1 Introduction

Throughout history, earthquakes have caused collapses and human casualties. Recent earthquakes, such as the 2017 Iran-Iraq earthquake, the 2018 Sulawesi earthquake and tsunami in Indonesia, the 2019 Albania earthquake, the 2020 Aegean Sea earthquake in Greece, the 2021 Haiti earthquake, and the 2022 Afghanistan earthquake, have demonstrated the continued loss of life and property. Indonesia is located between two major tectonic plates, the Australian Plate and the Eurasian Plate. Other than the Sulawesi earthquake, Indonesia has experienced several major earthquakes, including the 2004 Indian Ocean earthquake and tsunami in Aceh, the 2006 Yogyakarta earthquake, the 2009 West Java earthquake, the Sumatera earthquake, the Lombok earthquake, and the 2022 Cianjur earthquake. Because of the significant hazards caused by the earthquake, the structural performance and life safety of reinforced concrete buildings in Indonesia were to be prioritized. This tragedy has also given a very big challenge to the nation, especially in the construction industry, to come up with an analysis and design of structures that can withstand seismic loading (Hong et al. 2020). Therefore, it is important to consider seismic loading in the design of reinforced concrete buildings, especially for a building whose seismic resistance is of importance in view of the consequences associated with a collapse, such as an office and research laboratory building. The seismic performance of a building is influenced by the soil types, where the foundation soils are one of the main elements in performing a correct seismic design for structures (Galal and Naimi 2008; Jiang et al. 2012; Majid et al. 2017; Yön and Calayir 2015; Zebua and Wibowo 2022).

Some studies on soil-structure interaction include little to no information on how the building reacts to the varying settlement of the foundation. While excessive and uncalculated settlements may frequently happen throughout the lifespan of the construction, foundation settlement can be expected at the design stage (Hong et al. 2020). This is mostly the result of modifications to the loads and environmental factors, such as nearby new development (Mohammed et al. 2013), deep excavation (Camos et al. 2014), heavy flooding, or earthquakes (Son and Cording 2011). A ten-story reinforced concrete building that had its foundation differentially settled by 25 mm was the focus of an investigation by Lin et al. (2016). According to Indonesian National Standard 8460 (Badan Standardisasi Nasional 2017), for high-rise buildings, the value for the permitted differential settlement was recommended at less than 15 cm plus the width of the foundation (b) in centimeters divided by 600, as long as it could be demonstrated that the upper structure is still safe.

Meanwhile, Indonesia is located between two major tectonic plates, the Australian Plate and the Eurasian Plate. On September 2, 2009, the West Java region of Indonesia was struck by a MW 7.3 earthquake, one of the strongest in recorded history, and some areas were affected, including Bandung city, where the studied 3-story building is located. Furthermore, the Lembang fault is located nearby in the province of West Java. Based on the PUSGEN map, the Lembang fault is one of 81 active faults in Indonesia (Irsyam et al. 2018). Fig. 1 shows Bandung city and the Lembang fault location.

Fig. 1
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Location of study

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In this study, the effects of local soil conditions and foundation settlement have been evaluated. The aim of the study was also to evaluate the interaction between soil condition and structure, such as the lateral displacement, inter-story drift, and internal forces of the reinforced concrete office and research laboratory building, which have been studied in this research.

2 Methods

2.1 Structure Related Data

The structure used in this research is a three-story reinforced concrete office and research laboratory building. This building is an existing structure built in the early 1980s and located in Bandung, Indonesia. The layout and elevation of the building are shown in Fig. 2. The building measures 25.2 m in longitudinal directions with an additional 2.4 m, 14.4 m in transverse directions, and 3.6 m in story height. There are eight longitudinal frames (numbered 1–8) and four transverse frames (designated A-D). The longitudinal spans are 3.6 m. There are three types of spans in the transverse direction: 4.8 m (A–B), 2.4 m (B–C and 8–9) and 7.2 m (C–D). The building's lateral load-resisting system is made up of reinforced concrete moment-resisting frames (RC-MRF) in both directions. The roof is constructed by steel frames with a span of 14.4 m. The concrete compressive strength fc’ = 30 MPa and the reinforcement yield strength fy = 300 MPa were used in the analysis. The geometry of the structures involved in the study, along with the various details of the structural parameters, are shown in Table 1.

