Seismic performance of various structural configurations for RC building on sloped terrain considering soil-foundation-structure approach

The study aims to evaluate the seismic performance of reinforced concrete (RC) buildings on slopes using soil–foundation–structure (SFS) interaction modeling. This study investigates the seismic performance of different structural configurations for a five-story RC building on sloped terrain, incorporating bracings, shear walls, grade beams, stub columns, strap footings, and hybrid arrangements. Three critical slope locations—toe, crest, and center—at 20° inclination were analyzed using the SFS modeling approach in PLAXIS 3D, incorporating soil nonlinearity. The RC building was modeled to assess the inter-story drift ratio (ISDR) and lateral displacement as performance parameters. Results indicate that structures on sloping ground were much more vulnerable than those on level ground, with bare-frame structures exhibiting the worst seismic performance at all slope locations. Braced and shear wall buildings show remarkable improvements, with up to 90% reduction in both lateral displacement and inter-story drift ratio compared to typical bare-frame systems and hybrid configurations such as the M26 model, achieving reductions in critical shear force and bending moment exploitation ratios by as much as 2.3× and 1.5×, respectively, at the observed column. At the crest, optimal configurations showed a 91% reduction in lateral displacement. For buildings at the center of the slope, certain configurations reduced inter-story drift and roof displacement by up to 79% and 88%. The study provides valuable guidelines for creating seismically resilient structural designs, substantially improving the safety and performance of RC buildings under seismic loads in mountainous terrain. The study aligns with building sustainable cities and resilient communities (Sustainable Development Goals (SDGs) 9 and 11), which minimize the damage to the infrastructure and reduce social losses in a community. Few studies have been done on the structural configuration of buildings on slopes, where limited guidelines were provided in the Indian Standards. The study includes soil–structure interaction and varies the location of the building based on practical scenarios that prove to be novel research to identify the best possible resilient structural configuration for building construction on slopes.

1 Introduction

With the rise in population and development, there is significant pressure to expand construction activities to hilly regions due to scarce flat land. This rapid urbanization often results in unplanned and inadequately designed structures, which are more vulnerable to hazards like earthquakes, landslides, and erosion, posing a significant risk. Building on hilly terrain introduces unique structural challenges due to irregular geometry and complex load distributions requiring careful assessment and design (Daniel and Sivakamasundari, 2016; Jarapala and Menon, 2025).

Hilly regions are often located in high seismic zones, where the risk of earthquakes is consequential (e.g., the Himalayan belt in India). Earthquakes in such areas are more impactful due to geological conditions like slopes, which can amplify the ground motion (Gawande et al., 2012; Çağlar et al., 2021; Mazhe and Padmawar, 2019; Shylaja et al., 2022). Step-back, step-back set-back, and cut slope foundations are some common configurations in hilly regions, as shown in Figure 1 (Aggarwal and Saha, 2021; Magapu and Setia, 2023; Yu et al., 2017). However, buildings on slopes usually experience a short column effect, unsymmetrical mass, and stiffness distributions due to varying column lengths and irregular shape (Ramhmachhuani and Mozumder, 2024; Patel et al., 2014; Ingle and Kolase, 2017; Jakati and Saha, 2022).

Figure 1

Figure 1. Building elevation view: (a) step-back configuration, (b) step-back set-back configuration, and (c) split-foundation configuration.

Due to the above factors, the building’s center of mass and center of rigidity often do not coincide. This leads to increased torsional effects (rotational forces) during an earthquake, further destabilizing the structure. The uphill and downhill sides of the building experience different loads and movements during seismic activity (Deshpande and Mohite, 2014). This uneven force distribution increases the risk of shear failure in columns or the structure overturning. Therefore, it is very important to consider the effect of lateral forces and the consequent destruction in buildings in hilly regions after observing the effect of topography in various earthquakes, such as the 1985 Canal Beagle (Chile), 1987 Whittier Narrows, 1995 Aigio (Greece), and 2010 Haiti earthquakes (Singh et al., 2012; Kapse and Pande, 2015). Studies (Shabani et al., 2021a; Brennan and Madabhushi, 2009; Asadi Ghoozhdi et al., 2022) highlight that buildings on sloped terrain experience greater torsional effects than those on flat ground, leading to increased vulnerability during seismic events.

