Nonlinear time‑history analysis of the Evolution Tower resting on cellular raft due to earthquake loads

This study includes an investigation of using a cellular raft over piles on the seismic response of both a twisting and regular tower using the direct method, demonstrating the variance between a solid raft and a cellular raft. Both towers are 52 stories high and made of reinforced concrete. They were also built on a reinforced concrete piled-raft foundation. The soil model is thought to be multi-layered and has the same profile as the zone under investigation (New Mansoura, Egypt). All structural properties (dimensions, section properties, materials) are equal to allow a fair comparison of output response for both towers. The sole difference between the two towers is their elevation. The study is carried out under seismic loads using nonlinear time-history analysis. All analyses are carried out employing finite-element software (Midas GTS NX). Thus, seven distinct earthquake records with full 3D models were used for time-history research. According to the findings and discussions, it is concluded that adopting a cellular raft can reduce the dynamic response of the towers. Considering the soil–structure interaction, the maximum inter-story drift ratio decreases by 8.17% for the twisting tower and 5.58% for the regular tower while using the cellular raft. Furthermore, the regular tower is more effective than the twisting tower at resisting lateral loads.


Introduction
Most traditional structural design methods ignore the impacts of soil-structure interaction (SSI).Under seismic loading, SSI is seen as helpful since it causes the system to dampen more and extends the lateral fundamental period.According to recent studies, SSI can be hazardous, and ignoring its influence could lead to an unsafe design for both the superstructure and the foundation, especially for structures built on soft soil [1,2].Mylonakis and Gazetas [2] observed that SSI amplified structures' responses during different earthquakes despite potential dampening rises.They found that the earthquake particularly affected buildings with 10-12 stories, whose vibration duration increased due to the SSI from approximately 1.0 s to almost 2.0 s resting on soft clay.Several authors have made an effort to investigate how the SSI affects the seismic response of buildings.Veletsos [3], Nair [4], and Bielak [5] performed preliminary studies in this field.
The analysis of tall buildings with fixed bases is unsuccessful in accurately reflecting the seismic reaction, according to Yingcai [6], Lu [7], Julio et al. [8], Priyanka et al. [10], and Tahghighi, Mohammadi [14] that considered the interaction between soil and piles while examining the seismic behavior of framed structures.Anand et al. [9] studied how RCC structures respond to earthquakes under different soil conditions with and without shear walls.Xiao Lu et al. [11] quantitatively evaluated the effects of SSI on seismic reactions at Shanghai tower by using comparable static loads, response spectra, and time histories.Shehata et al. [12] studied the impacts of 329 Page 2 of 22 SSI on multi-story raft-supported buildings.Ebadi et al. [13] investigated the effects of seismic soil-pile-structure interaction on superstructure seismic responses; several numerical simulations were run on two types of superstructures and six types of piled-raft foundations.Sahil et al. [15] examined the soil-structure interaction effect on a four-story RC building resting on hill slopes.Kaddah et al. [16] studied the response of midrise concrete frame structures resting on silty sandy soil using ABAQUS software.Hokmabadi et al. [17,18] investigated the SSPSI phenomena by conducting shaking table tests on different structures, and results showed that SSI amplifies lateral deflections and inter-story drifts in structures supported by floating pile foundations, but reduces lateral displacements due to reduced rocking components.Nguyen et al. [19] stated that design engineers must carefully consider shallow foundation size and interaction parameters for safe, cost-effective seismic design in buildings.Reza et al. utilized the wavelet transform methodology for investigating the seismic response of soil-structure systems and to reduce the cost of calculations for the incremental dynamic analysis [20][21][22][23][24].
Reza et al. studied the improvement of high-rise buildings seismic performance considering SSI using outrigger systems and the optimization of its location [25,26], or by using different mass-tuned dampers [27,28].