Fig. 2
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Building configuration

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Table 1 Detail of structures
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2.2 Loading

The original structure was built in accordance with the 1971 edition of the Indonesian Reinforced Concrete Code (Peraturan Beton Bertulang Indonesia (Indonesian Concrete Reinforced Regulation), 1971) and the 1970 Indonesian Load Code (Peraturan Muatan Indonesia (Indonesia Load Regulation), 1970) (Peraturan Muatan Indonesia (Indonesia Load Regulation), 1970). The design was modified for this study in accordance with the provisions of the most recent 2019 edition of Indonesian National Standard 1726 (Badan Standardisasi Nasional 2019) for seismic design and Indonesian National Standard 1727 (Badan Standardisasi Nasional 2020) for load specification. According to the 2019 edition of Indonesian National Standard 1726, the structure was designed as an Ordinary Moment Resisting Frame (OMRF) building for seismic loads (R = 3, Ω0 = 3, Cd = 2.5). For the seismic design of a building, the parameters R, Ω0 and Cd represent the ductility-related factor, over-strength related factor, and lateral displacement magnification factor, respectively. The MCER response spectrum for Bandung was used to calculate the design base shear represents a 1.0% probability of collapse within 50 years.

Based on Fig. 3, design earthquake spectral response acceleration parameters at short periods, SDS, and at 1 s periods, SD1, shall be determined from Eqs. 1 and 2, respectively.

$${S}_{DS}=\frac{2}{3}{S}_{MS}$$
(1)
$${S}_{D1}=\frac{2}{3}{S}_{M1}$$
(2)

Where SMS = the MCER, 5% damped, spectral response acceleration parameter at short periods adjusted for site class effects. SM1 = the MCER, 5% damped, spectral response acceleration parameter at a period of 1 s adjusted for site class effects. SDS = design, 5% damped, spectral response acceleration parameter at short periods. SD1 = design, 5% damped, spectral response acceleration parameter at a period of 1 s

Fig. 3
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Design Response Spectrum (ASCE/SEI 7-16, 2016)

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As shown in Fig. 4, the foundation was assumed to be on soil represented by five site class (SA = hard rock, SBC = rock, SC = very dense soil and soft rock, SD = stiff soil and SE = soft soil).

Fig. 4
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Response spectrum (PuSGeN et al. 2021)

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The reinforced concrete office with laboratory research building had been modeled and analyzed using software for structural analysis and design. The loads that are considered in this analysis are gravity load (dead and live load), wind load, and seismic load. The structure was designed to withstand a superimposed dead load (SIDL) of 1.44 kN/m2 at floors, 3.1 kN/m2 for stairs, and 0.39 kN/m2 at the roof, and 2.35 kN/m2 for a brick wall, in addition to self-weight of the structural members, and a 2.4 kN/m2 live load at the office area, 3.83 kN/m2 at the corridor, 4.79 kN/m2 at the staircase and laboratory area, and 0.96 kN/m2 at the roof. For some office areas, live load is 0.72 kN/m2 for partition. The wind load is applied at 0.77 kN/m2 for closed or half-closed buildings and 0.38 kN/m2 for roofs. There are several combinations of load cases that were applied to the building in this research based on the most recent 2019 edition of Indonesian National Standard 1726 for seismic design. Fig. 5 shows a structure model without and with foundation settlement. The settlement is selected at 150 mm, which is in accordance with Indonesian National Standard 8460.

Fig. 5
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Frame without and with foundation settlement

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The key variable of all structure model is presented in Table 2. Structure models are labeled in two segments that are connected by hyphens. The label is led by description of soil type and followed by the depth of maximum settlement foundation.

Table 2 Structure model parameters
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3 Results and Discussion

The seismic base shear force that acts on the structure, lateral displacement, inter-story drift, and internal forces for RC structures are discussed and presented together with the factors that influence them.

