Introduction

In densely populated urban areas, locating level ground for constructing complex infrastructural facilities and buildings can be challenging. Instead, sloped and uneven natural terrain is often utilised to meet the increasing demand for building constructions. Soil nailing proves to be an effective method for stabilising these irregular surfaces through excavations. Due to urbanisation, cities and towns are rapidly growing and the available land is required to be utilised in the most efficient way possible. In such a scenario, the space that is available in the vicinity of a vertical cut stabilised using soil nailing may be in great demand and can be employed for the construction of any other structure, such as a multi-storeyed building. The presence of the multi-storeyed building constructed in proximity to the nail-stabilised structure may impact the characteristics of the nailed vertical cut, especially in a seismically active region.

Previous research suggests that the technique of soil nailing is effective when compared to other conventional methods and performs well under static as well as dynamic environments. The characteristics of soil-nailed structures under different load conditions were studied using different methods. The field-based performance of soil-nailed structures was determined by Plumelle and Schlosser (1990) and Wong et al. (1997). Wong et al. (1997) described the construction specifications, instrumentation and performance of a nail-stabilised wall constructed to retain a 9 m deep permanent cut of residual soil. The results signified that the nailed wall was effective in retaining the soil and even after three years of construction, the maximum horizontal displacement was below 0.4% of the wall height. Dynamic centrifuge testing on soil-nailed structural models were conducted by Vucetic et al. (1993), Tufenkjian and Vucetic (2000), Wang et al. (2010), Rotte and Viswanadham (2014), Zhang et al. (2014). Wang et al. (2010) performed centrifuge tests on reinforced and unreinforced slope models under dynamic loading to investigate the effect of nail lengths, nail spacing and slope inclinations.

The response of nailed structures to seismic loads was also studied by Hong et al. (2005), Giri and Sengupta (2009), Sahoo et al. (2016), Yazdandoust (2018) and El-Emam (2018) through shake table tests. Giri and Sengupta (2009) performed shake table tests to examine the behaviour of small-scale embankment model slopes under dynamic loading and also numerically simulated using FLAC software. The seismic response of 8 m high helical soil-nailed structures using shake table tests was conducted by Mollaei et al. (2022) to assess the impact of arrangement, orientation and length of nails on their performance. It was concluded that increasing both the length and inclination of nails enhanced the stability of the helical soil-nailed walls during earthquakes with increasing the nail length having a more pronounced effect. Other studies that explored the seismic response of soil-nailed structures include those by Sharma et al. (2020), Yang et al. (2021), Baziar et al. (2023) and Yazdandoust et al. (2024). Juran et al. (1990) Choukeir et al. (1997) Rawat and Chatterjee (2018) carried out analytical studies to understand and predict the performance of ground structures retained through soil nailing. As the mechanism of soil-nailed structures involves the complex mutual interaction between soil, nails and facing, it becomes difficult to capture their behaviour while performing small-scale experiments. So, in most of the literature, the behaviour of nailed structures has been studied with the help of rigorous numerical computational methods (Babu and Singh 2008; Fan and Luo 2008; Zhou et al. 2009; Giri and Sengupta 2009; Singh and Babu 2010; Rawat and Gupta 2016; Dashtara et al. 2019; Johari et al. 2020; Pak et al. 2021; Chen et al. 2022; Maleki and Hosseini 2022; Maleki et al. 2022).

Literature consists of studies of response analysis of multi-storeyed buildings using experimental as well as numerical methods (Maison and Ventura 1992; Chajes et al. 1996; Corbi and Rakicevic 2013; Tabatabaiefar et al. 2013; Fatahi and Tabatabaiefar 2014; Torabi and Rayhani 2014; Jayalekshmi and Chinmayi 2016). Chajes et al. (1996) performed dynamic analysis of a 47-storey tall steel-framed tower using finite element models. Fatahi and Tabatabaiefar (2014) through numerical analysis using FLAC 2D software studied the efficacy of a nonlinear approach over the equivalent linear approach used in dynamic analyses. Three midrise RC moment resisting building models (5, 10 and 15 storeys) were analysed under different soil types. Jayalekshmi and Chinmayi (2016) performed the transient analysis of multi-storeyed reinforced concrete building frames supported on a raft foundation using LS DYNA software by incorporating the soil-structure interaction, generally termed SSI. The buildings had 4, 6, 8, 12 and 16 storeys with a storey height of 3 m and consisting of 4 m wide three bays in either direction.

Under seismic loading, the response of excavated structures adjacent to tall buildings was investigated (Mo and Hwang 1997; O’Riordan and Almufti 2015; Yeganeh et al. 2015; Dashti et al. 2016; Jiang et al. 2022). Yeganeh et al. (2015) explored dynamic response of a high-rise building located near a deep excavation using the finite difference method. A 17-storey RC building having five spans located near a 13 m deep excavation was analysed incorporating soil-structure interaction to study the performance of both structures. A performance-based design was proposed by O’Riordan and Almufti (2015) after analysing a tall, heavy building 130 m high located 10 m outside an 18.3 m deep excavation subjected to various levels of dynamic shaking. Dashti et al. (2016) carried out centrifuge tests to assess the seismic effect of tall buildings on adjacent shallow underground structures. The seismic performance of an 8 m high tunnel and 12 m deep excavation, and their interaction with mid to high-rise (12 and 42 storeys) buildings was studied experimentally and numerically taking into account soil-structure-underground structure-interaction.

