20.1. Introduction Mine surveying includes underground surveying as practiced in mining and tunneling as well as the surface operations associated with underground work and open-pit mining.

Conditions underground are very different from those on the surface. Traverses maycontain very short legs and run along narrow, dusty corridors. Levels to establish elevations may have to be brought into the workings through deep shafts. Astronomic observations are not possible, so that underground orientation must be controlled by plumbing wires in a shaft or by means of a gyro theodolite. Rock movement can affect the stability of survey marks and may also cause more serious problems associated with cave-ins, property damage, or perhaps loss of life. The mine surveyor must monitor these rock movements and cooperate closely with geologists and other related specialists.

Because of the expanding role of surveyors in the mining industry (Ref. 3), it is not possible to cover all aspects of mine surveys in one chapter. Emphasis is concentrated on a few of the more basic tasks in underground and tunnel surveys, such as mine orientation procedures and the control of tunneling. However, many other equally important aspects, such as open-pit surveying, ground deformation monitoring, and three-dimensional mine modeling and mapping ha';"e been omitted.

20.2. Mining terminology The composite sketch in Fig. 20.1 illustrates some mining terms the definition of which follow:

Adit A horizontal or nearly horizontal passage driven from the surface for working or dewatering a mine.

Back The top of a drift, cross cut, or slope. Also called a roof.Back fill Waste rock or other material used to fill a mined out stope to prevent caving.Bedded deposit An ore deposit of tabular form that lies horizontally or slightly inclined and is

commonly parallel to the stratification of the enclosing rocks.Cage An elevator for workers and material in a mine shaft.Chute A channel or trough underground, or inclined trough above ground, through which ore falls or

is shot by gravity from a higher to a lower level (also spelled shoot).Collar The term applied to the timbering or concrete around the mouth or top of a shaft and the

mouth of a drill hole.Cross cut A horizontal opening driven from shaft to a vein across the course of the vein in order to

reach the ore zone.Dip The angle at which a bed, stratum, or vein is inclined from the horizontal.

tThis chapter was written by Dr. Adam Chrzanowski, University of New Brunswick, Canada, and Dr.A. J. Robinson, University of New South Wales, Australia.

\

Article 20.2 Mining terminology 839

Fig. 20.1 Cross section of a typical mining operation.

Drift A horizontal opening in or near a mineral deposit and parallel to the course of the vein or long dimension of the deposit.

Entry Manway, haulage way, or ventilation way below ground, of a permanent nature (i.e., not in anore to be removed).

Face End wall of a drift or cross cut or of bedded deposits.Foot wall The wall or rock under a vein or under other steeply inclined mineral formations.Gangue Undesired minerals associated with ore.Gangway A main haulage road underground.Hanging wall The wall or rock on the upper side of steeply inclined deposits. It is called a roof in

bedded deposits.Headframe A construction at top of a shaft which houses hoisting equipment.Level Mines are customarily worked from shafts through horizontal passages or drifts called levels.

These are commonly spaced at regular intervals in depth and are either numbered from the surface in regular order or are designated by their actual elevation below the top of a shaft.

Ore pass Vertical or diagonal opening between levels to permit movement of ore by gravity.Pillars Natural rock, or ore supports, left in stopes to avoid or to decrease the roof subsidence as

mining progresses.Raise A vertical or inclined opening driven upward in ore from a level.Rib Wall in an entry. Also simply wall.Roof See Back.Shaft A vertical or inclined excavation in a mine extending downward from the surface or from some

interior point as a principal opening through which the mine is exploited.Shoot See Chute.Sill Synonymous with floor.Stope Underground "room" or working area from which ore is removed.Strike The horizontal course, bearing, or azimuth of an inclined bed, stratum, or vein.Sump An excavation made at the bottom of a shaft to collect water.

840 Mining surveys Chapter 20

lQ[

Tunnel A horizontal or nearly horizontal underground passage that is open to the atmosphere at both ends.

Waste Mined rocks that do not contain useful minerals.Winze A vertical or inclined opening driven downwards (sunk) from a point inside a mine for the

purpose of connecting with a lower level or of exploring the ground for a limited depth below a level.

20.3. Design of horizontal control networks In underground mines Control networks consist of traverses (frequently open-end traverses) that must follow the existing net of mining workings and excavations. Since open-end traverses may often serve as basic control, they must be executed with the utmost care and are usually independently checked by a second resurvey.

Distances between the survey stations are generally very short, ranging from 10 to 20 ft (afew metres) to an average of 160 ft (50 m). Only in the main transportation roads may the distances be increased to about 1000 ft or a few hundred metres.

The control network consists of (1) first-order loops which serve as basic control and an; run in the permanent mine workings, (2) second-order traverses run into headings and development areas, and (3) third-order stations (short traverses) used for detailed mapping of excavated areas and daily checks of mining progress in stopes and headings.

The establishment of the underground control network is done in a reversed sequence from that used on the surface. The lowest-order control is established first and is subse- quently replaced by the higher-order control once the developed area allows for longer sights and for a loop closure of the traverses.

Typically, the following maximum errors in relative positions of the control points arepermitted:

first-order control (a) 1: 10,000 in small and medium-size mines(b) 1: 20,000 in large mines extended over areas of several kilometres in

diametersecond-order control 1 : 5000

third-order control 1 : 1000

The relative accuracies given above are usually interpreted as the ratio of the semimajor axis of the relative error ellipse (Art. 2.19), at the 95 percent probability level, to the distance between the points of interest.

20.4. Monumentatlon and marking of points The stations of the horizontal control network are usually marked in the roof (back) or walls of the mining workings. A hole is drilled, a wooden plug is inserted, and into this a spad (Fig. 20.2a) or a metal plug (Fig.20.2b), with a hole for the string of the plumb bob, is driven. The markers may also be cemented directly in the drilled holes, using, for instance, an epoxy glue.

I J

I J

I J

@(a)

Fig. 20.2 Roof markers.

(b)

The wall markers require either a special type of a portable bar (Fig. 20.3) which is inserted into the marker during the survey procedure, or the markers are used as eccentric stations to which the position of the survey instruments is referenced by measurements of short distances and/or angles (see Ref. 9). The latter method, although requiring some additional measurements and trigonometric calculations, has the advantage that the survey instruments can be set up in any convenient place without the time-consuming task of centering under the marker.

20.5. Angle measurements The old-type vernier transits, although still in use in some mines in North America, are being replaced by much smaller and lighter modern theodolites with the optical micrometer readout (Art. 6.30). The theodolites are equipped with electric illumination of the horizontal and vertical circles and the cross hairs. Vertical axes of the theodolite are marked on the top of the telescopes for centering under the roof stations.

Owing to the generally short sights in underground traversing, accurate centering of the instruments is very crucial. Centering under the roof markers is more difficult than the conventional centering above the marked points. If one adds to it the cramped conditions, darkness, and difficulties for setting the legs of the tripod on an uneven floor, the centering procedure requires a lot of experience. It is usually done by means of a string plumb. bob. The telescope with a centering marker must, of course, be set in a horizontal position during the centering procedure. The tips of the bobs should be very sharp and protected against any damage to ensure a good accuracy of centering. Optical zenith plummets attached on the top of the telescopes or interchangeable with the theodolite in the same tribrach, available as an optional accessory with some models (e.g., Wild Heerbrugg) of theodolites, are also used in centering under the roof markers.

First-order traversing is usually done by means of forced-centering traversing equipment,using interchangeable theodolite and targets fitted with detachable tribrachs (Art. 6.30).

Repeating theodolites with direct micrometer readouts of 20" to I' are usually sufficient for most of the control surveys except first-order traversing in very long headings and tunnels when precision theodolites are required.

Plumb-bob strings lighted from behind by means of a mining head lamp (covered with apiece of tracing paper) serve as the targets in third- and sometimes in second-order traversing. Traversing equipment with lighted targets (see Fig. 6.67) are used in first-order surveys. Special parabolic reflectors with 6-volt bulbs and with a changeable aperture have

Protective

Fig. 20.3 Wall markers. (From Ref. 16.)

~

to be used as the targets when distances exceed a few hundred metres (Ref. 21). A small helium-neon laser mounted on the telescope of a precision theodolite and small corner reflectors used as the targets have been successfully tested at the Department of Surveying Engineering of the University of New Brunswick in Canada in precision angle measurements in long tunnels.

Frequently, very steep sights are encountered when traversing through steep raises orother inclined openings. The influence of an error €f3 (expressed in seconds of arc) in leveling the theodolite on the accuracy of angle measurement can be very dangerous and is expressed by the approximate formula (Ref. 10)

(20.1)

where YI and Y2 are vertical angles of the sights and €L is the error of leveling the horizontal plate of the theodolite. For instance, if YI = Y2 =400 and a theodolite with a spirit level of asensitivity of 30" is misleveled by one division only (i.e., €L = 30"), then the error of themeasured angle €f3 = 36". Additional striding levels of a higher sensitivity must then be used in leveling the theodolite.

