GATE Mining Engineering Mining Geology, Mine Development and Surveying Flashcards

24 sample cards from the Mining Geology, Mine Development and Surveying deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. In surveying, define a level surface, datum, and reduced level (RL).

   A level surface is a curved surface everywhere perpendicular to the direction of gravity (e.g., still water surface). A datum is the reference level surface from which elevations are measured (commonly Mean Sea Level). Reduced Level (RL) is the height of a point above (or below) the chosen datum.

2. Differentiate a Backsight (BS), Foresight (FS), and Intermediate sight (IS) in levelling.

   Backsight (BS) is the first reading taken after setting up the level, onto a point of known RL (added to compute height of instrument). Foresight (FS) is the last reading before moving the instrument, onto a point whose RL is being established. Intermediate sight (IS) is any other staff reading taken between BS and FS from the same setup.

3. State the two methods of reducing levels and the arithmetic check for the Rise and Fall method.

   The two methods are the Height of Instrument (collimation) method and the Rise and Fall method. Rise and Fall check: $\Sigma BS - \Sigma FS = \Sigma \text{Rise} - \Sigma \text{Fall} = \text{Last RL} - \text{First RL}$. The HI method check is $\Sigma BS - \Sigma FS = \text{Last RL} - \text{First RL}$ only.

4. Give the combined correction for curvature and refraction in levelling/heighting.

   Curvature correction $C_c = -\dfrac{d^2}{2R}$ (depresses the line) and refraction correction $C_r = +\dfrac{d^2}{14R}$ (raises it). Combined correction $= -\dfrac{6}{7}\cdot\dfrac{d^2}{2R} = -0.0673\,d^2$ metres ($d$ in km), where $R$ is Earth's radius. Curvature dominates, so the net effect lowers apparent elevation of distant points.

5. What is the fundamental (face-left/face-right) relation among a theodolite's axes?

   For a correctly adjusted transit theodolite: (1) the vertical (rotation) axis is truly vertical; (2) the line of collimation (line of sight) is perpendicular to the horizontal (trunnion) axis; (3) the horizontal axis is perpendicular to the vertical axis; and (4) the plate level axis is perpendicular to the vertical axis. Observing on both faces eliminates collimation, trunnion, and vertical-index errors.

6. Distinguish the temporary adjustments of a theodolite from permanent adjustments.

   Temporary adjustments are done at each setup: Setting up (centring over the station with plumb bob/optical plummet and approximate levelling), Levelling up (using plate bubbles and foot screws), and Focusing/Elimination of parallax (focusing eyepiece and objective). Permanent adjustments correct the fixed relationships between the instrument's axes and are done occasionally by the instrument maker/surveyor.

7. What is the principle of tacheometry and the stadia distance formula?

   Tacheometry determines horizontal distances and elevations rapidly by optical means without a chain, using a telescope with stadia hairs and a graduated staff. For a horizontal line of sight: $D = K\,s + C$, where $s$ is the staff intercept between stadia hairs, $K$ is the multiplying constant (usually 100), and $C$ is the additive constant (≈0 for internal/anallactic lens).

8. Give the tacheometric distance and elevation formulas for an inclined line of sight (staff vertical).

   Horizontal distance: $D = K\,s\cos^2\theta + C\cos\theta$. Vertical component: $V = K\,s\cdot\dfrac{\sin 2\theta}{2} + C\sin\theta$, where $\theta$ is the vertical angle, $s$ the staff intercept, $K$ the multiplying constant, and $C$ the additive constant. RL of staff station $=$ HI $+ V -$ central hair reading.

9. What is triangulation and the principle on which it is based?

   Triangulation is a control-survey method in which a network of connected triangles is established; the angles of every triangle are measured precisely and one side (the baseline) is measured directly. The lengths of all other sides are then computed using the sine rule: $\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$.

10. Differentiate triangulation, trilateration, and traversing.

    Triangulation: measure all angles + one baseline, compute sides. Trilateration: measure all sides (distances, via EDM) and compute angles. Traversing: measure successive lengths and the angles between connected lines to form an open or closed traverse. Modern surveys often use triangulateration (both angles and distances).

11. What is the well-conditioned triangle in triangulation and why is it sought?

    A well-conditioned (strong) triangle is one whose angles are neither too small nor too large—ideally each angle near $60^\circ$, and in practice no angle below about $30^\circ$ or above about $120^\circ$. It is sought because small angles make the computed side lengths very sensitive to angular measurement errors (the sine rule amplifies error), so well-conditioned triangles minimize propagated error.

12. Define a contour line and contour interval.

    A contour line is an imaginary line on the ground (its plan projection on a map) joining points of equal elevation (reduced level). The contour interval is the constant vertical distance (difference in RL) between two successive contours; horizontal equivalent is the corresponding map distance between them, which varies with slope.

13. State four key characteristics/properties of contour lines.

    (1) Contours close on themselves (within or beyond the map). (2) Closely spaced contours indicate steep ground; widely spaced indicate gentle slopes; equally spaced indicate uniform slope. (3) Contours never cross except at an overhanging cliff, and merge at a vertical cliff. (4) A contour crossing a valley forms a V pointing upstream (uphill), and around a ridge/spur a U or V pointing downhill; closed contours with higher values inside indicate a hill, lower inside indicate a depression.