Literature reveals that under seismic conditions, the soil-nailed structures have been effective in withstanding strong ground motion. However, the seismic stability of a nail-stabilised vertical cut could be influenced by the response of any structure constructed adjacent to it. Hence, in this study, the influence of reinforced concrete multi-storeyed buildings constructed in the proximity of vertical soil-nailed retaining structures due to space constraints is evaluated under seismic excitation. This practical scenario and its interaction effects are not studied so far as evident from an extensive literature review. The factors such as the load carried by the building, its proximity from the soil-nailed structure and the connectivity between the two structures are incorporated in detail in the analysis to evaluate their significance in the variation in the characteristics of the soil-nailed structure from its seismic performance in the absence of the RC building. For this, the dynamic finite element analysis of a 6 m high nail-stabilised structure with the presence of an adjacent multi-storeyed building and the behaviour of the whole system under seismic loading has been studied. The numerical seismic simulation of such an integrated soil-nailed wall-building system has been performed using Plaxis 3D.

Methodology

The finite element simulation and analysis to evaluate the influence of adjacent multi-storeyed buildings on the performance of a vertical soil-nailed structure were conducted under the artificial time history of El Centro earthquake (1940) ground motion. The nailed structure was designed utilising specifications of the Federal Highway Administration (FHWA) (Lazarte et al. 2015) in such a way that a vertical cut of height (H) 6 m having a horizontal backslope ground was retained. The retention was done using grouted soil nails. The material properties utilised in the design and analysis of the nail-stabilised structure are tabulated in Table 1. The design was carried out assuming the length of the soil nail (L) to be 0.7 times the height of the soil-nailed wall (H) with nails placed horizontally. It was observed that the design of the nailed structure according to the values outlined in Table 1, met the safety factors recommended by FHWA. A study conducted by the authors to identify the effective inclination of soil nails (ί) and their length required for stabilisation of a 6 m high vertical soil-nailed structure under seismic load showed that the nail orientation of 15° with horizontal and nail length to wall height ratio of 0.7 was necessary for improving the seismic resistance of the nailed structure (Amrita et al. 2021). These parameters were found to yield the least deformation of the nail-stabilised cuts under seismic loads and the same values of above-mentioned parameters were chosen for this work. It was assumed that the groundwater table was positioned at a greater depth and thus applied at the base of the model.

Table 1 Details of integrated soil-nailed wall-building system
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Multi-storeyed buildings of three different heights were adopted maintaining the aspect ratio of 1.5. G + 3, G + 5 and G + 7 storeyed RC buildings having a storey height of 3 m were considered. These three buildings consist of 2bay, 3bay and 4bay, respectively with bay widths of 4 m each. The thickness of floor slab was taken as 150 mm at different storey levels and the building was subjected to a live load of 3kN/m2 (IS 13920, 2016; IS 456 2000).The building was founded on a raft foundation of 0.5 m thickness which extends by 1 m on the sides of the building. Other structural characteristics of the multi-storeyed building are tabulated in Table 1.

The seismic response of the nail-stabilised structure in the presence of the multi-storeyed building may also vary depending upon the position and the connectivity of the building to the nailed structure. Hence, different connectivities and positioning between the two structures were taken into consideration. The soil-nailed structure under seismic load was analysed initially in the absence of the multi-storeyed building. Then the multi-storeyed building was spaced at a distance of 4 m from the soil-nailed structure considering the normal boundary clearance at sites. Further, the multi-storeyed building was connected to the soil-nailed structure, thus forming an integrated system. The beams at the first and the second floor of the building were extended and connected to the soil-nailed structure. This type of connection in construction helps to effectively utilise the space between the two structures for parking and storage facilities. Another integrated system was considered in which the multi-storeyed building was placed near the nailed wall leaving no gap between the two structures, i.e., the building wall acts as the shear wall and also retains the nailed soil mass on the other side. In these two connectivity conditions, the two structures were connected to each other and thus formed an integrated soil-nailed wall-building system. The four different connectivity conditions used in the present study are listed below along with the notations used for each case. The schematic representation of the above four conditions for a G + 3 storeyed building is shown in Fig. 1.

  1. i.

    Only soil-nailed structure/Only building in the absence of the other structure, designated as ‘Only soil-nailed wall system’ and ‘Only building system’.

  2. ii.

    Soil-nailed structure and the building 4 m apart without any connection between the two structures designated as ‘No connection system’.

  3. iii.

    Soil-nailed structure and the building 4 m apart with the connection between the two structures at the first and second floor using beams, designated as ‘With connection system’.

  4. iv.

    No gap between the building and the soil-nailed structure, i.e., the building wall acts as the shear wall, designated as ‘Shear wall system’.

Fig. 1
figure 1

Schematic representation of different connectivity between soil-nailed structure and G + 3 multi-storeyed building

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The soil stratum at the site is assumed to be homogeneous. The soil mass retained by the soil nailing was considered to have the same properties as the foundation soil at the site. The impact of the multi-storeyed buildings on the behaviour of the nailed structure was assessed in different soil profiles at various sites. The details of soil sites were taken according to the classification given by the National Earthquake Hazards Reduction Program (NEHRP) (FEMA-450 2003) for seismic design. The soil site classification corresponding to soft soil, stiff soil and very dense soil having designation as Class E, Class D and Class C sites were chosen for the present study. The soil properties used in the analysis for different soil sites are tabulated in Table 2.