Setting and reading the micrometer on very steep sights may be most difficult or even impossible without using additional diagonal eyepieces which are available as optional accessories' with most models of modern theodolites. Some companies, for example Breithaupt, Keuffel & Esser, and Berger, produce theodolites with additional eccentric side telescopes for sighting downwards on very steeply inclined traverse legs. Kern Co. of Switzerland produces small additional telescopes which fit on the top of the main telescope of their model DKM-I theodolite. When using the side telescope, the mean of an angle turned with the telescope direct and reversed is free of the eccentricity influence of the side telescope. Use of the top telescope is inferior in this respect because it does not allow for direct and reversed measurements and, therefore, requires a very careful instrument adjust- ment prior to the measurements. Vertical angles measured with eccentric telescopes must be corrected for the eccentricity. Details of the adjustment and use of eccentric telescopes are given in Refs. 19 and 23.

In some cases the cramped space in the mining workings or an unstable and steeplyinclined floor do not allow the use of tripods in angle measurements. The theodolite must then be set up on special bars (Fig. 20.4) or supporting arms equipped with a bracket screwed or bolted to the timber. Also, telescopic beams stretched between the walls of the headings are used. The Wild and Zeiss companies, among others, produce special supporting bars for their theodolites for mining and construction survey applications. Any mining workshop should be able to make supporting arms at the request of the mine surveyor.

Reversed hanging theodolites (Fig. 20.5a), which fit on supporting bars screwed into wall timbering, are popularly used in the third-order surveys in coal mines in central and easternEuropean countries. They are very convenient to use in narrow and cramped conditions.

~-~~rIFig. 20.4 Supporting bars for theodolites. (From Ref. 16.)

Article 20.8 Error propagation in open-end traverses 843

Fig. 20.5 (a) Hanging theodolite.(Courtesy Academy of Mining andMetalurgy, University of Krakow, Krakow,Poland.) (b) Hanging spherical target. (a) (b)

They allow for very fast setting up and leveling. Small targets in a form of small spheres (Fig. 20.5b) or cones suspended on a short chain are interchangeable with the theodolite on the portable supporting arms, thus allowing for an automatic (forced) centering. Model Temin made by Breithaupt weighs only 2.5 kg, has 1 centigrade (about 30") interpolated accuracy of the readout, and 1.1 m shortest focusing distance.

20.6. Distance measurements Steel tapes are still the most popular tools in distance measurement. Lightweight, short-range electronic distance measurement (EDM) instruments (Arts. 4.29 to 4.35) have become popular in first-order traverse, but their use is still uneconomical for a daily application in traverses with very short distances. Mining regula- tions require that only fire- and damp-proof EDM instruments, such as the Zeiss Eldi-2 (Mining), may be used in gaseous mines.

Steel tapes are used mainly supported at the two ends (in catenary) unless the floor is flat and the procedure and corrections to be applied are practically the same as on the surface.

Optical distance measurements (stadia) with short fluorescent tacheometric rods or optical range finders, such as Zeiss-Jena BRT 006 telemeter, are very useful in stope measurements and in detail underground mapping. Their use ,in mining surveying, due to the specific conditions, will probably survive a much longer time than in surface measurements, where electronic tacheometry is rapidly replacing optical measurements.

20.7. Traverse computations Mining operations must be based on a framework of coordi- nated points. Coordinates of underground stations should be calculated in the surface coordinate system so that positions of details on the surface can be analytically correlated with details on individual levels and sublevels of the mine. Of course, this requirement also implies that both surface and underground systems have the same orientation. First-order and possibly second-order underground traverse loops should be simultaneously adjusted by the method of least squares (see Art. B.14, Appendix B).

20.8. Error propagation In open-end traverses As mentioned previously, most of the control surveys in the underground development areas are based on open-end traverses. A thorough analysis of the expected positional accuracy of the last point of the traverse should always be done before starting a new development survey.

Figure 20.6 shows a traverse 0 - K with known coordinates of points 0 and 1 treated aserrorless (belonging to the higher-order traverse). If angles {3i and distances d, are measured,

(1Al d

d

= -

844 Mining surveys Chapter 20

y

o~--------------------------------------------------xFig. 20.6 Traverse with measured angles and distances.

the coordinates of point K are calculated from

Xk = Xl + dl sin(Ao+ f31 -180°) + d2sin[Ao+ f31 + f32 - (2)(180)] + ...

+ dk-I sin[Ao+ f31 + f32 + ... + f3k-I- (k-l)180]Yk ~ YI + d, cos(Ao+ f31 -180) + d2cos[Ao+ f31 + f32 - (2)(180)] + ...

+ dk-I cos[Ao+ f31 + f32 + ... + f3k-1 - (k -1)180]

where Ao is calculated from the coordinates of points 0 and 1.

(20.2)

(20.3)

The propagated variances and covariances of the coordinates for point K, (1; , (1y2, and (1xy, k k k

can be found by applying Eqs. (8.33), Art. 8.23, to Eqs. (20.2) and (20.3). Standarddeviations of angles, (1(3 (in radians), and distance, (1d,., are estimated for this purpose.

The variances and covariances determined using Eqs. (8.33) allow calculation of the parameters of the error ellipse for point K using Eqs. (2.39) to (2.41), Art 2.19.

If azimuths of each traverse leg are measured (Fig. 20.7) using a gyrotheodolite, thecoordinates of K are calculated from

and

Yk = YI + d, cosA 1+ d2 COSA2 + ... + dk-l cosAk_1

(20.4)

(20.5)

In this case the error propagation will result in

k - 1 k - 1 ( X X )2(1X2k =.rt:.J "(

Yi+l- Yj )2 2 + " i + I - i.rt:.J (1t2:

4(20.6)

1 1 I

k 1 - k - 1 ( Y Y )2(1

2Yk = s"(: Xi + I - Xi

)2

(1A2

I +

" i + 1 - i.rt:.J (1t

2:

4

(20.7)

and1 1 I

~l 2 ~1 ~(1XYk kJ (Xi+ I - X;)( Yi+ 1- Y;)(1A; £.J (X;+ 1- X;)( Y;+ 1- Y;) 2

lId;

(20.8)

Comparing the Eqs. (8.33), Art. 8.23, with Eqs. (20.6) to (20.8) it can be seen that there is a significant difference in the propagation of errors of angle measurements versus errors of azimuth measurements. In long traverses with many stations, the positional accuracy of the last point may be smaller in a traverse with measured azimuths, compared to a traverse with measured angles even when the angles are measured with a much higher accuracy than theazimuths.

y

Article 20.8 Error propagation in open-end traverses 845o~------------------------------------------------~xFig. 20.7 Traverse with measured azimuths and distances.

11 (15")2

i

d2 a

t

y'

o 2 3 4 5 6 7 8 9 10 11 12

~----------------------------------------------------_.xFig. 20.8 Error propagation of angles vs. azimuths (Example 20.1).

Example 20.1 A traverse 5.5 km long (Fig. 20.8) is run from fixed, higher order stations 0 and 1 to station No. 12. All the distances are equal to 500 m. An option is available either to measure angles f3with (Jp = 4" or azimuth with (JA = 15". Which method will give smaller (JY12? (Note that in this examplethe X-coordinate of 12 is not affected by the errors of angles or azimuths because the traverse is parallel to the X axis).

SOLUTION Using angle measurements and applying Eqs. (8.33) to Eq. (20.3),

(Jy2 = 211: (X12-

X{)2

(4=

")»

2: =0.0476

m2

and

12 1 PUsing azimuth measurements [Eq. (20.7)]:

(Jy2 = 2: (X;+1 _X;)2 -,,- =0.0145 m2

12 1 P

where p" = 206,265" .

and

The results show that the azimuth measurements would give almost twice the positional accuracy of the angle measurements even though the azimuths would be measured with almost four times lower accuracy than angles.

Example 20.2 Given are approximate coordinates of traverse stations points 1 to 4 (Fig. 20.9):

Point X,m Y,m

1 +300.00 + 100.002 400.00 200.003 500.00 200.004 600.00 200.00

Points 0 and 1 are known and are treated as errorless. Find the standard error ellipse of point 4 if estimated standard deviations of measured angles and distances are (JfJ= 10", (Jd= 10 mm. First apply Eqs. (8.33) to Eqs. (20.2) and (20.3) to obtain propagated variances and covariances.

SOLUTION

3

2: (Y4 - y;)2(Jil= 23 mm2

1

3

(X4 -X;)2(Jil= 329 mm2

23: (Xi+1 -

X)2 (J2 = 250 mrn"

1 i

3

2: (Y4 - Y;)(X4 - Xi)(Jff = 71 mm 21 1'1

3 (Y _ y)2" ;+1 ; (J2 = 50 mm2£.J d21 ;

y

o

L-------------------------------------------------------xFig. 20.9 Positional error in an open traverse (Example 20.2).

" 206,265" V 2 2

where 0f3, is in radians. From the above:

o;4=273mm2 o$4=379mm2 o""Y4=-21 rnrn?

Placing these values in Eqs. (2.39) to (2.41), Art. 2.19, the parameters of the error ellipse are

8=20 mmb= 16 mm8= 100048'

:

20.9. Mine orientation surveys: basic principles and classifIcation If the mine is accessi-ble by means of adits or inclined transportation roads, the orientation process is compara- tively simple and limited to running a traverse between the surface geodetic network and points of the underground control net. Very often, however, the only access to the mine is by way of vertical shafts and then direct traversing from the surface is impossible. In these cases, one of the following three methods of mine orientation can be applied:

1. Shaft plumbing with two or more plumb lines in one vertical shaft.2. Shaft plumbing through two or more vertical shafts with one plumb line in each shaft.3. Gyro orientation with one plumb line.

