Seismic Analysis of RC High-Rise Buildings Rested on Cellular Raft

Abstract

This paper includes the investigation of the soil–structure interaction (SSI) effect on the seismic response of 20 and 30-story reinforced concrete moment resisting frames (MRFs) rested on a piled raft foundation using the direct approach. After that, a study is conducted to show the impact of using a cellular raft instead of the designed solid raft on the dynamic response of the building. A study is introduced to select the best gap size for the cellular raft. The soil model is assumed as a single layer of sandy clay. Time history analysis by the direct integration method is performed under seven earthquake records (El-Centro, Northridge, Kobe, Chichi, Friuli, Kocaeli, and Loma), which are scaled to the Egyptian Code for Loads (ECP-201) response spectrum using a full 3D model by a finite element software named (Midas GTS NX). It is concluded that considering SSI significantly affects the dynamic response of high-rise buildings, and using cellular rafts generally leads to a decrease in their dynamic response.

1. Introduction

The majority of civil structures include forms of structural members that have a direct connection with the ground. When exterior forces, such as seismic activity, impinge on these structures, neither the structure nor the ground displacements are independent of one another. Both soil responses and structural motions are influenced by each other, which is referred to as soil–structure interaction (SSI). Generally, the SSI effects are neglected in most conventional structural design methods, especially for light structures with relatively stiff soil. Under seismic loading, the role of SSI is often seen as positive for the structural system since it lengthens the lateral fundamental period and leads to higher damping of the system. Recent research indicates that SSI is harmful and that disregarding its impact could result in a risky design for both the structure and the foundation, particularly for structures built on soft soil [1,2]. Mylonakis and Gazetas [2] detected three earthquakes (Bucharest 1977, Mexico City 1985, and Kobe 1995) in which SSI increased the seismic response of structures despite possible damping increases. According to their reports, the Mexico earthquake was especially damaging to (l0–12)-story buildings built on soft clay, whose period of vibration rose from roughly 1.0 s (assumption of a fixed base structure) to nearly 2.0 s as a result of the SSI. Several writers attempt to determine the impact of the SSI on building seismic response. Veletsos and Meek [3], Veletsos and Nair [4], and Bielak [5] conducted initial studies in this field. Veletsos and Meek [3] evaluated the flexible base period (T) for a structure as follows:

$$\frac{\tilde{\mathrm{T}}}{\mathrm{T}}=\sqrt{1+\frac{{\mathrm{k}}_{\mathrm{l}}}{{\mathrm{K}}_{\mathrm{H}}^{\mathrm{d}}}+\frac{{\mathrm{k}}_{\mathrm{l}}{\mathrm{h}}^2}{{\mathrm{K}}_{\mathrm{R}}^{\mathrm{d}}}}$$

(1)

where $\mathrm{T}$ is the fixed-base structure’s period corresponding to the first mode and ${\mathrm{k}}_{\mathrm{l}}$ reflects the stiffness of the model for the first mode of a fixed-base structure. The equivalent viscous damping ratio is stated in terms of the structure’s viscous damping and the soil foundation system’s radiation and hysteretic damping.