Table 2 Soil site classification (Bowles 1996; FEMA-450 2003; ASCE7-02 2013; Plaxis 2022)
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The fundamental frequency of soil-nailed structures and multi-storeyed buildings was evaluated by free vibration analysis. It was conducted for different structures in different site soil profiles and the findings are summarised in Table 3. The fundamental frequency of the nail-stabilised structure in Class E soil site was obtained as 1.3 Hz. The time history earthquake data chosen for seismic analysis of the finite element models was El Centro earthquake data. This ground motion was having the peak ground acceleration (PGA) was 0.3 g and the duration of loading was 20 s. This El Centro earthquake data was selected for seismic analysis as its frequency content of excitation (1.2 Hz) was close to the fundamental frequency of the soil-nailed structure. The frequency of the structures in Class D and Class C sites increases due to the greater strength and stiffness of these soils. The frequency of the multi-storeyed buildings in the three soil sites decreases with the storey height as the increased height reduced the overall stiffness of the building. As can be noted, the natural frequency of G + 5 and G + 7 in soft soil are close to the frequency content of the ground motion.

Table 3 Fundamental frequency of structures in different soil sites
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Numerical modelling of the integrated system

The simulation, modelling and analysis of integrated soil-nailed wall-building systems under seismic loading were carried out using Plaxis 3D software (Plaxis 2022). The basic three-dimensional soil elements were simulated using ten-noded tetrahedral elements. The phreatic surface was placed at the base of the models so that the groundwater table does not influence the response of the structures.

Modelling of soil

A proper simulation of soil is an essential feature which determines the accuracy of the finite element analysis results. The numerical analyses of nail-stabilised structures were carried out by modelling soil using the traditional Mohr-Coulomb model. However, it was emphasised that employing an advanced soil model is necessary where the displacement of nail-stabilised structures is critical for the nearby structures and in the case of seismic analyses (Singh and Babu 2010; Zhang et al. 2015; Kim and Finno 2019; Maddah et al. 2021; Plaxis 2022). So, the Hardening soil with small strain stiffness (HS small) model was employed here. It is an advanced constitutive model used for simulating the dynamic behaviour of soil and it accounts for very small-strain soil stiffness and its non-linear dependency on strain.

The basic characteristics of the HS small model include three stiffness moduli namely, triaxial loading stiffness, oedometer loading stiffness and triaxial unloading-reloading stiffness, in addition to the initial shear modulus and the shear strain at which the secant shear modulus equals 70% of the initial shear modulus. Other parameters include unit weight, cohesion, angle of friction, dilatancy angle and Poisson’s ratio. The unloading-reloading modulus and oedometer loading modulus were taken equivalent to 3 and 0.8 times the triaxial loading modulus, respectively. The stress-dependent stiffness was formulated using a power law, for which the input parameter was adopted as 0.5 and the reference stress for stiffness was taken as 100 kPa (Plaxis 2022; Schanz et al. 1999). The initial shear modulus and the shear strain were calculated using empirical formulas provided by Brinkgreve et al. (2010). The unit weight, modulus of elasticity, angle of friction, dilatancy angle and Poisson’s ratio for three different classes of soil were taken from the corresponding range of values given in Bowles (1996), NEHRP (FEMA-450 2003) and FHWA (Lazarte et al. 2015). The various soil input parameters used for soft, stiff and very dense soil in analysis are tabulated in Table 2.

Modelling of structural elements

The integrated soil-nailed wall-building system consists of elements such as soil nails, facing, beams, columns, shear walls, raft foundations, etc. These structural elements were simulated as linear elastic-perfectly plastic materials. The facing of the nailed structure was modelled as plate elements while the soil nails were modelled as beam elements. These elements are based on Mindlin’s plate theory (Bathe 1982), which accounts for deflections caused by shearing and bending. The parameters for the grouted soil nail were determined considering the material properties of both reinforcement and grout material. The equivalent value of modulus of elasticity for the grouted soil nail was determines as:

$$Equivalent\;modulus\;of\;elasticity,\;{E_{eq}}\; = \;{E_n}\left( {\frac{{{A_n}}}{A}} \right)\; + \;{E_g}\left( {\frac{{{A_g}}}{A}} \right)$$

where A denotes the total cross-sectional area of the grouted nail, En and An denote the elasticity modulus and cross-sectional area of the nail while Eg and Ag denote the elasticity modulus and cross-sectional area of the grout. The input parameters of grouted nails and facing are outlined in Table 4. The properties of the grouted nails were assessed by taking into account the characteristics of both the reinforcement and the grout. The multi-storeyed building was simulated as a frame model. The storey floors and shear walls were simulated using plate elements while the columns were simulated using beam elements, based on Mindlin’s theory (Bathe 1982), which captures deflections due to bending and shearing. Plate elements were also utilised to model the raft foundation. The input parameters for each structural element were calculated based on the material properties specified in Table 1. The modulus of elasticity of concrete is calculated based on IS 456 code (IS 456 2000).

Table 4 Input parameters of soil nails and facing of soil-nailed structure
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Interface elements and meshing

The analysis of integrated systems was carried out by simulating the actual site behaviour which involves modelling of soil and buildings at the site. An apt simulation of soil-structure interaction thus becomes necessary. The interaction between various structural elements and soil was modelled with the help of interface elements. They were provided in regions where the soil made contact with the other elements. So, interfaces were provided between nails and soil, facing and soil and also between raft foundation and soil. Interfaces provide a thin layer of intensely shearing material at connections between the element and the adjoining soil. They have the material characteristics of the surrounding soil elements, except for the strength reduction factor, R. This factor R was taken as 0.8, which is used in the case of concrete-soil interface (Potyondy 1961; Maleki et al. 2022). This value determines the strength and stiffness parameters of the interface. Interfaces also account for the slippage occurring between the adjoining elements, thus minimising the stress-concentrated regions.

