Seismic Structure-Soil-Structure Interaction (SSSI) between piled neighboring bridges: Influence of height ratio

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 the (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 has been rarely studied, mainly due to the shortage of experimental or field-based case studies that confirm 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 toward the seismic loading direction.

SSSI has attracted extensive attention in the last decades; most previous research about (SSSI) has generally concentrated on the seismic behavior of neighboring tall buildings and skyscrapers. Nevertheless, there is rather a variance between the findings of these studies in the literature. In the numerical field, Kim [1] has employed a three-dimensional (3D) finite element (FE) 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, USA). Bolisetti and Whittaker [2] performed a series of numerical simulations and centrifuge experiments to assess the seismic effects of (SSSI) on buildings constructed in dense urban environments. They 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. [3] 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 FEs and boundary elements (BE). A thorough series of 2D numerical analyses were carried out by Bybordiani and Arici [4] to study the interaction effect between neighboring 5-, 15-, and 30-story clusters of structures and the surrounding viscoelastic half-space. They investigated the influence of the inter-building distance and the foundation material on the response of the adjacent buildings. The results revealed negligible effects of (SSSI) on the behavior of the identical low-rise structures and significant effects on the response of the identical high-rise structures. In the same manner, Isbiliroglu et al. [5] 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 [6] 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 [7] has conducted a wide (SSSI) analytical parametric study; the effects of mass, height of the superstructures, foundation types, embedment situations, and 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 spacings, Yahyai et al. [8] claimed a detrimental effect of (SSSI) on base shear forces and lateral displacement. Also, detailed numerical analyses for obliquely incident seismic waves were carried out by Álamo et al. [9]. They noted that the inter-building spacing and the seismic loading are crucial for the (SSSI) effects on short identical structures supported by pile foundations. In a related study, Rahgozar [10] has employed the direct method for evaluating the behavior of 3D FE 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. [11] conducted a comprehensive seismic analysis by using a nonlinear 3D FE model to determine the (SSSI) and the ground irregularity effect on the seismic response of nuclear power plants (NPPs). Roy et al. [12] 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 influenced by the existence of nearby heavy structures. Barrios and Chouw [13] performed a physical experimental study by using a sand-filled 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. [14] conducted a comprehensive analytical and numerical study on the (SSSI) effect among multiple foundations (without superstructures). Larkin et al. [15] performed shaking table tests with a laminar box for four neighboring buildings. They denoted that the (SSSI) effects are more evident for neighboring structures with different fundamental frequencies due to the mechanism of energy exchange between them. Ge et al. [16] conducted comprehensive experimental tests and numerical studies to investigate the (SSSI) effect between multiple high-rise buildings. The results revealed beneficial effect of (SSSI) on the acceleration responses of structures and adverse effect on the structures' deformations. Furthermore, two centrifuge tests were performed by Trombetta et al. [17] to assess the (SSSI) effects between midrise elastic shear wall buildings supported by a mat foundation and low-rise inelastic frame buildings built on individual spread footings. Andersen et al. [18] extended the validity of a semi-analytical model predicting ground vibration from rigid rectangular loads to enable it to estimate accurately the effect of heavy masses or plates set either on the ground surface or implanted into the soil. Similarly, Gan et al. [19] carried out 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 [20] employed the FE software (ANSYS) to analyze the (SSSI) effect between the surface structure built on viscoelastic soil layer and the adjacent underground station. The results denoted that the arrangement and the fundamental frequencies of the structures have crucial impact on the (SSSI) effect. Bard et al. [21] conducted extensive experimental, numerical, and theoretical cross-analyses 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 SSSI. Schwan et al. [22] 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 significantly alter the seismic response of both the construction site and the related buildings; also, they quantified the complex (SSSIs) at the city scale. Mason et al. [23] conducted centrifuge tests on two adjacent moment-resisting frame steel structures. The first 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 was carried out by Ngo et al. [24] to investigate the (SSSI) effects on the behavior of two adjacent structures with different mass, natural frequency, and height. Extensive numerical analyses were conducted by Alam and Kim [25] 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 [26] employed a novel 3D technology to investigate the (SSSI) effect between a tunnel, the soil, and existing structures. The building models were printed with brittle material behavior similar to masonry and tested in a geotechnical centrifuge. A thorough series of numerical analyses were conducted by Alfach [27] to examine the effect of the plan positioning of bridges toward the seismic excitation direction and inter-bridge spacing of three dissimilar adjacent bridges supported by a group of piles embedded in nonlinear clay. Knappett et al. [28] examined the seismic performance of an isolated structure and adjacent (similar and dissimilar) structures under a series of strong seismic excitations. The nonlinear dynamic centrifuge tests were accurately validated by a comprehensive nonlinear FE model. Furthermore, Ada et al. [29] investigated the (SSSI) effect between two neighboring frame structures through a series of 3D numerical analysis. They examined the influences 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 that the (SSSI) effect depended highly on the dynamic characteristics of the adjacent structures. Vicencio et al. [30] have discussed the pros and cons of the leading developments of (SSSI) and site–city interaction (SCI) effects with focusing on the theoretical idealization of SSSI by means of low-fidelity models with comparable predictive accuracy. Ghasemzadeh and Alibeikloo [31] developed a simple analytical solution for computing the dynamic interaction tensor for floating pile groups with batter piles. The governing differential equations were derived for an unloaded batter floating pile closely spaced to another loaded pile with the same properties. Asgarian et al. [32] studied the dynamic response of pile-supported structures by comparing the experimental and numerical dynamic responses of a prototype jacket offshore platform. Ghasemzadeh et al. [33] examined the effects of batter angle, slenderness ratio, spacing between piles, pile–soil stiffness ratio, and soil plasticity on pile–soil–pile interaction factors.

