Seismic Behaviour of High-rise Frame-core Tube Structures Considering Dynamic Soil-Structure Interaction

As the population grows and land prices rise, high-rise buildings are becoming more and more common and popular in urban cities. Traditional high-rise building design method generally assumes the structure is xed at the base, because the inuence of soil-structure interaction is considered to be benecial to the response of structures under the earthquake excitation. However, recent earthquakes and studies indicated that SSI may exert detrimental effects on commonly used structural systems. In this study, a numerical soil-structure model is established in Abaqus software to explore the impacts of SSI on high-rise frame-core tube structures. The seismic response of frame-core tube structures with various structural heights, height-width ratios, foundation types and soil types is studied. The numerical simulation results including maximum lateral deections, foundation rocking, inter-storey drifts and base shears of rigid and exible base buildings are discussed and compared. The results reveal the lateral displacement and inter-storey drifts of the superstructure can be amplied when SSI is taking into account, while the base shears are not necessarily reduced. Increasing the stiffness of the foundation and the subsoil can generally increase the seismic demand of structures. It has been concluded that it is neither safe nor economical to consider only the benecial effects of SSI or to ignore them in structural design practice.

response can be different. Firstly, the foundation is capable to resist large deformations because of its rigidity. As a result, the foundation fails to conform to the deformations of surrounding soil and thus the input motion is inconsistent with free eld motion. Secondly, the seismic response of the superstructure will probably cause deformation of the ground soil, which further modi es the input motion (Wolf and Deeks 2004). Therefore, the seismic behaviour of the superstructure is in uenced by the interaction between the superstructure and the underneath soil and a feedback loop will exist (Tabatabaiefar et al. 2013;Tabatabaiefar 2016;Far 2019a;Al Agha et al. 2021;). This feedback loop, in which the response of the soil affects structural behaviour and vice-versa is termed as soil-structure interaction (SSI) (Anand and Satish Kumar 2018).
It is widely believed in previous studies that SSI is bene cial to the seismic behaviour of buildings, since it elongates the natural period (Seed et al. 1976) and increases the damping of system (Wolf 1985), which tends to reduce the seismic demand of structures. Therefore, many current structure design codes recommend reducing the overall seismic coe cient when considering SSI or completely ignore SSI (NZS1170.5, 2007NBCC 2010;GB 50011 2010;IBC 2012). However, observations from a number of earthquake damaged sites proved that this design consideration is quite harmful. Take the 1985 Mexican earthquake as an example, a totally reverse result was noticed, wherein the soft subsoil resulted to a huge increase in the seismic forces (Sharma et al. 2018). In addition, remarkable examples including damage in pile-supported bridge structures and collapse of expressway can be found in Yashinsky (1998) and Mylonakis and Gazetas (2000). Recent studies have also justi ed this possibility. The exibility of foundation can increase the deformation and inter-storey drifts of the structure (Guin and Banerjee 1998;Tabatabaiefar 2012;Hokmabadi et al. 2014;Tabatabaiefar and Clifton 2016;Van Nguyen et al. 2017;Far 2019b).
Therefore, it is noted that there are some contradictory opinions when SSI is considered in the structural design practice (Mylonakis and Gazetas 2000;Far and Flint 2017). It is the complexity of SSI and lack of consensus among researchers with regard to the in uence of SSI that lead to very few structure design codes provide provisions related to it. Consequently, considering SSI in design practice of the most common and worldwide prevalent building typologies has been a rarity (Anand and Satish Kumar 2018). Therefore, in response to the need for critical investigation of SSI impacts, in this study, an enhanced numerical soil-structure model is adopted to investigate the effects of SSI on a typical high-rise building structure system: reinforced concrete (RC) frame-core tube structure. The seismic behaviour of frame-core tube structures with different structure heights, height-width ratios, foundation types and soil types are studied. The results including maximum lateral de ections, foundation rocking, inter-storey drifts and base shears for the rigidly supported and exibly supported structures are discussed and compared.