Yingcai [6], Lu [7], Julio et al. [8], and Priyanka et al. [9] studied the seismic behavior of framed structures by taking into account soil–pile interaction and concluded that analyzing tall buildings with a fixed base fails to represent the real seismic response. Anand et al. [10] investigated the seismic behavior of reinforced concrete (RC) buildings with and without shear walls under various soil conditions. Mengke Li, Xiao Lu, Xinzheng Lu, and Lieping Ye [11] considered the Shanghai Tower in their studies. The tower is 632 m high. The substructure technique is applied to estimate the SSI effect on seismic responses. Using equivalent static load, response spectrum, and time history methods, Shehata E., Mohamed M., and Tarek M. [12] looked into the effects of SSI on a typical multi-story moment-resisting building resting on a raft foundation. Mehdi Ebadi, Jamkhaneh Mohsen Bagheri, and Bijan Samali [13] ran a series of numerical simulations on two types of superstructures and six types of piled raft foundations to study the impacts of seismic soil–pile–structure interaction on superstructure seismic responses. S. Ismail, F. Kaddah, and W. Raphael [14] used ABAQUS software to investigate the response of mid-rise concrete frame buildings resting on silty sand soil. As a result, engineers are instructed to optimize their design between the many evaluated parameters to provide overall structure stability. A. Kamel and A. Andronic [15] used Abaqus to evaluate the effects of soil as a supporting material, as well as to clarify and highlight the importance of soil–structure interaction and its effect on the guiding efforts used in structural element design. Babu, N.J., Rao, B.K., and Reddy, C.R.K. [16] investigated mode shapes and response spectra for a reinforced concrete (RC) frame with isolated footings, with the interaction between footing and earth. As a result, while designing RC frames, not only gravity and lateral effects should be considered, but also the coupled effects of soil on the foundation. Cayci, B.T., Inel, M., and Ozer, E. [17] investigated the influence of soil–structure interaction (SSI) on the seismic response of mid- and low-rise residential structures was explored in a study that took into account linear and nonlinear structural behavior. The findings reveal that forecasts of displacement demand vary substantially based on ground motion records and modeling methodologies. Ravi et al. used Abaqus to analyze the effects of the number of stories (20, 25, and 30 stories) on seismic performance, as well as the size of the raft foundation with SSI effects; they performed a series of three-dimensional finite element calculations [18]. Jishuai Wang, Tong Guo, and Zhenyu Du investigated the effect of dynamic structure–soil–structure interaction (SSSI) on the reactions of two nearby structures using a three-dimensional finite element model. According to the findings [19], the SSSI influence on structural responses reduces as structure spacing grows, but the SSSI effect on structural seismic demands grows or decreases as structure size increases and seismic excitation direction varies. Vasiliki G. Terzi [20] investigated the effects of soil–structure interaction on the modal characteristics of an increasing mechanical complexity cantilever beam. Madany and PeiJun Guo [21] proposed a method for evaluating the enhanced seismic responses of two adjacent structures on the horizontally stratified ground due to seismic structure–soil–structure interaction and backfill soils. L. Scislo and M. Guinchard review the prediction and monitoring of civil engineering source-based vibration and their effects observed in the Large Hardon Collider (LHC) tunnel due to heavy machinery work or seismic activity using the transfer function approach [22]. Kim [23] calibrated a variety of transfer functions between translational and torsional foundation motions, as well as free field movement, against the observed foundation and free field behavior, which were developed by Veletsos [24] and Veletsos [25], respectively. L. Scislo presented the techniques implemented at the European Organization for Nuclear Research (CERN) to allow the tracking and monitoring of a seismic swarm, which is a series of earthquakes that occur in a small area over a short period [26]. Aurélien Mordret et al. used 2 weeks of ambient vibrations recorded by 36 accelerometers that were installed in the green building at the Massachusetts Institute of Technology (MIT) to monitor the shear wave speed and the apparent attenuation factor of the building [27]. Juan M. Mayoral et al. describe an unconventional foundation system’s static and seismic performance evaluation, comprised of a partially compensated box foundation structurally tied to an open-ended grid of stiffener walls [28]. K. Yamashita carried out a numerical simulation using the moderate earthquake motion recorded during the 2011 Tohoku Earthquake to evaluate the induced internal stresses in a cellular raft system against its capacity [29].

In this paper, the seismic analysis of 20- and 30-story RC moment resisting frames with plan dimensions of 25 m × 25 m rested on a piled raft foundation using the direct approach is included to investigate the SSI effect. Time history analysis is performed on three cases; the first is ignoring SSI; the second is considering SSI with a solid raft; the third is considering SSI with a cellular raft. The considered cellular raft has the same dimensions as the designed solid raft. It is presented to study sustainability based on material requirements and calculate the reliable dimensions for gaps that form the cellular raft.

2. Direct Method for Soil–Structure Interaction

This means modelling the complete structure–foundation–soil system in the time domain and analyzing it in a single step, as shown in Figure 1, taking into account variation in soil characteristics, material and geometric non-linearity, wave propagation complexities, and careful consideration of interface and boundary conditions. The major problem with the direct method of analysis is the very large size of the whole problem. Many methods are used in the direct approach, such as the finite element method (FEM), the finite difference method (FDM), and the boundary element method (BEM). The finite element method (FEM) is used in this research to model and evaluate the entire SSI system in a one-step. The SSI finite element model’s equation of motion is:

$$\left[\mathrm{M}\right]\{ü\}+\left[\mathrm{K}\right]\left\{\mathrm{u}\right\}=-\left[\mathrm{M}\right]\left\{{ü}_{\mathrm{g}}\right\}$$

(2)

where $\left[\mathrm{M}\right]$ is the mass matrix, $\left[\mathrm{K}\right]$ is the stiffness matrix, $\left\{\mathrm{u}\right\}$ is a displacement vector matching the degree of freedom of the SSI model’s internal node, and $\left\{{\mathrm{u}}_{\mathrm{g}}\right\}$. It is the input displacement vector for the nodes at the bottom of the model.

