Effect of Structure-Soil-Structure Interaction (SSSI) between Three Dissimilar Adjacent Bridges

The present study assesses the effect of Structure-Soil-Structure-Interaction (SSSI) on the seismic behavior of three dissimilar adjacent bridges by comparing their seismic responses with the seismic response of the isolated bridge including Soil-Structure-Interaction (SSI). To this end, an extensive series of numerical analyses have been carried out to elicit the effects of Structure-Soil-Structure-Interaction (SSSI) on the seismic behavior of three dissimilar bridges with different superstructure masses. The studied bridges are based on groups of piles founded in nonlinear clay. A parametric study has been performed for congurations of three dissimilar bridges with superstructure masses ratios of 200% and 300%, concentrating on the inuence of the inter-bridge spacing, and the geometrical position of the bridges towards each other and towards the seismic excitation direction. The numerical analyses have been conducted using a three-dimensional nite difference modeling software FLAC 3D (Fast Lagrangian analysis of continua in 3 dimensions). The results of the numerical simulations clearly show that the seismic responses of the dissimilar grouped bridges were strongly inuenced by the neighboring bridges. In particular, the results reveal a salient positive impact on the acceleration of the superstructure by a considerable drop (up to 90.63%) and by (up to 91.27%) for the internal forces induced in the piles. Comparably, the inuence of bridge arrangement towards the seismic loading were prominent on both of superstructure acceleration and the internal forces in the piles. The responses were as much as 27 times lesser for the acceleration and 11 times smaller for the internal forces than the response of the isolated bridge. Contrarily, the inter-bridge spacing has a limited effect on the seismic response of the grouped bridges.


