Three-Dimensional Simulation of Seismic Structure–Soil–Structure Interaction for Mid-Rise Buildings near Dense Shallow Sloping Soils Under the Impact of 6 February 2023 Kahramanmaraş-Pazarcık Earthquake

Abstract

During a seismic movement, each wave field incoming to a foundation by reflecting from the surroundings causes amplification. Therefore, the seismic response of any building is affected by both the topography and the adjacent building. In this study, the effect of the adjacent building on the seismic performance of a building located near a shallow slope is numerically assessed. In the adopted three-dimensional finite element simulation, nonlinear variation of soil stiffness and hysteretic damping, elastoplastic behaviour of the superstructure frame system showing significant deviations from linear behaviour beyond the limits of elastic behaviour and varying distances between the foundation edge and the adjacent building were employed. Two identical 10-storey moment-resisting buildings, 40 m thick dense clayey sand, and a 5 m high shallow slope were considered as a reference model and simulated using the direct method in the time domain. The seismic performance of the building was studied at a distance equal to the height of the slope from the crest. The results of the analyses represent an interaction in which both shallow slope and adjacent building effects are observed together. Incremental structure–soil–structure interaction effect, on the one hand, created additional shear stresses on the shallow slope and enhanced the foundation rocking of the building. On the other hand, as a natural result of dynamic cross-interaction, it resulted in a reduction in the maximum acceleration value captured at the foundation, a drop in the base shear demand, and a large change in the maximum storey displacements at the lower floors. As a result of these cases, storey drifts increased. The results highlighted that the structure–soil–structure interaction cannot be neglected in the presence of a slope.

1. Introduction

In seismic events, structural displacements and ground displacements are not completely independent of each other. The soil response influences the motion of the structure, and the motion of the structure influences the soil response. This phenomenon is called a soil–structure interaction (SSI). It is known that the local site effect can cause significant changes in the seismic behaviour of the superstructure depending on the SSI [1,2]. When there is more than one structure in the site, the soil–structure problem becomes a cross-interaction problem between multiple structures due to the interaction of structural responses with the soil. It was Luco and Contesse [3] who first introduced the definition of structure–soil–structure interaction (SSSI) for this study area. In the SSSI case, each foundation that diffracts the incident wave field can be regarded as a disturbance producing a secondary wave field affecting the adjacent ones [4]. In this direction, this leads to lengthening in the natural period of the system and a reduction in the structural demand compared to SSI. Although most of the studies on SSSI focus on the effects of structures on each other on flat terrains, the damage to structures located near artificial or natural slopes during strong ground motion necessitates a detailed examination of the combined effects of SSSI with topography. It has been proven by various researchers that the presence of a shallow slope in the environment plays an important role in modifying the seismic response of the structure near the slope [5,6]. The additional stresses induced in the slope by the superstructure with the changing centre of gravity in a seismic event can develop a large amount of shear stress in the soil under the foundation and subsequently result in significant foundation deformation and rocking of the superstructure. In this case, a system with sloping soil will experience an elongation of the natural period and deterioration of the seismic performance of the superstructure. In addition, previous studies also emphasise that there is no reduction in soil bearing capacity sufficiently far from the slope [7,8]. In a seismic event, inelastic structural behaviour is more accurately predicted by the performance-based design (PBD) approach, which considers the displacements of structural elements [9]. The damage parameters, such as storey shear demands, inter-storey drifts, and lateral displacements, are the performance objectives obtained by the PBD approach. IBC 2006 [10] reported that transient storey drifts should not exceed 2% in order to avoid drift failures in buildings during strong ground motions. Although both the problem of cross-interaction between structures and the superstructure seismic response located near a shallow slope have been much discussed by different researchers in different studies, the study of multiple structures together on non-flat soils has received much less attention from researchers. For example, multiple mid-rise buildings built near to slopes, including in the provinces within the region affected by the Kahramanmaraş-Pazarcık earthquake that occurred in the south of Turkey on 6 February 2023, shown in Figure 1, are frequently encountered in large cities due to increasing populations and the scarcity of flat land. For this reason, it is a necessity to consider multiple structures located on sloping soils together within the scope of structure–soil interactions and to accurately reveal their effect on the superstructure seismic performance.