3.1 Seismic Base Shear Force

The base shear is the total lateral force design at the base of the building. The base shear is calculated depending on the building's vibration period and the type of soil. The fundamental periods of the structures in x-and y-direction are 0.463s and 0.359s, respectively. Table 3 shows the spectral response acceleration and seismic base shear force that is acting on the model. It is observed that very dense soil and soft rock (SC) experienced the largest seismic base shear force, which is 454.06 tons in both directions. This result indicates that the magnitude of the base shear force does not depend on the type of soil.

Table 3 Sa and Base shear
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3.2 Lateral Displacement

Lateral displacement is important when structures are subjected to lateral loads like seismic or wind loads. Lateral displacement is affected by structure height and slenderness because structures become more vulnerable to lateral load as building height increases. Figs. 6, 7, 8 and 9 show lateral displacement in four directions under different base shear forces (depending on soil type) and foundation settlement. All the structure models are analyzed in the software structure analysis with the configuration shown in Fig. 2 and Table 1.

Fig. 6
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Story displacement of static analysis along X-direction positive

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Fig. 7
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Story displacement of static analysis along X-direction negative

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Fig. 8
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Story displacement of static analysis along Y-direction positive

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Fig. 9
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Story displacement of static analysis along Y-direction negative

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It has been seen from Figs. 6a, 7, 8 and 9a that with the change in soil type (which consequently changes the base shear force) and without foundation settlement, the value of lateral displacement varies. The largest lateral displacement value is 57.14 mm on structure model SC_0 at X-direction positive. The displacement of site soil SC is the greatest among the other models. The top displacement in the X and Y directions for SC_0 is greater than 50 mm. The smallest lateral displacement value is 33.59 mm on structure model SA_0 at Y-direction positive.

The effect of foundation settlement makes the lateral displacement larger, especially in the X-direction. In the X-axis direction, the highest increase occurred in hard rock (SA), which was 130%, while the smallest increase occurred in rock soil type (SBC), which was 80%. On the Y axis, the displacement value only increases by about 3% to 6% in all types of soil conditions.

3.3 Inter-Story Drift

Inter-story drift is the drift of one level of a multi-story building relative to the level below as the building sways during an earthquake. The inter-story drift can not only measure the damage degree and performance level of the structure but also intuitively reflect the deformation between the layers and the overall deformation of the structure. The maximum relative deformation between layers is used as the overall performance index of the structure, so that the overall performance index of the structure is obtained. Therefore, in this paper, when studying the response of a RC frame structure to different soil types and foundation settlement, the maximum inter-story drift of the structure is selected as an index for determination. The limit value of interstory drift of a RC structure under seismic load is 0.02hsx, where hsx is the story height. According to SNI 1726, the story drift in any story due to the minimum specified lateral load shall not exceed 72 mm.

To calculate inter-story drift based on Fig. 10 and Eq. 3, a three-story RC building under which five different soil types (hard rock, rock, very dense soil and soft rock, stiff soil and soft soil) is investigated.

Fig. 10
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Story Drift Determination (ASCE/SEI 7-16, 2016)

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The deflection at level x (δx) used to compute the design story drift, shall be determined in accordance with the following equation:

$${\delta }_{x}=\frac{{C}_{d}{\delta }_{xe}}{{I}_{e}}$$
(3)

Cd = deflection amplification factor (2.5). δxe = deflection at the location required by this section determined by an elastic analysis. Ie = Importance Factor (1.0)

Figs. 11, 12, 13 and 14 show the values of the maximum inter-story drift of structures with different soil types and settlement foundations. In general, the maximum inter-story drift of the structure increases with settlement and is location dependent.

Fig. 11
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Inter-story drift along X-direction positive

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Fig. 12
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Inter-story drift along X-direction negative

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Fig. 13
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Inter-story drift along Y-direction positive

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Fig. 14
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Inter-story drift along Y-direction negative

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As shown in Fig. 12(b), due to settlement of 150 mm, the value of the maximum inter-story drift at the second and third floors exceeds the limit of the elastic inter-story drift of 72 mm. The SC, SD, and SE soil types and inter-story drift on the 2nd and 3rd floors exceeded the permit limit, while the SA and SB soil types only on the 3rd floor exceeded the permit limit.