Introduction
As most structures in densely populated urban areas are constructed in clusters, and often with only a few meters apart, their seismic response is thoroughly affected by the dynamic behavior of the adjacent structures and their fundamental dynamic characteristics; this interaction is termed as Structure-Soil-Structure Interaction (SSSI). Whence, the study of (SSSI) effects has become increasingly inevitable to ensure an effective earthquake resilience of the structures constructed in dense urban environments. Furthermore, the accelerated lack of available space has led in some cases to construct new large structures near old smaller structures in new neighborhoods which impose additional complications to the (SSSI) effects. The state-of-the-art in (SSSI) analysis has been mostly concentrated on tall buildings and skyscrapers; the effect between neighboring bridges have been rarely studied, mainly due to the shortage of experimental or eld-based casestudies that con rm its effect on seismic response. The numerical analyses presented herein share the common goal of a better understanding of the phenomena of (SSSI), with particular attention to focusing on the effect of (SSSI) between three dissimilar adjacent bridges, different superstructure mass ratios, inter-bridge spacing, and the arrangement of the bridge towards the seismic loading direction.
Structure-Soil-Structure-Interaction (SSSI) has attracted extensive attention in the last decades; most prior research about (SSSI) have generally concentrated on the seismic behavior of neighboring tall buildings and skyscrapers. Nevertheless, there is rather a variance between the ndings of these studies in the literature. In the numerical eld,  has employed a three-dimensional (3D) Finite Element model to analyze the seismic interaction between three connectors and the surrounding soil at different bridge superstructure elevations of an existing bridge interchange at the intersection of Interstates 10 and 215 (San Bernardino, CA). Bolisetti and Whittaker (2015) have performed a series of numerical simulations and centrifuge experiments to assess the seismic effects of (SSSI) on buildings constructed in dense urban environments. They have asserted that the experiments and numerical results have revealed a slight effect of (SSSI) on the seismic response of the buildings considered in their research. Lu et al. (2020) have developed simple discrete models for simulating the static and dynamic interaction between multiple buildings. The developed models have been validated by comparison with the results of the simulation methods of Finite elements (FE) and Boundary elements (BE). A thorough series of 2D numerical analyses have been carried out by Bybordiani and Arici (2019) to study the interaction effect between neighboring 5-, 15-, and 30-story clusters of structures and the surrounding viscoelastic half-space. They have investigated the in uence of the inter-building distance and the foundation material on the response of the adjacent buildings. The results have revealed negligible effects of (SSSI) on the behavior of the identical low-rise structures and signi cant effects on the response of the identical high-rise structures. In the same manner, Isbiliroglu et al (2015) have conducted parametric numerical analyses to study the effects of (SSSI) for various arrangements of regular building clusters composed of three types of buildings of approximately 3, 13, and 40 stories. The results pointed out to considerable drop in buildings base motion at frequencies above the natural frequencies of the building-foundation systems. Likewise, both detailed numerical analyses and a set of centrifuge experiments have been employed by Bolisetti and Whittaker (2020) in order to investigate the effect of (SSSI) on three arrangements of low-to medium-rise frame buildings. They concluded that the existence of deep vault reduces uplift in the foundations and the peak spectral accelerations at the roof. Ogut (2017) has conducted a wide (SSSI) analytical parametric study; the effects of mass, height of the superstructures, foundation types, embedment situations and xed based natural frequencies of two and three closely spaced buildings on (SSSI) have been investigated. By studying the (SSSI) effect on 32 story neighboring buildings for different inter-building spacing, Yahyai et al. (2008) have claimed a detrimental effect of (SSSI) on base shear forces and lateral displacement. As well as detailed numerical analyses for obliquely incident seismic waves have been carried out by Álamo et al. (2015). They noted that the interbuilding spacing and the seismic loading are crucial for the (SSSI) effects on short identical structures supported by pile foundations. In a related study, Rahgozar (2015) has employed the direct method for evaluating the behavior of threedimensional nite element models of neighboring 15 and 30 story steel structures founded on different sandy and clayey soils. The results demonstrated the detrimental effect of (SSSI) for the case of neighboring tall buildings to short buildings. Nakamura et al. (2012) have conducted a comprehensive seismic analysis by using a nonlinear three-dimensional FEM model to determine the (SSSI), and the ground irregularity effect on the seismic response of NPPs (Nuclear Power Plants). Roy et al. (2015) have performed a detailed parametric study to analyze the impact of (SSSI) on the behavior of neighboring light structure to a heavy structure, and a heavy structure adjacent