## 1 Introduction  
In contemporary urban development, there is growing emphasis on prioritizing pedestrian traffic, leading to the creation of civil structures designed specifically for walkable use. This shift aims to enhance walkability and promote sustainable urban living [1]. However, the dynamic interaction between human-induced activity loads and the response of civil structures frequently limits serviceability owing to the development of excessive structural vibrations. Dynamic coupling between gait pedestrians and structural responses has been extensively discussed in the literature concerning civil structures, such as stairs [2; 3; 4], grandstands [5; 6; 7; 8; 9], slabs [10; 11; 12], and footbridges [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. The latter type of structure has become the most affected urban civil structure regarding vibration serviceability limits due to the increase in technical and aesthetic requirements, their condition of spanning large distances, and the ongoing integration of advanced materials that are more robust and lighter during and after the construction process. Grouping of these conditions allows for design optimization, resulting in relatively low mass and damping. Consequently, footbridges are becoming increasingly slender and flexible, increasing their dynamic sensitivity to excessive vibrations owing to human activity [13; 17; 25]. Normally, vandalism-induced human loadshave the greatest dynamic effect on the response of footbridges [18; 26]. However, owing to their intensity and wide frequency range, human-induced gait loads have the highest recurrence and potential to limit the structural serviceability due to the vibrations generated. In addition, the human gait frequency content is typically close to the dynamic properties of these types of structures, which poses a latent risk of synchronization phenomena affecting both footbridges and pedestrian traffic. The adaptive [17; 27; 28], random [29; 30], and nonstationary conditions [17; 29; 31] of human-induced gait loads have generated an interrelation phenomenon with structural vibrations known as structure-to-human interaction (S2 HI) [17; 32; 33; 34]. Concurrently, the dynamic properties of footbridges are influenced by the presence of these anthropic loads, and the participatory mass and damping provided by human loads are significant for these dynamically sensitive structures; this relationship is known as human-to-structure interaction (H2 SI) [23; 35; 36; 37]. In addition, dynamic effects between the gait pedestrians themselves have been observed and are denoted as human-to-human interaction (HHI) [38; 39; 40]. These interaction aspects are referred to in the literature as human-structure interaction effects (HSI) [13; 18; 20; 27; 41; 42; 43; 44]. These effects on footbridges represent an advanced case of dynamic synchronization and have become one of the most intriguing topics within the structural scientific community in recent years. Traditionally, human-induced gait load effects on footbridge dynamic responses have been numerically evaluated by assuming the behavior of these anthropic loads on vibrating surfaces without complete interrelation effects with the structural response, which underestimates the dynamic coupling effects and leads to a tendency to condition serviceability due to the low estimation of structural vibrations [21; 31; 45; 46; 47; 48; 49]. Likewise, S2 HI effects have been assessed on surfaces with lateral movement using instrument treadmills, which allows unidirectional or multidirectional analysis of the vibration effects on human-induced gait loads [17; 32; 33; 34; 50]. Although experimental tests allow better measurement of the human gait response due to controlled conditions and predefined protocols, limitations have generally been reported in the development of variability conditions under HHI effects and individual human gait disturbances [9; 14; 17; 51; 52].