Seismic Performance of Buildings with Various Configurations in Hilly Regions

Structures on incline ground are vulnerable to earthquakes because of irregularities in plan and elevation. The structural configurations on slopes have been observed, with stepback and stepback-setback configurations being the most common. In mid to high rise buildings, shear wall and C-shaped shear wall cores are commonly used lateral load resisting components. The current research focuses on comparing the seismic performance of L-shear walls(LSW) at the corners, C shear-walls at core(CSW) and Reinforced concrete-filled steel tube column (RCFST) at corners and cores in stepback, and stepback-setback configurations buildings considering the base of the structures fixed designed for Indian codes using response spectrum analysis. The structural analysis tool ETABS 2017 was used to perform seismic analysis. Buildings on a hill slope with various configurations are studied: bare frame, concrete blockwork infill, LSW full bay at corners, LSW half bay at corners, CSW and RCFST column at corners and core. The characteristic parameters such as base shear, forces in the columns at the ground floor, storey drift, maximum storey displacement, time period, the bending moment in columns at every floor level and storey shear in structures will be determined and analysed for the different structures at the sloping ground. Structures with corner LSW perform better than buildings with centrally located shear walls at the core, whereas LSW at half bay in the corner and RCFST columns at corners and core serve the dual objective of space constraint and improved performance.


Introduction
Strong earthquakes arise at any time, and constructions with irregularity have been shown to be the most susceptible. Construction activity on steep slopes is compelled by a scarcity of plain ground in the hilly terrain. Structures on inclines differ from those on flat land so that they are very uncertain and asymmetrical in both along and across incline directions. The mass and stiffness of such constructions vary vertically and laterally resulting in the centre of mass and rigidity on various floors do not coincide, leading to dominant torsional mode of vibration. Given the circumstances, it is necessary to explore the responses of such structures in order to make them earthquake-resistant and avoid their failure, hence minimising casualties. Due to the unpredictability of mountainous slopes, the influence of slope on structures subjected to seismic loads must be investigated.
A "Shear-wall" is a part of a structure that is subjected to lateral loads in its plane. The stiffness and strength characteristics of the wall determine the extent to which this wall shares the lateral load applied to the structure. The frame's strength and stiffness are enhanced by the shear wall and RCFST column. The shear-walls are capable of withstanding lateral stresses even those caused by seismic tremors and wind. The height of columns is not the same for buildings on sloping land, which impacts the building's performance during an earthquake. The purpose of the present work is to reduce the damage in structures built on sloping grounds by using shear wall, RCFST column etc.
For the Design Basis Earthquake, the performance of shear-wall and CSW buildings is Immediate Occupancy (IO), whereas the performance of shear-wall buildings is Life Safety (LS) and CSW buildings are Collapse Prevention for the Maximum Considered Earthquake (CP). As a result, it may be inferred that shear-wall construction has fared marginally better than CSW construction [1].
Plan irregularities are indicated by the existence of short columns on the uphill side, while vertical irregularities result from differences in strength and stiffness of succeeding stories all along the height, resulting in a complex dynamic response during seismic excitation [2].
Seismic analysis was conducted using RSA on an eight-story structure that included a bare frame and structure with shear-wall in seismic zone III, with the conclusion that when the contribution of the shear wall is considered, storey drifts and displacements are significantly reduced [3].
The floor at road level, simply if there should be an occurrence of downhill structures, is most vulnerable to damage, according to a dynamic analysis of a building at 450 slope and vertical cuts with varying heights for a bunch of five ground movements from Pacific Earthquake Engineering Research Centre database. Under cross incline excitation, stepback buildings are prone to significant torsional impacts, and storey drift there in upper three storeys of a sloping ground building is equivalent to that of a three-storey regular building; as a result, the pattern of inter-storey drifts varies between structures. The results of the analytical investigation are backed up by observations of the damage pattern during the Sikkim earthquake [4].
The stiffness, roof displacements, and seismic performance of RC buildings are all improved by infill walls. [5].
The seismic response of three different structures placed on sloping terrain is considered, and it is discovered that stepback-setback constructions are better appropriate on inclining terrain [6].
The performance of sloped structures is especially poor in the cross-slope direction, caused by torsional irregularities, resulting in disappointment at even lower intensities of shaking, according to a time history analysis of a sloped building using bidirectional components of time histories of seven recorded ground motions. Short columns displayed brittle shear failure at ground level, which is the fundamental reason for these structures' failure in both along and cross slope excitation [7].
When a shear wall is installed at two corners of a structure for 7.50, 150, and 300, it was discovered that the mode contributes to modal mass participation up to higher modes due to the building's asymmetry [8].
The base shear of the infill structure grows with the addition in stiffness of the structure, according to a pushover analysis on G+9 storey structures situated on sloping land at a 270 slope with and without infill walls. The storey drift of the soft storey structure is properly controlled by masonry infills within the bottommost storey, showing that the soft-story building's performance during earthquakes is more sensitive than the full-infill type [9].
On slanting terrain, stepback-setback building frames were found to be more acceptable than stepback frames [10].
SAP2000 is used to analyse the response system for four mathematical models. The maximum forces, displacements, and storey drift were also investigated. Short columns are the most important component for steep slope building. It is preferable to install the shear wall on the shorter column side to reduce shear force and bending moment. [11].
The collapse of hill structures is mostly caused by shear failure of short columns, according to stepback buildings planned and evaluated for gravity loads and specific moment resisting frame. Furthermore, when bidirectional ground movements are applied to a step-back structure, the highest inter storey drift is not always in the major direction [12].