to a heavy structure for several soil cases, foundation embedment depths, and separation distances. The results asserted that the SSSI response of light or heavy structures can be in uenced by the existence of a nearby heavy structures. Barrios and Chouw (2015) have performed a physical experimental study by using a sand-lled laminar box on a shaking table. The examined adjacent structures had identical mass and different fundamental periods. They concluded that the buildings with lower natural frequencies are less vulnerable to the (SSSI) effect than the buildings with higher natural frequencies. Ikeda et al. (2004) have conducted a comprehensive analytical and numerical study on the (SSSI) effect among multiple foundations (without superstructures). Larkin et al. (2016) have performed shaking table tests with a laminar box for 4 neighboring buildings. They denoted that the (SSSI) effect are more evident for neighboring structures with different fundamental frequencies due to the mechanism of energy exchange between them. Ge et al. (2017) have conducted comprehensive experimental tests and numerical studies to investigate the (SSSI) effect between multiple high-rise buildings. The results revealed bene cial effect of the (SSSI) on the acceleration responses of structures and adverse effect on the structures deformations. Furthermore, two centrifuge tests have been performed by Trombetta et al. (2014) to assess the (SSSI) effects between midrise elastic shearwall buildings supported by a mat foundation and low-rise inelastic frame buildings built on individual spread footings. Andersen et al (2017) have extended the validity of a semi-analytical model predicting ground vibration from rigid rectangular loads to enable it of estimate accurately the effect of heavy masses or plates set either on the ground surface or implanted into the soil. Similarly, Gan et al. (2020) carried out a thorough numerical analyses of the (SSSI) effect between three adjacent structures supported by pile-raft foundations embedded in viscoelastic half-space. The results revealed that the (SSSI) impact depends mainly on the structural characteristics, rather than the location of the structures. Wang (2018) has employed the nite element software (ANSYS) to analyze the (SSSI) effect between surface structure built on viscouselastic soil layer and the adjacent underground station. The results denoted that the arrangement and the fundamental frequencies of the structures have the crucial impact on the (SSSI) effect. Bard et al (2013) have conducted extensive experimental, numerical and theoretical cross-analysis to quantify multi-building interactions (SSSI) and site-city effect. An idealized experimental model of a city on a soft layer has been used to examine the effect of multiple Structure-Soil-Structure interactions (SSSI). Schwan et al. (2016) have performed a set of shake table tests on a designed elementary case study of multiple (SSSIs) between clusters of structures. The experimental data were compared with theoretical and numerical results. They demonstrated experimentally, theoretically, and numerically the fact that a city group effect can signi cantly alter the seismic response of both the construction site and the related buildings; also, they quanti ed the complex (SSSIs) at the city scale. Mason et al. (2010) have conducted centrifuge tests on two adjacent moment-resistingframe steel structures. The rst model structure is a one-story, lumped-mass frame structure based on embedded spread footings. The other model structure is a three-story, lumped-mass frame structure founded on a one-story aluminum basement. A comprehensive set of dynamic geotechnical centrifuge tests has been carried out by Ngo at al. (2019) to investigate (SSSI) effects on the behavior of two adjacent structures with different mass, natural frequency, and height.
Extensive numerical analyses have been implemented by Alam and Kim (2014) to explore the effect of uniform and nonuniform ground motions on the behavior of neighboring reinforced concrete (RC) frame structures. The results revealed a remarkable impact of the spatial variation of ground motions on the seismic response of the adjacent structures. Ritter (2017) has employed at novel three-dimensional technology to investigate the (SSSI) effect between a tunnel, the soil, and existing structures. The building models were printed with brittle material behaviour similar to masonry and tested in a geotechnical centrifuge. A thorough series of numerical analyses have been conducted by Alfach and Al Helwani (2019) to examine the effect of the plan positioning of the bridges towards the seismic excitation direction and inter-bridge spacing for two identical bridges supported by a group of piles embedded in nonlinear clay. Knappett et al. (2015) have examined the seismic performance of an isolated structure and adjacent (similar and dissimilar) structures under a series of strong seismic excitations. The non-linear dynamic centrifuge tests were accurately validated by a comprehensive non-linear niteelement model. Furthermore, Ada et al. (2019) have investigated the (SSSI) effect between two neighbouring frame structures through a series of 3D numerical analysis. They have examined the in uences of the stiffness of the underlying soil, layout of the structures, the clear distance between the structures, and the number of stories of the structures. They concluded the (SSSI) effect highly depended on the dynamic characteristics of the adjacent structures.