Shabani et al. [11] investigated the seismic behaviour of superstructures at the crest and heel of a slope and calculated larger acceleration values near the slope crest. Sucasaca and Saez [12] investigated the dynamic interaction of buildings on a slope close to the coastline; they concluded that a cautious approach should be taken to the design of low-rise buildings located behind deep excavations and near slope crests. Shamsi et al. [13] examined the earthquake performance of low- and medium-storey building groups located close to the slope crest and found that the heavier and taller the similar building group located near the slope crest, the more damage the building closest to the slope will be exposed to. Considering the studies on the subject, SSSI was investigated only by changing the number of buildings, and as a result of the studies, it was argued that SSSI can be neglected in the presence of a slope, whereas the presence of more than one building in the medium makes cross-interaction inevitable.

Thus, in the present study, three-dimensional numerical models consisting of a mid-rise building near the top of a shallow slope and a second identical building at varying distances from this building, which is exposed to the shallow slope effect in any case, were developed using the PLAXIS 3D V19 [14] software. These models allowed a detailed evaluation and comparison of SSI and SSSI subjected to slope effects. The nonlinear behaviour of the sloping soil and superstructures during seismic motion was taken into account, and the system was modelled and analysed in a single step using the direct method. The static and seismic stability analysis of the slope was performed by adopting a strength-reduction method and a time-history analysis, respectively. In the simulations, the acceleration–time record of the 7.7 Mw Kahramanmaraş-Pazarcık earthquake, one of the most destructive earthquakes in the world, which occurred in the south of Turkey in February 2023, was used, and data from a soil investigation report for the Kahramanmaraş-Pazarcık area were utilised. The results of the study are presented comparatively in terms of slope deformations, frequency response of the building nearest to the slope, rocking, and the objectives of the PBD approach (shear demands, storey displacements, and drifts). The combined effects of SSSI with a shallow slope are investigated carefully and in detail.

2. Site Investigations and Laboratory Tests

Geophysical studies are conducted to determine the elastic and dynamic parameters of the soil in the study area. A multi-channel analysis of surface waves (MASW) technique is used for S-type seismic velocity analysis. The method is based on the principle of analysing the Rayleigh-type surface waves present in the P-type field record by separating them into plane-wave components. The dispersion curve is determined from the phase velocity–frequency spectrum obtained as a result of the analysis, and an initial model is followed by iterative generation of the resulting S-type velocity–depth model. It is an effective way of obtaining shear wave calculations, which are an indicator of soil strength. The V_s30 value and the detection of thin layers can be calculated accurately with the MASW technique, one of the surface wave analysis methods. The Vs-Vp vertical velocity section and dynamic-elastic parameters of the soil are presented in Figure 2. Drilling and field studies are carried out for soil sampling and surface geological studies. In a total of 2 boreholes drilled to determine the type and stratigraphy of the soils in the study area, the distribution of soil properties according to depth is determined, as shown in Figure 2b; 0.00–2.00 m as fill and 2.00–20.00 m as dense clayey sand unit. In the drilling works carried out in the study area, a depth of 20 m is reached, and no groundwater is encountered. The test results on the samples taken from the borings drilled in the study area are presented in

Table 1. Laboratory test results of the soil sample.

Sample No	Depth (m)	No 4 Remaining %	No 200 Passing %	Liquid Limit %	Plastic Limit %	Plasticity Index %	Cohesion (c) kPa	Friction Angle (Φ) degree	Classification (USCS)	Unit Weight kN/m3
1	7.5	22.4	46.2	32.6	16.5	16.1	56.6	14.37	SC	19.17

.

3. Numerical Model

3.1. Superstructure and Foundation

In this study, a 30 m high 10-storey reinforced concrete moment-resisting building model was selected to represent mid-rise buildings that can be frequently seen in cities. In order to increase the number of buildings exposed to the slope effect, three 4 m openings in the direction of the slope extension and two 3 m openings in the opposite direction were utilized. The openings and storey height in the modelled building are 3 m each. The building frame was planned using SAP 2000 V14 [15], in accordance with the relevant building standards, EN 1992-1-1 and EN 206-1 [16,17]. Gravity loads, including dead load 7.5 kPa (6 kPa for the weight of roofs and 1.5 kPa for the weight of partitions) and live load 2 kPa corresponding to residential buildings in accordance with the recommendations in Eurocode 1 [18], were considered at each floor. Since the ratio of the ultimate load (i.e., 122.91 MN) to the building gravity load (i.e., 20.6 MN), which is 5.97, is the ratio of the ultimate load that the building foundation can support according to Hansen’s method [19] and is considerably greater than the required minimum factor of safety (FOS) 3, it is understood that the designed foundation is suitable. The designed foundation and building were modelled in the IdeCAD V10 [20] program and analysed in accordance with IBC 2006 [10], and all necessary safety conditions were provided. A similar building model has been adopted in some studies on SSI analysis [21,22]. The model of the superstructures and the reinforcing bars per unit length of reinforced concrete elements are shown in Figure 3. Rust covers were calculated as 2.5 cm and 1.5 cm for columns and slabs, respectively. The material properties used in reinforced concrete elements are summarised in

Table 2. Characteristics of reinforced concrete elements.