The process of orientation is supposed to give coordinates of at least one point and azimuth of one line of the underground network in the surface coordinate system. In the first two methods, the two plumb lines serve for a simultaneous transfer of the coordinates and of the azimuth directly from the surface, assuming that the plumb lines are truly vertical. This assumption is particularly critical in the first method in which the distance between the two plumb lines is comparatively short. This distance is usually not longer than 2 to 4 m even when the diameter of the shaft is larger because there are always many obstacles in the shaft such as cages, pipes, cables, etc. In this case two small random deflections, e} and e2, one for each plumb line separated by a distance b, will produce an error c" of the transferred

azimuth, A:

cA = b e} + e2 (20.9)

For example, random deflections, e} = e2 = 1 mm, of the plumb lines which are separatedby a distance of 3 m will produce an error of cA =97". Therefore, the method of shaft plumbing orientation through one vertical shaft requires the utmost care and experience in establishing the plumb lines in the shaft as it is discussed in detail in Ref. 3 and summarizedin the next section.

The. error of shaft plumbing caused by the possible deflections of the plumb lines is, of course, much smaller when two plumb lines are used in the two separate shafts. In that case the distance b in Eq. (20.9) is usually several hundred metres long and even large errors in the verticality of the plumb lines may be tolerated. The method of orientation through two or more vertical shafts is also called the fitted traverse method. This method usually gives much higher accuracy of mine orientation than shaft plumbing through one vertical shaft, and very often it may also give a better accuracy than the gyro orientation. Unfortunately, not every mine has an access to the surface through two or more vertical shafts from the mining levels which require the orientation.

Use of the gyro attachments has revolutionized mine orientation surveys. In this method, the shaft plumbing is used only for the transfer of coordinates of one point, and an error of even a few centimetres can be tolerated because the transfer of the azimuth, which is critical for the orientation of the underground network, is done independently of the shaft plumb- ing. Although shaft-plumbing methods may be considered obsolete in modern mine survey- ing under certain favorable conditions, shaft plumbing even through one vertical shaft can be competitive with gyro orientation. Examples of conditions favorable to shaft plumbing are shallow shafts, or the orientation of subway or hydro-development projects. Besides, precision shaft plumbing is still needed in the process of sinking new shafts (control of the

Article 20.11 Shaft-plumbing procedure 847

shaft construction) and in periodic deformation measurements of shafts, which is mandatory in 'many mines. Therefore, the gyro method and the shaft-plumbing methods are both discussed in more detail in the following sections.

There are no general specifications for the accuracy requirements for mine orientation. In each individual case the chief surveyor has to decide, depending on the importance of the orientation, what accuracy is needed. Generally, the relative position of the underground points in respect to the surface and other mining levels should be known with an accuracy better than 1 m. The accuracy requirements may be much higher, of the order of 0.2 m, when two mine workings from two different levels, or when two different mines are supposed to meet each other.

The process of mine orientation is one of the most responsible tasks of the mine surveyorand should not be entrusted to persons who do not have good experience and knowledge in all aspects of mine orientation, including error analysis.

20.10. Shaft plumbing through one vertical shaft: general methodology The basic idea of the method is shown in Fig. 20.10. Plumb lines PI and P2 serve as intermediate traverse

stations between known (coordinated) points A and B on the surface and C and D

underground. The only problem in the method is the determination of the angles /31 and /32'They cannot be measured directly because of difficulties in setting up theodolites in the shaft opening and centering them precisely in the locations of the plumb lines. One possibility is to establish points Band C exactly in line of the vertical plane of the two plumb lines. This method is time consuming and if high accuracy is required, special equipment such as micrometric sliding devices for the theodolites is necessary to bring them precisely in the plane of the plumb lines.

There are several other methods of connecting surveys which allow the determination of

angles /31 and /32' The most popular are Weissbach's method (or Weissbach's triangle method) and the quadrilateral method, which is also known in the literature either as theHause or the Weiss method.

20.11. Shaft-plumbing procedure

Selection of the plumb bob Thin steel wire with a heavy suspended plumb bob is the most popularly used plumb line in the orientation process. Precision optical or laser plummets will be briefly discussed later, but their application is not as popular as the mechanical plumb bobs.

Steel wires with very high tensile strength (200 kg/mm2 or larger) (piano wires) should be used for shaft plumbing. As a rule, the wire should be as thin as possible and the load (the bob) should be as heavy as possible. As a compromise, the weight of the bob is usuallyselected as equal to H 13 in kilograms, where H is the depth of plumbing in metres. Forsafety reasons the load should not exceed half of the maximum (breaking) load of the wire. Therefore, if wires with tensile strength of 200 kg/mm2 are used in a depth of H = 600 m, a

A

Fig. 20.10 Mine orientation using shaft plumbing (angles {31 and /32 must be determined indirectly).

848 Mining surveys Chapter 20

Fig. 20.11 Wire reel for shaft plumbing.

bob of 200 kg should be suspended on a wire with cross section of 2 mm2 (this corresponds to a diameter of 1.6 rom). The wire should be stored on special drums (Fig. 20.11) which allow for a slow lowering of the plumb bob to a desired mining level. The plumb bob consists of a rod and removable lead disks (Fig. 20.12), usually of 20 kg each.

Lowering and stabilizing the plumb bobs The wire drums are located near the shaft (Fig.20.13) and are securely fastened to the ground. Safety platforms are built across the shaft opening on the surface and at the oriented level. The wires are led over beams of the shaft head frame and over guiding pulleys (Fig. 20.14) in the preselected locations. Only small weights, of about 11 lb (5 kg), are attached to the wires during the lowering procedure. The main loads are suspended when the wires reach the bottom. The distance between the two safety platforms at the bottom should be designed according to the precalculated extension of the wire when the full load is suspended:

AH = PH m or ft (20.10)aE

where P= weight of the plumb bob, kga = cross section of the wire, cnr' or in2

H = depth, m or ft

E=(2.1)106 kg/cm2 (28 to 30 million Ib/in2)

For example, if H=600 m, P=200 kg, and a=0.02 cnr', then flH=2.9 m.The plumb line should be checked to ensure that it does not touch any obstacles in the

Fig. 20.12 Typical plumb bob with removable weight disks.

Article 20.11 Shaft-plumbing procedure 849

Fig. 20.13 Shaft-plumbing procedure.

shaft. For that purpose a small ring of wire is wrapped around the plumb line and allowed to drop. Another check is to compare the actual and theoretical period, T, of oscillations of the plumb line using the formula

T=2'lTYf (20.11)

where g=980 cmjsec2 and H is the depth of shaft in centimetres (g=32 ftjsec2 and H is in feet).

In shallow shafts, when the weight is small, the plumb bob should be submerged in a container of oil to dampen the oscillations of the. plumb line, which are produced by air currents and dropping water in the shaft. In very deep shafts it is impossible to completely dampen the oscillations, and the plumb line is in a continuous swing along ellipses a few centimetres in diameter. The vertical position of the wire may be found by taking readings of the extreme left and right deflections of the wire on a millimetre scale placed behind the wire at the oriented level. The readings are taken with a telescope of the theodolite, which

Fig. 20.14 Guiding pulley for plumb wire.

850 Mining surveys Chapter 20

Scales Wire

Fig. 20.15 Typical apparatus for setting plumb wire in its vertical position.

should be set up a few metres from the wire. Fractions of a millimetre are estimated when taking the readings of the left and right edges of the wire at its turning points.

Usually, a set of 10 readings of the turning points of the swinging wire is sufficient to calculate the mean "vertical" position of the plumb line. Care must be taken so that the plumb bob swings in a plane parallel to the scale, which should be perpendicular to the line of sight of the theodolite. This is done by holding the plumb bob near its center of gravity and gently deflecting it in the desired direction. The calculated mean reading on the scale serves as a target for angle measurements in the connecting surveys at the oriented level. Sometimes, for example in the aforementioned quadrilateral method of the connecting surveys, the plumb line must be clamped in its vertical position. Two perpendicular scales must then be used for observing the swings of the wire from two perpendicular directions, or a mirror is attached (Fig. 20.15) which allows observations on two scales from one station. More details on the procedure and instrumentation used in lowering and stabilization of the wires in their vertical positions is given in Ref. 3.

Influence of air currents The movement of air in the shaft exerts a force on the hanging wire (Fig. 20.16). If the plumb bob itself is screened from the air influence, as it should be, the approximate value of the deflection of the plumb line may be calculated (see Ref. 3) from the equation

e= 30(h)(H)(d)(v)2 mmp (20.12)

where h= portion of the wire in metres exposed to the side stream of air, m; it is taken as approximately equal to the height of the shaft opening at the shaft entrance

H = depth of plumbing, md = diameter of the wire, mv=velocity of air, mls at the cross section hP = weight of the plumb bob, kg

For example, if h=5 m, H=600 m, d=0.OOI6 m, v= 1.5 mis, and P=200 kg, the expected deflection would be e = 1.6 mm.