2 Overview Of The Structure-soil Model Three structural heights: 60 meters (20 stories), 90 meters (30 stories) and 120 meters (40 stories) are considered in this study to cover the commonly used height range of high-rise buildings. Besides, the height-width ratios of the superstructure are four, ve and six respectively, with three spans in each direction. Two prevalent foundation types: end bearing piled foundation and classical compensated foundation are adopted. The foundation embedment depth is assumed to be 9 metres, with three basement stories. The bedrock depth is 30 metres since the most soil ampli cation effect occurs in the upper 30 metres of the soil pro le. For each structure-soil model, two far-led earthquakes and two nearled seismic records are applied. Therefore, a total of 252 cases (36 xed base cases and 216 exible cases) were considered. The plan view of standard stories of frame-core tube structures is shown in Fig.   1 (a), which consists of the outer frame and the inner core tube. Figure 1 Characteristics of frame-core tube structure (a) plan view of standard storey (b) 20-storey framecore tube structure with end bearing piled foundation (height-width ratio=6) (c) 20-storey frame-core tube structure with classical compensated foundation (height-width ratio=6) (d) the nite-element model By referring to AS3600 (2018) and AS1170.4 (2007, the structural sections of buildings with various heights and widths were designed in SAP2000 software. After that, nonlinear time history analyses under four seismic records ( Fig. 2) was conducted to ensure inter-storey drifts of xed base structures with various parameters were less than 1.5% (life safe level). Grade 40 concrete with characteristic compressive strength (f' c ) of 40 MPa, modulus of elasticity (E c ) of 32.8 GPa and unit weight of 24.5 kN/m 3 (AS3600 2018) were adopted. In order to facilitate modelling in the subsequent nite element analyses, structures with the same height have the same dimensions of structural sections regardless of the height-width ratio. The dimensions of structural elements are summarised in Table 1. The superstructures founded on soil deposits with different geotechnical characteristics, which are summarised in Table 2  . The reason why the maximum shear-wave velocity of ground soil (V s ) adopted in this study is 600 m/s is that generally when the V s is greater than 600 m/s, the in uence of SSI is not signi cant (Tabatabaiefar et al. 2013).  Nowadays, the application of piled foundations for buildings has become increasingly common. The piled foundation generally transmits upper loads through the soft soil to the deep stiff soil or rock. In this study, end bearing piled foundation is adopted and all piles are rigidly connected with the base slab, and pile toes are xed at the bottom of the soil to simulate the socket end of piles in bedrock (Fig. 1b). The arrangement and characteristics of pile foundation have shown in Fig. 3 and Table 3. In addition, classical compensated foundation was selected for comparison with the piled foundation model because the compensated foundation tends to induce larger foundation rotation, and the superstructure can produce more obvious lateral de ection. Therefore, this study employs classical compensated foundation and piled foundation with three basement oors overlying a 1m-thick RC base slab ( Fig. 1b and c). The requirements for bearing capacity and maximum settlement of these two foundation types are satis ed (Bowles 2001).  This section introduces the modeling method of the structure, foundation, subsoil and contact surface, the setting of boundary conditions and the seismic motion input method in nite element software Abaqus 6.14. In the next section, the direct method will be adopted to study the seismic response of highrise frame-core tube structures with various parameters considering SSI.

Structural model
In order to improve computing e ciency, shell elements S4R are adopted to model shear walls and slabs and beam elements B31 are adopted to model beams and columns. Three dimensional eight-node reduced integration element C3D8R are employed to simulate the basement, base slab and piles (Fig. 1d).
The damping ratio of RC structures are assumed to be 5% and damping coe cients (α and β) are obtained based on the rst and second natural frequencies of the structure (Van Nguyen et al. 2017). In addition, elastic-perfectly plastic behaviour is adopted in structural elements and yield stress is speci ed. The yield stress, E c and density of concrete material are equal to the values introduced in section 2.