Compressive Strength of Concrete (fck) (MPa)	Elasticity of Concrete (Ec) (MPa)	Rebar Yield Strength (fyd) (MPa)	Elasticity of Steel (Es) (MPa)
30	17,143	435	210,000

.

In this study, reinforced concrete elements are modelled using frame elements. Reinforced concrete moment-resisting buildings withstand the incoming lateral forces with their ductility. Reinforced concrete elements continue to absorb energy by displaying plastic behaviour at stresses above elastic limits and can overcome structural failures. Accordingly, reinforced concrete elements were defined as elastoplastic (M-κ) to model the nonlinear behaviour of buildings. The behaviour of reinforced concrete elements under bending effect is typically defined through the moment–curvature relationship. The bending behaviour of a reinforced concrete section is defined using a user-defined M-κ diagram; curvature (κ), is specified in the unit of length and moment (M), in the unit of force times length per unit of width [23]. In an M-κ diagram, the behaviour of a reinforced concrete section under bending effect is described by means of several point identifications (Figure 4a). The moment at which rupture occurs defines the first point. The moment at which yielding of the rebar occurs defines the second point, and the moment at which the concrete material begins to yield defines the third point. The last point represents the failure [24]. Failure occurs, according to Eurocode 2 [16], at a concrete strain of 3.5‰. The points calculated in reinforced concrete elements are presented in

Table 3. Structural properties of reinforced concrete elements.

Specific Points	Parameters	Building Columns	Floor Slabs
Rupture moment	Moment (kN-m)	143.47	53.45
	Curvature (1/m)	0.0004	0.0012
Yielding of rebar	Moment (kN-m)	2084.50	162.82
	Curvature (1/m)	0.0083	0.0194
Concrete yielding	Moment (kN-m)	2301.20	166.27
	Curvature (1/m)	0.0098	0.0256
Failure	Moment (kN-m)	1992.83	171.46
	Curvature (1/m)	0.0131	0.0768

. Figure 4 indicates that the slopes between the points in the moment–curvature diagrams of reinforced concrete sections create more curvature with less additional moment beginning from the first slope. In this case, it can be inferred that the bending stiffness of reinforced concrete elements decreases under the effect of increasing moment. As can be seen in Figure 4a, since there is no axial force in reinforced concrete lateral elements, a more ductile behaviour will develop. In columns (Figure 4b), although the axial force increases the moment capacity to some extent, both ductility and capacity will decrease afterwards. The requirement that the columns used in earthquake-resistant structural design should be stronger than the beams was also realised in this way.

The structural damping is simulated using Rayleigh damping [25]. For the reinforced concrete structure, two target frequencies corresponding to the first vibration mode (f₁ = 1.07 Hz) and the second vibration mode (f₂ = 3.42 Hz) in the earthquake shaking direction of the structure in a damping ratio of 5% were used, in accordance with the recommendations in Eurocode 8 [26]. Figure 5 demonstrates the change of damping ratio with frequency for the model building. As can be seen in Figure 5, the damping ratios achieved along the two target frequency ranges calculated are very similar. Furthermore, the interface element was assigned to the contact surface between the soil and the shallow foundation, and the interface strength reduction factor (R_inter) was defined. The interface element reduction factor was defined as 0.75 in light of the information given in previous studies in order to capture the possible decrease in the strength of the soil interacting with the building foundation in the static state and during seismic motion compared to the nearby soil [27,28,29].

3.2. Substructure Characteristic

Soil exhibits hysteretic behaviour at small stresses and plastic behaviour at large stresses. It is important to define this behaviour of the soil in order to predict the seismic response of the system exactly. Therefore, a hardening soil small (HSsmall) model [30] is adopted in the present study. The HSsmall model can accurately simulate the depth-varying strength of the soil deposit and the hysteretic behaviour of the clayey sand [31]. Figure 6 exhibits the damping ratio curve and the normalized tangent shear modulus reduction curve for the soil deposit at the small strain range (10⁻³% ≤ γ_c ≤ 10⁰%). To determine the soil–structure interaction effects, it is necessary to identify the natural vibration frequencies of the soil and superstructure [32]. In this context, soil natural vibration frequencies are also determined in the current study. The Rayleigh method was used to estimate the soil damping, as in the case of superstructure damping. Whereas Rayleigh damping is frequency dependent in the superstructure, it is almost frequency independent in the soil [33]. Therefore, the ξ has been assumed to be 0.5% in this study. The first and second natural vibration frequencies of the soil were calculated as 3.44 Hz and 17.19 Hz, respectively, with the second natural vibration frequency being 5 times the first natural vibration frequency, in accordance with previous studies on SSI analysis [11,34]. The change of damping ratio with frequency for the soil deposit is shown in Figure 5. It can be seen in Figure 5 that the critical frequency range obtained for the soil deposit is wider than the critical frequency range obtained for the structures.

