Empirical formula for fundamental period of RC hillside buildings considering terrain slope and soil-structure interaction

Accurate estimation of the fundamental period is crucial for seismic design, as it influences a building’s response to earthquake forces. Traditional seismic codes often rely on simplified formulas based on building height or the number of stories, neglecting the effects of sloping ground and soil-structure interaction (SSI). While IS 1893:2016 uses the smallest building height, it tends to underestimate the period, leading to conservative base shear calculations. Conversely, other codes, such as Eurocode 8 and ASCE/SEI 7–16, which use the largest height, tend to overestimate it. This study investigates the fundamental period of reinforced concrete (RC) buildings on sloping ground (10°–40°) under stiff, medium, and soft soil conditions using modal analysis in SAP2000. A total of 211 models of three-, five-, and seven-story buildings with four and five bays (4 m and 5 m widths) were analyzed. To assess SSI, the Winkler foundation model was used. The results reveal that IS 1893:2016 underestimates the period by an average of 42.58%, while Eurocode 8, ASCE/SEI 7–16, and EGC 1993 overestimate it by 14.56%, 7.90%, and 1.29%, respectively. This study proposes using the average of the tallest and shortest building heights in code formulas. Additionally, a new multiple linear regression equation incorporating building height, bay width, number of bays, slope angle, and soil conditions is proposed to improve fundamental period estimation for hillside RC buildings.