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

Conventional Surveying methods

In order to determine the context in which traditional mine surveying techniques are used it is considered necessary to investigate conventional land-, mine- and tunnelling surveying methods used internationally. Common surveying methods used to establish the co-ordinates of a survey station include:

1. Traversing

Bannister defines a traverse as follows: “A theodolite traverse survey consists of the measurement of (a) angles between successive lines (or bearings of each line), and (b) the length of each line.” [28]. Two types of traverse exist, namely the “closed” and the “open” traverse. A brief discussion of the two types of traverse follows.

1. 
   Closed traverse
   

A closed traverse is defined as a traverse that is started from a known point and ended on a known point. In many cases the observed lines of such a closed traverse will form a polygon. This method of traversing is considered to be superior to open traversing as the start and end points of the traverse are fixed on known points with known co-ordinates. Any error in the traverse should become obvious when the final closing co-ordinates are calculated. Any identified error can be balanced using accepted adjustment techniques such as the Bowdich correction or a least squares adjustment. Bannister argues that “The closed-line traverse has the advantage over the closed loop traverse that mistakes in the finishing co-ordinates and bearings and in the scale of the distance measurement should be revealed” [28]

2. 
   Open traverse
   

An open traverse is the most common method of surveying tunnels and mining development ends²⁷, as the survey is carried from known surface beacons and transferred underground. Bernard et al have described the process of conducting an underground traverse in the following manner “If these workings are narrow and tortuous, the traversing will be difficult and less accurate. However, modern mechanized mining commonly requires more space, making surveying operations easier. Even so, traversing is the only practical means of carrying line and grade to the headings.” [82]. It is accepted that an underground survey network cannot be closed on known survey points unless a holing between levels is effected and a closure survey be made between the two open traverses. An open traverse is described in the SME Mining Engineering Handbook as “Traverses that do not close back on their starting point or on other known points are said to be “open,” meaning that there is no automatic check on the validity of the work.” [82]. The open traverse requires continuous check surveying, to verify the distance component of the survey and a gyroscope survey to verify the bearing of the survey. Kavanagh stated that an open traverse is a combination of a number of straight lines and therefore is impossible to obtain a geometric closure, and argued that “…the measuring technique must be refined to provide for field verification. As a minimum, distances are measured twice (once in each direction) and angles doubled.” [37]

Figure . Hangingwall Traverse diagram

2. Intersection

This method of surveying uses the intersection of observed directions to determine the position of a point, either by making observations from known points to an unknown point (commonly referred to as a triangulation) or by making observations to known points from an unknown point (commonly referred to as a resection). The City Engineers Department, Durban Corporation, defines intersections as follows: “Intersection is the method used to determine the position of an unknown point, by means of the intersection of rays observed either to or from two or more fixed points.” [34]

3. Triangulation

In a conventional triangulation observations are made from a fixed baseline of which the terminal points have known co-ordinates. The angle between the known reference point and the unknown point is observed from both sides of the baseline. The minimum number of observations needed to obtain a fix of position is considered to be two rays. Triangulation has remained the most preferred method of obtaining the position of a point in surface surveying, as stated by Kavanagh “…because the basic measurement, angles, could be more quickly and precisely taken than could distances.” [37]. Ashkenazi wrote that “triangulation … is the strongest geometrical layout for almost any practical combination of angular and linear observational accuracies...” [98].

Figure . Triangulation diagram

4. Trilateration

Trilateration is a type of intersection using the measuring of distances to the unknown point from known points, as opposed to the observation of angles used for normal triangulation. Bannister and Raymond clarified that EDM technology “…not only allows the measurement of base lines, but also the measurement of selected sides of the triangulation network, which leads to further reliability….” [99]. This method of intersection was thought to supersede triangulation in popularity with the widespread introduction of the EDM. In the Durban City Engineers handbook “… subsequent results have shown that the system is liable to a rapid accumulation of azimuth error” [34], and that triangulation still provides a superior check in the form of angles compared with the measurement of distances which has no such internal check. [34]. Ashkenazi supported this view when he observed that “when vertical displacements are also involved, pure trilateration determinations lead to ill-conditioned (unstable) geometrical layouts and should not be contemplated”. [100]. He previously i concluded that the use of pure trilateration “usually constitutes a weak network, particularly in terms of orientation control” [98]. The Figure illustrates the minimum observations made during a trilateration.