The following numerical simulations have been carried out for several configurations of three dissimilar bridges for two superstructure mass ratios (200% and 300%). The impact of two essential factors has been examined: 1) inter-bridge spacing and 2) the geometric position of neighboring structures toward each other and the seismic loading direction (parallel, perpendicular, crossing) configurations for the above-stated mass ratios.

3.1

Three bridges with superstructure mass ratio (200%)

3.1.1

Effect of inter-bridge spacing

The effect of 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 (Figure 2b) located between two lighter bridges with a superstructure mass of M_st = 350 t (Figure 2a). The numerical calculations were undertaken for a range of distances between the bridges, precisely S = 20, 30, and 40 m. All the geometrical and mechanical characteristics of soil and concrete mentioned in section 2.1 and Tables 1–3 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 Figure 10 includes 4176 zones of eight node solid elements and 552 3D structural elements of two node beam elements.

Figure 10:

3.1.1.1 Results and Discussion

The spread of plasticity in the soil for the two isolated bridges (M_st = 350 and 700 t) is presented in Figure 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, Figure 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).

Figure 10:

Figure 11:

The plasticity spread in the soil has slightly reduced with the increase of inter-bridge spacing as shown in Figure 11. However, plasticity dominated the comportment of the upper part of the soil (C = 150 kPa), while the behavior of the lower part stayed mostly elastic because plasticity started at the soil surface and extended gradually toward the base without attaining the base during the seismic loading time.

Table 7 indicates an important positive effect of (SSSI) on both superstructure acceleration and the internal forces induced in the piles. The mass acceleration of the light bridge (M_st = 350 t) drops sharply (up to 53.28%) due to the (SSSI) effect; similarly, the mass acceleration of the heavy bridge (M_st= 700) decreases by up to 50%. In the same manner, the cap acceleration of the heavy bridge (M_st = 700 t) and the light bridge (M_st = 350 t) reduces by up to 61.2%, and 54%, respectively. Regarding the impact of SSSI on the internal forces induced in the piles, the bending moment and the shear force induced in the piles of the heavy bridge (M_st = 700 t) reduced by up to 31.5% and 12%, respectively, as illustrated in Figures 12 and 13. Similarly, Figures 14 and 15 show a comparable effect of (SSSI) on the piles of the light bridge (M_st = 350 t) by decreasing the bending moment and the shear force by up to 16.6% and 20.6%, 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 significant diminution of both. Table 7 and Figures 12–15 demonstrate the slight influence of the inter-bridge spacing on the internal forces provoked in the piles of the three bridges, which is in accordance with the results of Alfach and Al Helwani [34] and Alfach [35] 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 increase 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 increase in inter-bridge spacing as found in Figure 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 Figures 14 and 15.