Aims
The main objective of this paper is developing better understanding of the seismic structure-soil-structure interaction (SSSI) between three dissimilar bridges with different superstructure mass ratios. Notably, the contents of this study focused on the effect of inter-bridge spacing and dissimilar bridge geometrical arrangements on the (SSSI) impact. In this paper, we enlarge the range of our former studies about the (SSSI) effect between two identical bridges in Alfach and Al Helwani (2019), and the (SSSI) effect between two dissimilar bridges in Alfach (2021) to study the case of three dissimilar bridges with different superstructure mass ratios. The numerical analyses were performed using a nite-difference modeling software FLAC 3D (Fast Lagrangian analysis of continua in 3 dimensions). The analyses have been undertaken for nonlinear clay.
More Speci cally, the research contributions in assessing the effect of the seismic structure-soil-structure-interaction (SSSI) could be summarized in these three points: -Identi cation of the nature of (SSSI) effect (detrimental, constructive, or neutral) between three adjacent dissimilar bridges with different superstructure ratios.
-Explore the impact of inter-bridge spacing on the seismic performance of the neighboring bridges.
-Investigation of the seismic e ciency of the planned alignment of adjacent structures with respect to each other and the epicentral direction (Parallel, Perpendicular, Crossing).

Soil-pile-bridge model
The (SSSI) system in this study consisted of three asymmetric reinforced concrete bridges. These bridges of lumped masses of (350, 700, and 1050 Tons) have been used for forming different neighborhood combinations. The used bridges were supported by oating piles groups of (6, 12, and 18 piles) respectively, for the purpose of retaining the single pile static axial load to (80 tons). The xed-head pile groups are embedded into homogeneous nonlinear cohesive layer (C=150 KPa, = 0) underlined by rigid bedrock as shown in (Figure 2). The soil behavior was simulated based upon the standard Mohr-Coulomb criterion through an elastoplastic law without hardening. Table (1) presents the essential geotechnical characteristics of the soil layer. The length and the diameter of the piles are (L p = 10.5 m) and (D p = 0.8 m) respectively. The piles are connected rigidly by a reinforced concrete cap of (1 m) thick as illustrated in gure (1). The comportment of the material of the structural elements (superstructure mass, bridge pillar, cap, and piles) has been de ned as elastic. Tables (2) and (3) lists the fundamental parameters of the superstructure and the pile groups, respectively.   In light of the high complexity of the subject of Structure-Soil-Structure Interaction (SSSI), a set of measures have been adopted: -Aiming to minimize the computational cost, the soil mesh density was decreased with increase of the distance from the soil center, where the major effect of (SSSI) could be taken place as shown in gure (2).
-The absorbent boundaries have been employed to avoid the seismic wave's re ection on the structures model zone.
-In order to prevent the potential soil-cap interaction, the cap was based a 0.5 m over the soil surface.
-In order to preclude the possible pile-pile interaction, the inter-piles distance was taken as (S =3.75D p =3 m).
To reduce the computation cost, the superstructure was simulated by lumped masses at the top of the pillars [M st =350, 700, Page 6/42 and its fundamental frequencies (assuming a xed base) are equal to [F st =2.5,7.09,5.78 Hz] respectively. The latter were computed by using the subsequent formulations: While the fundamental frequency of the soil layer is 3.2 Hz. The exible base frequencies of the superstructure taking into consideration the soil-structure interaction were calculated (using numerical methods) as F st, ex = 0.827, 0.71, and 0.7 Hz respectively.

Seismic excitation
The numerical analyses have been carried out under the seismic record of the Kocaeli Earthquake (Mw = 7.4) which occurred on August 17, 1999, in the North Anatolian Fault Zone in Turkey (Station AMBARLI; KOERI source). The peak horizontal acceleration and velocity of this earthquake are (PGA =0.247 g) and (PVA =40 Cm/s) respectively during the total duration of the record (t = 30.08 Sec). Nevertheless, the numerical analyses have been performed for a duration of (t=8.465 sec) to economize the computational capacity and the analyses durations. This step was adopted after rigorous analysis to ensure the equalization of the seismic excitation impact for the total duration (t = 30.08 sec) and the used duration (t=8.465 sec). Figure (3) presents the fundamental frequency of the seismic loading (F= 0.9 Hz) in the Fourier spectrum of the velocity record ( gure 3D). It is worth mentioning that the seismic loading fundamental frequency is between the fundamental frequency of the soil (F 1 = 3.2 Hz) and the exible frequency of the structure (F ss = 0.7 Hz) which justi es the choice of this seismic loading. Table 4 and gures (4) and (5)   As shown in gures (6) and (7) and table 5, the maximum internal forces induced in the piles of the bridge of (M st = 700 T)

Results and Discussion
are smaller by about (25 %) than those of the piles of the bridge of (M st = 350 T). Furthermore, the ampli cation factor at the mass was reduced by a ratio of (A amp =7.95). Also, it is noteworthy that the bending moment pro le has changed drastically by recording the maximum values at the top parts of the piles.  (8) and (9). Additionally, the mass and cap accelerations of the bridge of mass (M st = 1050 T) have dropped sensibly to (11.99) and (10.82) respectively as presented in table (6). Likewise, the ampli cation factor of the mass has decreased to (A amp = 5.64). 3. Bridge-soil-bridge System The following numerical simulations have been carried out for several con gurations of three dissimilar bridges for two superstructure mass ratios (200 % and 300 %). The impact of two essential factors have been examined: 1) Inter-bridge spacing and, 2) The geometric position of neighboring structures towards each other and the seismic loading direction (Parallel, Perpendicular, Crossing) con gurations for the above-stated mass ratios.

