Field-Calibrated Simplification of the F(x) Correction in Subsurface Drainage Design for Urban Heritage Sites

Rising groundwater levels pose a significant threat to urban heritage sites, highlighting the need for efficient subsurface drainage systems. The Hooghoudt equation is a foundational tool for such designs, yet its practical use is hindered by the complexity of computing the correction term F(x), which is critical in urban environments with irregular geometries. This study presents a two-phase investigation. The first phase involves a field-calibrated analysis of three historic mosques in Cairo, applying a refined 10-term series for F(x). Findings reveal that omitting this term can lead to discharge errors exceeding 40%. In the second phase, a simplified empirical formula for F(x) is developed using data from over 22,000 simulation scenarios. A hybrid exponential decay model delivers outstanding accuracy (R² >0.9999; maximum error < 0.01%). The resulting three-parameter equation, F(x) ≈ 5.432 + 2.832⋅exp(− 6.414x), offers a practical alternative to complex series computations. Accompanying tools, such as nomographs and lookup tables enable rapid and reliable drainage planning to support the preservation of heritage sites vulnerable to rising groundwater.