Article 20.11 Shaft-plumbing procedure 851

Fig. 20.16 Deflection of the plumb line by air current.

The direction of the wire deflection depends on the location of the wire in the horizontal cross section of the shaft. Generally, the direction coincides with the direction of the axis of the shaft opening, but it can differ by ±45°, so that the plumb bobs hanging in different positions may be deflected in different directions causing a large error in the orientation. Therefore, the air current should be dampened during the orientation process at all levels entering the shaft by shutting all the ventilation doors. The complete damping of the air stream in the shaft is not usually possible. The disconnection of the forced draft ventilationis not a sufficient precaution, as the speed of the natural air stream may be greater than 1m Zsec.

When the influence of the air current is too strong, a method of wire plumbing with two or more different loads may be used. Two positions '1 and '2 of the deflected wire are then determined on the scale (Fig. 20.17) using two different loads on the same wire (usually atthe ratio PI/ P2 = 1 : 2). The vertical position ('0 reading on the scale) of the wire can then beextrapolated from:

(20.13)

The double-weight method has, however, some disadvantages:

1. The point of the suspension of the wire on the surface may move when changing the weights of the plumb bob.

2. The smaller weight PI may be too small to counteract the spiral shape of the wire (see below).

Influence of the spiral shape of the wires During manufacture, and later during storage on small-diameter reels, the wire becomes permanently deformed and assumes a spiral shape. Even a very heavy load may fail to straighten the wire completely, and what appears to the naked eye as a long, straight wire may in fact be a long, small-diameter spiral (Fig.

852 Mining surveys Chapter 20

Fig. 20.17 Shaft plumbing with two weights.

20.18), with a radius r (em) calculated from Ref. 3:

'lTd4Er= 64RP (20.14)

where R is the radius of the spiral of the unloaded (free) wire in centimetres, d the diameter of the wire in em, P the weight of the plumb bob in kg. R is usually between 10 and 25 em,F or example, if d = 0.16 em, P = 200 kg, and R = 20 em are used, r = 0.17 mm. The same wireif loaded only with 50 kg would give r=0.7 mm.

The spiral shape of the hanging wire gives an error in the vertical projection of the suspension point at the head of the shaft; the maximum value of this error can be 2r if the observer on the surface sights the wire in point A while the observer at the oriented level uses point B when observing the scale.

20.12. Connecting surveys using the Welsbach method In this method the orientation angles {31 and {32 (see Fig. 20.10) are determined from measurements of the angle al and

A

Fig. 20.18 Spiral shape of the plumb wire. p

Article 20.12 Connecting surveys using the Weisbach method 853

. ~·0

Fig. 20.19 Weisbach method of orientation. ·A

distances a, b., and Cl in the triangle on the surface (Fig. 20.19) and measurements of a2 and distances b2 and C2 in the underground triangle. The distance a between the plumb wires is

also measured underground to approximately check the verticality of the wires. The measurements on the surface are made directly to the plumb wires. The measurement of the underground angle a2 is made to the predetermined vertical positions of the wires on the scales (one scale for each wire) perpendicular to the lines of sight. The distances C2 and b2

are taped directly to the swinging wires, averaging the readings on the tape. To complete the orientation measurements, the angles 01 and 02 are measured at stations Band C.

The angles /31 and /32 are calculated from the simple trigonometric relationships

. /3 bi sinal . /3 b2 sin a2SID 1 =

aand sm 2 = ---

a(20.15)

As a check, the angles 1'1 and 1'2 are calculated from

clsmalSinl'l=--- a

and (20.16)

and the closure to 1800 should be obtained in both triangles.Once the angles /31 and /32 are determined, the mine orientation procedure is completed by

calculating the azimuth of the line CD and coordinates of C from the traverse A-B-PI-P2-C- D as shown in Fig. 20.10, in which stations A and B on the surface have known coordinates.

The variance of the azimuth of the underground line CD with respect to the surface lineAB can be calculated from

(20.17)

Article 20.13 Connecting surveys using the quadrilateral (Hause) method 855

2

where fA is the influence of the deflections of the plumb lines calculated from Eq. (20.9) if the deflections el and e2 are treated as standard deviations of the verticality of the plumb lines. They are estimated approximately from the previously discussed errors due to the air current, spiral shape of the wires, and the error of the mean positions determined on the scales (adding them, of course, in square values, as random errors). Usually, only half of the calculated [Eq. (20.12)] influence of the air current is taken as the part of the estimated standard deviation, owing to the fact that both plumb lines are most probably deflected in a similar direction. The standard deviation of positioning the wires on the scales can be kept equal to or smaller than 0.2 mm if the plane of the oscillations of the plumb bobs is parallelwithin ± 10° to the scale, the amplitude is smaller than 10 em, and if at least 10 readings(with an estimation to 0.2 mm) of the left and right reversal positions are taken for the calculation of the mean position.

Standard deviations of angles 01 and 02 can be estimated in the usual way from anexamination (Ref. 10) of the survey method and instruments used. They can easily be kept within a few seconds if the angles are measured in four to six positions with a theodolite with20" or smaller nominal values. of the micrometer divisions.

The variances of the calculated angles' 13 are determined by applying the rule of error propagation [Eq. (2.42)] to Eqs. (20.15), obtaining (for 131 or 132)

a~= -ta-naf3 ;+ -ta-naf3 ;+ (b -tan2f3 ) a;2 2 2 (20.18)

b2 a

2 a cos2 13

Equation (20.18) allows for an easy optimization of the Weisbach method; the best accuracy will be obtained when f3~180° because then the errors of the distances can be neglected and then

(20.19)

or, analogically,

ca =-a (20.20)Y a a

if angles "I are used in the traverse computations.For optimum results, theodolite stations at Band C should be as close as possible to the

nearer wire, and almost in line with both wires, the distance between the wires should be as long as possible and the angles exshould be measured with a high degree of precision.

Errors in distance as large as 10 mm may be neglected if the angle a <; 30'. Generally, the Weisbach method is not applied when the angle ex must be larger than 10°, because the influence of the errors of the measured distances becomes critical. In this case other methods of connecting surveys, for example the quadrilateral method, are recommended.

20.13. Connecting surveys using the quadrilateral (Hause) method Typical configura- tions for connecting surveys by the quadrilateral method are shown in Fig. 20.20.

Generally, the following values are measured in the quadrilateral method: angles 01' 02' Yh and "12 and distances PIP2 and CD. The errors of the distances have no influence on the accuracy of the transferred azimuth; therefore, they do not need to be measured precisely.

Since the angles to each wire are measured from two different stations, the "vertical" position of each wire must be determined on two scales perpendicular to each other using the apparatus shown in Fig. 20.15. The blocking plug is removed to allow the wire to swing in directions perpendicular to each scale, changing the direction of the swing after observa- tions on the first scale are completed, and a set of observations is taken on each scale. The mean "vertical" positions are then calculated and the wire is fixed in this position by means of the blocking plug and slow-motion screws. The angles are then measured directly to the fixed wires.

tanf3= (Yc- Yp)(XP1 -Xp)-(Xc-XP)(YPI- Yp)

(Yc- Yp)(YPI- Yp)+ (Xc-Xp)(Xp)-Xp)

(a)

Fig. 20.20 Quadrilateral (Hause) method of orientation.

Since the distance CD is usually just a few metres, the accuracy of centering the theodolite and the target is critical. Forced centering is recommended or else two theodolites should be used simultaneously at stations C and D, each pointing at the cross hairs of the other (telescopes focused to infinity).

Calculation of the orientation angle f3 can be done as follows:

1. A local coordinate system is arbitrarily chosen for the calculation of the angle {3, taking, for instance, point C as the beginning of the system and the line CD as the + X axis.

2. The coordinates of PI and P2 are calculated in the local system by simple intersections from the base CD using angles 81 and "'(2 for point PI and angles 82 and "'(1 for point P2' An error in the distance b

will produce only a scale change of the figure without changing the shape (the angles) so that the accuracy of b is not critical in the calculation of {3.

3. Angle {3 is calculated from the known coordinates of points PI' P2, and C (in the localsystem).4. Angles 82 and "'(2 are calculated from the obtained coordinates and as a check are compared with

their original values.

Equations (9.3) and (9.4) (Art. 9.2) derived from the point slope [Eq. (8.13), Art. 8.21] are recommended for use in calculating the intersections. When coordinates Xp, Yp ,Xp, Yp

I I 2 2

have been computed, the angle f3 is found using

(20.21)

Once the angle f3 is calculated, the orientation calculations proceed the same way as described in the preceding section.

Error analysis (see Ref. 13) of the quadrilateral method shows that (1) the best geometrical shape for the connecting quadrilateral is a. sqD;p.re;(2) given a square figure, better results are obtained if the shaft can be entered from ¥lre~des (Fig. 20.20b) because in this case (Jf3 = (Ja'

where (Ja is the average standard deviation of the measured angles o}> 02, YI' and Y2, and for

856 Mining surveys Chapter 20

(20.24)

the case where the shaft can only be entered from one side (Fig. 20.20a), 0"f3 = 2.4oa; and (3)

by increasing the ratio of distance CD to distance PIP2 the standard deviation of the orientation is also increased.