Effect of Inter-Bridge spacing
The effect of the inter-bridge spacing on the (SSSI) effect between three different parallel bridges has been numerically analyzed; the central bridge is the heavier one with a superstructure mass of (M st =700 T) ( gure 2.b) located between two lighter bridges with a superstructure mass of (M st = 350 T) ( gure 2.a). The numerical calculations were undertaken for a range of distances between the bridges, precisely (S= 20 m,30, and 40 m). All the geometrical and mechanical characteristics of soil and concrete mentioned in section (2.1) and tables (1,2, and 3) have been adopted in these analyses. The numerical simulation is performed for the seismic loading of the Turkey earthquake (Kocaeli,1999). The applied mesh presented in gure (10) includes (4176) zones of 8 node solid elements and (552) three-dimensional structural elements of 2 node beam elements.

Results and Discussion
The spread of the plasticity in the soil for the two isolated bridges (M st =350 and 700 T) are presented in gure (10).
Foreseeably, the plasticity extension under the central part of the light bridge (M st = 350 T) is much smaller than its peer under the heavy bridge. Likewise, gure (11) illustrates the plasticity extension for the inter-bridge spacing (S= 20,30, and 40 m) between three parallel dissimilar bridges under the effect of seismic loading (Kocaeli, 1999).
The plasticity spread in the soil has slightly reduced with the increase of the inter-bridge spacing as shown in gure (11). On the other hand, the plasticity has dominated the comportment of the upper part of the soil (C= 150 KPa), whilst the behavior of the lower part stayed mostly elastic due to the fact that the plasticity has started at the soil surface and extended gradually towards the base without attaining the base during the seismic loading time.     (12) and (13). Similarly, Figures (14) and (15)  respectively. Hence, the interaction between three dissimilar bridges (SSSI) has valuable positive impacts on the superstructure acceleration and the piles internal forces by provoking a signi cant diminution of both. Table 7 and Figures  12, 13, 14, and 15 demonstrate the slight in uence of the inter-bridge spacing on the internal forces provoked in the piles of the three bridges, which are in accord with the results of Alfach and Al Helwani (2019) and the results of Alfach (2021) about the minor impact of the inter-bridge spacing. Substantially, the bending moment and the shear force induced in the piles of the light bridge (M st = 350 T) increase by (up to 6 % and 6.9 %) respectively with the rise of the inter-bridge spacing.
Likewise, the bending moment and the shear force of the heavy bridge (M st = 700 T) augment by (up to 4.9 % and 6.1 %) respectively. In the same manner, the mass and the cap accelerations increase by (up to 4.3 % and 7.41 %) respectively with the increase of the inter-bridge spacing as revealed in gure (16). It is worth mentioning that all the maximum internal forces induced in the piles have been obtained in the heads of the piles except the maximum bending moment induced in the piles of the bridge of (M st = 350 T), which has been obtained in the central part of the piles as seen in gures (14) and (15).
In the frequency domain, gure (17a)   In terms of the pile's internal forces, the minimum bending moments induced in the piles (1) and (2) (24) and (25).
Moreover, the internal forces induced in piles (1) and (2) were very close for the con gurations of perpendicular and crossing bridges as provided in table 8 and gures (24) and (25). Conversely, the maximum bending moment and shear force induced in piles (7) and (15) of the heavy bridge (M st =700 T) were reported for the perpendicular bridge con guration.
However, the minimum bending moment and shear force in the piles (7) and (15) were noted in the case of parallel bridges as shown in gures (22)  Similarly, the best impact of the (SSSI) on the cap acceleration was noted for the minimum cap acceleration of the heavy bridge of (M st = 700 T) which has attained (A cap = 1.34 m/sec 2 ) for the con guration of the crossing bridges, which agrees with the conclusions obtained by Alfach and Al Helwani (2019) and Alfach (2021). Howbeit, the minimum acceleration in the mass of the heavy bridge of (M st = 700 T) has been obtained for the perpendicular con guration with (A st = 1.83 m/sec 2 ) as shown in gure (26a). It is pertinent to note, the perpendicular and crossing con gurations have an uncommon impact on the vibration of the superstructure of the light bridge of (M st = 350 T) which was represented by generating the bigger accelerations in the cap by (A cap =6.52, and 6.47 m/sec 2 ) accompanied with much smaller accelerations in the mass (A st = 0.54, and 0.53 m/sec 2 ). Figure (27a) shows the spectrum Fourier analyses for the lateral seismic responses of the superstructure mass of the heavy bridge of (M st = 700 T) for the three studied con gurations (parallel, perpendicular, and crossing) bridges. The maximum dominant frequency (F=0.7 Hz) was obtained for the parallel bridge con guration; while the dominant frequencies of the crossing and perpendicular bridges con gurations were (0.473, and 0.4 Hz) respectively, with much smaller amplitudes. Conversely, for the light bridge of (M st =350 T), the maximum dominant frequency (F= 0.709 Hz) was attained for the crossing bridge con guration with a slight amplitude, while the dominant frequency of the perpendicular bridges is (F= 0.7 Hz) and the dominant frequency of the parallel bridges is (F= 0.6 Hz) with much bigger amplitude as illustrated in gure (27b).