The soil parameters used in this numerical model are obtained from a soil investigation report of the Kahramanmaraş-Pazarcık area. In the numerical models, the 40 m deep soil sitting on strong bedrock is simulated. No groundwater was encountered during the works carried out in the field. The soil deposit has a unit weight of 19.17 kN/m³ and an average shear wave velocity of 550 m/s. In addition, the cohesion (c), friction angle (ϕ), and Poisson’s ratio (υ) of the soil in the drained condition are taken as 56.6 kPa, 14.37°, and 0.30, respectively. Soil parameters according to the soil investigation report are presented in

Table 4. Soil parameters according to soil investigation report.

Failure Parameters		Basic Parameters		Advanced Parameters
Cohesion (c) (kN/m2)	56.60	$E_{50}^{ref}$: Secant stiffness (kN/m2)	332,000	$E_{ur}^{ref}$: Unloading/reloading stiffness (kN/m2)	995,000
Friction angle (Φ) (°)	14.37	$E_{oed}^{ref}$: Tangent stiffness for primary oedometer loading (kN/m2)	332,000	vur: Poisson’s ratio for unloading–reloading	0.30
Dilatancy angle (ω) (°)	-	m: Power for stress-level dependency of stiffness	0.5	pref: Reference stress for stiffnesses (kN/m2)	274
				$K_0^{nc}$: K0-valuefornormal consolidation	0.75

. The model prepared for a distance of 6 m between the buildings is illustrated in Figure 7. The slope height (H) and slope angle (θ) are 5 m and 2V:1H (i.e., 63.44°), respectively. The distance between the slope and the building nearest to the slope will be the key to understanding the structure–soil–structure interaction system in the presence of a slope. Therefore, the distance between the building nearest to the slope and the top of the slope was kept sufficiently large to overcome possible stability problems and was set at a ratio of 1 to the slope height (i.e., 5 m). This ratio is common in urban settlements. In order for the SSSI to be fully assessed, it is also a necessity that the second building be located within the slope effect. Fatahi et al. [35] calculated that the slope effect disappears at a distance of five times the slope height from the slope crest in a study investigating the safe approach distance to a slope of a building to be constructed near a 2 m high shallow slope. Similarly, in the present study, it was calculated that the slope effect disappears at a distance of approximately six times the slope height from the slope crest, and the second building was located within this domain. In the analyses performed in this study, only the number of buildings (1 and 2) and the distances between buildings (B = 6 m, 3B/4 = 4.5 m and B/2 = 3 m) were changed. The distance between the slope crest and the building nearest to the slope was kept constant and taken as 5 m in all analyses. The model prepared for the analyses is presented in Figure 7.

3.3. SSSI Modelling

A free-field boundary condition was used in the simulations. In the free-field boundary condition, the model boundaries are connected to the finite element mesh by viscous dampers. In this way, it is prevented that the ground motion is reflected at the boundaries of the model and creates amplifications that are not real. According to the suggestion of other researchers [35,36], the horizontal distance between the lateral boundaries along the earthquake shaking direction was set to be large enough (about 8 times the thickness of the soil layer) to minimise the negative effect of waves reflected from artificial boundaries in the SSSI analyses, as shown in Figure 8. It is known that strong ground motions cause serious damage to the superstructure. For this reason, data from the 6 February 2023 Kahramanmaraş-Pazarcık earthquake, one of the most destructive earthquakes that occurred in Turkey and the world throughout history, are used. In this study, the acceleration–time record of the 7.7 magnitude Kahramanmaraş-Pazarcık earthquake recorded by the NAR coded station was used. As can be seen in Figure 8, considering the simulation prepared for the analyses, the earthquake motion applied in the x-direction is suitable for seismic analyses. In Figure 9a, the earthquake acceleration–time records from the Turkish accelerometric database and analysis system can be observed [37]. Figure 9b delineates the frequencies derived from the Fourier spectra of the earthquake motions. In addition, the main characteristics of the strong ground motion applied in the seismic analyses are presented in

Table 5. The main characteristics of the strong ground motion.