20.14. Orientation through two vertical shafts If two vertical shafts are sunk to the mining level, the orientation process is performed in the following steps:

1. One plumb line is established in each shaft and coordinates XI' YI and X 2' Y2 of the plumb lines PI and P2 (Fig. 20.21) are determined at the surface by means of a connecting survey to the nearest points of the geodetic control network.

2. The azimuth AI,2 and distance dl,2 between the plumb lines are calculated from

X2-XIA 1,2 = arctan y _ Y (20.22)

2 1

and

3. An underground traverse is measured from PI to P2 using the shortest possible route.

(20.23)

4. Distances in the underground traverse are reduced to the reference level of the surface coordinatesystem by adding corrections:

dBild.= -,-

I R

where H is the vertical distance to the reference surface and R the mean radius of the earth.5. The underground traverse is calculated in a local XY coordinate system having the coordinates of PI

in the surface system as an origin and with the + X axis aligned with the first traverse leg (Fig.20.21). Thus, coordinates of D, E, and P2 (Fig. 20.21) are calculated in the XY system.

6. The distance dl,2 and azimuth ..41,2 are calculated from the local coordinates of Pl and P2 andcompared with previously calculated dl,2 and A 1,2 on the surface, giving the rotation angle w of the local coordinate system:

and the scale

w=A1,2-AI,2 (20.25)

(20.26)

.i->:

o 20 40 60 80 m

Fig. 20.21 Mine orientation through two shafts.

7 .. Coordinates for points in the underground traverse are now calculated in the XY surface coordinate system using distances multiplied by A and the azimuths of the first and subsequent legs rotated by the angle co (similarity transformation).

A least-squares adjustment may be used in the adjustment of the underground traverse at this point. However, with only one redundant observation in the traverse, the value of such an adjustment is questionable.

The accuracy of the orientation angle w can be determined by finding the standard

deviations of A and A and applying the rule of error propagation to Eq. (20.25). One should

note that the error of A has two components: one component is the result of random errors in angle and distance measurements in the underground traverse; and the second compo- nent occurs as the result of the possible deflections of the plumb lines expressed by the errorfA [Eq. (20.9)]. If aX is defined as a standard deviation of A caused only by the errors of theunderground traverse, the total value of the standard deviation Ow can be calculated from

(20.27)

·If·variances and covariances of the coordinates of PI and P2 on the surface are known, the value of aA is found by applying error propagation Eq. (2.42) to Eq. (20.22)~ obtaining (in radians/)

2 ~X2

(2 2 ) d y2 (2 2 2 )0A = --d4 Oy + Oy - 20y y

I 2 I 2

tlXdY

+ -4d - Ox I + ax

2 - ax

Ix

2

+2 d4 (OY1X2 +OY2XI-OYIXI-OY2X) (20.28)

where ~X=X2-Xl and dY= Y2- YI•

The value of ox underground is obtained in a similar manner, except that in this case thecoordinates of PI have to be treated as errorless because the errors in A are caused only byrelative positional errors of P2 with respect to PI in the local system. Therefore,

(20.29)

The variances and covariances of the coordinates X2 and Y2 can be calculated using Eq. (8.33), Art. 8.23, with estimated accuracies for angle and distance measurements.

The calculated standard deviation of w gives the accuracy of the determination of the azimuth of the first leg of the underground traverse. In order to calculate the accuracy of any leg in the traverse,. the full variance covariance matrix for coordinates of all the traverse points would have to be known. This can be obtained by a simultaneous error analysis of the combined surface and underground connecting surveys, including the squares of the esti- mated deflections of the plumb lines as additional variances of the coordinates of PI and P 2'

A detailed description of the combined error analysis is beyond the scope of this chapter. If more than two vertical shafts with plumb lines are connected by an underground network, a simultaneous least-squares adjustment using the technique of indirect observations is recom-mended (Example B.IO, Art. B.14). Variances and covariances for adjusted coordinates are aby-product of this adjustment, so that error analysis of the orientation is possible.

Orientation through two or more vertical shafts can give an accuracy better than 20 seconds of arc in transferring the azimuth from the surface to the mine if the accuracy and survey methodology of the connecting surveys are properly designed.

Example 20.3 A design of a mine orientation through two shafts is shown in Fig. 20.21. Two plumb lines, P1 and P2, are to be established in the shafts, at a distance d of about 195 m and connected by

two independent traverses to the reference control stations A and B on the surface. Underground, atraverse P1 - 0- E- P2 will be measured. Approximate coordinates (scaled graphically from a

a~ =2.5+89.9= 92.3 rnrn". a~=0.1 +77.5= 77.8 mm2

a$, = 0.7 + 110.3 = 111.0 rnrn" a$2 = 0.5+ 22.3 = 22.8 mm2

2

a:

1 2

aX

large-scale plan) of the points are as follows:

Point

P1

X,m

515

Y,m

235C 505 270A 548 2908 677 293P2 705 278E 675 2080 535 206

Determine the accuracy of the orientation angle w if:

1. Points A and B are treated as errorless.2. Standard deviations of plumbing e1 = ~ = 5 mm.3. All angles are measured with aa = 5" .4. All distances, are measured with ad = 10 m.

First, the three component errors used in Eq. (20.27) are calculated. Next, the influence of the shaft plumbing is calculated using Eq. (20.9):

e'A= p; ye12+ei = 7.5"

where o" = 206,265." The influence of the connecting surveys on the surface, aA' is calculated from Eq. (20.28). The variances and covariances of coordinates of P1 and P2 are calculated by propagating

errors in the open-end traverses A - C- P1 and 8- P2 using Eqs. (8.33), (Art. 8.23), yielding:

aX Y1 = - 0.9 + 11.9 = 11 .0 mm 2 aX Y

= 0.3 - 41 .5 = - 41 .2 mm 2

Finally, using Eq. (20.28)

a1= 142 + 9 + 15 = 166 and

(Note that traverses A - C - P1 and 8 - P2 are uncorrelated and, therefore, the covariances between coordinates of P1 and P2 are zero.) Influence of the errors in the underground traverse is calculated from Eq. (20.29), holding point P1 and direction P1 - 0 as errorless (arbitrarily selected underground coordinate system). Using given variances and aJ in Eqs. (8.33) yields

a~2= 7.0+147.8=154.7mm2

a~2 = 38.7 + 152.3 = 191.0 mm2

and

2Y2 = -13.2 - 9.1 =- 22.3 mm

obtaining

aj=203+8+11 =222"2 and aA'= 14.9"

The total orientation error (error of the azimuth of the direction P1 - D)

aw= Val+aj+el =Y166+222+56 =21"

If the distances and angles are measured with twice the accuracy (ad = 5 mm and aa = 2.5"), the orientation error would become

aw=Y41.5+55.5+56 =12"

20.15. Gyroscopic methods of mine orientation: IntroductIon Orientation may be de- termined by means of the gyro theodolite. The basic theory of the gyro attachment is

applicable to the gyrotheodolite and is discussed briefly in Art. 11.46. The reader is referred

Article 20.15 Gyroscopic methods of mine orientation: introduction 859

to Refs. 1 and 14 for an account of the interesting historical development of the gyrotheodo- lite and for a detailed mathematical treatment of the theory. The gyro theodolite is available in two forms, one in which. the gyro is a separate unit and is attached above the theodolite, such as the Wild GAKI manufactured by Wild Heerbrugg Instruments, Inc. This instrument is described in Art. 11.46 (Figs. 11.30 and 11.31) and will also be discussed in this chapter. The other form available is one in which the gyro is mounted below and forms an integral part of the theodolite, such as the GYMO GijBI, marketed by Gyro, a division of Plessey Canada (Fig. 20.22). The accuracy of the azimuth determination of this latter type is usually

.greater than for the attachment, a standard deviation of 3 seconds of arc being quoted for the Gymo Gi/Bl. Consequently, instruments of the latter type have been used to determine azimuth for geodetic control (Ref. 11).

There are two basic approaches for azimuth determination, one in which the gyro is allowed to precess about the meridian while the observer reads the horizontal circle of the theodolite or the time of oscillation and the amplitude of the swing. With this technique the damping of the gyro movement is very small and the gyro usually spins about 22,000

rev jmin. The other approach is to use the torque acting on the spinning gyro when it is not aligned in the meridian and, from several observations of this torque, east and west of the meridian, determine the azimuth. This principle is applied in the P .I.M. (Precision Indicator of the Meridian, British Aircraft Corporation, Ref. 23).

The latest gyro theodolite to be developed makes use of a heavier gyro which rotates at aslower speed and is heavily damped. An example of this type of instrument is the Meridianweiser MW77, which was developed by Westfalische Berggewerkschaftskasse, In- stitut fiir Markschiedewesen, Bochum, West Germany. It is not yet available in North America.

The gyro attachment is very popular because of its compact size and because it is anattachment for a theodolite. The theodolite on which it is mounted is usually a direct-read- ing type (direct to nearest minute, estimation to 0.1 minute of arc), and it is used in other survey work associated with the mine. The standard deviation for an azimuth determined with the Wild GAK 1 is given as 20 seconds (this value is considered to be comfortably

Fig. 20.22 Gyrotheodolite, GYMO Gi/81. (Courtesy Gymo, a Division of Plessey Canada Ltd.)