State of the Art
In this paper, the state of art on seismic analysis, behaviour, and analytical modelling of elements of building on hill slopes with various configuration i.e., stepback-setback and stepback building has been brought out. The buildings in hilly region have different dynamic properties when compared with the buildings built on level ground [19].
In buildings resting on sloping ground, within a particular storey there is huge variation of column forces and the columns with higher bending moment at the upper side of the slope are affected severely during earthquake [20].
Stepback and setback building frames are observed to be more reasonable on slanting ground, contrasted with stepback frames [21].
The purpose of present work is to improve the performance of the structures built on sloping grounds. The same is compared by placing shear wall in various orientations and by using RCFST column instead of shear wall.

Scope of the Study
Seismic analysis is carried out on a building on plain ground and two types of buildings resting on slopes, namely stepback and stepback-setback, by response spectrum approach using finite element software ETABS Version 2017. An attempt has been made to strengthen these buildings which are formed commonly due to architectural purpose with the help of shear walls at different locations, RCFST column at corners and blockwork infill in the open ground storey by reducing the response of such building in terms of drift, displacements, time period and storey shear etc. In the long run, a suitable plan of attempting to be used in a hilly region is proposed.

Modelling and Analysis
Shear walls are regarded shell elements while beams are considered 2-noded beam elements with 6dof at each node. The floor slabs are represented as 4-noded shell components with 6dof at each node and are expected to behave as diaphragms, ensuring integrated action of all vertical load resisting parts. Columns are considered to be square. To support the notion of a strong-column weak-beam, the beams' cross-sectional area is kept less than that of the columns. In the modelling, the material is assumed to be isotropic. The concrete block infill wall's deadweight is assigned to the beam as a uniformly distributed load. The concrete block infill wall is modelled as an equivalent diagonal-strut member pinned with eccentric back bracing. The angle of the diagonal-strut for the full panel infill wall is taken as 26.5650 and that for the half-panel infill wall as 44.740 as per clause 7.9 of IS 1893 (Part I) [13]. Storeys with one way slanted at 280, with a dimension in the plan as 30 m x 25 m and storey height of 3.2 m, as illustrated in Figure 1.
For the built-up RCFST composite column 550 mm × 550 mm, Reinforced cement concrete (RCC) column of 450 mm × 450 mm is embedded in the 50 mm thick Fe345 steel tube as demonstrated in Figure 2. The RCFST composite column is designed using section designer in Etabs 2017 [14].

Models Investigated
Three distinct building configurations, Regular, Stepback, and Stepback-Setback, are used in this study, as indicated in Figure 3, with plan view of shear wall positions and RCFST column configuration in Figure 4, and thirteen models as indicated in Figure 5 are investigated as follows: P: Bare Frame on plain ground. 1S: Stepback bare frame at a slope.

2S:
Stepback frame at a slope with Concrete block infill walls and open ground storey.
3S: As with model 2S, only the corner panels have L type shear wall till top.
4S: As with model 2S, only the corner half panels are infilled with L type shear wall till top.
5S: As with model 2S, only the centre core of building is infilled with C type shear wall core till top.
6S: As with model 2S, the columns at corner and core are replaced RCFST Composite column. 1SS: Stepback-Setback bare frame at a slope. 2SS: Stepback-Setback frame at a slope with Concrete block infill walls and open ground storey.
3SS: As with model 2SS, only the corner panels have L type shear wall till top.
4SS: As with model 2SS, only the corner half panels are infilled with L type shear wall till top.
5SS: As with model 2SS, only the centre core of building is infilled with C type shear wall core till top.
6SS: As with model 2SS, the columns at corner and core are replaced RCFST Composite column.