Soil model
The soil element is modeled by solid elements C3D8R and the Mohr-Coulomb failure criterion is employed. To achieve this in Abaqus, cohesion and internal friction angle (Table 2) and the tension cut off option are speci ed.
In order to take into account the nonlinearity of subsoil, the cyclic shear strain (γ c ) depended shear modulus (G/G max ) curves ( Fig. 4 and 5) and damping ratio (ξ) curves ( Fig. 6 and 7) provided by Sun et al. (1998) and Seed et al. (1986) are adopted for cohesive soils (D e and E e soil) and cohesionless soils (C e soil), respectively. After that, the trial and error were employed to calculate the strain-compatible values of soil damping and shear modulus under four seismic records ( Fig. 2 and Table 4). The detailed steps of this process can be found in Tabatabaiefar et al. (2013) and Fatahi and Tabatabaiefar (2014). The soil strain-compatible parameters is presented in Table 5.
Rayleigh damping is adopted to consider the energy losses in the ground soil under the action of earthquakes. In this process, it is very important to select soil frequencies because it determines the damping coe cients α and β. In this study, the method introduced by Park and Hashash (2003) that the selection of soil frequencies should partially cover the main frequency range of the seismic record is used. Table 5 provides the Rayleigh damping parameters of subsoil calculated by this method.

Contact surface
Surface to surface contact (standard) in Abaqus is adopted to simulate the interaction between the foundation and surrounding soil during seismic loading. In this process, the master surface is the foundation surface, and the slave surface is the soil surface. This is because the mesh sizes of these two surfaces are similar, and the material of foundation is more stiff. Besides, nite sliding formulation and surface-to-surface discretisation method are employed.
The contact interaction property includes two parts: normal direction and tangential direction. In the normal direction, the default relationship between contact pressure and clearance in Abaqus, hard contact, is applied, in which the amount of pressure that can be transmitted between the contact surfaces is not limited; when the contact pressure becomes negative or zero, the two contact surfaces will separate, and contact constraints on the corresponding nodes will be invalid (Van Nguyen et al. 2017). In the tangential direction, penalty friction formulation and contact-pressure-dependent data are adopted to simulate Mohr-Coulomb failure model between the contact surface of foundation and soil.

Boundary conditions
In order to avoid re ection of outward propagating waves on the boundary and capture the recovery ability of the semi-in nite ground, viscous-spring boundary is applied on lateral and bottom surfaces of soil domain. To achieve this goal, independent springs and dampers in one normal and two tangential directions were set on the boundary nodes (Gu et al. 2007), as shown in Fig. 8. The coe cients of the springs K T and K N and coe cients of dampers C T and C N (subscripts T and N indicate tangential and normal directions, respectively) can be calculated by the characteristics of the surrounding soil as follows: Where α T , α N are modi ed coe cients, α T = 0.67, α N = 1.33 (Liu et al. 2006); R is the distance between the wave source and boundary nodes; ρ and G are the density and shear modulus of the subsoil, respectively; V s and V p are shear wave velocity and P wave velocity of the subsoil, respectively.