Figure . A diagram of a Trilateration.

5. Resection

A resection is a form of intersection where the observer sets up at an unknown point and observes known points to determine the position of the unknown point [101]. Watt defined a resection as “… a method of a point position determination which requires only the observation of directions from the point itself to a minimum of five well-spaced control points” [102] McCaw observed that the resection method has been known for a long time and dated the application thereof “In the Philosophical transactions for 1685, there is a paper of direct interest to surveyors., This paper in Vol XV, No 177 (December) pp 1231-6,...,”the solutions of Three Chorograpic Problems. [103] A number of methods of calculation can be used to determine the co-ordinates of the unknown point, including Cassini’s [104] method was recorded by Klinkenberg and Tienstra’s method [105] referred to by Van der Sterr , the latter author remarked that “the above formula are suitable for machine computation and are identical with the results obtained by Mr. Surveyor J.M. Tienstra in Tydschrift voor Kadaster en Landmeetkunde, 1926, No I.” [105]. This method of surveying has traditionally been considered as primarily a surface surveying application. The reluctance of Mine Surveyors in using resections even on surface has been expressed by Morton when he observed that “Resection has never been accepted by the majority of surveyors as a reliable method of obtaining a “fix”. This is due to the fact that unless the problem of resection is fully understood, serious errors may be introduced and not detected during calculation.” [14]

The general design of survey networks in the underground environment is constrained by the long narrow environment and it is argued that this environment accommodates the conventional traversing method and therefore narrow tunnels are not considered to lend themselves to the method of resection used in surface surveying. It is interesting to note the progressive shift in opinion of the resection method from 1951 when Shewmon discussed the possibility of a pure angular resection method to 2006 when Uren and Price described the freestation method [95]. In 1951, Shewmon alluded to the fact that the resection was not considered accurate enough for underground surveying: “Speaking of random setups in general, not just the method described above, it should be noted that transit men are occasionally prohibited from using random setups because a superior believes them to be too inaccurate. Actually, a random setup can be made with almost any accuracy desired up to 1ft in 400ft, through the use of strong triangles with four of five significant figures in the sides.” [106] By the mid 1980’s, in a technical guideline published by the Johannesburg Consolidated Investments Company it was stated that it is possible to use the resection method if the correct procedures are in place and the geometry of the resection is within the correct limits [107]. It is interesting to note that at that time EDM technology was not used underground. The method described a process of using steel tapes and angular measurements with the position determination being calculated by a programmable calculator. In 2006, Uren and Price described two types of resection possible, namely resections making use of observed angles and resections making use of measured distances. The authors remarked that “…these are particularly useful for coordinating temporary control points on site which are called free station points because they can be established anywhere convenient.” [95].
McCaw argued that the efficiency and accuracy of the resection method of fixing the position of an unknown point should convince surveyors to adopt this method as a primary method of surveying: “This method of interpolating positions possesses considerable advantages from the point of view of speed, economy, and convenience. In certain kinds of work its advantages are so overwhelming that practically no other course is open to the surveyor;” [103]

Figure . A Resection observation

6. “Vertical” Resections

A further refinement of conventional resection is described as the vertical resection. The method is not well known in the Mine Surveying field, but has a wider application than what would be apparent at first glance. This method is most obviously used in the position determination method used by Global Positioning Systems, however the method can be applied in terrestrial surveying where observations can be made to elevated points with known co-ordinates. Allan argued that the vertical resection method could be used when as little as two points are available [108], as long as at least one of the points has an elevation. Should both points be elevated, it would be possible to obtain an independent check on the survey position.