These effects of slope topography have been studied numerically, analytically, and experimentally, and they show amplification in ground motion due to soil topography (Shabani et al., 2021b; Brennan and Madabhushi, 2009; Ramhmachhuani and Mozumder, 2024; Talukdar et al., 2018; Hasan and Serker, 2021). Seismic loading increases the lateral earth pressure on retaining walls and other structural and non-structural elements of the building. Settlement of foundations, variation in column height, and the soft story effect are some other prominent responses to lateral forces (Rave-Arango and Blandón-Uribe, 2012; Mitra and Tamizharasi, 2024; Ghandil and Behnamfar, 2015). To address these issues, Aggarwal and Saha (2021) examined the effectiveness of moment-resisting frames and found that optimizing beam-column connections improves overall lateral stability. It is also essential to consider the impacts of soil–structure interaction (SSI) for structures situated close to or onto slopes. SSI is a phenomenon where the behavior of a structure influences the soil it is built on, and conversely, the soil’s response affects the structure’s motion. Recent studies emphasized the role of SSI in modifying seismic responses and underscoring the need for site-specific design considerations (Bapir et al., 2023; Das and Maheshwari, 2024; Reddy and Badry, 2022; Birajdar and Nalawade, 2004). Some articles aim to provide engineers with the effects of seismic forces on slopes, considering foundation–structure interaction on relative displacement and residual inter-story drifts in case of mid-rise buildings on slopes, ensuring safe design (Fatahi et al., 2020; Bahuguna and Firoj, 2022; Shabani et al., 2021a; Göktepe and Coşkun, 2025).

Various lateral force-resisting systems have been introduced and are prominently used in mid- to high-rise buildings worldwide (Lu et al., 2024). Halkude et al. (2015) demonstrated that shear walls increase resistance against seismic forces, but their efficiency depends on strategic placement within the structure. Along with shear walls, composite columns can also be used as an efficient lateral force-resisting system (Verma et al., 2025; Zhu et al., 2024). Another common system for resisting lateral forces is bracing. Bracing has been adopted as a feasible and reliable source of lateral force resistance (Chaudhary and Tiwary, 2023; Hejazi et al., 2024; Tirca et al., 2016). Another study by Mazza and Labernarda (2023) demonstrates the effectiveness of hysteretic damped braces in reducing structural drift and controlling damage. That study also highlights the importance of considering out-of-plane behavior and the variability of masonry infill properties in the design process. Different bracing types have been configured and integrated with other systems to improve performance (Hessek et al., 2017; Ahmed et al., 2024; Beigi et al., 2014; Ebrahimi et al., 2024).

Further research compared braced frames with shear wall systems, concluding that bracing significantly minimizes the inter-story drift and corresponding base shear while maintaining structural integrity (Birajdar and Nalawade, 2004). Additionally, Roshan & Pal (2023) explored dual systems combining shear walls and bracing, which proved to be the most resilient under seismic loading conditions. Infill walls are also seen as lateral force-resisting systems but are mainly used on flat terrain (Demir and Sivri, 2002).

During an earthquake, the soil and structure interact and deform mutually, significantly influencing the structural response (Gouasmia and Djeghaba, 2006). Nonlinear finite element (FE) analysis captures the complex interaction between soil, seismic waves, and topography. Surface geology and topographic irregularities must not be neglected in site-specific seismic hazard assessments (Jaber et al., 2018; Derghoum and Derghoum, 2023). Various studies done by Raj et al. (2018), Wu et al. (2022), Maheshwari and Das (2023), and Jahanpanahi and Shamim (2024) demonstrate that slope geometry, soil or rock strength, load eccentricity, and seismic effects critically reduce footing capacity, highlighting the need for advanced site-specific design methods. Special care is necessary for foundations on slopes to prevent downslope movement and provide anchorage (Shabani et al., 2022). It is important to identify and characterize complex failure modes, often overlooked in simplified designs (Magapu and Setia, 2023). When an embedded strip footing applies a load near or on a slope, the failure mechanism differs from classical bearing capacity failure on flat ground (Das and Maheshwari, 2023; Kumar and Korada, 2022).