Research objectives
As considering the soil-foundation system in the analysis of high-rise buildings leads to lengthening the vibration period because of the buildings base flexibility and also leads to increase the sway along the buildings height, a lot of research is concerned with applying different methods to decrease or control at least the lateral deformation along towers during earthquakes.This paper presents the study of using cellular rafts instead of solid rafts under high-rise buildings.Dynamic analyses of both 52-story reinforced concrete (RC) twisting and regular towers are carried out using time-history analysis under seismic loads.Both towers are analyzed in two cases: using a solid raft on piles as the tower foundation considering soil-structure interaction (SSI) and the same case but replacing a solid raft with a cellular one.All rafts are made of reinforced concrete (RC) through multi-layer soil.The only difference between both towers is the shape of the elevation.All analyses are carried out using finite-element software (Midas GTS NX).The twisting tower is a simulation of the Evolution Tower in Moscow.The behavior of using cellular rafts instead of solid ones against seismic loads is discussed by showing the dynamic response difference between the twisting tower and the regular tower with the same dimensions and properties.

Methods of analysis
The method used to analyze the interaction between soils and structures in this research is the direct method, which will be illustrated below.
• Direct method The basis of this method is the inclusion of the soil medium in the mathematical model created for dynamic analysis, as shown in Fig. 1.Finite element discretization of the domain with suitable absorbing/transmitting boundaries is often used to achieve this.To model the impacts of an unbounded soil medium, which calls for the seismic energy to disperse from the source of vibration, these unique boundary elements are required.Boundaries that are both absorbing and transmitting stop seismic energy from reflecting into the problem region.Despite the method's conceptual simplicity, applying it to the analysis of real-world situations is a challenging computational endeavor.Because the soil strata must be included in the mathematical model for dynamic analysis, a very complicated system of equations must be solved.Models and evaluations of the entire SSI system in one step are often made with the finite element method (FEM).SSI finite element model's equations of motion can be stated as: (1) [M] represents the model mass, [K] represents stiffness, displacement, [u] represents the displacement vector for nodes in the interior of the model, and input displacement [u g ] represents the displacement vector at the bottom.Although the direct approach can tackle the soil and the superstructure with similar precision, it usually necessitates a significant computing effort and is difficult to implement.

Structure modeling
3D models are created using the finite element program (Midas GTS NX), which is verified in this type of analysis by Shaaban et al. [29].A 52-story RC twisting tower and a regular tower with the same dimensions and properties are the main subjects of a nonlinear time-history analysis.The twisting tower is a simulation of the Evolution Tower in Moscow, which is an office skyscraper with a reinforced concrete frame.The structure rises 246 m and has 52 stories above ground.The Evolution Tower has a circular core in the center and a square plan overall.The creative construction utilizes twisted square floor slabs with an octagonalshaped central core and eight columns to support a vertical reinforced concrete frame.The building's central core is surrounded by floors that are constantly rotated at a fixed angle of 3°, creating a clockwise twist from the bottom to the top of the structure of around 135° [30] and [31], as shown in Figs. 3 and 4. Soil and raft are modeled as 10-node pentahedral solid elements.Beams and columns are modeled as beam elements with six degrees of freedom on each node.Piles are modeled as beam elements with interface elements to simulate friction with the soil, as shown in Fig. 2.
The building structure's material is considered as reinforced concrete (RC), and for nonlinear time-history analysis, geometric nonlinearity for the structure is considered (Figs. 3, 4).RC properties are introduced in Table 1.The cross-sectional details are shown in Table 2.

Loading
Scaled time histories of the El-Centro, Northridge, Kobe, Chichi, Friuli, Kocaeli, and Loma earthquakes are used for nonlinear time-history study.Scaling was conducted using the Egyptian Code (ECP-201) for these records [32] (New Mansoura Zone).The seismic features of this zone are the 2nd seismic zone with ground design acceleration (ag = 0.125 g).The soil is classed as (C).The target response spectrum due to ECP-201 is shown in Fig. 5, and the response spectrum curve for the seven earthquake records is shown in Fig. 6.The seven earthquake records after being scaled to the target response spectrum are introduced in Fig. 7. Rayleigh damping was adopted to take damping into consideration during the time-history analysis with coefficients of (α = 0.108535398 and β = 0.0049548014), which are calculated using the two fundamental periods of the building (T 1 = 5.458918 s and T 2 = 0.3301475 s) from the following equations:  where is the natural circular frequency, is the damping ratio which is assumed as 5%.