Table 7:

Influence of the spacing inter-bridge on the seismic response of three dissimilar parallel bridges system.

S (m)	ast (m/s2)		acap (m/s2)		Internal forces
					Central piles				Corner piles
					Pile (2) (Mst = 350 t)		Pile (16) (Mst = 700 t)		Pile (1) (Mst = 350 t)		Pile (7) (Mst = 700 t)
					Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)
One bridge (Mst = 350 t and S = 0)	23.02		14.39		2244	1218			2189	1604
One bridge (Mst = 700 t and S = 0)	18.09		14.9				1640	1134			1732	1233
S (m)	Bridge (Mst = 350 t)		Bridge (Mst = 700 t)		Three dissimilar parallel bridges
	ast	acap	ast	acap	Pile (2) (Mst = 350 t)		Pile (16) (Mst = 700 t)		Pile (1) (Mst = 350 t)		Pile (7) (Mst = 700 t)
20	11.5	6.61	8.45	5.78	1981	1169	1123	998	1824	1310	1218	1090
30	11.8	6.88	8.63	5.94	2021	1200	1156	1006	1870	1273	1222	1118
40	12	7.1	8.81	6.05	2035	1242	1176	1037	1935	1361	1278	1157

Figure 12:

Figure 13:

Figure 14:

Figure 15:

Figure 16:

In the frequency domain, Figure 17a compares the three dominant frequencies of the mass of the heavy bridge of M_st = 700 t for the configuration of three adjacent bridges for three inter-bridge spacings (S = 20, 30, and 40 m) with the dominant frequency of the isolated bridge of M_st = 700 t. The dominant frequency peak (F = 0.732 Hz) of the isolated bridge of M_st = 700 t drops to F = 0.7 Hz for the configuration of three neighboring bridges. Likewise, for the light bridge (M_st = 350 t), Figure 17b shows that the dominant frequency decreases from F = 0.709 Hz for the isolated bridge to F = 0.6 Hz for the case of adjacent three bridges for the three aforementioned inter-bridge spacings.

Figure 17:

3.1.2

Effect of bridge plan alignment with respect to each other and the seismic loading direction

Three combinations of bridges with respect to the direction of seismic excitations composed of three dissimilar configurations (parallel, perpendicular, and crossing) have been considered for the above-mentioned heavy bridge of M_st = 700 t and light bridge of M_st = 350 t. An extensive series of numerical calculations were carried out on the three mentioned configurations of parallel, perpendicular, and crossing bridges to evaluate the influence of the direction of the bridges toward each other and toward the seismic loading direction on the (SSSI) effects. The numerical analyses were performed for an inter-bridge spacing of S = 20 m and under the seismic record of Turkey (Kocaeli, 1999) presented in Figure 3. Furthermore, the mechanical and geometrical properties shown in Figure 1 and Tables 1–3 have been used in these calculations. The adopted mesh for perpendicular and crossing configurations displayed in Figures 18 and 19, respectively, includes 77,990 nodes and 552 beam structural elements of two nodes.

Figure 18:

Figure 19:

3.1.2.1 Results and discussion

Figure 20 demonstrates the deep extension of the plasticity under the perpendicular isolated bridge of M_st = 350 t; differently, the plasticity prolongation was substantially smaller for the heavy isolated bridge of M_st = 700 t. Similarly, the plasticity zones under the light bridges of M_st = 350 t and the heavy bridge of M_st = 700 t reduced significantly for the perpendicular and crossing configurations presented in Figure 21. Nevertheless, the plasticity prolonged and attained the soil base under the heavy bridge of M_st = 700 t for the crossing bridges' configuration.