Effect of Inter-Bridge spacing
A set of numerical analyses have been carried out to examine the in uence of inter-bridge spacing on the (SSSI) effect between three different parallel bridges with superstructure masses ratio of (300 %). The same geometrical and mechanical characteristics mentioned in section (2.1) for the light bridge of (M st = 350 T) as shown in gure (2.a) and the heavy bridge of (M st = 1050 T) as presented in gure (2.c) have been adopted. The numerical study has been performed under the velocity record of the Turkey earthquake (Kocaeli,1999) and for a range of inter-bridge spacing precisely (S = 20 m, 30 m, and 40 m). . In a similar manner, the shear force induced in the piles of the heavy bridge has signi cantly reduced by (77.7 %) and by a much inferior ratio for the piles of the light bridge (7 %). A slight effect of the inter-bridge spacing was highlighted in table 9 and gures (31a to 34a). More precisely, the bending moment provoked in the piles of the heavy and light bridges has increased by (10.47 %) and (7.17 %) respectively with the inter-bridge spacing rise. Alike, the shear force induced in the piles of the heavy and light bridges has grown by (7.2 %) and (14.38 %) with the augmentation of the interbridge spacing as shown in gures (31b to 34b). It must be mentioned that all the maximum internal forces induced in the piles have been reported in the top of the piles, except the maximum shear force in the piles of the light bridge, which has been obtained in the central part of the piles. Similarly, the shear force induced in the corner piles of the bridge (M st = 350 T) decreased by (4.96 %) with the increase of the inter-bridge spacing as described in gure (33b). In contrast, the bending moment in the corner piles and the internal forces (bending moment and shear force) in the central piles of the bridge of (M st = 350 T) varies marginally (up to 11 %) without showing an evident trend as illustrated in table 9 and gures (33)  3.2.2 Effect of bridge plan alignment with respect to each other and the seismic loading direction Two additional numerical analyses have been carried out to examine the effect of the Perpendicular and Crossing bridges con gurations on the overall effect of the (SSSI). The analyses were performed for the same geometrical and mechanical properties used in the former section (3.2.1) while choosing the inter-bridge spacing of (S= 20 m) as shown in gures (37) and (38). The numerical analyses have been conducted under the seismic loading record of Turkey (Kocaeli,1999). The employed mesh revealed in gures (37) and (38) includes (8104) zones of (8) nodes and (690) three-dimensional structural elements of 2 nodes. Unpredictably the plasticity under the isolated light perpendicular bridge of (M st = 350 T) has prolonged heavily and deeply to the base of the soil, whereas the plasticity spread is substantially smaller under the central portion of the cap of the heavy perpendicular bridge of (M st = 1050 T) as illustrated in gure (39). The interaction between the three bridges has incited a substantial change in the plasticity extension through the soil. The interaction between the three bridges in gure (40a) has reduced considerably the plasticity under the heavy bridge of (M st = 1050 T) with a slight effect on the zones under the light bridge of (M st = 350 T) and inter-bridges zones. Moreover, gure (40b) demonstrates that the plasticity extension almost vanished under the three bridges in the case of interaction between three perpendicular bridges, but it has increased considerably under the heavy bridge for the crossing con guration as shown in gure (40c). Table 10 elucidates the valuable impact of the (SSSI) on both superstructure acceleration and the internal forces induced in the piles.
Due to the interaction between the three bridges, the mass and cap accelerations of the heavy bridge have hugely reduced by ( (42). It should be mentioned that the bending moment and the shear force of the heavy bridge vary by (37.9 %) and (66.5 %) respectively with the bridge con guration changing between (parallel, perpendicular, and crossing), while the con guration change of the bridges has a bigger in uence on the superstructure acceleration by variation of up to 74.45 % as demonstrated in table 10. Contrarily, the minimum internal forces (bending moment and shear force) induced in the central and corner piles of the light bridge of (M st = 350 T) have been achieved for the con guration of crossing bridges as illustrated in table 10 and gures (43) and (44). Precisely, the minimum bending moment (M min =360.8 KN.m) has been obtained in the corner pile (1), while the minimum shear force (T min = 110.6 KN) was attained in the central pile (2). Moreover, the minimum superstructure accelerations have been gained also for the crossing con guration with mass and cap accelerations of (A st = 0.51 m/se 2 ) and (A cap = 6.3 m/sec 2 ). It is worth noting that the mass accelerations of the light bridges for the perpendicular and crossing con gurations are hugely smaller than the cap accelerations. Table 10 indicates an evident tendency to a signi cant drop in the superstructure acceleration, bending moment, and shear force by up to (95.6 %), (82.3 %), and (90.69 %) with the bridge con guration change starting from parallel to perpendicular and nally crossing bridges. T) with (A st = 2.81 m/sec 2 ) in the case of perpendicular bridges con guration, while the mass accelerations values for the parallel and crossing bridges con gurations are very close. In addition, it is worth noting the time lag between the three accelerations. Contrarily, the maximum lumped mass acceleration of the light bridge of (M st =350 T) has been obtained for the con guration of the parallel bridges with (A st = 11.6 m/sec 2 ), whereas the mass accelerations for the perpendicular and crossing con gurations are hugely smaller and has semi-constant value as shown in gure (45b). Figure (46a) shows the Fourier spectral analyses of the lumped mass velocity of (M st = 1050 T) for the three studied con gurations. The dominant frequency of the parallel con guration (F= 0.827 Hz) dropped to (F= 0.6 Hz) for the crossing con guration and to (F= 0.473 Hz) for the perpendicular con guration. Conversely, for the dominant frequency of the lumped mass of (M st =350 T) shown in gure (46b), the dominant frequencies are constant (F=0.7 Hz) for the three con gurations, but with much smaller amplitude for the perpendicular and crossing con gurations.