860 Mining surveys Chapter 20

attainable, as noted in Refs. 1 and 12) and hence is suitable for most mining and tunneling work.

20.16. Azimuth determination Azimuth determinations with the gyro attachment are usu- ally classified as approximate and accurate. The approximate or quick method is employed when there is no azimuth available from the existing survey records. The results of this determination are then used as the initial setting for the second classification type, the accurate methods.

Quick method The basic principle of this method is to observe two reversal points.The gyro theodolite is set up and carefully leveled, the gyro is run up to its operating

speed, lowered, and allowed to precess. The observer must track the gyro (use the upper tangent motion of the theodolite) so that the gyro mark remains in the center of the V notch (see Fig. 11.32). When a reversal point is reached, the gyro mark slows down and momentarily stops before moving in the opposite direction. At the reversal point the observer stops tracking and reads the horizontal circle of the theodolite, reading UI• The

gyro mark is then tracked until a second reversal point is reached, where the observer stops tracking and reads the horizontal circle of the theodolite, reading U2• The approximate

orientation is given by (see Fig. 20.23)

(20.30)

Accurate methods Two methods are considered, the reversal-point and transit methods. The reversal-point method requires an experienced observer to track the gyro mark ac- curately, keeping it in the V notch, and to read the horizontal circle of the theodolite at the reversal points (i.e., where the gyro mark changes its direction of movement). Generally, eight reversal points are recorded, taking the observer about 20 to 30 min, depending on the latitude of the place of observation.

The transit method This method was invented by H. R. Schwendener (Ref. 20) and is based on the fact that the first 20 percent of the swing curve (which is a sine curve) is a straight line and hence there is a linear relationship between time and change in direction (Fig. 20.24).

The north direction N is given by

N=N'+!:lN

u, + u2N=--2-

Fig. 20.23

Article 20.16 Azimuth determination 861

N N'

/I~Gyro indicated north

I Approximate north setting

I II-- AN (correction)

III

ell

E i=

Fig. 20.24

Angular displacement

N=N' + AN

where N' is the approximate north setting and!:lN is a correction to N' to give N. It can be shown (see Ref. 20) that

!:IN = catxt (20.31)

where c=constant (and is dependent on latitude, see Art 20.17)a = average amplitude of swing right and left in scale divisions

!:It = time difference in seconds between the time for a swing to the right and the time for a swing to the left

The method of observation is as follows. The gyrotheodolite is centered over the station and carefully leveled, direct and reversed observations are taken on the reference object, and the theodolite is oriented to the north direction. This orientation must be within 10 to 20 minutes of arc or closer to the north direction. The horizontal circle reading at this setting is read and recorded. Since any error in this reading enters directly into the resulting azimuth determination it is important to check this observation. The nonspinning gyro readings are taken, then the gyro is run up to its operating speed and carefully released. The amplitude ofthe gyro mark is adjusted to be about + 10 to -10 scale divisions. (If the setting is exactlytrue north, both amplitudes would be the same.) A stopwatch with a trailing hand is started when the gyro mark passes through the center of the V notch and the amplitude of the swing to the left or right is observed and recorded. When the gyro mark passes through the V notch the time is again taken, and the amplitude in scale divisions is also observed and recorded. Times are observed for eight transits of the gyro mark through the V notch, and at least two left and two right amplitudes are recorded. The gyro is then clamped, allowed to run down or braked, and the final nonspinning readings are observed. Finally, direct and reversed observations are taken to the reference object. The recorder calculates the swing times to the left, which should agree to about 0.2", and the swing times to the right, which should also agree to 0.2". The recorder also calculates the individual !:IN values [!:IN =

(c)(al)!:ltd, which when averaged ought to equal (c)(a)av(!:lt)av.The value of aN is added to or subtracted from the initial setting N' to obtain the circle

reading for the gyro indicated north (G.I.N.). The calibration value E and the mean

horizontal circle reading to the reference object must be applied to the value for N to obtain the azimuth to the reference object.

An example of this method is shown in Fig. 20.25 and Table 20.1 (after Ref. 1).

20.17. Determination of the constant c The constant c, used in the calculation of /1N, can be determined by observations. Two determinations of north are necessary for the calcula- tion; one determination is carried out with a setting of about 20 minutes of arc west of north and the other 20 minutes of arc east of north. Thus, the direction of. the meridian must be known to determine the constant c. True or astronomic north is given by each determina-tion:

N=NI +/1NI =N2+/1N2

where NI and i1Nl refer to the first determination and N2 and /1N2 refer to the second determination. Thus,

so that

N2-N1C = -....,.---.,---

al /1t1- a2i1t2

(20.32)

(20.33)

An example of the determination follows:

First determination Second determination

N1 = 0010'0081 = 10.45

flt1 = - 23.9"359055 ' - 3600 10 '

c= (10.45)( - 23.9) - (10.30)(7.4)

= 0.0460' jdivisionjsecond

~ = 359055'00~ = 10.30

fl~=7.4"

It was stated previously that the initial orientation of the theodolite should be within 20' for the transit method.

Using the calculated value of c=0.046 and letting a= 10 divisions and /1t=45" (these are about the maximum values within the 20' limit),

AN= (0.046)(10)(45)=20.70"=0°20'42"

If the value of c is changed to 0.0459, then AN is 0°20'39.3"; that is, a change in c of 0.0001 gives a change in azimuth of about 3".

The constant c is dependent on latitude and it can be shown (Ref. 20) that a change in latitude of about 10 will causethe factor c to change by 0.0001. Therefore, the same c factor may be used within a radius of about 100 km, the resulting azimuth error being about 3".

20.18. Calibration value E The calibration value E is the horizontal angle between the plane of the meridian and the direction of the line of sight of the theodolite's telescope determined by the exact symmetry of the gyro oscillations (Ref. 24). The mamrlacturer cannot always set the E value to zero but attempts to construct the instrument so that the E value is stable. It is recommended that the value of E be regularly checked, particularly if the gyro has been in storage, has been transported over long distances, or is suspected of having been bumped.

The E value is determined by a direct comparison on a line, the azimuth of which has been determined from astronomical observations (see Arts. 11.32 and 11.39). If the azimuth of the line determined by gyrotheodolite (using one of the accurate methods) is designated

Article 20.18 Calibration value E 8~3

Ij

(a) (b) (c)

Fig. 20.25 The transit method. (a) Right (west) reversal point, amplitude aw= -7.7. (b) Transit, take the time. (c) Left (east) reversal point, amplitude ae= 8.0. (Note: The north index mark moves in the opposite sense to the north-seeking end of the axis.) (Courtesy Ref. 3.)

AG and the astronomic azimuth is A, then

E=A-AG (20.34)

When a line of known azimuth in a plane coordinate system is available, it may be usedfor the determination of E provided that correction for convergence of the meridians is applied to convert the grid direction to a geodetic azimuth. In this case

E = grid azimuth ± convergence of meridians - AG

0./04

Spinning Gyro Readings

864 Mining surveys Chapter 20

Table 20.1 (After Ref. 1)

Gyro-theodolite Survey - Transit Method

Place Erinda/e Co//eqeDate Apr;I7/78 Time 1440 ES. 1. Line ASTRO to STARObserver A.JR Recorder A.C. Battery lnf.Theod. TIt;. 205404 Gyro GAKI. 25818 Run up time C,6 sees Braking Time 55 sees

Ref. Obj. Circle Readings

Start FinishF.L. F.R. F.L. F.R. Means

348-S0'OO" 1&.8'50'00" 348DSOO6/1 108'SO'OC," Start 34B'{X)'OO"50'00" .50'00" 50'06/1 50'0&;/f Finish 341)50'0(0"50'00" 50'00" 500~" 50'0&;/1 Mean 348"50'03" ( 4)

Means 348"50'00" 1t:,8'SO'00" 348'50'O~" 108"SO'O/IC,

Start

Non-Spinning Gyro Readings

FinishLeft + Right -

-9.8Mean Left +

/5.4Right - Mean

10.0 (-9.75) 0./25 (/5.35) -/4.5 - O.075(9.95) -9.7 0./25 /5.3 (/4.45) - 0.075

9.9 (- 9.7) 0.100 (15.32 -14.4 -0.050

(9.92 -9.7 0./00 +/5.3 (-14.352 -0.025

9.9 (9. C;51 0./25 . (15.25) -/4.3 -0.025

(9.7) -9.~ 0.050 /5.2 (-14.32 -0.050

9.8 -14.3

Mean Mean -0.050

Transit Time Swing Time ~t

Swinging to left _

Auxiliary Scale

Left Right ~N = c.a. ~t

Swinging to Right Q!:_.Qg:'Q_} lL_1_

+ ------_3_M_/7_~4_ =.-L2_ 8.0

_L7

~ .22_:_J._ + ~_!'}; !2_ -4.0 _ 1.1 _ _ -:l.:_4_j- _

L_.1_§_: 1_a 2J_:_~_

-3 17.5 -_------ -4./ _8.0_

+ } /_2;_4:_ -=4.2_ -=l :.!f §._

-/._2£_!_~ J_J_c_1_ - i_fl~_ ~i_3_ _--1.52_L9_ _ _}_~.l_ +.}__/ _1:_.L

.::1_..?__ -_j_·2£_

?? ~Q_Z_ -- J_ _ (_]_._3_

Mean-4;/17 Mean -1.49 ~2)

c. Q.Q1_~ c.a. = Q:2~LCalculation of Azimuth

a. = J_!i2

Circle Setting N' se: _O_Q' QQ':_ 1

Mean ~N -01 29 2

N = N' + AN _j_.2_9 2§ 2L 3 = 1 + 2Mean R.O. Circle Reading 348 50 03 4

Gyro Azimuth j_j-'§ !iL_2£_ 5 = 4 - 3

E -/2 30 6

Azimuth of R.O. 348 39 02 7 = 5 + 6

20.19. Meridian convergence The orientation of a mine (see Art. 20.9) may be considered to be the angular difference between the gyroazimuth of the surface line and the gyroazi- muth of the underground line plus or minus a correction for convergence of meridians. Referring to Fig. 20.26, this angular difference, w, can be determined as follows:

w= (ACD - Bc) -(AAB-BA)=AcD -AAB - (Bc -BA)

