8.9 Tunnelling, Mining Surveys and Deformation Monitoring

7.2 Tunneling, Mining Surveys & Deformation Monitoring

Underground engineering, tunneling, and mining surveying present unique geometric challenges. Surveyors must project precise surface geodetic coordinates and true directional orientation down vertical shafts into dark, enclosed underground workings without access to satellite GNSS signals or surface line-of-sight. Furthermore, monitoring structural deformations in tunnels, mines, dams, bridges, and high-rise structures requires sub-millimeter measurement techniques. This section examines shaft correlation, gyrotheodolite orientation, Nigerian mining regulations, and structural deformation monitoring frameworks.

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1. Underground Shaft Correlation Methods

Shaft correlation (or shaft plumbing) is the process of transferring surface control coordinates $(X, Y)$ and an azimuth baseline ($\theta$) down vertical mine or tunnel shafts to establish an underground control network aligned with the surface coordinate system.

Mechanical Wire Plumbing

Two high-tensile steel wires (plumb wires) are suspended down the shaft from surface control points, weighted by heavy plumb bobs ($50\text{ to }100\text{ kg}$).

• Oscillation Dampening: To minimize pendulum oscillations caused by air currents and falling water droplets, plumb bobs are submerged in tanks filled with high-viscosity oil or heavy grease.
• Wire Reading: Optical scale readers record the extreme swing positions (reversal points) of each wire to compute the true mean equilibrium position.

The Weissbach Triangle Method

When the space inside a vertical shaft is constrained, the two plumb wires ($W_1$ and $W_2$) are placed close together (often $2\text{ to }4\text{ meters}$ apart). An instrument station ($S$) is set up at a short distance from the wires, forming a very narrow triangle known as the Weissbach Triangle.

The instrument position $S$ is placed almost in line with $W_1$ and $W_2$ such that the angle at $S$ ($\alpha = \angle W_1 S W_2$) is extremely small ($< 2^\circ$, ideally $< 30'$).

• Let $a = W_1 W_2$ (distance between wires, measured with micrometer tape).
• Let $b = S W_2$ (distance from instrument to far wire).
• Let $c = S W_1$ (distance from instrument to near wire).

Applying the Sine Rule to calculate the angle $\beta = \angle S W_1 W_2$:

$\frac{\sin\beta}{b} = \frac{\sin\alpha}{a} \quad \implies \quad \sin\beta = \frac{b}{a} \sin\alpha$

Because $\alpha$ and $\beta$ are small, $\sin\theta \approx \theta\text{ (in radians)}$, yielding:

$\beta'' = \frac{b}{a} \alpha''$

Where angles are expressed in seconds of arc ($''$). This formulation allows computing the exact azimuth of the baseline $S-W_1$ relative to the wire baseline $W_1-W_2$ with high precision, minimizing error propagation underground.

The Weiss Quadrilateral Method

In larger shafts or setups requiring independent geometric redundancy, four stations (two surface/underground instrument stations $S_1, S_2$ and two plumb wires $W_1, W_2$) form a quadrilateral. Angles and distance measurements across the quadrilateral provide independent condition equations, enabling rigorous least-squares adjustment of the transferred coordinates and azimuth.

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2. Gyrotheodolite Orientation Underground

While wire correlation transfers direction down vertical shafts, error accumulation in long underground drives necessitates independent azimuth verification. A Gyrotheodolite provides an absolute determination of true astronomical north underground without surface visibility.

Operating Principle of the Gyrotheodolite

A gyrotheodolite consists of a high-precision surveying theodolite integrated with a suspended, high-speed gyroscopic rotor ($20,000\text{ to }24,000\text{ RPM}$).

1. Gyroscopic Inertia & Precession: The spinning rotor resists directional changes. As the Earth rotates with angular velocity vector $\mathbf{\Omega}$, the horizontal component of Earth's rotation ($\Omega \cos\phi$, where $\phi$ is latitude) exerts a precession torque on the spin axis.
2. North-Seeking Behavior: The precession torque forces the gyro axis to oscillate back and forth around the meridian plane (True Astronomical North).