IS 14243:1995 recommends that buildings be constructed only on terrain with slopes less than 30° (Bureau of Indian Standards, 1995). Larijani and Tehrani (2024) studied critical incident angles at which maximum damage occurs, ensuring that designs are safe under worst-case directional loading.

This study explores structural aspects of multi-story buildings on sloped terrain using a nonlinear continuum model investigated numerically. The seismic response of a conventional reinforced concrete (RC) building is compared with shear wall and bracing configurations on soil slopes, aiming to identify designs that enhance seismic resilience by analyzing parameters such as inter-story drift and displacement. This research proposes an optimized structural system for improved seismic safety and performance.

2 Methodology

The pictorial representation of the detailed methodology adopted in this study is shown in Figure 2.

Figure 2

Figure 2. Flowchart of the methodology.

2.1 Finite element modeling

A three-dimensional (3D) model of a five-story building is designed and analyzed primarily in ETABS to determine optimum section sizes, considering flat terrain (Computers and Structures Inc., 2020). Then, 24 3D numerical models were developed considering SSI by providing similar section and material properties obtained from ETABS, which are listed in Table 1 and Table 2, respectively. PLAXIS 3D V24 (Hemeda, 2024; Bentley Systems, 2024) was used for the simulations as it is well suited for handling complex structures considering the nonlinear and anisotropic behavior of soils. The models were placed at three distinct locations along a slope with a 20° angle, as shown in Figure 3, and were subjected to seismic force at the base of the soil model. Various structural configurations were adopted, such as bracing systems, shear wall systems, and belt bracing systems (Sec. 2.2) to resist the lateral forces and study the behavior of the structure through a soil–foundation–structure approach. A typical detailed geometry of the structure is shown in Figure 4.

Table 1

Table 1. Section properties of RC structures.

Table 2

Table 2. Material properties for soil and structure.

Figure 3

Figure 3. Two-dimensional schematic diagram of the sloped terrain with different building locations and boundary conditions.

Figure 4

Figure 4. Typical plan and elevation of the building.

2.1.1 Constitutive modeling

In this study, a soil model is created for two layers: one hard stratum at the base and medium sandy soil on top. The size of the soil model is shown in Figure 3. The model is 500 m in the transverse direction. A hardening soil model with small-strain stiffness (HSS) has been adopted for the sandy soil material. Unlike simple Mohr–Coulomb models, the HSS model effectively simulates different stress paths, including primary loading, unloading, and reloading with distinct stiffness moduli. This capability is crucial for modeling, to capture the response to seismic loading to ensure stable convergence for finite modeling and to avoid any unrealistic amplification of acceleration in sloped soil profiles under strong ground motions. Table 2 lists the required parameters for the HSS constitutive model along with the description. These parameter values and damping ratios for soil have been adopted from Das and Maheshwari (2024).

For hard strata, at the bottom, a Hoek–Brown constitutive model has been adopted to capture the nonlinear shear strength envelope and tensile strength, enabling better representation across varied stress states. The index properties are assumed based on the shear wave velocity as V_s = 815 m/s and a damping ratio of 2%. The required parameters are listed in Table 2.

For the building, a concrete model defined with an elasto-plastic material has been considered. This approach considers combined Mohr–Coulomb (compression) and Rankine (tension) yield criteria, enabling detailed simulation of cracking and crushing behavior under multiaxial stresses. The model accounts for strain hardening, softening, and time-dependent property evolution, with fracture-energy-based regularization to ensure mesh-independent results. The material properties are provided in Table 2. The target damping for the building is assumed to be 1%.

2.1.2 Element meshing and boundary conditions

Using the finite element analysis (FEA) software, a 15-node, tetrahedral element has been used for the soil, six-node triangular elements were used for the model footing, and five-node line elements have been adopted for the beam and column sections. The models were discretized using auto mesh in PLAXIS 3D, accounting for soil strata, structural members, and loads with boundary conditions. At the lateral side of the slope free-field, a boundary condition was applied with the compliant base assigned to the bottom of the slope to prevent wave reflection of the seismic loading back into the model domain. This enables the propagation of earthquake ground motion through prescribed surface displacement. In addition, as can be observed in Figure 3, the boundaries are placed far enough away so that wave reflections do not interfere with the slope’s response, ensuring that the dynamic behavior is not distorted by boundary effects and closely represents actual wave propagation in the soil.