Finite element discretisation of the model was done through meshing after the simulation of the integrated system. For the study, mesh sensitivity analysis was performed to evaluate the effect of mesh size and configuration. The software provides five global levels of meshing where the relative element size varies as 2, 1.33, 1, 0.67 and 0.5 corresponding to very coarse, coarse, medium, fine and very fine meshing, respectively. The analysis results gave converging results for the fine mesh density. So, the fine meshing was used for the discretisation of the whole finite element model. To enhance the accuracy of results, the areas near the multi-storeyed building and the soil-nailed structure in every model were further refined.

Dimension of finite element boundary

It is essential to determine the boundary dimensions of the three-dimensional finite element models so that the analysis results do not get affected by the model boundaries. For this purpose, sensitivity analysis was performed. The width of the soil layer beyond the nailed wall and the multi-storeyed building and the thickness of the soil stratum below the foundation level of the building were determined. Hence, these dimensions were incrementally varied and analyses were performed to ascertain the final finite element boundary dimensions. The finalised dimensions of the model utilised for the evaluation of the seismic response of integrated soil-nailed wall-building systems are represented in Fig. 2. All dimensions are shown in terms of the width of the raft footing, B. The soil stratum of length 4.5B was extended on all four sides of the multi-storeyed building. The depth below the footing level influencing the response of the integrated system was determined as 3B. Hence, the overall model dimensions were obtained as 10B x 10B x 3B.

Fig. 2
figure 2

Layout representing boundary dimensions of the finite element model

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Dynamic variables

Under dynamic load, the dissipation of energy caused is defined using damping characteristics. The viscous properties of the material are responsible for the material damping. Here, the damping properties of the material were modelled using Rayleigh damping. A damping ratio of 5% was adopted for the dynamic analysis (IS 1893 Part 1 2016) and the corresponding Rayleigh coefficients were calculated based on the fundamental frequency of the structure and the frequency content of the input dynamic loading. During the analysis, the bottom boundary of the model was completely restrained while the four lateral side extremities were equipped with viscous boundaries representing the infinite soil continuum. The appropriate viscous boundaries simulate actual soil site behaviour by avoiding the seismic wave reflection from the boundary into the soil domain and it also absorbs the incremental stresses produced by the loads under seismic excitation. The seismic load was imposed at the base of the finite element model of the integrated system through the prescribed displacement. The ground motion of El Centro earthquake was used for seismic loading, which is displayed in Fig. 3. The width of the vertical cut was taken as equivalent to 4 times the width of the footing (B) adjacent to the multi-storeyed building for initial analysis. The analysis results were similar to the integrated models when the width of the vertical cut was equivalent to the width of the footing with sides having infinite boundary conditions. So, the present study was conducted by taking the width of the cut as equivalent to the width of the raft footing. Figure 4 illustrates the three-dimensional finite element model of the integrated soil-nailed wall-building system generated in the software.

Fig. 3
figure 3

Modified time history data of El Centro earthquake (1940)

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Fig. 4
figure 4

Finite element model of (a) No connection system (b) Cross-section through the centre of soil-nailed wall

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Validation of numerical modelling

The validation of the finite element simulation and analysis of soil-nailed structure using Plaxis was accomplished using experimental results of dynamic centrifuge testing conducted by Vucetic et al. (1993). Different levels of horizontal shaking were conducted in dynamic centrifuge testing for models of soil-nailed excavation, with a scale factor of 50 applied. The prototype excavation height for the structure was 7.6 m. The soil nails were provided horizontally at 0° inclination with the horizontal and the length of the nail was taken in the range between 0.33H and 1H, where H represents the height of the nailed wall. The nails were grouted nails whose prototype diameter was 152 mm. Three rows of nails were positioned in a diamond-shaped format. The horizontal and vertical arrangement of soil nails were done with spacing of 2.5 m and 1.9 m, respectively. The prototype facing thickness was 160 mm. The cohesion, frictional angle and unit weight of soil used for testing were 7.2 kPa, 36° and 14kN/m3, respectively. A schematic sketch of the centrifuge test model is displayed in Fig. 5.

Fig. 5
figure 5

Longitudinal section of soil-nailed excavation model in dynamic centrifuge test (Vucetic et al. 1993)

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Modelling and analysis of this soil-nailed excavation model subjected to dynamic centrifuge test were conducted with fine meshing of finite element model in Plaxis. The nail length was taken as 0.76H. The soil was modelled as the HS small model and plate elements were used to represent the facing and beam elements for the soil nails. Nails were embedded in the soil mass and the interaction between the soil and structural elements was modelled with the help of interface elements. The model was subjected to a sinusoidal acceleration with an amplitude of 0.28 g applied at its base. The displacement of nails and settlement of the ground surface were evaluated.

Finite element analysis solutions were compared with those of the experimental results, as presented in Fig. 6. It was observed that the results of numerical analysis were consistent with the experimental outcomes. The variations in results were found as less than 15%. Hence, similar modelling and analysis employing Plaxis software were used for the present study to carry out the evaluation of the integrated soil nailed wall-building system.