Figure 20:

Figure 21:

Table 8 and Figures 22–26 demonstrate the key constructive role of (SSSI) on the seismic behavior of the neighboring bridges. Both superstructure acceleration and the piles' internal force reduced significantly under the crucial impact of (SSSI). Concerning the acceleration of the superstructure, the mass and cap accelerations of the light bridge of M_st = 350 t decreased considerably (up to 42.8% and 42.5%, respectively). Correspondingly, the mass and cap accelerations of the heavy bridge of M_st = 700 t reduced drastically (by up to 58.8% and 53.72%, respectively). The beneficial impact of (SSSI) on the piles’ internal forces was much pronounced through very large reduction of the bending moment and the shear force of the light bridge of M_st = 350 t by up to 88.49% and 88.7%, respectively. Similarly, but by smaller ratios, the bending moment and the shear force of the heavy bridge (M_st = 700 t) dropped by up to 44.53% and 74.2%, respectively.

Table 8:

Influence of different positioning of three dissimilar bridges on the seismic response system.

Position	ast (m/s2)		acap (m/s2)		Internal forces
					Central piles				Corner piles
					Pile (2) (Mst = 350 t)		Pile (15) (Mst = 700 t)		Pile (1) (Mst = 350 t)		Pile (7) (Mst = 700 t)
					Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)
One perpendicular bridge (Mst = 350 t)	20.1		11.5		3979	1268			4093	1330
One perpendicular bridge (Mst = 700 t)	20.53		12.49				2196	1325			2061	1294
Position	Bridge (Mst = 350 t)		Bridge (Mst = 700 t)		Three dissimilar bridges
	ast	acap	ast	acap	Pile (2) (Mst = 350 t)		Pile (15) (Mst = 700 t)		Pile (1) (Mst = 350 t)		Pile (7) (Mst = 700 t)
Parallel	11.5	6.61	8.45	5.78	1981	1169	1218	1090	1890	1309	1218	1090
Perpendicular	0.54	6.52	1.83	1.44	501.9	155.4	1508	363.1	490.4	161.2	1438	328.6
Crossing	0.53	6.47	2.46	1.34	457.8	143.2	1367	545	478.7	159.6	1367	545.2

Figure 22:

Figure 23:

Figure 24:

Figure 25:

Figure 26:

In terms of the pile's internal forces, the minimum bending moments induced in piles (1) and (2) of the light bridge of M_st =350 t were reported in the configuration of crossing bridges with M_min1 = 478.7 kN m and M_min2 = 457.8 kN m accompanied by the minimum shear forces (T_min1 = 159.6 kN and T_min2 = 143.2 kN) as found in Figures 24 and 25. Moreover, the internal forces induced in piles (1) and (2) were very close for the configurations of perpendicular and crossing bridges as shown in Table 8 and Figures 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 configuration. 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 Figures 22 and 23. It is noteworthy that the minimum accelerations in the superstructure elements (mass [A_st = 0.53 m/s²] and cap [A_cap = 6.47 m/s²]) have been observed in the case of crossing bridge configuration for the light bridge of M_st = 350 t as depicted in Figure 26.

Similarly, the best impact of (SSSI) on the cap acceleration was noted for the minimum cap acceleration of the heavy bridge of M_st = 700 t, which attained A_cap = 1.34 m/s² for the configuration of the crossing bridges, agreeing 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 was obtained for the perpendicular configuration with A_st = 1.83 m/s² as shown in Figure 26a. It is pertinent to note that the perpendicular and crossing configurations have an uncommon impact on the vibration of the superstructure of the light bridge of M_st = 350 t, which was represented by generating bigger accelerations in the cap by A_cap = 6.52 and 6.47 m/s² accompanied by much smaller accelerations in the mass (A_st = 0.54 and 0.53 m/s²). 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 bridges with the three studied configurations (parallel, perpendicular, and crossing). The maximum dominant frequency (F = 0.7 Hz) was obtained for the parallel bridge configuration, while the dominant frequencies of the crossing and perpendicular bridges' configurations 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 configuration 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 Figure 27b.