2.1.3 Soil–foundation interface

An interface for soil–structure interaction was provided between the soil layer and the bottom of the foundation. A joint element was used to provide the proper interface. This bonds the soil and footing, which will act as a single unit. This was done to have a relative displacement/behavior of the structure along with soil displacement, as, in reality, concrete and soil are not always rigid. The interface was given the same properties as the adjacent soil material.

2.1.4 Damping

Amorosi et al. (2016) suggested viscous damping and Rayleigh formulation to increase the accuracy of soil–foundation–structure performance. In this method, forming the damping matrix involves combining the mass and stiffness matrices by the linear relationship given in Equation 1.

$\left[C\right]={\alpha }_r\left[M\right]+{\beta }_r\left[K\right].(1)$

In Equation 1, [C], [M], and [K] indicate the damping coefficient, mass, and stiffness, respectively. The damping coefficients are represented as ${\alpha }_r$ and ${\beta }_r$ (Table 3), which are determined using Equation 2 for the two distinct modes of vibration, along with their respective natural frequencies.

$\left(\begin{array}{l}{\alpha }_r\\ {\beta }_r\end{array}\right)=\frac{2\mathrm{\xi }}{{\omega }_i+{\omega }_j}\left[\begin{array}{c}{\omega }_i{\omega }_j\\ 1\end{array}\right],(2)$

where ${\omega }_i$ and ${\omega }_j$ (Table 3) represent two natural modes and their frequencies. ξ is the assumed damping value for the natural mode, as the structural seismic response will be affected significantly at the first two modes (Fatahi et al., 2020). Equation 3, which was provided by Kramer (1996), was used to determine the natural frequency of the soil.

$f_n=\frac{V_s}{4H}\left(2n-1\right),(3)$

where $f_n$ = natural frequency of the respective mode, $V_s$ = shear wave velocity, $H$ = soil deposit depth, and $n$ = mode number.

Table 3

Table 3. Rayleigh damping coefficients.

2.2 Structural configurations

Numerous configurations combining lateral force-resisting elements like bracings, shear walls, and struts, were examined to assess the effectiveness of these systems in lateral deformations and inter-story drift ratio and how these systems help to mitigate the seismic force demands. The studied models are listed in Table 4. Figure 5, shows the building configurations for the center of the slope. Similar models were developed for the toe and crest.

Table 4

Table 4. Summary of the structural configurations studied.

Figure 5

Figure 5. Structural configurations for a step-back building at the center of the slope.

3 Ground motion characteristics

3.1 Selection of ground motion

The 1999 Chamoli earthquake recorded at Gopeshwar station was used for the present study because it had the highest peak ground acceleration recorded in the Himalayan region of 0.359 g. The Chamoli earthquake serves as a relevant case study for a worst-case seismic scenario in a hilly region. The input ground motions were taken from the Consortium of Organizations for Strong-Motion Observation Systems (COSMOS). The suitability of ground motion records was decided based on the factors like magnitude (Mw) range of 4.5–7.5, and the near field region having a source-to-site distance of 5–50 km and medium soil type. Figure 6a shows the time history data for the scaled response spectrum value attained for 0.36 g as per IS 1893.

Figure 6

Figure 6. (a) Time history data for the matched response spectrum and (b) matched response spectrum considering 5% damping.

3.2 Scaling of ground motion

Scaling was carried out using SeismoMatch software (SeismoSoft, 2025), where the input is the unscaled ground motion. The target spectrum is defined considering zone, response reduction factor, importance factor, and damping ratio as per IS 1893 (Bureau of Indian Standards, 2016). These parameters are defined in Table 5. The standard scaling procedure prevents scaled average response spectra from falling below the target spectrum, which ranges from 1 + 15T to 1.36/T, where T is the fundamental period of fixed-base structures ranging from 0 to 4 s. Over this time range, the recorded earthquake motion was adjusted such that its response spectrum matches the target spectrum for zone V as per IS 1893, which is characterized for severe seismic-prone regions. Figure 6b shows the scaled response spectrum characteristics of the selected ground motion. This scaled ground motion was applied to the base of the hard stratum in numerical modeling for the nonlinear time history analysis.

