Urban Highway Realignment in Portland, Oregon

Scenario

A city-led infrastructure upgrade required realigning a 420-m segment of SW Barbur Boulevard to accommodate new light rail integration and reduce flood-prone cut sections. The site featured variable glacial till and weathered basalt bedrock, with strict noise and vibration limits near residential zones—limiting blasting and requiring precise volume control to minimize truck hauls. Right-of-way constraints prohibited widening beyond existing corridor boundaries, necessitating accurate cut-and-fill balancing.

Given Data

• Length of road alignment: 420 m
• Cross-sectional areas (m²) at 50-m stations: [8.2, 14.7, 22.3, 19.6, 16.1, 25.4, 31.8, 27.5]
• Segment length: 50 m (consistent stationing; final segment adjusted to 20 m)

Calculation

The tool applies the trapezoidal rule per segment (standard for earthwork estimation when cross-sections are regularly spaced):
For segments i to i+1:
$$V_i = \frac{L}{2} (A_i + A_{i+1})$$
where L = segment length (50 m for first 7 intervals; last interval = 20 m).

Cross-sections provided at 0 m, 50 m, 100 m, ..., 350 m → 8 stations → 7 full 50-m segments + one 20-m segment (350–370 m), but total length is 420 m → correction: stations at 0, 50, 100, 150, 200, 250, 300, 350, and 420 m → 9 stations. Since only 8 values were given, the tool interpolates the 9th area using linear trend from last two:
Slope = (27.5 − 31.8)/50 = −0.086 m²/m → A₉ = 27.5 + (420−350)×(−0.086) = 27.5 − 6.02 = 21.48 m².

Segment volumes:

• 0–50 m: (50/2)(8.2 + 14.7) = 25 × 22.9 = 572.5 m³
• 50–100 m: 25 × (14.7 + 22.3) = 925.0 m³
• 100–150 m: 25 × (22.3 + 19.6) = 1047.5 m³
• 150–200 m: 25 × (19.6 + 16.1) = 892.5 m³
• 200–250 m: 25 × (16.1 + 25.4) = 1037.5 m³
• 250–300 m: 25 × (25.4 + 31.8) = 1430.0 m³
• 300–350 m: 25 × (31.8 + 27.5) = 1477.5 m³
• 350–420 m: (70/2)(27.5 + 21.48) = 35 × 48.98 = 1714.3 m³

Sum = 9,106.8 m³ total volume.
To separate cut and fill: field survey data embedded in cross-section signs — negative values indicate cut (excavation), positive indicate fill. Recalculating with signed areas: [−8.2, −14.7, −22.3, −19.6, −16.1, +25.4, +31.8, +27.5, +21.48].
Cut sum (absolute): segments where both ends ≤ 0 → first 5 intervals fully cut: 572.5 + 925.0 + 1047.5 + 892.5 + 1037.5 = 4,475.0 m³.
Fill sum: remaining segments (partially or fully positive): 1430.0 + 1477.5 + 1714.3 = 4,621.8 m³, plus partial fill in 200–250 m (where A₅ = −16.1, A₆ = +25.4 → zero-crossing at 200 + 50×16.1/(16.1+25.4) ≈ 219.4 m → fill portion = (50−19.4)/2 × (0 + 25.4) ≈ 387.3 m³). Total fill = 4,621.8 + 387.3 = 5,009.1 m³.
Thus:

• Total volume = 9,106.8 m³
• Cut volume = 4,475.0 m³
• Fill volume = 5,009.1 m³
  Net import = 534.1 m³.

Result and Decision

The model confirmed a net fill deficit of ~534 m³ — well within allowable borrow material tolerance (<1,000 m³). The project team selected an on-site borrow pit 1.2 km east (within city-owned land) instead of off-site hauling, reducing transport emissions by 62% and avoiding $48k in disposal fees. Final grading plan was approved with 5% swell factor applied to cut volumes (per ASTM D698 Proctor data), increasing estimated cut to 4,699 m³ — still sufficient to meet fill demand after compaction losses.

Lesson

Always apply material-specific swell and shrinkage factors before balancing cut and fill — unadjusted volumetric balance misleads mass-haul planning, especially in heterogeneous soils like Portland’s glacial till.