Conclusions
An extensive set of detailed 3D numerical analyses have been performed to evaluate the effects of Structure-Soil-Structure-Interaction (SSSI) between three dissimilar neighboring bridges under seismic excitations. The analyses have focused on the impact of the adjacent superstructures lumped masses ratios (200 %, and 300%) on the (SSSI) effect. Moreover, the effects of the prominent factors such as the inter-bridge spacing, and the position of the three neighboring bridges towards each other and towards the seismic loading direction have been investigated. The three-dimensional code (FLAC 3D) based on the nite-difference elements method has been used in the numerical calculations, in which hysteretic damping has been considered for both soil and bridges, and linear assumptions have been put forward for the bridges and non-linear assumptions for the soil behavior to simulate the realistic seismic behaviour of the soil in this rigorous three-dimensional modeling. These numerical analyses have been performed under a real single record, the real record of Turkey (Kocaeli 1999). Further analysis under different earthquake records will be pursued in the future to con rm the conclusions drawn.
The main question of this research is in what situations the seismic Structure-Soil-Structure Interaction (SSSI) effect could be bene cial or detrimental for the individual elements of the system? Furthermore, what are the key factors that may control the degree of multi-structural interactions?
This research has led to the following principal conclusions based on the cases studied: -Intriguingly, the results revealed substantial bene cial effects of (SSSI) between the three dissimilar bridges on both superstructure acceleration and the internal forces induced in the piles, particularly for the case of neighbouring superstructures lumped masses ratio of (300 %). Differently, the (SSSI) effects between two identical bridges (M st = 350 T) has modest effect (rather positive) on the seismic response of the two bridges and the internal forces induced in the piles, according to the results of Alfach and Al Helwani (2019).
-The consideration of (SSSI) effect between dissimilar bridges incites a sharp drop in the superstructure acceleration (up to 90.63 %) for the case of adjacent superstructures masses ratio of (300 %).
-The (SSSI) effect sharply reduce the bending moment and the shear force induced in the piles by (up to 91.18 %) and (up to 91.27 %) respectively for the case of neighbouring superstructures lumped masses ratio of (300 %).
-Substantially, in case of interaction between adjacent different bridges, the level of the (SSSI) effect on the response of the bridges highly depend on the neighboring superstructures lumped mass ratios.
-The inter-bridge spacings have slight effect on the superstructure acceleration by reduction of the closest spacing (up to 6.9 %). Similarly, the bending moment and the shear force decline by (up to 10.47 %) and (up to 14.38 %) respectively, which agrees with the conclusions obtained by Alfach and Al Helwani (2019) for the effect of inter-bridge spacing between two identical bridges of (M st = 350 T).
-Finally, the geometrical position of the bridges towards each other and towards the seismic loading direction has signi cant impact on the seismic behavior of the system, particularly for the light bridges, which is re ected by huge reduction for the crossing at 45 o case of the superstructure acceleration, the bending moment and the shear force by ratios up to (97.46 %), (91.18 %), and (91.27 %) respectively, which agrees with the results of Alfach and Al Helwani (2019) for the interaction between two identical bridges of (M st = 350 T).