Table 5

Table 5. Seismic parameters for ground motion scaling (IS: 1893–2016).

3.3 Nonlinear time history analysis approach

In a nonlinear time history approach, ground motion in terms of acceleration-time history was applied at the bedrock level. The structural responses, such as roof displacement and story drift, were monitored for the entire duration of the considered earthquake. In this study, the direct analysis method was adopted for the simulation of soil–foundation–structure (SFS) interaction systems. The soil and the structure were modeled and analyzed simultaneously in consecutive steps by solving the equation of motion. The soil was described as a continuum medium and linked to the foundation/footing with interface elements. Suitable boundary conditions were assigned. In this approach, the complete model was analyzed with respect to the time domain, considering free-field motion as input. The governing equation of motion (Chopra, 2007) for a soil–structure system is written as per Equation 4:

$\left[M\right]\ddot{u}+\left[C\right]\dot{u}+\left[k\right]u=\left[M\right]{\ddot{u}}_g+F_{vb},(4)$

where [M], [C], and [K] represent the matrices for mass, viscous damping, and stiffness, respectively. The vectors $\ddot{u},\dot{u},u$ represent acceleration, velocity, and displacement, respectively. The force vector $F_{vb}$ denotes the viscous damping boundaries, and ${\ddot{u}}_g$ shows the acceleration induced due to ground motion applied at the base of the hard strata.

In this study, time history analysis was conducted by accounting for the nonlinearity of soil material behavior and the elasto-plastic behavior of structural members. The cracked sections of beams and columns were accounted for by considering 0.35× and 0.7× the uncracked bending stiffness, respectively (IS 1893 part 1, 2016). This approach evaluates the reliable response of soil–structure systems due to seismic events.

4 Verification

The numerical model was verified by comparing the horizontal displacement patterns obtained from the nonlinear time history analysis in PLAXIS 3D with those reported by the numerical model of Das and Maheshwari (2024). Both analyses considered a G+5 building on a slope with the sectional properties as adopted by Das and Maheshwari (2024). The unscaled Chamoli 1999 earthquake time history was used for the verification.

The contour in Figure 7 visually shows how horizontal displacement extends laterally along the slope, revealing a progressive increase from point “a” to point “d,” with point “d” experiencing the highest displacement below the foundation.

Figure 7

Figure 7. Horizontal displacement contour of the slope.

The values of these displacements are noted and compared in Table 6. Although the values greatly differ, the result shows a similar pattern in horizontal displacement to that reported by Das and Maheshwari (2024).

Table 6

Table 6. Comparison of horizontal displacement patterns.

5 Results and discussion

5.1 Comparison between fixed and flexible base

A numerical analysis considering a five-story building was carried out in ETABS, having a fixed base and PLAXIS 3D on soil strata (flexible base), to study the effects of soil–structure interaction. Figures 8a,b show the model geometry for the respective software. Figure 8c shows that the displacement at the roof for a fixed base is 21.738 mm, and the displacement is 50.481 mm for the flexible base.

Figure 8

Figure 8. Modeling (a) 3D view of building on soil strata, (b) 3D view of a building with a fixed base, (c) comparison of displacement with fixed and flexible bases, and (d) deformed shape of the building due to SSI.

The trend line shows a similar behavior in the building deflection. However, in a flexible base, the lateral displacement is amplified more than two-fold. This is due to the effect of slope and foundation rotation, as can be seen in Figure 8d.