Fig. 6
figure 6

Displacement profile of soil nailed excavation model obtained from finite element analysis

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Results and discussion

This section discusses the results of analyses performed to evaluate the seismic response of integrated soil-nailed wall-building systems under El Centro ground motion incorporating SSI effects. The behaviour of the whole system with four different connectivities between the two structures was studied under different site soil profiles. The influence of various heights of multi-storeyed building on the response of integrated system were determined. The deformation profile and acceleration patterns of the soil-nailed structure and the multi-storeyed building were recorded and presented. These results are organised in three parts. In the first two parts, the representative results of seismic response of the 6 m high nailed wall and the G + 3 storeyed building founded in soft soil with different combinations of connectivities are discussed. The third part comprises results obtained for the different heights of multi-storeyed buildings in different soil sites under seismic excitation.

Seismic response in soil-nailed structure

Displacement profile

The displacement profile of the 6 m high soil-nailed structure under the influence of the adjacent G + 3 multi-storeyed building in its proximity under seismic loads is discussed here. The dynamic excitation resulted in lateral displacement of the nailed wall which was maximum at the crest of the wall. Figure 7 displays the maximum lateral displacement of the soil-nailed wall having different connectivities to the nearby G + 3 multi-storeyed building under El Centro excitation in the soft soil profile (Class E site) in terms of the height of nailed wall. The lateral displacement of the soil-nailed wall is represented as δ and the maximum horizontal displacement is represented as δmax. The displacement of the nailed wall (δ) is expressed as a percentage of the wall height (H). The graph shows that for all models, δmax occurs at the crest of the nailed wall and it reduces towards the toe. From the graph, it can be noted that the highest value of δmax is obtained for the wall in the absence of the multi-storeyed building. The displacement is 0.75% of the nailed wall height. The seismic performance of the nail-stabilised structure is affected by the nearby multi-storeyed building and its presence reduces δ of the nailed wall. When compared to Only soil-nailed wall structure, δmax value decreases for the No connection system. Further reduction in the value of δmax is observed when the two structures are connected to each other.

When the soil-nailed structure stands independently without any neighbouring buildings, the seismic activity induces lateral deformation of the wall primarily influenced by the input ground motion and the reinforced soil characteristics. However, the presence of structural load adjacent to the nail-stabilised structure affects its performance and limits the unrestricted lateral movement of the nailed wall when subjected to dynamic load, thereby reducing its deformations. The integration between the two structures further helps in the distribution and sharing of the seismic loads coming from the other structure. The seismic load of the building helps in effectively bracing the nailed structure while the load from the nailed wall is transferred to the foundation by the building and yields lower deformations. The lateral displacement is minimal in the Floor connection system. The percentage reduction in δmax of the nailed wall in the presence of G + 3 storeyed building is 32.67%, 49.08% and 47.92% for No connection, Floor connection and Shear wall in comparison to Only soil-nailed structure, respectively.

Fig. 7
figure 7

Maximum lateral displacement of soil-nailed wall in the presence of G + 3 building

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Due to land scarcity, when the space near a soil-nailed structure is being utilised for constructing a multi-storeyed building, the effective way to enhance the seismic stability of the nailed structure is through the integration of the building with the nailed structures such as Floor connection and Shear wall systems. The Floor connection system yields minimum deformation of the soil-nailed wall under El Centro excitation, which produces near-resonant condition in stand-alone case.

The lateral deformation profile of different integrated systems obtained from the numerical analyses is depicted in Fig. 8. Under seismic excitation, the Only soil-nailed wall system shows deformation of the nail-stabilised vertical cut in the form of a wedge. δmax occurs at the crest of the cut and the displacement reduces towards the toe and a large volume of soil mass is seen deformed in an inclined manner. In the No connection system, the sliding pattern of the soil mass is different with the presence of the G + 3 multi-storeyed building. The deformation of the wall reduces and the volume of displaced soil mass is also reduced. The soil mass deformation in the Floor connection and Shear wall connection is much less and the whole system acts as a single unit due to the integration between the two structures.

Fig. 8
figure 8

Maximum lateral deformation of integrated systems with soil-nailed structure and G + 3 building

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The time history representative of lateral deformation obtained at the crest of the soil-nailed wall for 20 s during seismic excitation in the presence of G + 3 multi-storeyed building is shown in Fig. 9. The above-discussed results can also be viewed from the graph. The maximum deformation of the nailed wall occurs in the Only soil-nailed wall system and the least is obtained in integrated Floor connection and Shear wall systems.

Fig. 9
figure 9

Time history of lateral deformation at crest of soil-nailed wall in the presence of G + 3 building

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Pseudo spectral acceleration (PSA) response spectrum

Figure 10 discloses the pseudo spectral acceleration (PSA) response spectrum of the nail-stabilised structure in the presence of G + 3 multi-storeyed building. The graph shows the variation of PSA of the nail stabilised wall with the natural period. It is apparent that the spectral acceleration obtained at the crest of the nailed wall increases with the period and reaches the peak value near to the natural period of the system. The highest peak of the PSA curve is obtained for Only soil-nailed system. The peak acceleration of 0.22 g corresponds to a period of 0.56s. The presence of G + 3 multi-storeyed building in the proximity of the nailed structure causes the acceleration of the nailed wall to reduce. For the No connection system, the peak of the PSA curve is at 0.15 g. When the two structures are connected to each other either through beams or as the shear wall, the acceleration decreases when compared with the Only soil-nailed wall system. The peak values of 0.18 g and 0.2 g are obtained for Floor connection and Shear wall systems, respectively. The decrease in acceleration is attributed to its connection with the multi-storeyed building and additional mass from the structure acting during seismic excitation. The seismic load of the multi-storeyed building effectively braces the soil-nailed structure and helps in reducing its acceleration response.