Declarations Ethics Declaration
The authors declare that they have no con ict of interest.

Figure 10
Parallel bridges System 3D numerical mesh with adsorbing boundaries (552 structural elements and 41361 nodes)

Figure 11
Distribution of plasticity (red zones) for two single isolated bridges (Mst=350 T) and (Mst=700 T).

Figure 12
Distribution of plasticity (red zones) for different spacing between the three dissimilar bridges (Mst= 350 T, Mst= 700 T,

Figure 13
Three dissimilar parallel bridges: Internal forces at corner pile (7)  Three dissimilar parallel bridges: Masses Accelerations.

Figure 18
Three dissimilar parallel bridges: Fourier spectra diagram.

Figure 29
Parallel bridges System 3D numerical mesh with adsorbing boundaries (552 structural elements and 33072 nodes)

Figure 30
Distribution of plasticity for two single isolated bridges (Mst=350 T) and (Mst=1050 T). Three dissimilar parallel bridges: Internal forces at corner pile (7) of Bridge (1050 T).

Figure 35
Three dissimilar parallel bridges: Internal forces at central pile (2) of Bridge (350 T).

Figure 37
Three dissimilar parallel bridges: Fourier spectra diagram.  Three dissimilar bridges: Internal forces at corner pile (7) of Bridge (1050 T).