Geometric and hydraulic parameter correlations with cross pipe culvert extension requirements in road rehabilitation works

Abstract

Highway rehabilitation often results in modifications to the existing embankment geometry and roadway prism, necessitating the extension of cross-pipe culverts to maintain hydraulic and geometric continuity. These extensions are commonly determined through subjective judgment or rule-of-thumb methods, causing design inconsistencies, project delays, and cost overruns. The absence of scientifically established literature guiding the quantification of culvert extension lengths limits a replicable and consistent approaches for extension length determination. This study develops and validates a predictive, data-driven framework that integrates Digital Terrain Model (DTM)–derived parameters with analytical and hydraulic principles to quantify culvert extension lengths and improve design-stage consistency. Using the Alwii–Nebbi corridor (Uganda) as a case study, Digital Terrain Models (DTMs) derived from topographic surveys were integrated with roadway geometry to extract governing variables—shoulder elevation (Z), invert elevation (V), lateral offsets (Xz, Xv), embankment slope (S), culvert gradient (g), diameter (Ø), and wall thickness (t)—across 61 culvert sites (122 inlet/outlet cases). From the roadway–embankment–culvert cross-section, explicit closed-form expressions for upstream (Lu) and downstream (Ld) extensions were derived, with √(〖(g〗^2+1)) capturing barrel inclination and (S ± g) distinguishing inlet/outlet configurations. Terrain analysis revealed corridor variability (Z−V ≈ 2.0–3.5 m; Xv ≈ 5.0–6.5 m) and diagnostic negative extensions indicating regrading needs rather than pipe addition. Validation showed strong agreement between analytical predictions and DTM-measured lengths (R² > 0.9; low RMSE) and hydraulic adequacy under design flows (Hw/D ≤ 1.2 via HY-8). Sensitivity and correlation analyses identified vertical separation ΔZV = Z − (V + Ø + t) and lateral placement (Xv − Xz) as dominant controls; Xv offers the most actionable field lever for fine-tuning lengths. Descriptive statistics indicated a modest downstream bias (mean Ld ≈ 1.64 m vs. Lu ≈ 1.45 m; Δ ≈ +0.19 m) with typical extensions between 1.0 and 2.0 m, supporting modular sizing (1.0–1.5–2.0 m) while retaining site-specific optimization. The study contributes a reproducible, terrain-sensitive, and hydraulically verified framework suitable for specification adoption. It recommends institutionalizing the DTM → analytical sizing → HY-8 check workflow in design manuals and Terms of Reference (ToRs). Future research should focus on evaluating the structural performance of culvert extension joints and joint treatment during installation, and on integrating the developed equations into civil engineering platforms such as AutoCAD Civil 3D, ArcGIS, and HY-8 to enable automated optimization in culvert extension planning.