This behavior, due to the flexible base, cannot be observed in fixed-base analysis of a building on a sloped terrain, where the displacement profile shows a steeper slope in the building than that shown in the analysis of the flexible base. Hence, it is necessary to include the soil–structure interaction to study the behavior of the building situated on sloped terrain. Additionally, the increase in roof displacement from 22 mm (fixed base) to 50 mm (flexible base) in the flexible base model indicates that SSI can enhance the system’s total flexibility, increase the natural period, and lower seismic force demand (base shear). Nevertheless, it adds complex deformation behavior at the base. In contrast, the fixed-base model underestimates roof displacement because it excludes the soil–foundation system’s interaction and deformation capacity. Figure 8d also shows the torsional irregularity forming at higher story levels, showing that the building is susceptible to torsion if it is situated on a slope. The same was not observed in the case of modeling only the structure and assuming it was fixed at the base.

5.2 Story drift and lateral displacement

The performance of each proposed building configuration is examined, considering a mid-rise building located at the toe, center, and crest of a slope. The inter-story drift ratio (ISDR) curve was developed for each model with various structural configurations along with a lateral force-resisting system. Inter-story drift is the ratio difference in horizontal displacement between the top and bottom of a story and the story’s height.

Lateral displacement for different structural systems shows notable variation in terms of the resistance capacity of various structural configurations. Lateral displacement in structures refers to the sideways movement caused by lateral loads like wind or earthquakes.

5.2.1 Building located at the toe

The ISDR curve was developed for various building models found at the toe of the slope (Figure 9a). Model M11 and M14 give the largest story drift ratio of 0.252%. In the braced building (M12) and the building with shear walls (M13), the maximum ISDR is reduced to approximately 93% compared to the bare frame. The models M15, M16, and M18 also show reduced inter-story drift compared to the bare frame. M17 shows a substantial reduction in story drift to 97% compared to the bare frame. Negative story drift is induced in almost all the models found at the toe due to the slope and lateral movement of the foundation in sloped terrain. Furthermore, when the story drift of M17 is compared with those of M12 and M13, the difference in reduction is not very large. M17 shows a reduction of only approximately 0.009% with respect to M12 and M13. Therefore, considering the feasibility aspect along with ISDR analysis, the models M12 and M13 also perform well at the toe of the slope.

Figure 9

Figure 9. (a) Inter-story drift and (b) absolute lateral displacement for a building located at the toe.

The absolute lateral displacement curve (Figure 9b) shows almost the same maximum displacement (30.483 mm and 30.248 mm) of the top story for models M11 and M14, respectively. The bracing configuration (M12) and shear wall configuration (M13) show promising reductions in the lateral displacement of 90.8% and 90.7%, respectively, compared to M11. M15, M16, and M18 give a reduction in lateral displacement of 92.6% with respect to M11. M17 reduces the lateral displacement by 97.7%, and the maximum displacement in this model is very low, at 0.696 mm.

5.2.2 Building located at the center

Among the models located at the center of the slope, the bare frame, as expected, yields the maximum story drift value of 0.35% from the ISDR curve (Figure 10a). For M22, the maximum ISDR is reduced by 64%, while for M23, the drift 53% compared to the bare frame. M24, M25, M26, and M28 also show a reduction in story drift compared to the bare frame. In the case of M27, the 89% reduction is notable. Models M22 and M23 also have considerable performance while maintaining their feasibility.

Figure 10

Figure 10. (a) Inter-story drift and (b) absolute lateral displacement for a building located at the center.

In Figure 10b, M21 shows the maximum lateral displacement of 50.481 mm. M22 shows a 63% reduction of displacement. M23 and M24 reduce displacement by 63% and 50%, respectively, with respect to the bare frame. M25 and M26 show reductions of 68% and 79%, respectively. M27 has a displacement reduction of 88%. M28, on the other hand, exhibits an 81% reduction compared to the bare frame.

5.2.3 Building located at the crest

The ISDR curve of a building located at the slope crest is shown in Figure 11a. As expected, the bare frame shows a maximum story drift of 0.341%. M32 indicates a smaller movement between the levels, with the drift value being reduced by 53%. M33, on the other hand, has a negative drift close to the first level due to the slope effect. When strap footing, a grade beam, and stub columns are introduced, the model shows a reduction in drift of 24%, which is not very large compared to the other models at the crest. M35 shows a maximum drift at the lower levels. The maximum value was in the negative; however, the value shows reduced ISDR compared to the bare frame. This reduction is due to the bracing provided, which helps with a further reduction in the drift along the above floors as well, compared to the bare frame. M36 and M37 show somewhat similar performance in terms of drift. However, the increase in the drift near the mid-level is larger for M36. M38 gives a considerable reduction in the drift for the building model located at the crest of the slope.