Soil modeling
A square R.C. raft measuring 47.0 × 47.0 m and 3.5 m in depth supports both towers.This raft was supported by 34.0 m-long, 1 m-diameter piles, as shown in Fig. 8.For this model, a soil profile was considered as taken by [33].This profile can be considered for the chosen zone for the analysis (New Mansoura, Egypt), as shown in Fig. 9.
The Mohr-Coulomb model, widely regarded as the most widely used constitutive model in soil media modeling, was utilized to characterize the material nonlinearity for soil.Friction and cohesiveness are the only two strength parameters used to explain plastic behavior [34].
To achieve optimal soil dimensions, absorbing borders are added at a suitable distance from the structure to mimic energy radiation.Gosh and Wilson [35] revealed that the distance between the foundation center and the soil HL border should be three to four times the base radius, and the distance between the foundation center and the VL border should be two to three times the foundation radius, in order to obtain fairly minimal reflexive wave effects.Moreover, (2) Rayhani and El-Naggar [36] showed that furthermost seismic activity amplification occurs in the first 30 m of the soil profile and that increasing the soil border from 5 to 10 times the structure's breadth only produces a 5% difference in output.Moreover, there are a lot of studies in that point like Kumar et al. [37] and Visuvasam and Chandrasekaran [38].Therefore, the soil dimensions were taken at 245 m × 245 m × 60 m.

Cellular raft modeling
A cellular raft is composed of a configuration of two-way interlocking foundation beams with a suspended slab on top and a ground-bearing slab beneath.I sections are often created by combining the upper and lower slabs with the beams.The large slab is effectively divided into continuous, tiny panels that span both directions by the intersecting beams, as shown in Fig. 10.The advantages of the cellular raft are discussed in more detail by Williams and Pellissier [39] and include: 1.The cellular raft is at least two to four times more rigid in bending than the ordinary raft.2. The cellular raft shows an even greater increase in the torsional stiffness than in the bending stiffness.3.Because the webs are closely spaced, the cellular raft offers the advantage that a flexible architectural plan may be achieved and that the internal walls' location is not determined by the position of the beams.Different decrease percentages in raft volume are studied for determining the optimal gaps dimensions in the cellular raft, which are (5-50% with 5% increment) from • As the raft volume reduction increased from 5 to 45%, the max.top floor sway dropped and subsequently began to grow as shown in Fig. 11.
• Furthermore, when the reduction percentage was increased, the max.relative sway of the top floor dropped, as indicated in Fig. 12. • As the reduction percentage increased from 5 to 35%, the max.stresses on the soil reduced, then began to grow as indicated in Fig. 13.
Fig. 7 (continued) • The max. raft stresses grew with increasing the reduction percentage till it dropped while adopting 35% and 40%, then rose again as indicated in Fig. 14. • Evaluating the punching shear stress of the piles on the raft according to the punching shear limitations prescribed by ECP 203 [40], it has been discovered that the utmost reduction percentage that may be applied till failure is 42.15%.Therefore, 35% has been utilized in the final analysis for all models for higher safety.The cellular raft model is shown in Fig. 15.
Fig. 8 The twisted tower model in MIDAS GTS NX including multi-layer soil Fig. 9 Soil layer engineering parameters [33] 329 Page 10 of 22

Results and discussion
Time-history analysis is performed on the different models used for the study taking into consideration the previously mentioned earthquake records.Results of the analysis showed that: Effect of using cellular raft on the twisting tower (due to El-Centro as an example): leads to variation in performance against seismic loads.• Figures 20 and 21 show the power spectra density function (PSDF) for the input (scaled El-Centro and the outputs (top floor acceleration) for the twisting tower using the solid raft and the cellular raft, respectively.
• Figure 22 shows that the maximum relative sway along the tower height is decreased while using cellular raft for each tower story.In addition, the maximum relative drift through using cellular raft is smaller than using solid raft by 6.749% (from 0.003882 to 0.00362), as shown in Fig. 23.  the outputs (top floor acceleration) for the regular tower using the solid raft and the cellular raft, respectively.• Figure 30 shows that the maximum relative sway along the tower height is decreased while using cellular raft for each tower story.In addition, the maximum relative drift through using cellular raft is larger than using solid raft by 1.319% (from 0.002501 to 0.002534), as shown in Fig. 31.• Tables 3 and 4 show a comparison between maximum relative sway and drift ratio for the used seven seismic records applied to all cases in the study.

