper examines the permissible error in orienting underground mine surveys through a single vertical shaft and argues that the uniform tolerance then prescribed by technical instructions is inadequate. It critiques the fixed requirement that two independent orientations differ by no more than 3 minutes, noting that orientation accuracy depends on mine depth, airflow, plumb-line geometry, shaft conditions, and the required accuracy of mine plans. Using an example based on the allowable positional error at the end of a 5.5 km mine-field wing, the paper shows how a stricter permissible orientation error may be derived from survey accuracy requirements and checked against the minimum expected error under actual conditions. It concludes that admissible orientation errors should be set case by case, and that alternative methods or protective measures should be considered when geometric orientation through one shaft cannot meet the required accuracy.
Full Text
On the Admissible Orientation Error Through a Single Vertical Mine Shaft
G. F. Lysov
(Presented by the scientific seminar of the Department of Mine Surveying and Geodesy)
The question of establishing the admissible orientation error through a single vertical mine shaft is not new. The history of this question has repeatedly been discussed in the mine-surveying literature; therefore we shall not dwell again on those changes in the requirements of instructional documents that have occurred at various times. At present, as is known, § 211 of the current mine-surveying instruction \[1\] requires that the difference of the direction angles of one and the same side of an underground survey, computed from two independent orientations, not exceed \(\pm 3'\).
The present state of knowledge of the causes that give rise to errors in orienting a mine makes it possible, in our opinion, to reconsider this requirement critically. The point is that § 211 of the technical instruction ignores the actual conditions of orientation. It should be recalled here that even in the note to § 325 of the 1939 technical instruction \[2\] it was stated that “the norm of \(3'\) established by the present paragraph should be considered temporary until its dependence on the length of the wings of the mine, its depth, and other factors is clarified.” Thus, as early as 1939 the need was recognized to revise the tolerance of \(\pm 3'\) from the standpoint of taking into account the actual conditions of orientation. Indeed, it is difficult to agree that the admissible difference of the direction angles of one and the same side of an underground survey should be the same when orienting different mines 1000 and 100 m deep, with an air-flow velocity in the shaft of \(0.2\ \text{m/sec}\) and \(3\text{--}5\ \text{m/sec}\), with a distance between plumb bobs of 2 and 5 m, and so on. If under certain “favorable” orientation conditions (for example, with a small mine depth, low air velocity in the shaft, a large distance between the plumb bobs, etc.) it is possible without particular difficulty to “fit” within the indicated tolerance, then in another, more complicated, situation it is not always possible to ensure that the divergence of the direction angles of the first side of the underground survey remains within \(\pm 3'\).
Paragraph 211 also does not take fully into account the requirements imposed on the accuracy of compiling plans of mine workings from the standpoint of safe operation of the mine and the guarantee of correct solution of technical problems. Thus, with different lengths of the wings of mine fields, it is obvious that, in order to comply with the established standards of accuracy, …
drawing up plans of mine workings [1], it is necessary to orient different mines with different accuracy. It follows from this that, for mines having a small length of the wings of the mine field, the magnitude of the permissible error of a single orientation may be more than \(\pm 2'\), and, conversely, for mines whose workings are considerably distant from the shaft, the permissible orientation error may be less than \(\pm 2'\).
Therefore we believe that at the present time it would be more correct to establish the permissible orientation error in each individual case separately, on the basis of considerations based, for example, on the requirements imposed on the accuracy of compiling mine-surveying plans from the standpoint of rational and safe operation of the mine. To this it should be added that the magnitude of the permissible error of orientation through one vertical mine shaft by geometrical methods should not be taken as less than the minimum possible orientation error, determined by a special preliminary calculation, the essence of which is set forth in works [3, 4].
Let us explain what has been said by an example. Let the length of the wing of the mine field be \(5.5\) km. Suppose that the operating conditions of this mine require that the error of the most remote point, located in the mine workings, relative to the approach point not exceed \(\pm 4.0\) meters [1]. In any case, because of the presence of errors in measuring angles and side lengths in double traverses of underground polygonometry of class 1 with a total length of \(5.5\) km, a limiting error in determining the most remote point [1] may be allowed, equal to \(\pm \frac{5500}{1500} = \pm 3.71\) meters. Consequently, the part of the total limiting error of the most remote point that falls to the “share” of the mine orientation must not be greater than a value equal to \(\pm \sqrt{4^2 - (3.7)^2} = \pm 1.6\) meters. Hence the limiting permissible orientation error \(M_{\mathrm{or}}\) may be found by the simple calculation
\[ M_{\mathrm{or}} = \pm \frac{1.6 \cdot 206000}{5500} = \pm 60''. \]
Thus, the permissible difference of the direction angles of the first side of the underground survey, computed from two independent orientations, in this case must not exceed \(\pm 2M_{\mathrm{or}} = \pm 120''\) (i.e., less than \(3'\)), while the error of one orientation must not exceed \(\pm 85''\).
Having then determined by preliminary calculation, for the given specific conditions (depending on the depth of the shaft, the velocity of the air flow, the height of the station or of the lower part of the plumb line subjected to air pressure, the possible form of the connecting figure, and the possible distance between plumb lines), the value of the minimum expected error of a single orientation, and having made sure that this error does not exceed \(\pm 85''\) in magnitude, one may adopt the final decision on the permissible orientation error.
In the case where, as a result of the preliminary calculation, the minimum expected error proves to be more than \(\pm 85''\), measures should be taken to shield the lower part of the plumb lines with pipes (the possibility of using this variant must also be checked by preliminary calculation), or else one should abandon orientation through one vertical mine shaft by the geometrical method and apply another, more accurate method of orientation. In especially difficult cases, if they allow
operating conditions and safety practices, it is advisable to reconsider the question of the magnitude of the limiting error of the most distant point of the underground survey.
Conclusions
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The magnitude of the permissible error of the connecting survey should be established depending on the requirements imposed on the accuracy of compiling mine-surveying plans of mining operations from the standpoint of safe operation of the deposit and of ensuring the correct solution of various technical problems.
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The requirement of § 211 of the technical instruction [1] that the permissible difference of the direction angles of the first side of the underground survey, computed from two independent orientations, must in all cases not exceed \(\pm 3'\), should, in our opinion, be considered obsolete and not corresponding to the present state of knowledge of this question.
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The question of the method for determining the magnitude of the permissible orientation error of a mine through a single vertical shaft is debatable and should be discussed in broad circles of mine-surveying specialists.
References
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Technical Instruction for the Performance of Mine-Surveying Work. Ugletekhizdat, 1959.
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Technical Instruction for the Performance of Mine-Surveying Work, GONTI, 1939.
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D. N. Ogloblin. Mine-Surveying Work in Underground Mining of Deposits. Part III, Metallurgizdat, 1963.
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G. F. Lysov. On the question of choosing the magnitude of the weight and the diameter of the wire for plumb lines in mine orientation. Proceedings of TPI, No. 118, Tomsk, 1962.