Article 20.18 Calibration value E 8~3(20.35)

I

e

Article 20.20 Optical and laser plummets 865iI

Gyro north

Grid north

c.;o:;

o(J,)

'2'0.0. ('Q

E'0c.s

.";0:

(J,)

E

+-' C (J,)

U

Gyro north

. B

~----------------x~------------------~

Fig. 20.26

where AAB= gyro azimuth at AACD = gyroazimuth at C

BA = convergence of the meridian at ABc = convergence of the meridian at C

I1BcA = convergence of the meridians from C to A

Convergence should always be calculated and applied to azimuth determinations even when the distance between two stations is very short because its value may be significant.

For example, suppose that station A is 200 Ian from the central meridian at latitude 4S~0and station Cis 20S km from the central meridian at latitude 4S.1 ", Then I1BcA = Be - 0;:' =66S0.1/1 -646S.3/1 = 184.8/1 by Eq. (19.1), where Bc and BA were computed individually using their respective latitudes and distances from the central meridian and assuming thatR=6730 km,

20.20. Optical and laser plummets Several models of precision optical plummets (zenith and/ or nadir) are available using tubular spirit levels, self-compensating leveling systems, or a mercury surface as a reference for setting the line of sight in the vertical direction. Table20.2 shows characteristics of four optical plummets.

Table 20.2 Precision Optical Plummets

Magnifi-

Manufacturer Model Type cation Achievable accuracy

Zeiss-Jena PZL Self-compensating 31.5 1 : 100,000 (2/1)zenith

Kern OL Spirit level, zen- 22.5 1 : 100,000 (2/1)ith and nadir

Breithaupt TELIM Spirit level, 40 1 : 50,000 (4/1)nadir

Wild GLQ Mercury horizon, 40 1 : 200,000 (1/1)nadir

866 Mining surveys Chapter 20

Fig. 20.27 Optical plummet Wild GLQ. (Courtesy Wild Heerbrugg Instruments, Inc.)

The Wild GLQ model (Fig. 20.27) sets the line of sight in a vertical direction with an auto collimating telescope by achieving coincidence of the cross hair with its image reflected from a surface of mercury. The pool of mercury is removed from the field of view of the telescope after setting the line of sight vertical. Use of optical plummets in shaft plumbing is limited to a short range only (100 to 200 m) because of the poor visibility usually found in the shaft atmosphere.

Slightly longer ranges can be achieved by using a collimated laser beam as the plumb line. A laser optical plummet (Fig. 20.28a) and a laser interference plummet (Fig. 20.28b), both

utilizing mercury reference surfaces, have been developed at the University of New Bruns- wick in Canada. Practical tests with laser plummets indicate a repeatability in setting the vertical lines with a standard deviation of better than 0.5 seconds of arc. Details of these

plummets are given in Refs. 4 and 7.Other models of precision laser plummets are being developed, for example, by the

National Physical Laboratory in England and by the optical industry in Poland. Some simple laser applications in plumbing are also possible by projecting a laser beam through telescopes of existing optical plummets or through precision automatic levels (see Ref. 5) equipped with 90° pentaprisms placed in front of the objective lenses. A commercially available laser plummet is illustrated in Fig. 18.4, Art. 18.5.

Laser plummets may be very useful in controlling shaft-sinking procedures and in transferring coordinates (shaft plumbing) when using the gyro or the two-shaft method of mine orientation. Their accuracy is, however, not sufficient for shaft-plumbing orientation through one vertical shaft.

Article 20.21 Vertical control surveys and leveling 867

He-NeLaser

] [Adjustablemirror Beam

iL ~ .~_:~~- - -+-::z:f.~ ~

ttl Autocollimating

I telescope

MerCUrY~

-Removablepool

Oil

(~)) (b)

Fig. 20.28 Optical laser plummet. (a) Prototype. (Courtesy University of New Brunswick.) (b)Schematic cross section.

20.21. Vertical control surveys and leveling Special steel tapes of lengths up to 1000 m (see Refs. 13 and IS) stored on large reels (Fig. 20.29) are available for the transfer of heights from the surface to the underground workings. The principle of the height transfer is shown in Fig. 20.30. The tape is slowly lowered to the required level and a weight is suspended at its end. The weight should preferably be equal to the tension used during the standardization of the tape (usually 20 to 45 lb or 10 to 20 kg). A bench mark, tied to the existing leveling network on the surface, is established near the collar of the shaft. Underground bench marks of the same type as those on the surface are cemented in the walls of the oriented levels near the shaft opening. Two survey crews with spirit levels take simultaneous readings on the tape at the surface and at the level. Usually, a set of 10 readings is taken changing the position of the tape (lowering or raising) by a few centimetres between the readings. The tapes are usually marked every 10 cm. Therefore, additional short scales with l-mm divisions are clamped to the tape at the reading heights.

Fig. 20.29 Shaft tape for height transfer. (Courtesy Ref. 10.)

868 Mining surveys Chapter 20

1

Fig. 20.30 Procedure for the height transfer with a special tape.

The elevation of the bench mark B,HB, at the oriented level is calculated from

HB=HA -h+rodA -rodB (20.36)

where HA is the elevation at A, rod , and rodj, are the respective rod readings at A and B,

and h is the mean difference between readings h2 - hI on the tape corrected by (1) standardization correction !1hd; (2) temperature correction !1ht; (3) stretch by the tape's own

weight, correction !1hw; and (4) stretch by the applied weight (if different from the standard tension), correction !1hp-

The first correction is analogous to the tape correction Cd described in Art. 4.16 and doesnot require any explanation. The temperature correction is the same as C, in Art. 4.18 but is more complicated because of the nonlinear change of temperature in the mining shaft. Temperatures should be measured at different levels (100 to 150 ft or every 30 to 50 m) in the shaft just before the height-transfer procedure and a weighted mean temperature is thencalculated from (see Ref. 16)

n

L [(hi+ 1- hi)(Ti + Ti+1)]

i= 1T= ----------

(20.37)

where T; is the temperature at a depth hi'2(hn - hI)

The correction Sh, is calculated using Eq. (4.13), repeated here for convenience

!1ht = haC T - To) (20.38) where To is the temperature of standardization and a the thermal coefficient of

expansion, which is equal to (11.6)10-6 per 1°C [(6.45)10-6 per 1OF] for steel.The stretch correction

t.hw = a~ ( Lh - ~2) (20.39)

where w=weight of one unit of length of the tapea = cross-sectional area of the tape, cnr' or in2

E = modulus of elasticity, which for steel is usually given as 2.1 X 106 kg/ cm2 (28 to 30 million lb /in2)

L= total length of the tape freely suspended, m or ft (same units as h)

The last correction, 6.~, is analogous to Cp given by Eq. (4.14) in Art. 4.19, repeated here for convenience:

(P-Po}L6.hp= aE

where P=applied weight, kg or lbj> 0 = standardization tension, kg or lb

a, L, E are as defined for Eq. (20.39)

(20040)

The value of the product aE may be checked experimentally (it is recommended to do this) by measuring 6.h for two different weights, say 20 lb and 100 lb (10 kg and 50 kg) and calculating aE from Eq. (20040).

Transfer of the heights to the mine through a vertical shaft may also be made with electro-optical distance measuring (EDM) instruments (Arts. 4.29 to 4.35) if the visibility conditions are favorable. In this case the EDM instruments should be clamped in a vertical position above the shaft opening. It requires some ingenuity on behalf of the surveyor and the cooperation of the mining workshop to make the necessary adaptors and brackets to fasten the instrument in this manner. The heights of the center of the instrument and of the reflector must be carefully determined by means of spirit leveling from bench marks. Another possibility in the use of EDM equipment is to use the instrument in its upright position near the shaft opening using a good quality mirror (first surface coating) to direct the electromagnetic signal down the shaft. Laser instruments with visible radiation should be used to facilitate the search for the reflector at the bottom of the shaft and to find a reference light spot on the mirror so that it can be referenced to the bench mark by spirit leveling.