Characteristic	Value
Earthquake	Kahramanmaraş-Pazarcık
Country	Turkey
Date	6 February 2023
Station Name	NAR
Peak Ground Acceleration (PGA) (cm/s2)	678.49

. Data representing bedrock motion (acceleration–time, velocity–time, displacement–time) used to simulate an earthquake and analyse the seismic response of the superstructure can be defined as input motion. Since the records taken from the station located in the study area were obtained as a result of the local site response, the acceleration–time record was scaled using a coefficient of 0.5 to represent the bedrock motion and applied directly to the lower nodes of the model. The predictions of the simulations are presented and discussed in the following sections.

4. Results and Discussion

4.1. Site Response

Figure 10 presents the acceleration–time history of the bedrock, ground surface, and slope crest subjected to the 2023 Kahramanmaraş-Pazarcık earthquake. The natural vibration period range and damping ratio are selected while preparing the response spectra. In the present study, a wide period range is used (0.01 s–4 s) and applied for 5% damping values to include all structures in the study area. Figure 11 demonstrates the spectral acceleration–period curve of the bedrock, ground surface, and slope crest, together with the standard design response spectrum characterising the sparse earthquake ground motion with a 10% probability of exceeding the spectral magnitudes in 50 years, in accordance with IBC 2006 [10]. By comparing the response spectra, it is obvious that the spectral accelerations are affected by both local site effects and the shallow slope, causing significant amplifications. Figure 11 demonstrates that the spectral accelerations obtained from the ground surface and the slope crest during the 2023 Kahramanmaraş-Pazarcık earthquake were greater than the design spectrum in almost all periods. This is in good agreement with the findings of previous studies [6,7,35], where topographic irregularity during seismic excitation led to some increase in period and spectral acceleration values.

4.2. The Effect of SSSI on the Frequency Response of the Building Nearest to the Slope

In this study, frequency response comparison was not neglected to investigate SSSI effects. For this purpose, the frequency response of the building nearest to the slope subjected to the earthquake was analysed under changing conditions. Within the scope of frequency response comparison, the spectral accelerations captured at the natural vibration frequency of the building and the frequency-dependent variation of the Fourier acceleration amplitude were investigated. Figure 12 shows the acceleration–time history of the building foundation nearest to the slope subjected to the 2023 Kahramanmaraş-Pazarcık earthquake in varying numbers of buildings and inter-building distances. In the time steps where the highest acceleration values were obtained during the earthquake duration, the highest and lowest acceleration values were captured at 1 and 2-B/2, respectively. The ratio with SSI of the spectral acceleration obtained at the natural vibration frequency of the building nearest to the slope and the frequency-dependent variation of the Fourier acceleration amplitude are presented in Figure 13a and Figure 13b, respectively. Higher spectral acceleration at building frequency and larger amplitudes at almost all frequencies are obtained at SSI. The amplitude of the earthquake waves decreased with an increasing number of buildings and decreasing inter-building distance. Despite the slope effect, SSSI resulted in decreased spectral acceleration and amplitude compared to SSI. This finding obtained from frequency analysis in the present study is in agreement with the findings of previous studies on SSSI [38,39].

4.3. Slope Stability and Deformations

Seismic slope stability is one of the important topics of geotechnical earthquake engineering. Static slope stability is of great importance on slopes with high existing shear stresses in static equilibrium, since low dynamic stresses may cause instability. For this reason, static and seismic analyses of the shallow slope were carried out for all varying conditions within the scope of the present study. Static slope stability was investigated using stress-strain finite element simulation, and seismic slope stability was investigated using a finite element method. The seismic FOS of the slope was calculated assuming that displacements of 500 mm and above would cause failure of the slope. To define the slope deformation, three points were selected on the top, centre, and bottom of the slope (shown in Figure 7), and the average of these points was taken as the slope deformation. The FOS of slope and maximum lateral deformations obtained from static and seismic stability analyses are presented in Figure 14a and

Table 6. The maximum lateral displacements recorded in the slope during seismic movement.

Number of Buildings	Distance	Point A (mm)	Point B (mm)	Point C (mm)
1		371	379	375
2	B	374	382	377
	3B/4	375	387	378
	B/2	378	389	381

, respectively. In all cases considered within the scope of the study, the FOS of the slope was calculated to be above 1. Therefore, it is understood that no instability of the slope will occur in both static and seismic conditions, no shear failure is expected, or no engineering measures are required to be taken to increase the slope stability. It can be seen in Figure 14a that strong ground motion significantly alters the slope FOS. In the case where the adjacent building is nearest to the existing building (i.e., 2-B/2), the seismic slope FOS is calculated to be approximately 40% less than the static FOS. In addition to these results, the static and seismic FOS of the slope exhibited similar behaviour under changing conditions. As the distance between buildings shortened and the number of buildings increased, both the static and seismic FOS of the slope decreased. In harmony with previous studies [40,41,42,43,44], the fact that the FOS of the slope decreases with the increase of structural loads transmitted to the slope has been proven once more.