Fig. 10
figure 10

PSA spectrum at crest of soil-nailed wall in the presence of G + 3 building

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Seismic response in multi-storeyed building

Displacement profile

Although evaluation of the seismic response of nail-stabilised structures in the presence of multi-storeyed buildings is the primary purpose of the study, the seismic performance of the multi-storeyed building is equally important for human safety and hence recorded and discussed in this section. Under El Centro earthquake excitation, the deformation of G + 3 multi-storeyed building in the presence of adjacent nail-stabilised structure is presented in Fig. 11 in the form of inter-storey drift. The displacement of one floor level of the building relative to another level either above or beneath it, is referred to as storey drift. This quantity helps in understanding the response and behaviour of the structure under seismic loads. The deformation of the multi-storeyed building depicts similar patterns to the deformation of the soil-nailed wall. The presence of the nailed structure affects the performance of the G + 3 building under seismic load. In case of the Only building system, the maximum lateral displacement obtained at the roof level of the G + 3 storeyed structure is 28.25 mm and the maximum inter-storey drift recorded is 0.06%. The inter-storey drift in the No connection system reduces by 8.46% when compared to the Only building system. In the case of integrated soil-nailed wall-building systems wherein the two structures are connected, the inter-storey drift in the building further decreases. When the connection is provided between the two structures, the load from the building and soil-nailed wall gets distributed and rearranged. The inter-storey drift in Floor connection and Shear wall systems decreases by 57.64% and 66.82%, respectively in comparison to Only building system. As per the codal provisions of IS 1893 Part 1 (2016), the maximum translational relative displacement between two consecutive floors due to earthquake forces should be within the limits of 0.004 times the level difference between these floors, i.e. the inter-storey drift should be less than 0.4%. In the integrated soil-nailed wall-building systems, the inter-storey drift decreases compared to the Only building system and is within the specified limits. The integrated system is found to be seismically stable under the applied earthquake loading having a PGA of 0.3 g. The time history representative of lateral deformation at the roof of G + 3 multi-storeyed building with various connectivities with the soil-nailed wall for 20 s under seismic excitation is depicted in Fig. 12. As it is evident, the deformation of the building is more in Only building system and No connection systems in comparison to Floor connection and Shear wall systems.

Fig. 11
figure 11

Inter-storey drift of G + 3 building in the presence of soil-nailed structure

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Fig. 12
figure 12

Time history of lateral deformation at roof of G + 3 building in the presence of soil-nailed structure

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PSA response spectrum

The pseudo spectral acceleration response spectrum at the roof of G + 3 building in the presence of the nail-stabilised structure in Class E soil profile under El Centro earthquake loading is presented in Fig. 13. With the rise of the period, the spectral acceleration increases reaching the peak value near the natural period of the structure. Further increase of the period results in a fall in the acceleration. The peak PSA value for Only building system is obtained as 0.62 g near to 0.66 s. The acceleration response slightly decreases in the case of No connection system. Whereas for Floor connection and Shear wall systems, the peak value is found to considerably decrease and this peak is obtained at lower periods. The graph represents a lateral shift in the period of the integrated system under different connectivities showing the additional stiffness incorporated. The peak PSA value for G + 3 building in No connection, Floor connection and Shear wall system is observed to be 0.61 g, 0.31 g and 0.32 g at the period of 0.66, 0.55 and 0.55 s, respectively.

Fig. 13
figure 13

PSA spectrum at the roof of G + 3 building in the presence of soil-nailed structure

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Site-specific seismic response of integrated systems

Deformation profile of soil-nailed wall

The influence of multi-storeyed buildings on the seismic response of the soil-nailed structure under different soil profiles has been discussed in this section. Parametric studies considering varying heights of multi-storeyed buildings (G + 3, G + 5 and G + 7) founded in different soil sites and different connectivities between the two structures were conducted.

Figure 14 illustrates the displacement profile of the nail-stabilised wall in the presence of adjacent multi-storeyed buildings of different heights in various soil sites under seismic loading. The lateral displacement of the soil-nailed wall (δ) is expressed in percentage of the height of the wall (H). It is evident that for all models, the maximum δ occurs at the wall crest and reduces towards the toe of the nailed wall. For all the cases, the Only soil-nailed system results in maximum deformation of the nailed wall. The reduction in δ is noticed with the presence of multi-storeyed building adjacent to it. The maximum displacement profile obtained in the Only soil-nailed system is followed by the displacement profile in the No connection system. The displacement is minimal in the Floor connection and Shear wall system. A similar pattern is observed in all three multi-storeyed buildings of different heights, irrespective of the soil site. The additional load that comes abutting the soil-nailed wall in the form of the building restricts the lateral movement of the nailed wall to some extent. When the two structures are connected to each other either through beams at the first and second floor or as a shear wall, the horizontal movement of the nailed wall is further hindered by the presence of the building. The deformation of the nailed wall also reduces as the strength and stiffness of the retained soil increase. The reduction in δ of the nailed wall under seismic load is profound in Class E soil sites. The displacement of the wall for the integrated systems in Class D and Class C soil sites reduces and the percentage reduction in δ of the nailed walls is also less in these sites.