Figure 27:

3.2

Two bridges with superstructure mass ratio (300%)

3.2.1

Effect of inter-bridge spacing

A set of numerical analyses have been carried out to examine the influence 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 Figure 2a and for the heavy bridge of M_st = 1050 t as shown in Figure 2c 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 of precisely S = 20, 30, and 40 m. Figure 28 reveals the 3D meshed model used in the analyses.

Figure 28:

3.2.1.1 Results and discussion

Predictably, the soil plasticity under the isolated heavy bridge of M_st = 1050 t has been prolonged deeper than the one under the isolated light bridge of M_st = 350 t, except under the cap limits of the light bridge in the x-direction, where the plasticity extended to about two-thirds of the soil depth as shown in Figure 29. However, the (SSSI) effect resulting from the interaction between the three dissimilar bridges has considerably changed the plasticity extension under the three bridges as illustrated in Figure 30. The plasticity prolongation in the zones under the light bridges of M_st = 350 t is much deeper than the one under the central heavy bridge of M_st = 1050 t. Furthermore, Figure 30 reflects the negligible impact of the inter-bridge spacing on plasticizing of the soil. Furthermore, Figure 30 reflects the negligible impact of the inter-bridge spacing on plasticizing of the soil. Table 9 reveals the valuable effect of (SSSI) on both acceleration of the superstructure and the internal forces induced in the piles. In further detail, the mass accelerations of the heavy bridge of M_st = 1050 t and the light bridge of M_st = 350 t dropped sharply by 71.8% and 42.28%, respectively. Similarly, the bending moment induced in the piles of the heavy bridge (M_st = 1050 t) and light bridge (M_st = 350 t) decreased considerably by 42.6% and 52.8%, respectively. In a similar manner, the shear force induced in the piles of the heavy bridge significantly reduced by 77.7% and by a much inferior ratio for piles of the light bridge (7%). A slight effect of the inter-bridge spacing is highlighted in Table 9 and Figures 31a–34a. More precisely, the bending moment provoked in the piles of the heavy and light bridges increased by 10.47% and 7.17%, respectively, with the inter-bridge spacing increase. Similarly, the shear force induced in the piles of the heavy and light bridges increased by 7.2% and 14.38%, respectively, with augmentation of the inter-bridge spacing, as shown in Figures 31b–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 was obtained in the central part of the piles.

Figure 29:

Figure 30:

Table 9:

Influence of inter-bridge spacing on the seismic response of three dissimilar parallel bridges system

S (m)	ast (m/s2)		acap (m/s2)		Internal forces
					Central piles				Corner piles
					Pile (2) (Mst = 350 t)		Pile (15) (Mst = 1050 t)		Pile (1) (Mst = 350 t)		Pile (7) (Mst = 1050 t)
					Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)
One bridge (Mst = 350 t and S = 0)	20.1		11.5		3979	1268			4093	1330
One bridge (Mst = 1050 t and S = 0)	20.53		12.49				2196	1325			2061	1294
S (m)	Bridge (Mst = 350 t)		Bridge (Mst = 1050 t)		Three dissimilar bridges
	Ast	acap	Ast	acap	Pile (2) (Mst = 350 t)		Pile (15) (Mst = 1050 t)		Pile (1) (Mst = 350 t)		Pile (7) (Mst = 1050 t)
20 m	11.6	11.6	5.78	4.58	2091	1189	1260	294.8	1929	1236	1496	426.3
30 m	12.1	12.2	5.95	4.79	2166	1271	1322	305.4	1969	1283	1517	428
40 m	12.7	12.7	6.15	5.12	2241	1360	1392	316	2017	1333	1552	433

Figure 31:

Figure 32:

Figure 33:

Figure 34:

Similarly, the shear force induced in the corner piles of the bridge (M_st = 350 t) decreased by 4.96% with an increase of inter-bridge spacing as described in Figure 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 varied marginally (up to 11%) without showing an evident trend as shown in Table 9 and Figures 33 and 34. It is worth noting that the maximum bending induced in the piles of the bridge of M_st = 350 t was in the central part of the piles according to Figures 33a and 34a, while all the other internal forces were obtained in the heads of the pile as shown in Figures 33b and 34b.