The effect of foundation settlement makes the inter-story drift larger, especially in the X-axis direction. The highest increase occurred in hard rock (SA), which was 270%, while the smallest increase occurred in medium rock (SC), which was 160%.

On the Y axis, the increase in value of inter-story drift is less than 2% in all types of soil conditions. Figs. 13 and 14 show the value of maximum inter-story drift along Y axis. This shows that even if a 150 mm settlement occurs, the maximum inter-story drift ratios do not exceed the limit.

3.4 Bending Moment and Shear Force

The shear force and bending moment results for ten structure models have been taken from the analysis results, which are tabulated below. The bending moment and shear force are calculated for each load combination and seismic zone.

Bending moment and shear values in columns and beams are shown in Tables 4, 5, 6, 7, 8, 9 and 10. For column structures C1, C2, and C3 as well as beams B1 and B2, there was no significant increase in bending moments and shear forces between before and after foundation settlement. Column C1 has a change of less than 1.5%, both an increase and a decrease in the value of the moment, while for the shear force there was an increase of approximately 3.0% to 4.5% for all soil types. In column C2, the moment changes from 6.0 to 9.5%, while the shear force increases from 15 to 25%.

Table 4 Comparison maximum bending moment and shear force for column C1
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Table 5 Comparison maximum bending moment and shear force for column C2
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Table 6 Comparison maximum bending moment and shear force for column C3
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Table 7 Comparison maximum bending moment and shear force for beam B1
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Table 8 Comparison maximum bending moment and shear force for beam B2
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Table 9 Comparison maximum bending moment and shear force for beam B3
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Table 10 Comparison maximum bending moment and shear force for beam B4
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For column C3, the increase in moment and shear due to foundation settlement is 1.85–2.71%. The rock soil conditions experienced a maximum increase and decrease in the moment and shear values in the C1, C2, and C3 columns.

As a result of the decrease, beam B1 experienced an increase in the value of the moment by 16 to 24% for the moment, and 2.3 to 11.5% for the shear force. The smallest increase value occurred in SC soil conditions, while the largest increase occurred in SE soil conditions.

The increase in the moment and shear values in Beam B2 is not too large, around 3.9–5.5% for the moment and 2.9–3.91% for the shear. SC soil conditions have the smallest increase in percentage value, while SA soil conditions have the largest increase.

Significant value changes occurred in beams B3 and B4 whose values increased by more than 50%. The moment value in beam B3 increased by 24–39.84%, while the shear value increased by approximately 42–60.14%. SC soil conditions experienced the lowest increase, while SA soil conditions experienced the largest increase. According to Figure 2, the maximum shear force and moment bending beam B3 occur at 2nd floor grid B7-8 and stair landing grid D2-3, respectively. For structures with foundation settlement, maximum, shear force and moment bending beam B3 happen at 2nd floor grid C7-8 and stair landing grid D2-3, respectively.

Figure 2 depicts shear force and moment bending beam B4 without foundation settlement at stair landing grids 9B-C and D′8-′9. Maximum shear force and moment bending beam B4 occur at 2nd floor grid D′8-9 for foundation settlement structures.

4 Conclusions

In this paper, the effect of different soil types and foundation settlement on the structure’s performance is studied by comparing the maximum lateral displacement, inter-story drift, and internal forces under seismic load. The following are the main findings and conclusions of this research:

  1. (1)

    Even though it is an old building, if there is no foundation settlement, the inter-story drift is still within allowable limits;

  2. (2)

    The inter-story drift value exceeds the permit limit due to foundation settlement;

  3. (3)

    SC (very dense soil and soft rock) soil type results in the largest values of base shear, displacement, inter-story drift, and internal force;

  4. (4)

    The hard rock soil type SA produces the largest increase in internal forces when the structure has a foundation settlement.