4.4. Foundation Rocking

The foundations of buildings shake during strong ground movements. The rocking foundation affects structural rotation and damping. Structural rocking, on the one hand, limits the force demand and, on the other hand, transfers the ductility demand from the superstructure to the soil [45]. Foundation rocking is measured in terms of the rocking angle. To determine the rocking angle in the direction of strong ground motion during the time history analysis, in every time step, the angle between the foundation slab and the horizontal plane was calculated. Figure 15 presents the rocking time history of the building foundation nearest to the slope subjected to the 2023 Kahramanmaraş-Pazarcık earthquake. The foundation rocking angle of the building nearest to the slope was affected by the variation of both the number of buildings and the distance between buildings. During the earthquake duration, the highest foundation rocking angles were recorded for the 2-B/2 case, and the lowest were recorded for the 1 case. The maximum transient and residual foundation rocking angles captured in the changed conditions are also recorded and presented in Figure 14b. In this study, the effect of the presence of a slope on the rocking element was clearly seen. The decreasing FOS of the slope in Figure 14a and the increasing foundation rocking angle in Figure 14b are in good agreement. As the number of buildings multiplies and the distance between the buildings shortens, the raise in the loads transmitted to the slope decreased the FOS of the slope, and the increasing slope deformations enhanced the vertical displacements in the soil under the foundation and the rocking element effect. The maximum foundation rocking angle calculated at 2-B/2 (i.e., 0.24°%) is 41.18% higher than that calculated at 1 (i.e., 0.17°%).

4.5. Shear Forces in Superstructure

In order to calculate the storey shear force, the absolute shear force developed in all columns in that storey at the time step when the highest shear demand on the columns occurred during the earthquake duration was calculated and is presented in Figure 16a. The ratio of the shear demand on the storeys to the base shear demand is also calculated and presented in Figure 16b. It is clearly understood that shear failure will not occur for all cases considered, since the maximum shear demand on the storeys during the earthquake movement is below the shear capacity determined in accordance with IBC 2006 [10]. Figure 17 shows the base shear demand of the building nearest to the slope in changing conditions. The base shear demand, which was calculated as 275.64 kN in the presence of only one building near the slope, decreased as the distance between buildings shortened in the presence of two buildings and was calculated as 265.20 kN in the case of 2-B/2 (i.e., a 3.80% decline). It is seen that a behaviour contrary to the changing foundation rocking parallelwise to the slope deformations shown in Table 6 and Figure 14 occurs in the base shear demand. Contrary to previous studies [5,7,8,35] that found that increasing slope deformations enhances the shear demands of the building near the slope, the present study calculated that the base shear demand diminished despite the decreasing FOS of the slope. Despite the slope effect, the presence of a second building in the vicinity or the shortening of the distance between the buildings caused a relative decrease in the base shear demand through the dynamic cross-interaction between the buildings. Isbiliroglu et al. [38] concluded that in the presence of adjacent buildings in the environment, a decrease in the base shear demand is expected since the peak horizontal velocities of the building base motion decrease during seismic motion. Bybordiani and Arici [39] investigated the dynamic cross-interaction of adjacent buildings with the ground on a flat-surfaced soil model and found that increasing the distance between adjacent buildings decreases the SSSI, and the base shear demand for mid-rise building clusters is estimated to be lower than a single building solution depending on the soil conditions.