14. Distinguish systematic (cumulative) errors from random (accidental) errors in surveying.

    Systematic errors follow a definite physical law, have a consistent sign/magnitude under the same conditions, are cumulative, and can be computed and corrected (e.g., temperature, sag, and standardization corrections in taping). Random (accidental) errors are small, equally likely positive or negative, follow the laws of probability, partly cancel, and are treated by least-squares adjustment; mistakes/blunders are gross errors that must be eliminated, not adjusted.

15. How does the most probable value and its weighting relate to random errors?

    The most probable value of a quantity from repeated equally reliable observations is the arithmetic mean. When observations have different reliabilities, weights $w$ are assigned (weight $\propto \frac{1}{\sigma^2}$, inversely proportional to the square of the standard error), and the weighted mean $\bar{x} = \dfrac{\sum w_i x_i}{\sum w_i}$ is the most probable value. The probable error of the mean decreases as $\dfrac{1}{\sqrt{n}}$.

16. What is correlation in mine surveying and why is it required?

    Correlation is the process of orienting and connecting the underground survey to the surface survey so that both share a common coordinate system and direction (bearing). It transfers the surface azimuth/orientation and coordinates down the shaft to underground workings, which is essential for correctly directing drivages, connecting workings between shafts, and ensuring holing-through accuracy.

17. Describe the principal methods of shaft correlation (transferring orientation underground).

    Through a single shaft: the two-plumb-wire method (Weisbach triangle), where two suspended wires define a line whose surface bearing is transferred underground using a small (Weisbach) triangle solved by the sine rule. Other methods include using a shaft plumbing template/co-planing, gyro-theodolite (which gives true north directly underground), and optical/laser plumbing. With two shafts available, orientation is transferred by traversing between them.

18. In the Weisbach triangle method of correlation, what configuration minimizes error?

    The theodolite is set up close to and almost in line with the two plumb wires so that the small angle at the instrument is minimized. The Weisbach triangle should be very acute (the angle subtended at the theodolite kept as small as possible, and the instrument as near the near wire as practicable), because this minimizes the effect of angular measurement error on the computed bearing transferred underground. The wires should also be as far apart as the shaft allows.

19. What is a gyro-theodolite and its advantage in mine correlation?

    A gyro-theodolite is a theodolite fitted with a gyroscope that seeks and indicates the direction of true (geographic) north independently of magnetic effects. Its advantage in mine surveying is that it can establish absolute azimuth directly underground without needing plumb-wire correlation through the shaft, providing fast, reliable orientation immune to magnetic interference and steelwork.

20. Define the closing error of a closed traverse and how it is distributed by Bowditch's rule.

    Closing error is the small gap between the computed and known coordinates of the starting point of a closed traverse, $e = \sqrt{(\Sigma L)^2 + (\Sigma D)^2}$ (sum of latitudes and departures). Bowditch's (compass) rule distributes it in proportion to line length: correction to a line's latitude/departure $= \text{total error} \times \dfrac{\text{length of that line}}{\text{perimeter}}$, assuming angular and linear errors are of equal precision.

21. Classify metamorphism by its main types/agents.

    Contact (thermal) metamorphism—driven mainly by heat near igneous intrusions. Regional (dynamothermal) metamorphism—driven by combined heat and directed pressure over large areas during orogeny, producing foliation. Dynamic (cataclastic) metamorphism—driven by directed pressure/shearing along fault zones. Plus hydrothermal and burial metamorphism. Foliated products include slate→phyllite→schist→gneiss with increasing grade.

22. What is the geological time/structural concept of an ore shoot versus a vein?

    A vein is a tabular, sheet-like mineral body filling a fracture or fissure in the host rock, often formed by hydrothermal deposition. An ore shoot is a localized zone of economically rich, payable ore within the larger vein (or lode) where conditions favoured concentration; the rest of the vein may be sub-economic. Identifying ore shoots guides selective mining.

23. What is rock quality designation (RQD) and how is it computed?

    RQD is an index of rock mass quality from drill core: $\text{RQD} = \dfrac{\sum \text{lengths of intact core pieces} \geq 100\ \text{mm}}{\text{Total length of core run}} \times 100\%$. Classification: $<25\%$ very poor, $25\text{–}50\%$ poor, $50\text{–}75\%$ fair, $75\text{–}90\%$ good, $90\text{–}100\%$ excellent. It influences access drivage support and mechanical cuttability.

24. Give the peak-particle-velocity scaled-distance relation used to control blast vibration.

    Ground vibration is predicted by $PPV = K\left(\dfrac{D}{\sqrt{W}}\right)^{-n}$, where $PPV$ is peak particle velocity (mm/s), $D$ is distance from the blast (m), $W$ is the maximum charge per delay (kg), and $K,n$ are site/rock constants. $\dfrac{D}{\sqrt{W}}$ is the square-root scaled distance; limiting PPV (e.g., for structures) sets the allowable maximum instantaneous charge per delay.

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