7. Freestations

Although no text references could be located for the combination of distance measuring and the normal resection method, this method of surveying is becoming increasingly popular. Bannister referred to this method of surveying when he stated that “many total station instruments, and nearly all data loggers, contain software that will give co-ordinates of points,..., following observation of distances and angle on to reflectors established at two stations, A and B. this is known as a freestation.” [28]. According to Uren and Price both methods of resections (using distances or angles) could be considered freestations as the observer has the freedom to set up at any convenient point. [95] Riccardus and Allman argued that “Since it is indifferent at which point the distance measuring instrument has been set up, there is in fact no distinction between intersection and resection by distance measurement” [101] One surveying equipment supplier described the method used by the on-board software of one of their instruments to calculate a resection as follows: “This method can be used to calculate the two or three-dimensional local coordinates for the instrument …from distance and angular measurements to two target points.” [109]. This method of surveying does not seem to be used to its full advantage as referred to in McCormack’s article [110] on surveying in Australia. Within the software of the instrument provision is made to observe the two known stations only once with no closure on the original reference object. The guide does make reference to the sequence in which observations should be made in order to set up the instrument according to local co-ordinates. It is unclear what the impact of the observation sequence will be on the accuracy of bearing calculations as some articles makes reference to the likelihood of error propagation specifically in azimuth. Nindel remarked in a software user’s guide that “…the instrument has the ability to calculate the position of a freestation by means of a least squares adjustment or a robust adjustment” [111]. According to Zimmerman, the provisional co-ordinates of the “freestation” point is calculated using “each possible unique observation combination” including triangles, resection(s) and a helmert transformation. These unique solutions are used to determine the differences between the differences between observed values and calculated values (OMC’s). The provisional co-ordinate solution is then calculated from the group of observations with the smallest number of large OMC’s between calculated and observed values. The final position determination is made by robust least squares adjustment, not the OMC values and weighting is applied to all observations. [112] The method of selecting OMC’s is illustrated in Figure .

Figure . Software freestation method

A current instrument manual made reference to the importance of additional observations when it is stated that: “although a position fix can be obtained by observations onto two stations, as shown above, for accurate work the surveyor should sight a third station for a check on the data.” [109].

8. Three-dimensional two-point resection

Wolf and Ghilani argued that the position of an unknown point can be determined from angle and distance observations “…to two other stations of known positions.” [36], they proposed that such a procedure would be convenient in mines. [36]. This three dimensional two-point resection would be similar to the vertical resection described by Allan [108] although Allan argues that at least one of the points should be elevated and that both points should be elevated if an independent check is required.

9. Triangulateration

The combination of triangulation and trilateration is sometimes referred to as triangulateration. In this method all angles and distances are observed to the unknown point using electronic distance measuring equipment. As far as could be determined, this method is not used in the South African underground environment. Kavanagh stated that “… with the advent of EDM instruments, traditional triangulation techniques have given way to (1) combined triangulation and trilateration techniques (2)simple trilateration, and (3) precise traverses.” [37] In his paper Morton referred to this method stating that “one instrument setup can now give both angle and distances, ensuring a more accurate result.” He referred to this method as “a combination of triangulation and trilateration, in which all the angles and sides are measured,…” arguing that as a result “ill-conditioned” figures may be used. [14] This method of surveying is sometimes referred to as an intersection or resection and used as such in Australian mines as described by Jaroz and Shepard, who stated that this method has “…gained widespread acceptance in underground metalliferous mines in Western Australia” [96]. McCormack argued that “if resection is performed instead of traversing then surveyors could set up anywhere they wanted, as long as they were in sight of two known points.” [96]^. Arthur supported McCormack, when in a paper presented at the International Mine Survey conference in 2010 he noted that the “wall station resection method has been used extensively since underground operations started in 2003. It has led to a safer, more productive and efficient method of surveying.” [43]. The term resection is used frequently in Australian papers but in the case where observations are taken to only two points as stated in these papers, the term resection could be considered to be contradictory. A more appropriate term would be a “random setup”, intersection or trilateration. The term “resection” implies the fixing of an unknown point by observations to at least three known points. Morton defined the difference between triangulation and resection as “The basic difference between obtaining a fix by resection and triangulation, is that in the former method back rays are used and in triangulation forward rays. The minimum number of rays in the first case being three while in the second case two rays will establish a fix.” [14]. Moffitt commented on the advantage of this method of surveying, stating that “the internal accuracy and reliability of such a network is greatly enhanced by a hybrid triangulation-trilateration system.” [113].