Statistical analysis for all results:
Table 5 shows a statistical analysis for all results obtained from time-history analyses under the three earthquake records.Results showed that: • The maximum top floor sway decreased by 5.034% and by 4.352% in the case of using the cellular raft for the twisting tower and the regular tower, respectively.Moreover, it increased by 0.908% while using the solid raft and increased by 1.633% while using the cellular raft, while considering the regular tower instead of the twisting tower.• The maximum top floor velocity decreased by 0.601% and by 9.758% in the case of using the cellular raft for the twisting tower and the regular tower, respectively.Moreover, it increased by 2.886% while using the solid raft and decreased by 6.593% while using the cellular raft, while considering the regular tower instead of the twisting tower.
• The maximum top floor acceleration decreased by 2.303% and increased by 1.564% in the case of using the cellular raft for the twisting tower and the regular tower, respectively.Moreover, it remained nearly the same while using the solid raft and increased by 3.9584% while using the cellular raft, while considering the regular tower instead of the twisting tower.• The maximum base shear increased by 12.859% and by 10.175% in the case of using the cellular raft for the twisting tower and the regular tower, respectively.Moreover, it increased by 23.627% while using the solid raft and increased by 20.687% while using the cellular raft, while considering the regular tower instead of the twisting tower.• The maximum relative story drift decreased by 8.173% and by 5.578% in the case of using the cellular raft for the twisting tower and the regular tower, respectively.Moreover, it decreased by 0.962% while using the solid raft and increased by 3.814% while using the cellular raft, while considering the regular tower instead of the twisting tower.• From the values of mean and standard deviation, ranges for the responses of the same structural systems and the same response spectrum are reached; for example, the maximum base shear ranges from 67,964.66 to 86,767.16kN and from 88,980.37 to 102,309.49kN while using the solid raft, and ranges from 84,143.371 to 90,485.869kN and from 101,029.363 to 109,724.64 kN while using the cellular raft for the twisting tower and the regular tower, respectively.In addition, the maximum relative story drift ratio ranges from 0.002527 to 0.003297 and from 0.002501 to 0.003379 while using the solid raft and also ranges from 0.002451 to 0.002897 and from 0.002567 to 0.002985 while using the cellular raft for the twisting tower and the regular tower, respectively.

Conclusions
This research investigated the effect of using a cellular raft in twisting building analysis for seven earthquake records matched to the ECP-201 response spectrum and comparing the cellular raft effect between the twisting tower and a regular one with the same structural properties.Midas GTS NX considers full 3D models for all scenarios.Based on the findings and discussions, it can be concluded that: • A cellular raft often reduces the dynamic response of high-rise buildings slightly.Furthermore, using a cellular raft minimizes the concrete utilized in the foundation of the building.This leads to material requirement-based sustainability.• The maximum sway along the tower height is decreased by 5.8% for the twisting tower and by 2.6% for the regular tower while using the cellular raft considering the soil-structure interaction • The maximum inter-story drift ratio is decreased by 8.17% for the twisting tower and by 5.58% for the regular tower while using the cellular raft considering the soil-structure interaction • Using a cellular raft leads to increase stresses over the raft, so increases should be taken into consideration during design.• Base shear enlarged by 12.859% for the twisting tower and by 10.175% for the regular tower while using the cellular raft considering the soil-structure interaction.
• The twisting tower is more affected with the gravity loads than the regular tower due to the inclination of outer columns and slabs rotation.Therefore, the gravity load leads to a side sway of nearly 18 cm in the case of the twisting tower.tem.Therefore, the study will be extended to other statistical systems such as outrigger and diagrid.

Fig. 1
Fig. 1 Direct approach in soil-structure interaction illustration

Fig. 27
Fig. 27 Base shear of the regular tower (El-Centro)

Fig. 29
Fig. 29 PSDF for the input (scaled El-Centro) and the output (top floor acceleration), regular tower, cellular raft

Table 2
Details of the Evolution Tower structural elements crosssections •The reliable volume for cellular raft gaps can range from 35 to 42% of the solid raft volume as the allowable limits of the punching shear.

Table 3
Comparison between some output for the used seven seismic records and the average response (twisting building)

Table 4
Comparison between some output for the used seven seismic records and the average response (regular building)