Spatial positioning of sidewall stations in a narrow tunnel environment: a safe alternative to traditional mine survey practice

Conclusion

The sidewall survey station has been proven to be a safe, practical and accurate alternative to conventional hangingwall surveying techniques under most mining conditions. The method has been proved to obtain the same minimum standards of accuracy required by the MHSA under certain conditions. The main conditions to be met are that of ensuring an absolute minimum of three reference points to be observed and that proper observation protocols should be followed if Class “A” minimum standard of accuracy is required. It is essential for all surveyors and supervisors to understand that software and advanced technology cannot act as a substitute for good fundamental survey procedures and common sense.

Chapter 9. Three dimensional mining control using sidewall stations, a solution.

1. The requirements for direction and gradient mark-up.

The term ‘marking up’ in South African mining terminology is referred to as ‘taking lines and grades’ for the purpose of marking-off a development end in preparation for drilling and blasting. The primary function of the mine surveyor within the production environment is to provide accurate vertical and horizontal control of all underground workings in order to ensure safe working conditions. In order for development ends to open up ore reserves and provide access to the ore body, accurate setting-out control in three dimensions are required. The gradient⁴⁵ and direction of mining excavations are set-out based upon pre-determined mine design specifications and must be adhered to rigorously preventing cost and scheduling over run.
The sidewall survey station method of surveying will have an impact on the traditional methods used by surveyors and production personnel to mark-up the required blasting pattern to control the 3D position of an excavation in relation to the mine design. Implementation of sidewall stations for survey control requires an alternative method of providing the production crew with direction- and gradient control the excavation. Such a method considered must be easily understood and implemented by the persons, including non-surveyors, required to perform the daily routine of marking off the new blast pattern of a tunnel.

1.1.Direction lines and gradient control by conventional means.

Conventional setting-out⁴⁶ methods normally consist of two direction lines installed in the roof of the excavation and two sets of gradepegs installed in the sidewall of the tunnel. By aligning the strings and projecting the gradient to the face of the excavation the drilling pattern is marked-up using this horizontal line as a reference.

1.2. Setting-out gradient using the minor dip method.

The method of installing sidegrades using the relationship between minor dip [162] and minor dip is known in industry but due to the number of calculations required underground was not standard practice before the introduction of total stations. Following from this, the basic formula to calculate the angle between major and minor dip is used:

( )

where:

d° is the Minor dip from the instrument to the grade peg

D° is the Major dip⁴⁷ from the instrument in the direction of mining

x° is the Horizontal angle⁴⁸ between the Minor dip and the Major dip

The method of installing sidegrades using the minor dip is known in industry but had not been standard practice before the introduction of total stations. Possibly the greatest advantage of this method is that the position of the grade peg can easily be moved should the condition of the sidewall or obstructions make the required position unviable. In addition the positioning of these gradepegs does not have to be at right angles to the direction of mining to be effective. The installation of accurate gradepegs using this method forms the basis for the proposed method of setting-out direction and grade from the gradepegs. Such position will allow for much safer and quicker installation of gradepegs, in fact the stations that are established for control should double as gradepegs. Alternatively gradepegs could be installed separately from the survey control points when these are required closer to the working face of the excavation.

1.3. An application of the theorem for the intersection of two lines.

The required design string of a tunnel (required bearing) will intersect the line joining two grade pegs installed at a certain position. This position can be determined graphically from the mine design and set out using on-board totalstation software. This method is based on first-principles to determine the intersection point(s) between a grade line and direction line. The position where the gradestring and the required centreline of the excavation meets is marked on the string and used to mark offsets for setting-out of the reference line of a tunnel. This method is used to stake out a tunnel laser for long-term directional control of the tunnel. The principle used is described by the following formula:

y = mx + c ( )

where:

m is the slope of the line determined by:

( )

c is the point of intersection and can be calculated by substituting y and x.

By calculating m and c for the two lines, the point of intersection between the two lines is calculated. In the design of a Microsoft Excel spreadsheet the following functions is used to determine the variables:

m = SLOPE ( known_y's, known_x's ) ( )

c = INTERCEPT ( known_y's, known_x's ) ( )

In this manner a line normally described in terms of bearing and direction or Polar co-ordinates is converted into a straight line equation. By converting the required design string line and the gradestring line into this format the two equations is solved. The y co-ordinate (Y_int1) is the point where the two lines intersect and by substituting y the x co-ordinate (X_int1) is calculated. Repeating the method, the second gradestring intersection point is calculated. As a check, a polar (join) direction calculated between the two intersection points (Y_int1; X_int1) and (Y_int2; X_int2) must be the same as the required (design string) bearing (α).

Quadrant Angle QA is ( )

( )

Figure . Diagram of the intersection of lines

Calculating a polar (join) between the gradepeg co-ordinates and the intersection point co-ordinates a “tie⁴⁹” distance can be calculated. This distance will be the shortest distance between the two points and describes the radius of an arc between the points. Using two of these tie distances the intersection between two arcs is described. These points can be measured out by mining personnel to determine the position of the direction line on the gradestring. Taking a sighting over the two positions on the gradestring a direction line is projected to the face of the tunnel.

Tie distance calculated from radius ( )

Join distances A-P1, D-P1, B-P2 and C-P2 were calculated from the co-ordinates of intersecting lines using the principle outlined. The operator use a standard soft tape to swing the arc distances A-P1 and D-P1 to determine point P1 on the grade line A-B and the arc distances B-P2 and C-P2 to determine point P2 on the grade line C-D. By joining the marks made at point P1 and point P2 the direction of the tunnel must be set-out every time a direction line needs to be verified. As a check to the calculation, a join between point P1 and point P2 should be the same as the required bearing. Additional tie distances may be supplied to check the set-out position of the marks from other gradepegs.






Figure . Tie distances from intersecting lines

With the tie method, the production crew is able to align the direction marks using a grade-stick, ranging rod, laser pointer or mounted laser to mark-up the direction and gradient of the excavation from the set-out control on a daily basis. For ease of reference these marks are then painted-in to provide a reference for further marking up. The advantage of this method is that the gradepegs serve a dual purpose of providing spatial reference and construction control. The straight line sight will facilitate a standard offset to be carried forward until the next control is set-out.

2.