Fig. 14
figure 14

Maximum lateral displacement of soil-nailed wall in various soil sites in the presence of (a) G + 3, (b) G + 5, (c) G + 7 building

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The percentage reduction in δ obtained at the crest of the nailed wall as a result of integration with multi-storeyed buildings of various heights under El Centro excitation in different soil sites is tabulated in Table 5. δmax at the crest of the nailed wall in Only soil-nailed system is 45.03 mm, 22.15 mm and 22.14 mm in site classes E, D and C, respectively. The maximum percentage reduction in δ of the nailed wall with the G + 3 building system is 49.08% in the Shear wall system when compared to the Only soil-nailed system in Class E soil site. For the G + 5 building, the maximum percentage reduction in δ is 39.88% in the Shear wall system and for the G + 7 structure, 41.31% reduction is noticed in the Floor connection system in the soft soil site. A higher reduction in δ of the nailed wall is obtained in the presence of G + 3 buildings than in G + 5 and G + 7 buildings. This is because the natural frequency of G + 5 and G + 7 multi-storeyed buildings are close to the frequency content of the input ground motion and thus resonance conditions occur in these models. This results in higher deformation of the nailed wall and thus the percentage reduction is less than that observed in the presence of G + 3 building.

Table 5 Percentage reduction in lateral displacement at crest of soil-nailed wall
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So, it can be inferred that the presence of the structural load adjacent to the nail-stabilised structure reduces its deformations when subjected to dynamic load. The minimum deformation is obtained by the integration of the soil-nailed wall-building system (Floor connection and Shear wall systems) and a significant reduction in δ is found in the soft soil site.

Acceleration of soil-nailed wall

Figure 15 shows the acceleration response of the nailed wall represented in normalised form when multi-storeyed buildings of heights 12 m, 18 m and 24 m are constructed in its vicinity in various soil sites. The maximum acceleration of the soil-nailed wall is normalised to the peak ground acceleration of the input ground motion, representing the amplification factor (Safaee et al. 2021; Yazdandoust et al. 2022). The acceleration amplification factor along the height of the soil-nailed wall varies non-linearly with greater amplification observed at the crest of the nailed wall in all models. These findings align with the results reported by Yazdandoust (2018) and Mollaei et al. (2022).

It is noticed that irrespective of the height of multi-storeyed building, the maximum acceleration amplification is registered for Only soil-nailed system when the analysis is performed in the Class E soil site. With the multi-storeyed building placed next to it at a distance of 4 m apart, the amplification of acceleration of the nailed wall decreases in the No connection system. The acceleration amplification further decreases when the two structures are connected to each other either through beams or as shear wall. The minimum amplification of acceleration of the nailed wall is observed in the Shear wall system. As discussed in previous sections, the movement of the nailed wall is restricted in integrated systems due to the presence and connection with the multi-storeyed building and thus the acceleration of the nailed wall decreases. Higher acceleration is obtained in the presence of G + 5 and G + 7 storeyed buildings when compared with the G + 3 building, which is due to the near-resonant condition occurring in these systems. This pattern is observed in all three different soil sites.

Fig. 15
figure 15

Maximum horizontal acceleration amplification factor of soil-nailed wall in various soil sites in the presence of (a) G + 3, (b) G + 5, (c) G + 7 building

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A similar trend is noted in Class D and Class C soil profiles. The acceleration amplification is maximum at the crest of the nailed wall and is observed in the Only soil-nailed system. Irrespective of the height of the multi-storeyed building, the amplification of acceleration of the nailed wall at the crest in integrated systems is lower than that in the Only soil-nailed system. The maximum percentage reduction in acceleration of the nailed wall is noticed in the Shear wall system in the presence of the three different heights of the multi-storeyed buildings. For the G + 3 building, 41.92% reduction is observed in the Class E site and for G + 5 and G + 7 buildings, 27.5% and 36.67% reduction is obtained in the acceleration of the wall in the Class E site, respectively.

So, it is concluded that the acceleration of the nailed-stabilised wall is influenced by the close proximity of the multi-storeyed building. The influential factor depends significantly upon the properties of the soil being retained by the structure and the characteristics of the soil site.

Deformation profile of multi-storeyed building

This section gives insight into the behaviour of the multi-storeyed building in various site soil profiles in the presence of soil-nailed structure under seismic excitation. Figure 16 shows the inter-storey drift in G + 3, G + 5 and G + 7 multi-storeyed buildings in site classes E, D and C when the integrated systems are subjected to time history loading of El Centro earthquake. As it can be observed from the figure, when the multi-storeyed building is constructed adjacent to the soil-nailed structure, the seismic response of the building is influenced by the nailed structure. These results align with the findings reported by Hashash et al. (2018) and Fatahi et al. (2020), who studied the influence of braced excavation and shallow slopes on the seismic response of adjacent tall buildings, respectively. The deformation along the height of the building can be seen to decrease for the integrated systems under different parametric studies. Factors such as the height of the building and the soil properties on which the structures are founded tend to play a substantial part in governing the deformation pattern of the multi-storeyed building. It can be noted that for the G + 3 building, the maximum storey drift is obtained in the Only building system, irrespective of the site soil profile. The storey drift reduces in the No connection system and minimum drift is obtained in the integrated systems. The presence of the soil-nailed structure adjacent to the multi-storeyed building reduces its deformations under seismic loads, thereby reducing inter-storey drift. Integrating the building and the soil-nailed structure offers restraining effects in Floor connection and Shear wall systems. The soil-nailed structure provides additional lateral support to the building, limiting the ability of the building to move laterally and thus decreasing the inter-storey drift in these integrated configurations. Similar results are obtained for G + 5 and G + 7 storeyed buildings in Class E soil sites. The reduction in the storey drift for the integrated systems is significant in the G + 3 storeyed building in comparison to G + 5 and G + 7 buildings.