4.6. Maximum Displacements of Superstructure

Figure 18 shows the maximum (transient) lateral deformations of the building nearest to the slope subjected to the 2023 Kahramanmaraş-Pazarcık earthquake. The storey shear forces had more significant effect on the lateral displacement than the rocking component in the present study. In the face of changing conditions, it is understood that while near-lateral displacement values are obtained at the upper floors of the building, as the lower floors descend, the displacements change considerably due to the effect of the SSSI. While it is expected that the increasing rocking foundation angle will increase the lateral displacements at the building floors, this decrease is a result of the SSSI effect. In this study, where shallow slope and adjacent building effects were observed together, the rocking component was shaped by the slope effect, and the base shear demand and maximum storey displacements were shaped by the adjacent building effect. The structure–foundation–slope interaction has a significant effect on the rocking component. The additional load transmitted to the slope raised the slope deformations, and the increased slope deformations shaped the rocking element characteristic by increasing the vertical displacements of the soil under the building foundation nearest to the slope (Figure 14b). The structure–soil–structure interaction had a more pronounced effect on the storey shear demand and maximum storey displacements. The adjacent building foundation caused a reduction in the maximum acceleration amplitudes transmitted to the building foundation nearest to the slope by altering, reflecting, or refracting the earthquake waves (Figure 13b), resulting in a relative reduction in the base shear demand and a change in the storey shear demand (Figure 17). In this study, under changing circumstances, similar storey shear demands were obtained at the upper storeys of the building; as the lower storeys descend, the storey shear demand decreased due to the SSSI effect (Figure 16). As a consequence of this, the maximum storey displacements varied more at the lower storeys (Figure 18). The SSSI decreased the peak acceleration value at the foundation of the building nearest to the slope, and as a result, the base shear demand and the peak displacements calculated, particularly at the lower floors, decreased. In this context, the building nearest to the slope experienced the highest base shear demand and lateral displacements in SSI. While the maximum lateral displacement of 31.2 cm was calculated at the 1st floor of the building, this value decreased to 26.0 cm (i.e., 16.67% reduction) at 2-B/2. Ghandil et al. [46] investigated the cross-interaction problem of two adjacent buildings with the underlying flat surface soil and determined that the displacements change much more in the lower floors in SSSI compared to SSI.

4.7. Inter-Storey Drifts of Superstructure

Inter-storey drifts are one of the targets in the PBD approach and are used to identify the seismic performance of a superstructure. The present study has not neglected to investigate the SSSI effect on inter-storey drifts. The maximum transient and residual inter-storey drifts are determined by the ratio of the difference between the maximum and residual horizontal displacements of the building floors to the storey height, respectively. Figure 19a and Figure 19b show the maximum transient and residual inter-storey drifts of the building nearest to the slope subjected to the 2023 Kahramanmaraş-Pazarcık earthquake, respectively. The highest inter-storey drift occurred at the 3rd floor in all cases. The drift ratio, which was calculated as 0.35% at the 3rd floor of the building nearest to the slope when it was alone, increased to 0.50% at distance B/2 of the adjacent building. Since the maximum inter-storey drift ratio calculated for each storey is below the drift limit (2%) determined in accordance with IBC 2006 [10], drift damage is not expected to occur for the superstructure in all cases considered in this study. Both maximum transient and residual inter-storey drift ratios of the building nearest to the slope incremented with the approach of the adjacent building to the slope, which is the natural result of the interaction of slope and adjacent building effects. Both the rise in the foundation rocking angle and the large alteration of the largest storey displacements in the SSSI effect enhanced the storey drift ratios at all storeys.

5. Conclusions

In this study, the effect of an adjacent building on the seismic response of a building near a slope is investigated. To that end, simulations were prepared by using the earthquake acceleration record of the 6 February 2023 Kahramanmaraş-Pazarcık earthquake, which is one of the most destructive earthquakes in the history of the world, a real soil investigation report of the Kahramanmaraş-Pazarcık area, and the model of a mid-rise building. In this study, a three-dimensional finite element numerical model consisting of a 40 m thick sloping soil deposit and two adjacent 10-storey superstructures is analysed in time domain within the scope of soil–structure interaction and considering the nonlinearity of the soil and superstructure. The results show that SSSI cannot be neglected in the presence of a slope. In addition, the results are in good agreement with previous studies, which reported that the seismic response increases with increasing SSSI influence. The effect of the adjacent building on the seismic behaviour of the building nearest to the slope was obtained by comparing frequency analyses and PBD performance objectives, respectively. The findings obtained are listed below.

1. Expectedly, as a result of the site response analysis, large spectral acceleration values at periods close to the bedrock-dominant period (high frequencies) are obtained in the lower layer, while in the upper layer and the top of slope, it is observed that the high acceleration values spread over a wide period range. For almost all periods, and notably at low periods (0–0.5 s), the spectral accelerations captured at the top of the slope are higher than the upper layer (Figure 11).

2. The frequency domain analyses showed that the consideration of SSSI in the mid-rise building results in a decrease in the maximum acceleration values of the seismic excitation to the foundation of the building and a decrease in the spectral acceleration and acceleration amplitudes at the building frequency and other frequencies (Figure 12 and Figure 13). In addition, in the scope of frequency response comparison in this study, the spectral acceleration and acceleration amplitudes recorded at the building foundation nearest to the slope during the seismic event were evaluated, and other structural responses were not considered in this scope.