The leveling network in the mine is divided into three orders of accuracy similar to thehorizontal network. Height measurement in the third-order network is carried by trigono- metric leveling (Art. 5.5) simultaneously with the traverse measurements in the horizontal control surveys. The roof markers serve as bench marks. Vertical angles are measured to a mark made on a plumb-bob string which usually serves as the target and vertical distances are measured with pocket tapes from the mark and from the horizontal axis of the theodolite to the bottom of the roof mark. Trigonometric leveling is also frequently used in second- and first-order networks when running the leveling traverses through raises and other inclined openings. Because of the comparatively short distances and usually quite stable atmospheric conditions, the accuracy of trigonometric leveling in the mine is competitive with spirit leveling if proper precautions are made in the measurements of the height of the instruments and the targets.

Spirit leveling is usually done between wall bench marks. When a connecting survey to aroof station is required, special inverted leveling rods have to be used.

Similar to the theodolites, spirit levels sometimes have to be used on supporting arms fixed to the wall lining or timbering. Detailed descriptions of different types of levels and specialadaptors used in the mines are given in Refs. 13 and 15.

20.22. Problems

20.1 A tunnel 11 km long is driven from reference point 1 to point 12 as shown in Fig. 20.B. The tunneling procedure is controlled by the straight traverse 0 - 1 - 2 ... 12. All distances between successive traverse points equal 1 km. Coordinates of reference point 1 and azimuth of the reference

line 0 - 1 are fixed and errorless. What misclosure in the Y coordinate of point 12 would you expect ifthe angles in the traverse are measured with a standard deviation (Jf3 = 2"?20.2 Answer Prob. 20.1 if the angle measurements are replaced by azimuth measurements of each traverse leg using a gyrotheodolite with standard deviations of the gyroazimuths of (J A = 20". Which of the two traverse measurements (angles vs. gyroazimuths) would give a smaller lateral deviation of the tunnel at point 12?

20.3 A mine orientation survey is to be done using two mechanical plumb lines in one vertical shaft. The depth of the oriented level H= 300 m. The distance between the two plumb lines is 4 m. Steel wires of tensile strength 200 kg/mm2 are available for plumbing. The height of the shaft opening to the oriented level h = 5 m and the average air velocity in the cross section of the opening v= 1 m/ s. There are no other openings to intermediate levels between the surface and the orientedlevel. Answer the following questions:

(a) What diameter (d) of the plumb wires and what weight (P) of the plumb bobs would you use for the orientation purpose?

(b) What should be the distance between the safety platforms at the oriented level?(c) What will be the period of swing of the plumb lines (for checking purposes)?(d) What error of the transferred azimuth would you expect as a result of the air current and spiral

shape of the wires [take R= 15 cm and use values of d and P as obtained from part (a)].

20.4 Mine orientation of the level H= 300 m has been performed using the Weisbach method as shown in Fig. 20.19. The plumbing procedure has been performed according to the previous design (see Prob. 20.3). The following values of the measured angles and distances have been obtained:

On the surface: a=4.001 m, b, =8.030 m, c; =4.035 m, 01 =160°20'20",0::1 =0°08'10" withstandard deviations of distances (J = 2 mm and angles (J = 4" .

Underground: a=3.997 m, ~=7.005 m, C:2=3.015, 0::2=0°16'00", O2=178°25'40'' with stan- dard deviations of distances (J = 5 mm and angles (J = 6" .

Calculate coordinates of point C, azimuth of the line CO, and standard deviation of the azimuth CD. Coordinates of point B on the surface are YB = + 360.320 m, XB = + 538.435 m, and the azimuth AB= 310° 15'20". The coordinates of B and azimuth AB are treated as errorless. (Note: In the calculations of the error of the azimuth of the line CD you should include the error of shaft plumbingas calculated in Prob. 20.3.)20.5 Grid azimuth of a line AB (Fig. 20.26) is equal to 26°16'30". A gyrotheodolite was calibrated on the line AB giving the gyroazimuth of the line equal to 2]D 14'00". The same gyrotheodolite was used at station C in order to determine the grid azimuth of the line CD. The gyroazimuth of CD was72 ° 20' 00". What is the grid azimuth of the line CD if X' A = 101250 m, X' c = 102416 m, and thelatitudes are <l>A=43°20'30" and <l>c=43°21'OO"?

References

1. Bennett, G. G., "New Methods of Observation with the Wild GAK-1 Gyrotheodolite," UnisurveReport No. 15, University of New South Wales, Australia, 1969.

2. Chrzanowski, A., and Derenyi, E., "Role of Surveyors in the Mining Industry," ASP-ACSM

Semi-annual Convention, St. Louis, Mo., October 1967.3. Chrzanowski, A., Derenyi, E., and Wilson, P., "Underground Survey Measurements, Research for

Progress," The Canadian Mining and Metallurgical Bulletin, June 1967.4. Chrzanowski, A., "New Techniques in Mine Orientation Surveys," The Canadian Surveyor, Vol.

24, March 1970.5. Chrzanowski, A., and Jansses, H.D., "Use of Laser in Precision Leveling," The Canadian

Surveyor, December 1972.6. Chrzanowski, A., and Masry, S., "Tunnel Profiling Using a Polaroid Camera," The Canadian

Mining and Metallurgical Bulletin, March 1969.7. Chrzanowski, A., Jarzymowski, A., and Kaspar, M., "A Comparison of Precision Alignment

Methods," The Canadian Surveyor, Vol. 30, June 1976. ,8. Chrzanowski, A., Ahmed, F., and Kurz, B., "New Laser Applications in Geodetic and Engineering

Surveys," Applied Optics, Vol. 2, February 1972. .9. Chrzanowski, A., and Steeves, P., "Control Surveys with Wall Monumentation," The Canadian

Surveyor, Vol. 31, June 1977.10. Chrzanowski, A., "Design and Error Analysis of Surveying Projects," Department of Surveying

Engineering, University of New Brunswick, Lecture Notes No. 47, November 1977.11. Gregerson, L. F., "An Investigation of Gyroscopic Theodolites," Paper presented to the 62nd

Annual Meeting of the Canadian Institute of Surveying, Ottawa, Canada, 1969.12. Hodges, D. J., and Brown, J., "Underground and Surface Orientation Measurements with

Gyrotheodolite Attachments," The Mining Engineer, October/November 1972.13. Kowalczyk, Z., Miernictwo Gornicze, Vol. 2, Wyd. Slask., Katowice, 1965; Vol. 3, 1968 (in Polish).

1

References 871

14. Laut, G. B., "The Gyrotheodolite and Its Application. in the Mining Industry of South Africa,"Journal of the South African Institute of Mining and Metallurgy, Vol. 63, March 1963.

15. Neset, K., Oulni Merictvi, SNTL, Praha, 1966.16. Richardus, P., Project Surveying, North-Holland Publishing Company, Amsterdam"1966.17. Sheehan, J. F., "Mine Surveying at Mount Isa," Presented at the 11th Congress of Institution of

Surveyors Australia, Brisbane 1968 (Australian Surveyor, March 1969).18. Smith, R. C. H., "A Modified GAK1 Gyro Attachment," Survey Review, Vol. 24, No. 183, January

1977.19. Staley, W. W., Introduction to Mine Surveying, 2d. ed., Stanford University Press, Stanford, Calif.,

1964.20. Strasser, G. J., and Schwendener, H. R., "A North Seeking Gyro Attachment for the Theodolite as

a New Aid to the Surveyor, II Wild Heerbrugg, Switzerland.21. Wasserman, W., "Underground Survey Procedures," New Zealand Surveyor, March 1967.22. Williams, H. S., "A 'New' Method for Gyrotheodolites Operable in the Non-tracking Mode," The

South African Survey Journal, April 1978.23. Winiberg, F., Metalliferous Mine Surveying, 5th ed., Mining Publicatjons Ltd., London, 1966.24. Wild Heerbrugg, Handbook GAK1, Gyro Attachment.

Answers to problems in Chapter 20 Mining Surveys by Chrzanowski and Robinson

20.1 O'Y12 = ± 0.218 m

20.2 O'Y12 = ± 0.322 m

20.3

a) d = 1.128 mm, assumed available for remainder of problem; P = 100 kg b) L\H = 1.429, between platforms

c) T = 34.8 seconds

d) e air current = 0.51 mm; e spiral shape = 0.222 mm; e scale = 0.2 mmso total error, cA = 28" [over b = 4.000 m]

20.4 Xc = 532.888 m; Y c = 369.878 m; ACD = 3280 32' 18" ± 32"

20.5 ACD = 710 21' 54"

library of Congress Cataloging in Publication DataMain entry under title:

Surveying, theory an~ practice.

Fifth ed. published in 1966 entered under R. E. DavisIncludes bibliographies and index.1. Surveying. I. Davis, Raymond Earl, dates

II. Davis, Raymond Earl, datesSurveying, theory and practice.TA545.D45 . 1981 526.9 80-15878ISBN 0-07-015790-1

SURVEYING: THEORY AND PRACTICE

Copyright © 1981, 1966 by McGraw-Hill, Inc. All rights reserved.Copyright 1953, 1940, 1934, 1928 by McGraw-Hill, Inc. All rights reserved. Copyright renewed 1956, 1962, 1968 by R. E. Davis and F. S. Foote.Printed in the United States of America. No part of this publication may be reproduced,stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher.

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