Seismic motion input method
After the viscous-spring boundary is applied, the arti cial boundary node should conform to the free eld motion to supply conditions identical to in nite model. Generally, one-dimensional free-eld grid is set on the periphery of the model, parallel to the main grid, and connected to the main grid nodes through springs and dampers. However, this method will increase the number of elements, and it is di cult to implement in Abaqus due to the large number of boundary nodes. In this study, the free eld motion is transformed into the equivalent node force F b applied on boundary nodes (Ma et al. 2020), and F b comprises three parts: the rst two parts is used to compensate the in uence of springs and dashpots, and the third part is the free eld stress on the boundary: Where u b ff and v b ff are free eld displacement and velocity vectors at boundary nodes, respectively; σ b ff is the free eld stress tensor; K b and C b are coe cient vectors of springs and dashpots on the boundary, respectively. A b is the in uencing area of boundary nodes and n is the cosine vector of the normal direction outside the boundary. By compiling a simple program in MATLAB software, the amplitudes of F b in one normal direction and two tangential directions of each boundary node were obtained.
The validity and accuracy of the numerical model have been veri ed by comparison between experimental shaking table test results and numerical outputs by Zhang and Far (2001). After that, the seismic response of high-rise frame-core tube structures with various parameters considering SSI was numerically studied and the results can be found in Section 4. Compared with xed base counterparts, almost all the maximum lateral de ections of exible base structures have been ampli ed, regardless of the structural height, height-width ratios, foundation and soil types. This is because the degree of freedom of the soil-structure system increases after considering SSI and the natural period is prolonged, and the displacement response spectrum curve generally increases with the increase of the natural period of the system. As a result, the ampli cation of the displacement response of high-rise buildings was observed.
It is also can be seen that when the superstructure parameters are the same, the maximum lateral de ections of piled foundation structures only change slightly with the type of soil, but the variation of displacement response of classical compensated foundation structures is relatively dramatic, especially under the action of far-eld earthquakes. This means that the end bearing pile foundation supported structures is less susceptible to the type of soil.
In addition, the maximum lateral de ections of piled foundation structures are not necessarily smaller than that of classical compensated foundation structures. For example, under the action of far-eld earthquakes, the deformation of piled foundation structures (with little difference between each other) is usually smaller than that of classical compensated foundation structures resting on the type E e soil; however, under the action of near-eld earthquakes, the deformation of piled foundation structures does not decrease obviously in comparison to classical compensated foundation structures. It is also worth pointing out that under the action of far-eld earthquakes, with the soil type changes from C e to E e , the maximum lateral de ections of structures increase gradually, especially for classical compensated foundation structures. In contrast, under the action of the near-led earthquakes, the deformation of structures usually decreases with the subsoil modulus decreases.
The effects of height-width ratio on the maximum lateral de ection is complex. On one hand, the increase in the width of buildings can increase the stability of structures and decrease the foundation rotation. On the other hand, the increase in the width means the increase in the mass of buildings, which will increase the inertial force and structural distortion in seismic excitations. Therefore, the maximum lateral de ection follows different patterns as the height-width ratio changes. Hachinohe earthquake (c) Kobe earthquake (d) Northridge earthquake 4.2 Foundation Rocking Different from xed base structures, lateral de ections of structures modeled with soil include rocking and distortion components (Kramer 1996). Table 6, 7 and 8 record the proportion of the foundation rocking induced lateral de ection in the total de ection of the top oor of 20-, 30-and 40-storey structures, respectively. The restriction of structure width on the rotation of the structure is not signi cant, whereas the soil type can considerably restrain the foundation rocking, and this phenomenon is more obvious in classical compensated foundation supported models. Similarly, the pile foundation can also effectively restrain the rotation of the foundation. For classical compensated foundation structures founded on E e soils, the foundation rotation induced displacement accounts for an average of more than 90% of the total displacement, which means buildings are more likely to rotate overall. In contrast, this value is only 17.03% in the case of piled foundation models.
However, as observed in Section 4.1, although the end-bearing piled foundation can effectively reduce the foundation rocking, the maximum lateral de ections of piled foundation structures is not always smaller than that of the classical compensated foundation structures. Table 6 The proportion of foundation rocking induced lateral de ection of 20-storey structures (%)  Table 7 The proportion of foundation rocking induced lateral de ection of 30-storey structures (%)

Inter-storey Drifts
The inter-storey drifts of 20-, 30-and 40-storey structures with different height-width ratios, foundation types and soil types is shown in Fig. 18, 19 , 20, 21, 22, 23, 24, 25 and 26. The inter-storey drifts were obtained adopting the method based on AS1170-4 (2007. Similar to lateral de ections, inter-storey drifts of almost all exible base cases have increased and the maximum value of many near-eld earthquake cases and several far-led earthquake cases have exceeded 1.5%, which means the performance levels were changed from life safe towards near-collapse or collapse level after SSI is taken into account (BSSC 1997). In classical compensated foundation models, the inter-storey drifts usually present an approximately vertical line, indicating that inter-storey drifts only change slightly with the structural height. In other words, the foundation rotation induced lateral de ection accounts for a large part of the total maximum lateral de ection in the classical compensated foundation models. Moreover, compared with classical compensated foundation cases, inter-storey drifts of piled structures with the same height, height-width ratio and seismic record do not change signi cantly with the soil type. Besides, it is worth noting that a considerable increase of inter-storey drifts is found in structures resting on C e soil under near-eld earthquakes and structures with compensated foundation resting on E e soil under far-eld earthquakes. This is related to the difference between the shape of response spectra of near and far earthquakes. Figure 26 Inter-storey drifts of 40-storey structure (height-width ratio=4) with various foundation types and subsoil types under different seismic records: (a) El Centro earthquake (b) Hachinohe earthquake (c) Kobe earthquake (d) Northridge earthquake 4.4 Base Shear Table 9, 10 and 11 compare the base shear of exible base cases () and xed base cases (V). The ratios /V are not always less than 1, which means the base shear of the structure may increase or decrease after considering SSI, depending on the foundation type and the soil type. For example, the base shears of the classical compensated foundation structures constructed on soft soils (type E e and D e ) are usually less than that of xed base counterparts, while the base shears of the classical compensated foundation models resting on C e soil and the piled foundation models are generally ampli ed. That means increasing the stiffness of the foundation and subsoil can absorb more seismic energy, making the traditional assumption that SSI can always reduce the seismic demand of the structure invalid. This result is consistent with Van Nguyen (2017). Therefore, although the piled foundation can reduce the foundation rocking, it will probably increase the seismic shear force and in turn increase the lateral displacement of the structure, which also explains why the deformation of the piled foundation model is not necessarily less than that of the classical compensated foundation model in Sections 4.1 and 4.3. In addition, although the absolute value of the base shear increases with the increase of the height-width ratio, the change of height-width ratio will not exert a critical impact on the relative value of the base shear (/V). Table 9 Base shear ratio of 20-storey structures