3. The presence of the adjacent building and its proximity to the slope caused additional stresses on the slope in both static and seismic conditions and increased the lateral displacements on the slope. The static and seismic FOS of the slope reduced by 8.16% and 4.29%, respectively, in the case 2-B/2, where the adjacent building is nearest to the slope. Since the FOS of the slope is above 1 in all cases considered, it is assumed that there is no shear failure in the slope (Table 6 and Figure 14a).

4. Increasing slope deformations led to higher vertical deformations in the soil under the building nearest to the slope, and as a result, the foundation rocking angle intensified. The correspondence between the FOS of the slope and the foundation rocking angle is shown in Figure 14. A similar tendency to the slope deformations occurs when the number of buildings increases and the distance between the buildings decreases; the maximum transient and residual foundation rocking angles at the foundation of the building nearest to the slope are presented in Figure 15. Increased rocking worsens the superstructure seismic performance. In the scope of this study, it has been proved once again that rocking increases in the superstructure under the slope effect. It is also understood that the rocking element characteristic has a significant effect on the superstructure seismic performance. Figure 15 shows that at the distance where the adjacent building is nearest to the slope (i.e., 2-B/2), generally, higher foundation rocking angles were calculated during the earthquake duration. The lowest foundation rocking angles were calculated when the building nearest to the slope was alone (i.e., 1). The maximum foundation rocking angle calculated at 2-B/2 (i.e., 0.24°%) is 41.18% higher than that calculated at 1 (i.e., 0.17°%).

5. Since the maximum shear demands captured at the storeys of the building nearest to the slope in changed cases are below the maximum permissible shear capacity in accordance with IBC 2006 [10], no shear failure occurs at the building storeys for all cases (Figure 16a). Contrary to previous studies [5,7,8,35] where it was inferred that increasing slope deformations and decreasing the FOS of the slope increase the base shear demand of the superstructure near the slope, in this study it is clearly understood that the base shear demands are largely shaped by the SSSI effect. Figure 17 represents the base shear demand for the building nearest to the slope, which decreases with the presence and proximity to slope of the adjacent building. The base shear demand of the building nearest to the slope is 275.64 kN if the building is alone (i.e., 1), while the base shear demand decreases to 265.20 kN (i.e., 3.80% reduction) in the presence of the adjacent building and in the location nearest to the existing building (i.e., 2-B/2). The reduction in the base shear demand of the building nearest to the slope in the presence and proximity to slope of the adjacent building is in agreement with previous studies [38,39].

6. The maximum storey displacements were shaped according to the storey shear demand. The ratio of the storey shear demand of the building nearest to the slope to the base shear demand increased with the SSSI effect, especially at the lower storeys (Figure 16b). As a result of this situation, the maximum storey displacements were near in the upper storeys of the building in which the base shear demand did not change much in the changed conditions, while the maximum storey displacements decreased in the lower storeys with the SSSI effect. As shown in Figure 18, while the maximum lateral displacement of 31.2 cm is obtained at the 1st storey of the building alone, this value decreased significantly with the SSSI effect and reduced to 26.0 cm at 2-B/2 (i.e., 16.7% reduction). The significant change in the displacements of the lower floors of the existing building with the proximity of the adjacent building is consistent with the previous study [46] on SSSI.

7. The combined effect of the rocking element characteristic and the storey shear demand on the storey drift ratios can be mentioned. Both the rise in the foundation rocking angle and the large alteration of the largest storey displacements in the SSSI effect enhanced the storey drift ratios at all storeys (Figure 19).

8. The findings of this study are influenced by the key factors used in the analysis (seismic records, soil type, and building characteristics) and therefore may not be valid if any of these key factors are altered or if other variables that could affect the results are present.

The results of this study investigating the effect of the presence and changed location of an adjacent building on the building nearest to the slope represent an interaction in which both slope and adjacent building effects are observed together. The additional shear stresses on the slope against the changed conditions (increasing the number of buildings and the adjacent building getting closer to the existing building) increased the rocking and storey drifts of the building nearest to the slope. On the other hand, the displacements of the lower storeys changed more than the upper storeys, and the storey drifts increased with the rise of SSSI effects. Comparing cases 1 (where the building is alone) and 2-B/2 (where the adjacent building is located at the nearest distance to the existing building), a 4.29% decrease in the seismic FOS of the slope, a 41.18% increase in maximum foundation rocking angle, a 3.80% decrease in base shear demand, and a 23.27% alteration in maximum storey displacement of the ground floor were calculated. As a result of these conditions, maximum storey drifts of more than 50% occurred in the lower storeys of the building.