Volume Computations

Volume reconciliation between mine survey and plant feed is a monthly KPI in Indian mines. Prismoidal formula gives higher accuracy than trapezoidal when end and mid-section areas differ significantly — examiners often provide three sections to test method selection.

Drone photogrammetry now generates dense point clouds for stockpile volume; traditional cross-section method remains exam standard. Bulk density must match moisture state (ROM vs dry) for tonnage conversion.

DGMS expects documented survey method for reserve reporting — Hartman & Mutmansky warn against mixing methods within one deposit without reconciliation.

Relation 1 —

Write this relation with symbols exactly as in Dass Mine Surveying — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 2 —

Write this relation with symbols exactly as in Dass Mine Surveying — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 3 —

Write this relation with symbols exactly as in Dass Mine Surveying — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Prismoidal formula V = (A₁ + 4A_m + A₂)/6 × L applies to three sections equally spaced: end areas A₁, A₂ and mid-area A_m at half spacing. Simpson's one-third rule analogue — exact for cubic variation of area with distance.

Trapezoidal V = (A₁ + A₂)/2 × L is simpler but underestimates or overestimates when curvature of area-distance plot is significant. Use when mid-section is unavailable and sections are closely spaced.

Strip method divides plan into strips of width w, area A_i per strip: V ≈ Σ A_i × w. Common in irregular pits with contour map — planimeter or GIS integration for areas.

Tonnage T = V × ρ_bulk where ρ_bulk includes moisture and voids (SWELL factor for bank vs loose). Match density to material state: in-situ reserve vs blasted loose cubic metres. Conversion errors between BCM and LCM are a classic mine accounting mistake.

State assumptions explicitly before using any relation for volume computations — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.

Wrong assumptions invalidate the entire solution even when the formula is correct. In Mine Surveying viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

1. Read the question and list given data with SI units (common in Mine Surveying papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to volume computations.
4. Use equation 1: .
5. Use equation 2: .
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Volume Computations appears in mine planning and statutory records. In Indian mining curricula this topic is tested because it connects theory to underground and surface surveys.

GATE and semester exams often combine volume computations with earlier units — revise prerequisites before attempting mixed problems.

Industry interview panels sometimes ask: "Where did you use volume computations?" — answer with a lab, mini-project, or plant visit example if possible.

• Using prismoidal formula with unequally spaced sections without modification
• Forgetting to convert area units (m²) and length (m) consistently before volume
• Applying loose density to in-situ volume or vice versa
• Trapezoidal formula when examiner explicitly expects prismoidal (three areas given)

Before attempting volume computations problems, confirm you can:

1. Open-pit volume from survey sections
2. Stockpile volume from drone/terrestrial scan
3.

Revise the solved examples in Dass Mine Surveying — Standard reference and one previous-year GATE or university paper for this unit.