Spectral velocity analyses of Fourier presented in Figure 36 exhibit a negligible effect of inter-bridge spacing on the dominant frequencies for the studied spacing of S = 20, 30, and 40 m between the three bridges. The dominant frequency was almost constant (F = 0.827 Hz for the heavy bridge of M_st = 1050 t and F = 0.709 Hz for the light bridge of M_st = 350 t).

Figure 35:

Figure 36:

3.2.2

Effect of bridge plan alignment with respect to each other and the seismic loading direction

Two additional numerical analyses were carried out to examine the effect of the perpendicular and crossing bridges configurations on the overall effect of 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 Figures 37 and 38. The numerical analyses were conducted under the seismic loading record of Turkey (Kocaeli, 1999). The employed mesh shown in Figures 37 and 38 includes 8104 zones of eight nodes and 690 3D structural elements of two nodes. Unpredictably, the plasticity under the isolated light perpendicular bridge of M_st = 350 t prolonged heavily and deeply to the base of the soil, whereas the plasticity spread was substantially smaller under the central portion of the cap of the heavy perpendicular bridge of M_st = 1050 t, as illustrated in Figure 39. The interaction between the three bridges incited a substantial change in plasticity extension through the soil. The interaction between the three bridges shown in Figure 40a reduced the plasticity under the heavy bridge of M_st = 1050 t considerably, with a slight effect on the zones under the light bridge of M_st = 350 t and inter-bridge zones. Moreover, Figure 40b shows that the plasticity extension almost vanished under the three bridges in the case of interaction between three perpendicular bridges, but it increased considerably under the heavy bridge for the crossing configuration as shown in Figure 40c. Table 10 elucidates the valuable impact of (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 hugely reduced by 86.3% and 90.63%, respectively. Similarly, the mass and cap accelerations of the light bridge considerably dropped by 97.46% and 45.2%, respectively. Moreover, the (SSSI) effects incited a substantial decline in the bending moment and shear force in the piles of the heavy bridge by up to 52.55% and 78.6%, respectively. Similarly, for the piles of the light bridge, the bending moment and the shear force hugely decreased due to the (SSSI) effects by up to 91.18% and 91.27%, respectively.

Figure 37:

Figure 38:

Figure 39:

Figure 40:

Table 10:

Influence of different positioning of three dissimilar bridges on the seismic response system.

Position	ast (m/s2)		acap (m/s2)		Internal forces
					Central piles				Corner piles
					Pile (2) (Mst = 350 t)		Pile (15) (Mst = 1050 t)		Pile (1) (Mst = 350 t)		Pile (7) (Mst = 1050 t)
					Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)	Mmax (kN m)	Tmax (kN)
One perpendicular bridge (Mst = 350 t)	20.1		11.5		3979	1268			4093	1330
One perpendicular bridge (Mst = 1050 t)	20.53		12.49				2196	1325			2061	1294
Position	Bridge (Mst = 350 t)		Bridge (Mst = 1050 t)		Three dissimilar bridges
	ast	acap	ast	acap	Pile (2) (Mst = 350 t)		Pile (15) (Mst = 1050 t)		Pile (1) (Mst = 350 t)		Pile (7) (Mst = 1050 t)
Parallel	11.6	11.6	5.78	4.58	2091	1189	1260	294.8	1929	1236	1496	426.3
Perpendicular	0.54	6.47	2.81	1.17	411.8	113.4	1580	282.7	388	130.5	1578	456.2
Crossing	0.51	6.3	5.67	2.39	370.2	110.6	1042	589.7	360.8	123.2	2412	1274

