Topographic Amplification of Urban Slopes with Local Geometric Irregularities: Insights from Pardis City

Local observations in buildings constructed on slopes, ridges, and hills reveal considerable and often unanticipated structural damage, even in code-compliant structures. Although seismic design codes address this issue through topographic amplification factors (AF), studies have shown that these AFs often underestimate the effects—especially in regions with complex topographic features. This study shifts focus to a prevalent but under-investigated scenario: the seismic response of slopes with engineered, local geometric irregularities common in urban development, using Pardis City, Iran—a rapidly developing area with complex terrain—as a case study. Field observations identified 144 distinct irregularity patterns across four main scenarios: horizontal, vertical, triangular, and multi-step excavations. These patterns were analyzed using finite element (FE) modeling in Abaqus, under sinusoidal acceleration excitations of varying frequencies. The numerical models were verified based on mesh size/type, material properties, and comparison with AFs from previous studies. Parameters including horizontal (AF _h ) and vertical (AF _v ) amplification factors, wave propagation mechanisms, and AF variations at and behind slope crests were assessed. Results show that AF increases with slope steepness. For example, for patterns A and B (w/H = 0.2, h/H = 0.2) at H/λ = 0.2, AFₕ increased by approximately 11.5% and 3.7%, respectively, as the slope angle α increased from 90° to 85°. A key finding is that these local irregularities generally reduce both AFₕ and AFᵥ compared to regular slopes. For instance, in pattern D (α = 85°, H/λ = 0.2), AFₕ and AFᵥ decreased by about 13% and 27%, respectively, for sub-pattern D1. Furthermore, the analysis introduced the spatial parameter τ ( AF _(max)bcr )/ AF _Crest ), revealing that irregularities significantly alter amplification patterns behind the crest, with τ exceeding 2.0 at higher frequencies—an effect absent from current code considerations. Wave propagation analysis showed these irregularities redirect wave reflections, reducing induced acceleration at the crest. AF was highly sensitive to excitation frequency, exhibiting uniform reduction at lower frequencies (<5 Hz) and oscillatory behavior with peaks 25–75 m behind the crest at higher frequencies. The findings highlight current code limitations and provide a quantitative framework to advance code provisions beyond a single topographic factor toward more precise, geometry-specific assessment for complex urban terrains.