Analysis Method
All of the models in this study are analysed using the linear static method i.e., Equivalent static method (ESM) and the linear dynamic method i.e., Response spectrum method (RSM). The software ETABS 2017 is used to do linear analysis. Buildings have been assigned dead and live loads according to IS 875 Part I and II. All of the structures are designed as per IS 1893 and IS 13920. To analyse the seismic response of the structures, ESM and RSM analyses are carried out and the findings compared. Mode shapes are usually acquired in a normalised form in modal analyses; hence the results of the RSM must be suitably scaled. The scaling in this study was done by equal the base shears acquired from ESM and RSM according to IS1893 (2016). A minimum number of modes was considered for each structure instance, with the entire sum of modal masses equating at least 99 per cent of the overall seismic mass. Accidental eccentricity and torsional effect are considered. Damping is estimated to be 5%. Table 1 shows the properties that were used for the buildings.

Results and Discussion
The various models were analysed using Etabs 2017. The outcomes are presented in a way that is acceptable for each of the study's models.

Time Period
The natural time periods from IS: 1893-2016 codal provision and Etabs analysis results for Model P to 6SS are presented in Table 2. The natural time periods obtained from the code do not match the analysis results, as seen in Figure 5 and Figure 6. Their variation in along and across slope direction is illustrated in Figure 6 and Figure 7. As per the equivalent static method, in IS 1893(Part 1):2016, the empirical relation is given cannot portray the right values of the time period in both along and across the slope direction, whereas Response spectrum analysis using free vibration analysis produced better results. It is seen that time period decreases as the seismic weight of the structure decreases as seen in P, 1S and 1SS. It is noticed that as the structural stiffness increments, time period decreases. Buildings with LSW at corners have the shortest period of vibration.

Axial Force Distribution
Axial force down the storey height of various structures setup has appeared in Table 3. From Figure 8, contrast between axial force distribution down the storey of different models is noticed. Axial force is maximum in models having an L-shear wall at full panel then half-panel and then at shear wall core, due to the higher stiffness provided by shear walls. Bare frame models have the least storey shear. Axial force in stepback-setback models decreases after 6 th storey because of setbacks which results in less seismic weight of storeys as compared to stepback building. As the model is laying on an inclined base, the measure of axial forces in the stepback-setback models is lower than the stepback models.     Table 4 lists the base shears for all of the models. Base shear is an element of mass as well as stiffness of the structure. However, due to increase in seismic weight of structure due to shear wall and composite columns, there is an increase in the base shear. The infill structure's base shear increases as the structure's mass increases. Maximum base shear is seen in models having a shear wall due to increased stiffness. Least base shear is seen in Regular building on levelled ground and highest in the stepback building. Base shear in Half panel L-shear wall and full panel L-shear wall is approximately near. Figure 9 depicts the base shear variations of various models.

Time Period (T) and Modal Mass Participation (P k )
Dynamic mass participation ratios and fundamental periods in the first three modes are illustrated in Tables 5  and Table 6 for all building configurations along and across the slope direction. According to IS 1893:2016 building in seismic zone IV and V, the initial 3 modes together, in each principal plan direction, ought to contribute at least 65per cent mass participation factor to avoid irregularity in lateral storey in a principal plan axis. This is well satisfied in all the models. Because of design inconsistency, mass participation in the fundamental mode in the case of working on a slope is significantly lower than in ordinary construction. The participation of higher mode is more in building resting on sloping ground. In stepback-setback, when an earthquake strikes in the direction of the slope, it endures stiffness irregularity. But, when subjected to earthquake across the slope; besides stiffness irregularity, buildings undergo torsion response, due to non-coincidence in the centre of stiffness and mass. This emphasises how important it is for a structure's stiffness and mass to be distributed uniformly along its elevation to maintain uniform lateral force distribution.

Lateral Displacement
The maximum displacements at every storey level concerning the ground determined using ESM and RSM for various configurations are displayed both along and across the slope in Figure 10 and Figure 11. To represent the impact of torsion, the displacements are seen both along and across directions when force is acting in a specific direction. The storey displacement is largest for top storey, steadily decreasing down the structure until it is nearly insignificant at the bottom storey.
With models resting on slope; as the centre of mass and rigidity of different configurations buildings do not overlap because of irregularity, bi-directional displacement(along and across) for unidirectional force is seen. In stepback and stepback-setback models, it is seen that the taller side of the model displaces more than the shortened side as the taller side has columns longer than that of the shorter side. Because of this explanation, the taller side acts more flexible in comparison to the shorter side when subjected to a similar measure of force.
Models with L-shear wall at corner showed excellent displacement control than shear wall core and composite column models. But stepback-setback models RCFST columns are proved more beneficial in displacement control than only infill model and shear wall core. When earthquake forces are applied across the direction, the top storey displacement is much higher than when they are applied along the direction.

