7.3 Mineral and Mining Surveys, Hydrographic Surveying, Route Alignment, and Construction Layout

7.3 Mineral and Mining Surveys, Hydrographic Surveying, Route Alignment, and Construction Layout

Geodetic Engineers in the Philippines are authorized under Republic Act 8560 (as amended by RA 9200) to conduct specialized engineering surveys, including mineral land location surveys, hydrographic mapping, route curve alignments, and high-precision construction layouts. This section covers statutory requirements, geometric derivations, and field procedures across these technical domains.

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Mineral and Mining Surveys (RA 7942 - Philippine Mining Act)

Mineral land surveys establish legal boundaries for mining claims, exploration permits, and mineral agreements under Republic Act No. 7942 (Philippine Mining Act of 1995) and DENR Administrative Order No. 2010-21.

1. The Meridional Block System

Under RA 7942, mineral land administration in the Philippines uses a standardized global grid called the Meridional Block System:

• Block Size: Exactly 30 seconds ($30''$) of latitude by 30 seconds ($30''$) of longitude.
• Area per Block: Approximately 81 hectares (varies slightly depending on latitude).
• Boundaries: Bounded by geographic meridians and parallels conforming to the Philippine Reference System of 1992 (PRS92) / PTM grid projection.

2. Lode vs. Placer Mining Claims

3. Underground Surveying Techniques

Underground mining operations require transferring surface coordinates and azimuths down vertical shafts to mine drifts and stopes:

• Shaft Plumbing (Shaft Connection Survey): Heavy plumb bobs (15-50 kg) suspended on steel piano wire inside viscous oil containers (to damp oscillations) transfer surface coordinates down vertical shafts. Alternatively, high-precision optical zenith/nadir plummets or gyro-theodolites are used.
• Underground Traverse: Roof spads (expansion plugs with brass eyelets set in the mine ceiling) serve as traverse stations to prevent disturbance by heavy mining equipment. Mining transits equipped with illuminated targets and side telescopes (to clear steep sight lines) are standard.

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Hydrographic Surveying and Marine Datums

Hydrographic surveys map underwater topography (bathymetry), measure water depths (sounding), and establish tidal datums for navigation, port engineering, and coastal zone management.

1. Hydrographic Vertical Datums

Vertical references in marine environments differ significantly from topographic land survey datums:

• Mean Lower Low Water (MLLW): The average of the lower low water height of each tidal day observed over a 19-year National Tidal Datum Epoch. In the Philippines, MLLW is the standard reference datum for hydrographic soundings and nautical charts published by NAMRIA (National Mapping and Resource Information Authority).
• Mean Sea Level (MSL): The average height of the sea surface for all stages of the tide over a 19-year epoch. Used as the zero datum for topographic elevations and geodetic leveling networks.

2. Sounding Reduction Formula

Water depth measured by an echo sounder or lead line at time $t$ must be reduced to the chart datum (MLLW): $h_{\text{chart}} = h_{\text{measured}} - \Delta h_{\text{transducer}} + (Z_0 - h_{\text{tide}})$ Where:

• $h_{\text{measured}}$ = Raw depth measured from acoustic transducer or water surface
• $Z_0$ = Height of tide station benchmark above MLLW datum
• $h_{\text{tide}}$ = Observed tide gauge height at the time of sounding

3. Hydrographic Positioning Methods

• Historical / Optical: Two-sextant resection observing three known onshore signals (solving the classic Three-Point Problem / Kaestner method).
• Modern / Electronic: Real-Time Kinematic GNSS (RTK-GNSS) or Differential GPS (DGPS) integrated with Single-Beam (SBES) or Multi-Beam Echo Sounders (MBES).

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Route Surveying and Geometric Alignments

Route surveying deals with the design and layout of transportation corridors (highways, railways, pipelines, canals).

1. Horizontal Curves

Horizontal alignments connect straight tangent sections using circular and transition curves:

A. Simple Circular Curve Elements

$\text{Tangent Distance: } T = R \tan\left(\frac{I}{2}\right)$ $\text{Length of Curve: } L = R \cdot I_{rad} = \frac{\pi R I^\circ}{180^\circ}$ $\text{Long Chord: } LC = 2 R \sin\left(\frac{I}{2}\right)$ $\text{External Distance: } E = R \left( \sec\left(\frac{I}{2}\right) - 1 \right)$ $\text{Middle Ordinate: } M = R \left( 1 - \cos\left(\frac{I}{2}\right) \right)$ Where $R$ is radius of curve, and $I$ is total intersection angle between forward and back tangents.