Figure 11

Figure 11. (a) Inter-story drift and (b) absolute lateral displacement for a building located at the crest.

Figure 11b shows the building models located at the crest of the slope. The bare frame without a lateral force-resisting system shows the maximum lateral displacement of 45.178 mm. M32 shows a reduction of 62.5%, while M33 shows a reduction of 89% in lateral displacement with respect to the bare frame. M34 and M35 show reductions in displacement of 39.8% and 88%, respectively. M36 shows an 88.6% reduction. M37 and M38 show reduced displacement of 85% and 91%, respectively. Therefore, at the crest of the slope, M38 shows good performance.

5.3 Shear force and bending moment

Shear force and bending moment values were measured for the critical column in the bare frame model near the foundation level and compared with other models at each location (toe, center, and crest of the slope). The column was selected by considering the most critical location of the soil at the center of the slope under displacement due to the building’s movement (Figure 12).

Figure 12

Figure 12. Selected location of Column A at the slope.

Later, the bending moment and shear force obtained from different models were normalized (M/Mur and V/Vur) with respect to the resistance provided by the column due to bending moment (M) and shear force (V). Mur and Vur are the ultimate moments of resistance and shear force resistance provided by the column.

5.3.1 Building located at the toe

Figure 13 shows that for the selected column (shown in Figure 12), the shear force and bending moment ratios are higher in the bare-frame model (M11). As we include the shear walls (M13) and bracing (M12), this ratio reaches (1.66, 0.33) for shear force and bending moment, and at (1.64, 0.4), the column becomes more prone to the lateral forces. The exploitation ratio, V/Vur, is > 1, indicating shear failure for column A in models M11, M12, and M13. Models consisting of a grade beam show a reduction in these bending moment and shear force exploitation ratios, reducing the concentration at that location. The lowest values can be seen in model M15, which uses a strap footing, a grade beam, and a stub column at the bottom, with corner bracing at above-story levels. M15 shows almost 2.75× and 2.4× reductions in shear force and bending moment exploitation ratios, respectively, compared to M11.

Figure 13

Figure 13. Exploitation ratio curve of Column A for a building at the toe.

5.3.2 Building located at the center

Figure 14 shows that the bare-frame model (M21) experiences the maximum degree of shear force and bending moment, with an exploitation ratio of (0.68, 0.28), respectively. A moderate increase in shear force and bending moment can be observed in model M23. For the M22 model, a slight decrement in shear force is observable. However, the column becomes more susceptible to bending moments. An RC building consisting of corner bracing and a V-column arrangement shows a considerable decrease in shear force and bending moments. An effective decrease can be seen in the M26 model, with 2.3× and 1.5× reductions in shear force and bending moment exploitation ratios, respectively, showing good functional use of stub column, strap footing, and belt bracings on the above-story levels. The exploitation ratio, V/Vur, is larger in the M21–M23 models than in other hybrid systems.

Figure 14

Figure 14. Exploitation ratio curve of Column A for a building at the center.

5.3.3 Building located at the crest

For a building located at the crest, as shown in Figure 15, the criticality of the column increases as we add lateral resisting elements. Figure 15 shows that of models M33–M38, model M38 shows the highest V/Vur and M/Mur values. These results are opposite to the ones above, showing that any addition of elements without properly addressing the issue may result in RC buildings being more vulnerable to seismic forces. The M34 model shows remarkably better performance than other structural configurations at the crest, indicating the reduction in the concentration of force demands on the selected column. However, the increment in the exploitation ratios of M38 indicates that the overturning of the entire building during a seismic event could be resisted by introducing a V-column at the front of the building. The results show an increment in V/Vur and M/Mur of 1.8× that of M31.

Figure 15

Figure 15. Exploitation ratio curve of Column A for a building at the crest.