Methods of True North Observation

• Reversal Point Method: The surveyor observes the extreme left and right turning points ($u_1, u_2, u_3, \dots$) of the gyro index on a scale reticle. The mean position of zero torque gives true astronomical north ($\text{N}_{true}$):

$N_{zero} = \frac{u_1 + 2 u_2 + u_3}{4}$

• Transit Method: The time elapsed as the oscillating index passes through the central scale zero mark is measured using precise digital timers, calculating true north based on harmonic oscillation dynamics.

Advantages in Underground Surveying

• Does not rely on surface optical visibility or plumb wires.
• Immune to local magnetic anomalies caused by steel rails, electrical cables, or iron ore bodies.
• Achieves directional accuracy of $\pm 2''\text{ to }\pm 5''$ of arc, ensuring precise breakthrough alignment in long tunnels.

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3. Nigerian Mining Survey Regulations & Statutory Requirements

In Nigeria, mining surveys are governed by strict statutory frameworks to ensure boundary security, resource accounting, operational safety, and environmental protection.

Legal Framework & Administrative Bodies

• Minerals and Mining Act 2007 (NMA 2007): The principal legislation regulating all exploration, extraction, and surveying activities across Nigeria's solid mineral sector.
• Mining Cadastre Office (MCO): Responsible for the administration, processing, and recording of mineral titles (Exploration Licences, Mining Leases, Small Scale Mining Leases, and Quarry Licences) using a transparent Cadastral grid system based on the WGS84 datum.
• Surveyors Council of Nigeria (SURCON): Mandates that all statutory mine survey plans, boundary demarcations, and underground stope maps be executed and signed by a Registered Surveyor.
• Office of the Surveyor-General of the Federation (OSGOF): Oversees national geodetic framework integration and boundary standard enforcement.

Statutory Mine Survey Requirements

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4. Engineering Deformation Monitoring Systems

Deformation monitoring involves systematic measurement of physical changes in shape, position, or tilt of natural slopes or man-made structures (dams, bridges, tunnels, high-rise buildings, tailings dams) over time.

Precise Spirit Leveling Networks

For vertical settlement monitoring, Precise Spirit Leveling using digital levels and invar barcode staves remains the gold standard.

• Accuracy: Achieves sub-millimeter loop closure error ($< 0.3\text{ mm} \sqrt{K}$, where $K$ is distance in km).
• Procedure: Permanent benchmark hubs are established in stable bedrock well beyond the zone of influence. Leveling runs measure vertical movements of target pins fixed to the structure.

Geotechnical & Structural Instrumentation

• Tiltmeters & Electrolytic Level Sensors: Fixed to structural walls or bridge piers to continuously record angular inclination (tilt) down to $\pm 1$ arcsecond.
• Convergence Meters & Tape Extensometers: Measure distance changes across tunnel walls to detect ground convergence or squeezing rock phenomena.
• Borehole Inclinometers: Flexible casing pipes installed in soil/rock slopes to measure lateral shear movements at various depths.

Automated Motorized Total Stations (AMTS)

AMTS networks provide continuous 24/7 real-time 3D displacement monitoring of critical infrastructure.

• Robotic Prism Tracking: The motorized total station automatically cycles through a network of fixed reference prisms (stable ground) and structural monitoring prisms at programmed intervals.
• Environmental Corrections: Real-time temperature and pressure sensors apply atmospheric refraction corrections.
• Least-Squares Analysis: Software processes coordinate shifts $(\Delta X, \Delta Y, \Delta Z)$ against baseline epochs, triggering automated alarms if velocity or acceleration thresholds are exceeded.

Satellite GNSS & InSAR Monitoring

• Continuous GNSS Networks: Dual-frequency GNSS receivers mounted on dam crests or bridge pylons process continuous carrier-phase observables to detect millimeter-scale displacements.
• Interferometric Synthetic Aperture Radar (InSAR): Satellite radar imagery (e.g., Sentinel-1) processes phase differences across multiple passes (Persistent Scatterer InSAR - PS-InSAR) to map regional surface subsidence over entire mining basins or urban infrastructure corridors with millimeter annual precision.