B. Compound and Reverse Curves

• Compound Curve: Consists of two consecutive circular arcs curving in the same direction with different radii ($R_1 \neq R_2$) meeting at a Point of Compound Curvature (PCC).
• Reverse Curve: Consists of two circular arcs curving in opposite directions meeting at a Point of Reverse Curvature (PRC). Caution: Prohibited on high-speed highways due to abrupt change in superelevation.

C. Spiral Transition Curve (Clothoid)

Spiral curves provide a gradual transition from a straight tangent ($R = \infty$) to a circular curve of radius $R$. The radius of curvature decreases linearly with spiral length $L_s$: $R \cdot L_s = A^2 \quad (\text{Clothoid constant } A)$ Spirals allow smooth introduction of centrifugal acceleration and vehicle superelevation runoff.

2. Vertical Parabolic Curves

Vertical curves connect intersecting gradient lines ($g_1$ and $g_2$) using equal-tangent vertical parabolas:

• Rate of Change of Grade ($r$): $r = \frac{g_2 - g_1}{L}$
• Elevation ($Y$) at any distance $x$ from the PVC (Point of Vertical Curvature): $Y(x) = Y_{\text{PVC}} + g_1 x + \frac{r}{2} x^2 = Y_{\text{PVC}} + g_1 x + \frac{g_2 - g_1}{2L} x^2$
• Location of High / Low Point ($x_{\text{max}}$ from PVC): $\frac{dY}{dx} = g_1 + r x = 0 \implies x_{\text{max}} = \frac{-g_1}{r} = \frac{-g_1 L}{g_2 - g_1}$

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Construction Layout and Earthwork Calculations

1. Setting Slope Stakes

Slope stakes mark the exact intersection of a cut or fill side slope with the natural ground surface: $d = \frac{B}{2} + s \cdot h$ Where:

• $d$ = Distance from centerline to slope stake
• $B$ = Roadway formation width (roadbed width)
• $s$ = Side slope ratio (horizontal : vertical, e.g., 1.5 : 1)
• $h$ = Depth of cut or height of fill at the stake location

2. Earthwork Volume Calculations

Cross-sectional area of cut/fill at successive stations $A_1$ and $A_2$ separated by distance $L$:

• End-Area Method (Average End Area): $V_{\text{end}} = \frac{A_1 + A_2}{2} \cdot L$
• Prismoidal Formula (for precise earthwork volumes): $V_{\text{pris}} = \frac{L}{6} \left( A_1 + 4 A_m + A_2 \right)$ Where $A_m$ is the cross-sectional area evaluated at the mid-station.

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Worked Example: Simple Circular Curve Computation

A proposed highway survey in Laguna requires connecting two tangents intersecting at an angle $I = 40^\circ 00'$. The curve radius is selected as $R = 250.00\text{ m}$. Stationing of the Point of Intersection (PI) is $\text{Sta } 2 + 150.00$.

Step 1: Compute Tangent Distance ($T$)

$T = R \tan\left(\frac{I}{2}\right) = 250.00 \times \tan(20^\circ) = 250.00 \times 0.363970 = \mathbf{90.99\text{ m}}$

Step 2: Compute Length of Curve ($L$)

$L = \frac{\pi \cdot R \cdot I}{180^\circ} = \frac{\pi \times 250.00 \times 40}{180} = \mathbf{174.53\text{ m}}$

Step 3: Compute Stationing of PC (Point of Curvature) and PT (Point of Tangency)

$\text{Sta PC} = \text{Sta PI} - T = (2+150.00) - 90.99 = \mathbf{\text{Sta } 2 + 059.01}$ $\text{Sta PT} = \text{Sta PC} + L = (2+059.01) + 174.53 = \mathbf{\text{Sta } 2 + 233.54}$

Step 4: Compute Long Chord ($LC$) and External Distance ($E$)

$LC = 2 R \sin\left(\frac{I}{2}\right) = 2 \times 250.00 \times \sin(20^\circ) = 500.00 \times 0.342020 = \mathbf{171.01\text{ m}}$ $E = R \left(\sec(20^\circ) - 1\right) = 250.00 \times (1.064178 - 1) = 250.00 \times 0.064178 = \mathbf{16.04\text{ m}}$