Conclusions
In order to investigate the seismic response of the high rise frame-core tube structure considering SSI, 20-, 30-and 40-storey building models with different height-width ratios, foundation types and soil types were established using Abaqus software. The numerical simulation results including maximum lateral de ections, foundation rocking, inter-storey drifts and base shear of structures with different in uencing factors are discussed and compared. The following conclusions can be draw: Compared to xed base cases, the maximum lateral de ections and the inter-storey drifts of almost all structures modelled with subsoil as exible base models are ampli ed to different extent, regardless of height width ratios, foundation types and soil types.
The maximum inter-storey drifts of many near-eld earthquake cases and several far-led earthquake cases have exceeded 1.5%, which means the performance levels of structures have been changed after considering SSI. As a consequence, conventional design procedures excluding SSI may not be adequate to guarantee the structural safety of high-rise frame-core tube structures.
The piled foundation can effectively reduce the foundation rocking compared with classical compensated foundation. However, the maximum lateral de ections of piled foundation models are the largest in many cases, especially under the action of near-eld earthquakes. The reason is that the shear forces of piled foundation structures is generally larger than that of compensated foundation structures and xed base structures.
When the superstructure parameters are the same, the type of soil has minor effects on the deformation of the pile foundation structures, but it has dramatic effects on classical compensated foundation structures, especially under the action of far-eld earthquakes. In other words, the seismic performance of piled foundation structures is less susceptible to the type of soil.
The stiff soil can considerably restrain the foundation rocking, and this phenomenon is more obvious in classical compensated foundation supported models. For classical compensated foundation structures constructed on soft soils, the foundation rocking induced lateral de ection accounts for a large proportion of the total lateral de ection.
The base shear of the structure may increase or decrease after considering SSI, depending on the foundation type and the soil type. As a result, blindly increasing the stiffness of the foundation and subsoil may absorb more seismic energy, making the structure neither safe nor economical.
Although the absolute value of the base shear increases with the increase of the structural heightwidth ratio, the change of the height-width ratio will not exert a signi cant impact on the relative value of the base shear (/V). Figure 1 Characteristics of frame-core tube structure (a) plan view of standard storey (b) 20-storey frame-core tube structure with end bearing piled foundation (height-width ratio=6) (c) 20-storey frame-core tube structure with classical compensated foundation (height-width ratio=6) (d) the nite-element model Inter-storey drifts of 20-storey structure (height-width ratio=5) with various foundation types and subsoil types under different seismic records: (a) El Centro earthquake ( Inter-storey drifts of 30-storey structure (height-width ratio=5) with various foundation types and subsoil types under different seismic records: (a) El Centro earthquake ( Inter-storey drifts of 40-storey structure (height-width ratio=4) with various foundation types and subsoil types under different seismic records: (a) El Centro earthquake (b) Hachinohe earthquake (c) Kobe earthquake (d) Northridge earthquake