6 Conclusion

The study examines various structural configurations for building construction on slopes in hilly areas. A mid-rise building on the crest, toe, and center of a slope was considered in this study. Dynamic analysis was performed to assess the building’s seismic performance in each case. Based on the comprehensive investigation into the seismic performance of reinforced concrete (RC) buildings on sloped terrain, several key conclusions can be drawn.

• Structures built on slopes are much more susceptible to seismic load because of irregular shape, non-uniform distribution of loads, and amplification of the ground motion due to slope topography. Considering soil–structure interaction (SSI) in analysis shows a more realistic behavior of structures. The flexible base model indicates larger roof displacement and system flexibility than the fixed-base model, indicating the need to include SSI for proper seismic assessment.

• Employing braces and shear walls highly enhances building stability. It minimizes floor-to-floor drift by up to 90%. This advantage holds for buildings located in all regions at the base, center, or top of a slope. Hybrid systems with bracing, grade beams, and struts provide the maximum resilience, reducing both drift and displacement under seismic loading. The models also exhibit reduced shear forces and bending moments at column locations of critical importance. However, the feasibility and economy of this hybrid system must still be verified using conventional available techniques.

• Structures at the toe of the slope have the highest intensity of shear forces and bending moments, so bottom floor columns nearer to the foundation experience higher seismic demand forces. The toe structural systems from M13 to M18 perform almost equally effectively in terms of lateral displacement and inter-story drift ratio. M15 configurations can be adopted for a building located at the toe of the slope based on the practical implementation feasibility to reduce the design demands, such as shear force and bending moment.

• The bracing belt system configuration M26 distributes seismic forces effectively, and roof movement and drift across floors are greatly reduced for the structure at the middle of a slope. Constructing a building in the middle of the slope with this technique is practically feasible and hence is suggested. The crest has lesser forces in general, but some columns (such as those toward the rear or front ends, based on the configuration) are still critical, and judicious use of bracing or V-columns (M38) enhances the performance of a structure at the crest of the slope.

• Based on the location of the structure, efficient configurations must be adopted for better seismic performance. In the case of the toe and the crest, the hybrid system with bracing and a shear wall performs well. In the case of the center of slope, which is the critical location, the new proposed hybrid system M26 (bracing belt with all M22 configurations) shows promising results.

• Exploitation ratios were observed to be >1 in the bare-frame and conventional configurations, like bracing and shear wall at the toe location, showing that short columns are more prone to shear forces at the toe location. Hybrid systems such as M15 showed better performance in reducing these shear forces. Similarly, for a building located at the center of the slope, M28 shows a decrease in shear forces at the location of column A compared to the M21–M23 models.

• The traditional structural systems cannot be adopted directly for all structure locations, as the seismic performance on sloping ground shows an increase in design demand in the column near the foundation level, especially at the toe of the slope.

The results highlight that traditional structural systems are not sufficient for achieving uniform seismic performance on sloping ground, and optimal structural setups involve combinations of shear walls, bracing, and proper attention to soil–structure interaction influences. This study provides valuable guidelines for creating seismically resilient structural designs, substantially improving the safety and performance of RC buildings under seismic loads in mountainous terrain.

7 Limitations and future scope

The study is limited to the type of building considered. Different building geometries must be considered to have broader results. Future studies should focus on extensive experimental validation through shake table testing and field monitoring, which would substantially improve the validity of numerical predictions and yield valuable insights into real structural behavior.

Research on innovative foundation systems, specifically deep foundations and hybrid foundation systems, should be investigated to maximize seismic performance for slope development.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

DP: Software, Methodology, Writing – original draft, Formal Analysis, Investigation. NP: Formal Analysis, Writing – original draft, Methodology, Software, Data curation, Validation, Investigation. AT: Writing – original draft, Formal Analysis, Methodology, Investigation, Software, Data curation. PS: Conceptualization, Validation, Writing – review and editing, Supervision, Data curation, Visualization, Project administration.

Funding

The authors declare that financial support was received for the research and/or publication of this article. This work was financed by Vellore Institute of Technology, Vellore.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The authors declare that no Generative AI was used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

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