Mountainous Rural Access Road in Appalachia, West Virginia

Scenario

A USDA-funded rural development project constructed a 2.8-km (2800 m) all-weather access road connecting three isolated communities in McDowell County. Terrain included steep slopes (up to 45°), shallow coal-seam overburden, and seasonal seepage zones. Environmental constraints mandated zero discharge into headwater streams and required all excavated material to be reused onsite (no external disposal). Tight budget ($1.2M cap) demanded minimal import/export — ideal for cut-fill optimization.

Given Data

• Length of road alignment: 2800 m
• Cross-sectional areas (m²) sampled every 100 m (29 stations): [0, 3.2, 7.8, 14.1, 22.5, 31.7, 40.2, 45.6, 48.9, 50.1, 49.3, 46.7, 42.1, 36.8, 30.2, 24.6, 19.8, 15.3, 11.7, 8.9, 6.5, 4.8, 3.6, 2.7, 2.1, 1.6, 1.2, 0.9, 0.5]
• Segment length: 100 m (final segment = 0 m since 28 × 100 = 2800 m → exact fit)

Calculation

With 29 cross-sections at 0, 100, 200, ..., 2800 m, there are 28 segments of 100 m each. Using trapezoidal rule:
$$V_i = \frac{100}{2}(A_i + A_{i+1}) = 50(A_i + A_{i+1})$$
All areas are positive — interpreted as cut (removal) in embankment zones and fill (placement) in excavation zones. Per standard convention in mountainous alignments: areas above existing ground = cut; below = fill. Surveyor notes indicated all sections represent cut (road built on bench cut into hillside), except stations 0, 27–28 where area < 1.0 m² — deemed negligible. Thus, all volume is cut — no fill required.

Summing adjacent pairs:
Total = 50 × Σ(Aᵢ + Aᵢ₊₁) for i = 1 to 28 = 50 × [(A₁+A₂) + (A₂+A₃) + ... + (A₂₈+A₂₉)] = 50 × [A₁ + 2A₂ + 2A₃ + ... + 2A₂₈ + A₂₉]
= 50 × [0 + 2(3.2 + 7.8 + ... + 1.2) + 0.5]
Compute inner sum:
A₂ to A₂₈ = 27 values. Sum = 3.2+7.8+14.1+22.5+31.7+40.2+45.6+48.9+50.1+49.3+46.7+42.1+36.8+30.2+24.6+19.8+15.3+11.7+8.9+6.5+4.8+3.6+2.7+2.1+1.6+1.2 = 622.2
Then total = 50 × [0 + 2×622.2 + 0.5] = 50 × (1244.4 + 0.5) = 50 × 1244.9 = 62,245.0 m³
Since all sections are cut, cut_volume = 62,245.0 m³; fill_volume = 0 m³; total_volume = 62,245.0 m³.

Result and Decision

The tool output confirmed a massive net cut — far exceeding local fill needs. To comply with zero-discharge and reuse mandates, the team designed a series of engineered retaining walls and terraced embankments using processed overburden (crushed shale/siltstone) as structural backfill. Excess material (≈18,000 m³ after wall construction) was stockpiled under erosion-control blankets for future community use (e.g., school playground surfacing, trail base). Bid documents were revised to require contractor reuse — saving $210k in off-site disposal and eliminating 1,200+ truck trips.

Lesson

In steep terrain, early recognition of dominant cut or fill conditions — validated via rapid volumetric estimation — enables proactive material reuse strategies that satisfy environmental rules and improve cost performance; never assume balanced earthwork.