The minimum internal forces (bending moment and shear force) induced in the corner pile (7) of the heavy bridge of M_st = 1050 T have been obtained for the parallel bridge configurations with a bending moment of M_min = 1496 kN m and a shear force of T_min = 426.3 kN as shown in Table 10 and Figure 41. Whereas the maximum bending moment (M_max = 2412 kN m) and the maximum shear force (T_max = 1274 kN) have been obtained in the case of crossing bridge configuration. Alongside, the minimum accelerations of the superstructure (mass and cap) accompanied by minimum shear force in the central pile (15) of the heavy bridge (M_st = 1050 t) occurred in the case of perpendicular bridges configuration as shown in Table 10 and Figure 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 configuration changing between parallel, perpendicular, and crossing configurations, while the configuration change of the bridges has a bigger influence on the superstructure acceleration by variation of up to 74.45% as shown in Table 10.

Figure 41:

On the contrary, 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 were achieved for the configuration of crossing bridges as shown in Table 10 and Figures 43 and 44. Precisely, the minimum bending moment (M_min = 360.8 kN m) was obtained in the corner pile (1), while the minimum shear force (T_min = 110.6 kN) was obtained in the central pile (2). Moreover, the minimum superstructure accelerations were also gained for the crossing configuration with mass and cap accelerations of A_st = 0.51 m/s² and A_cap = 6.3 m/s², respectively. It is worth noting that the mass accelerations of the light bridges for the perpendicular and crossing configurations were hugely smaller than the cap accelerations. Table 10 indicates an evident tendency to a significant drop in the superstructure acceleration, bending moment, and shear force by up to 95.6%, 82.3%, and 90.69%, respectively, with the bridge configuration change starting from parallel to perpendicular and finally crossing bridges.

Figure 42:

Figure 43:

Figure 44:

Table 10 and Figure 45a reveal a significant drop in the acceleration of the lumped mass of the heavy bridge of M_st = 1050 t with A_st = 2.81 m/s² in the case of perpendicular bridges configuration, while the mass acceleration values for the parallel and crossing bridges configurations are very close. In addition, the time lag between the three accelerations is worth noting. On the contrary, the maximum lumped mass acceleration of the light bridge of M_st = 350 t was obtained for the configuration of parallel bridges with A_st = 11.6 m/s², whereas the mass accelerations for the perpendicular and crossing configurations were hugely smaller and had a semi-constant value as shown in Figure 45b. Figure 46a shows the Fourier spectral analyses of the lumped mass velocity of M_st = 1050 t for the three studied configurations. The dominant frequency of the parallel configuration F = 0.827 Hz dropped to F = 0.6 Hz for the crossing configuration and to F = 0.473 Hz for the perpendicular configuration. Conversely, for the dominant frequency of the lumped mass of M_st = 350 T shown in Figure 46b, the dominant frequencies were constant (F = 0.7 Hz) for the three configurations, but with much smaller amplitude for the perpendicular and crossing configurations.

Figure 45:

Figure 46:

An extensive set of detailed 3D numerical analyses have been performed to evaluate the effects of SSSI between three dissimilar neighboring bridges under seismic excitations. The analyses have focused on the impact of the adjacent superstructures' lumped mass ratios (200% and 300%) on the (SSSI) effect. Moreover, the effects of prominent factors such as the inter-bridge spacing and the position of the three neighboring bridges toward each other and toward the seismic loading direction have been investigated. The 3D code (FLAC 3D) based on the finite 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 nonlinear assumptions for the soil behavior to simulate the realistic seismic behavior of the soil in this rigorous 3D modeling. These numerical analyses have been performed under a real single record of Turkey (Kocaeli, 1999). Further analysis under different earthquake records will be pursued in the future to confirm the conclusions drawn.

The main question of this research is in what situations the seismic SSSI effect could be beneficial 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 beneficial 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 neighboring superstructures' lumped mass ratio of 300%. Differently, the (SSSI) effects between two identical bridges (M_st = 350 t) had 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).