Storey Drift
According to IS 1893(Part 1): 2016 storey drifts in any storey should not outperform 0.004 times the storey height [9]. Storey height of 3.2m has got 12.8mm. Figure 12 and Figure 13 show the highest storey drift at each storey level derived using ESM and RSM for the various configurations, as well as both orientations of the slope, i.e., along, and across. In all methodologies, stepback-setback models indicate maximum storey drift in top storeys. Ground storey drift is maximum in the model on the plain ground due to stiffness. Models with L-shear walls at corners in full panel show extremely less inter-storey drifts.

Storey Stiffness
The overall stiffness provided inside a storey by its walls, lateral load resisting elements, and columns is referred to as the storey's stiffness. The stiffness of every storey for each model is shown in Figure 14 as per ESM and RSM. It is observed that in both RSM and ESM, stiffness variation along the storey heights is comparative. Models on the slope show exceptionally less stiffness in both the methods, which is most susceptible in the event of an earthquake. To prevent this, shear walls are provided to overcome the issue of stiffness deficiency. L-shear wall at corners proved more beneficial than shear wall core in respect of performance.

Bending Moment in Column
Bending moment in the column at each storey level and in each model is shown in Figure 15. It is seen in both ESM and RSM, the measure of moment in each column of every storey in model P is practically comparative. The greatest bending moment is at the columns of bottommost storey and as the storey height increments, the value of bending moment lessens in the model on the plain ground i.e., P. Models with shear wall have the least bending moment in columns of ground storey. Strangely, in the stepback-setback models i.e., SS category models despite having similar tallness of columns on one or the other side of the structure, enormous variation in column bending moment have been seen inside a specific storey. The columns at the upper level of the slant are confined to a greater bending moment than the columns at the bottom level of the slant which is overcome by providing an L-shear wall at the corners and RCSFT columns at corners.

Shear Force in Columns at Ground Level
Shear force at ground level columns in each model is shown in Table 7. In the building on levelled ground, shear force in the ground level columns is almost the same in all columns and both along and across the slope direction. When compared to the remainder of the columns on the bottommost floor, the shear force in the extreme right column is much larger along the slope of the stepback building. Comparatively, in the extreme left column and adjoining column (frame A and B) at ground level, the value of shear force is only 1 to 2% of that of the extreme right column. Across the slope, value of shear force in the extreme right column (frame F) at ground level is less than the corresponding values obtained for earthquake forces along the slope direction. From a design perspective, it is clear that the size and stiffness need of the extreme right column at ground level must be carefully considered such that it is safe even in the worst probable load combinations both along and across the slope's direction.
In contrast with stepback building, stepback-setback building experiences less shear force in the extreme right column (frame F) in both the direction.
It is seen that due to the presence of the shear wall in Model 3S, 4S, 3SS and 4SS, shear force value is reduced to approximate nil.
According to Table 7, it is seen that the actions needed for design purposes are predominant when earthquake forces are in along the slope direction.

Conclusions
The seismic response of the two typical configurations of building on slopes and building on flat terrain was studied by performing Response spectrum analysis.
The ends drawn from the above investigation were summed up underneath: 1. In comparison to the CSW building, it can be determined that the LSW at corners in full and half-panel has performed better. Nonetheless, both of the structures designed per the Indian code perform admirably. 2. Structures on slanted terrain are shown to be more vulnerable than those on flat ground. 3. The models on sloping terrain have been observed to move orthogonally under unidirectional force. 4. Due to the reduction in column height, columns on the higher side of the slope are likewise susceptible to increased bending moments. 5. When the L-shear wall at corners and RCFST columns are employed, there is a large reduction in lateral displacement and lateral drift requirement, and therefore the building's performance improves. In setback buildings, shear walls and RCFST composite columns have been proven to be phenomenally successful in decreasing lateral displacements. 6. The addition of shear walls increases base shear for all models, which is related to the increased seismic weight of the building. 7. When structures are subjected to lateral stresses, the presence of a shear wall affects the overall behaviour of the structures. Displacement and storey drift are much minimised due to shear walls contribution. 8. In regular type building without any setback on sloping ground, with incorporation of shear walls at various locations reduction is found in lateral displacement up to 3-5times, in fundamental time period up to 70-80% and increment found in base shear up to 2-3times in all the suggested models. 9. In stepback-setback models on incline ground, with incorporation of shear walls at various locations reduction is found in lateral displacement up to 5-7times, in fundamental time period up to 50-80% and increment found in base shear up to 2-2.5times in all the suggested models. 10. A dual-type structural system with properly placed shear walls is more effective than a moment-resisting frame system in resisting earthquake stresses and can be employed efficiently for structures on slopes. 11. Shear walls with a spreader construction exhibit superior torsional control, however the difficulty with shear walls is that they limit access to the open ground level, reducing the structure's functional efficiency and concentrating stiffness at a certain point but the stiffness of RCFST composite columns is equally dispersed on entire base of the building, and the RC column cross section does not change at the junction, therefore they can be selected where more space access is required.