Fig. 16
figure 16

Inter-storey drift of (a) G + 3, (b) G + 5, (c) G + 7 building in the presence of soil-nailed structure in various soil sites

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Table 6 provides the percentage reduction in the drift of the three multi-storeyed buildings in various soil sites under consideration when subjected to El Centro excitation in the presence of the nailed structure. In the G + 3 storeyed building, the maximum percentage reduction in lateral drift of the building is recorded as 66.82% for the Shear wall system in comparison to the Only building system in the Class E site. For the G + 5 building, the maximum reduction is obtained as 44.36% for the Shear wall system in the Class E site and for the G + 7 structure, it is 19.32% in the Class D site. Even though the horizontal drift of multi-storeyed buildings in the presence of soil-nailed structure in different soil sites vary differently, the inter-storey drift of these buildings in every model is recorded to be within the code specified limits of 0.004 times the level difference between the floors i.e. 0.4%. (IS 1893 Part 1 2016)

Table 6 Percentage reduction in the storey drift of multi-storeyed building
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Acceleration of multi-storeyed building

The amplification of the acceleration response of multi-storeyed buildings in the presence of the soil-nailed structure in different soil sites under seismic loading is presented in Fig. 17 represented in normalised form. The maximum acceleration response is noted at the roof level of the multi-storeyed building. It is evident that the acceleration of the multi-storeyed building is influenced by the nailed structure in its vicinity. The maximum acceleration amplification of the building is obtained in the Only building system and the acceleration amplification of the No connection system is almost similar to the Only building system. However, the roof acceleration amplification of the integrated systems reduces when compared to the Only building system and the reduction is significant in G + 3 storeyed building in comparison to G + 5 and G + 7 storeyed buildings. Integration between the soil-nailed structure and the building enhances the stability and resistance to deformation resulting in reduced acceleration of the building. The soil-nailed structure offers additional lateral support, which helps in absorbing and dissipating seismic energy. It acts as a buffer against seismic forces, thereby reducing the acceleration experienced by the building. Additionally, the interaction between the building and the soil-nailed structure introduces additional damping into the system. This increased damping decreases the amplitude of seismic excitations leading to lower accelerations throughout the building.

The maximum reduction in acceleration of the multi-storeyed building is observed in case of the Shear wall system compared to the Only building system. In the shear wall system, G + 3 building shows a maximum reduction of 37.37% in Class E site whereas G + 5 results in 33.42% and G + 7 results in 30.02% reduction in Class C sites.

Fig. 17
figure 17

Maximum horizontal acceleration amplification factor of (a) G + 3, (b) G + 5, (c) G + 7 building in the presence of soil-nailed structure in various soil sites

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From the seismic response of the integrated soil-nailed wall-building systems, it is concluded that the deformation and acceleration of the building reduce with the integration between the soil-nailed structure and the building. Such integrated systems can be effectively constructed in regions with space constraints as they perform well under dynamic loads.

Conclusion

A novel concept of integrating the soil-nailed structure with multi-storeyed buildings for the optimum utilisation of scarcely available space in urban areas has been studied in detail. For this, the three-dimensional finite element models of integrated soil-nailed wall-building systems were simulated and analysed under seismic excitation. The parametric studies including different heights of multi-storeyed buildings, different soil sites and different connectivities between the two structures were conducted. The conclusions drawn from the results of the analyses are:

  • The integration between the soil-nailed structure and the multi-storeyed building as in Floor connection and Shear wall systems imparts better seismic stability to the whole system under strong ground motion in comparison to the stability of the structure in the absence of such integration with adjacent structures.

  • The integrated structure restricts the lateral movement of the nailed wall under seismic load and reduces its displacement by about 40%. It also results in the reduction of acceleration of the wall.

  • Irrespective of the height of the multi-storeyed building, the inter-storey drift in the building decreases as a result of integration with the nailed wall and the reduction is more significant in G + 3 building in soft soil site. The building acceleration also shows a declining trend under excitation as an outcome of integration.

  • The maximum displacement and acceleration of the systems occur in the Class E soil site. The integrated systems are efficient in this soil site resulting in the maximum percentage reduction in the displacement of the nailed wall and the storey drift in the building.

The numerical analyses of integrated soil-nailed wall-building systems under seismic loading suggest that the integration through Floor connection and Shear wall systems provides better seismic stability to both structures. Thus, such integrated systems can be constructed by utilising the whole available land near similar structures and are recommended for regions with space constraints, especially in soft soil sites.

Limitations

The present study was conducted with a 6 m high soil-nailed structure to understand how integration affects the seismic response of the entire system. A uniform layer of soil stratum was considered, and El Centro time history data was used for dynamic loading. For this study, the groundwater table was assumed at the base of the finite element model, which neglects the effect of porewater pressure during seismic analysis. Thus, further investigation could explore the impact of different heights of nailed cuts in a heterogeneous soil stratum beneath the foundation subjected to various actual time history ground motions by accounting for the effect of groundwater table during seismic analysis, providing future scope of the work.