By assuming a lumped mass formulation and no external dynamic forces, the linear equations of motions of the whole system become:

$$\left[\begin{array}{cc}\begin{array}{cc}\begin{array}{c}{\mathrm{M}}_{\mathrm{S}\mathrm{S}}^{\mathrm{S}}\\ 0\\ 0\end{array}& \begin{array}{c}0\\ {\mathrm{M}}_{\mathrm{i}\mathrm{i}}^{\mathrm{S}+\mathrm{G}}\\ 0\end{array}\end{array}& \begin{array}{c}0\\ 0\\ {\mathrm{M}}_{\mathrm{g}\mathrm{g}}^{\mathrm{G}}\end{array}\end{array}\right]\left\{\begin{array}{c}{ü}_{\mathrm{S}}^{\mathrm{t}}\\ {ü}_{\mathrm{i}}^{\mathrm{t}}\\ {ü}_{\mathrm{g}}^{\mathrm{t}}\end{array}\right\}+\left[\begin{array}{cc}\begin{array}{cc}\begin{array}{c}{\mathrm{K}}_{\mathrm{S}\mathrm{S}}^{\mathrm{S}}\\ {\mathrm{K}}_{\mathrm{i}\mathrm{S}}^{\mathrm{S}}\\ 0\end{array}& \begin{array}{c}{\mathrm{K}}_{\mathrm{S}\mathrm{i}}^{\mathrm{S}}\\ {\mathrm{K}}_{\mathrm{i}\mathrm{i}}^{\mathrm{S}+\mathrm{G}}\\ {\mathrm{K}}_{\mathrm{g}\mathrm{i}}^{\mathrm{G}}\end{array}\end{array}& \begin{array}{c}0\\ {\mathrm{K}}_{\mathrm{i}\mathrm{g}}^{\mathrm{G}}\\ {\mathrm{K}}_{\mathrm{g}\mathrm{g}}^{\mathrm{G}}\end{array}\end{array}\right]\left\{\begin{array}{c}{\mathrm{u}}_{\mathrm{S}}^{\mathrm{t}}\\ {\mathrm{u}}_{\mathrm{S}}^{\mathrm{t}}\\ {ü}_{\mathrm{S}}^{\mathrm{t}}\end{array}\right\}=\left\{\begin{array}{c}0\\ 0\\ 0\end{array}\right\}$$

(3)

where S denotes structure and G denotes soil.

3. Software Verification

The finite element software (Midas GTS NX) is used in this research to create the 3D models. Midas GTS NX is capable of performing static and dynamic analysis while considering soil–structure interaction. Mohsen Bagheri, Mehdi Ebadi Jamkhaneh, and Bijan Samali [13] conducted a series of numerical simulations on two types of superstructures and six types of piled raft foundations to examine the impacts of seismic soil–pile–structure interaction (SSPSI) on the seismic responses of the superstructures. The structure is modelled as a 15-story steel building with three bays; each bay is 4 m wide with a total height of 45 m. The beams and column sections are shown in

Table 1. Structure model including beams, columns, and pile section details.

Structural Model
Levels	Beams Section	Columns Section	Pile Section
(1–3)	IPE300	Box 550 × 25	Diameter = 1.2 m
(4–6)	IPE300	Box 500 × 20
(7–9)	IPE300	Box 450 × 15
(10–12)	IPE270	Box 400 × 12
(13–15)	IPE270	Box 350 × 10

. Soil is selected as a class (E_e) due to AS1170 (Standards Australia 2007), with properties as shown in

Table 2. Material Properties from the study.

Material Properties
Reinforced Concrete	Unit weight = 2350 kg/m3 Modulus of elasticity = 28,284 MPa Compressive strength = 32 MPa
Steel	Yield stress = 280 MPa Tensile stress = 410 MPa
Soil	Shear modulus = 33,100 GPa Shear velocity = 150 m/s Poisson’s ratio = 0.4 Cohesion = 20 kPa Friction angle = 12° Unit weight = 14.42 kN/m3

.

Five cases were investigated to study the effect of soil–structure interaction; (1) fixed base, (2) building over raft foundation, and (3, 4, 5) building over piled raft foundation with different piles lengths.

All cases are modelled using MIDAS GTS NX as shown in Figure 2. The mathematical models are generated from the software material libraries. All beams, columns, and piles are modelled as 1D-beam elements with six degrees of freedom (DOFs). In addition, slabs are modelled as four-node shell elements with three DOFs in each node. Furthermore, the soil and raft are modelled as solid elements (Tetrahedral) with six DOFs at each node.

A time history analysis under the El-Centro earthquake is performed for the verification process. Two cases are selected from the research to be verified: (1) fixed base as shown in Figure 3a, and (2) SSI using 10 m piles on the raft as shown in Figure 3b. A comparison between the results is presented in

Table 3. Comparison between results of top floor maximum sway under El-Centro record.

	Fixed Base		SSI (Pile Length 10 m)
	Mohsen [13]	Author	Mohsen [13]	Author
Top Floor Max. Sway, mm	102	98.543	330	332.44
Accuracy	98.91%		99.27%

.

4. Structures Modeling

4.1. Structures Identification

The Egyptian Code for Design and Construction of Buildings (ECP-203) [30] is used to design the simulated buildings. The plan of the buildings is bi-symmetrical, with five equally spaced bays and a typical bay width of 5 m for both directions, as shown in Figure 4 and Figure 5. Every story’s height is 3 m. Structure cross-sections and material properties are tabulated in

Table 4. All structural properties for the models of the buildings.

Structural Geometric Properties
Member	Cross-Section
Beams	30.0 cm × 60.0 cm
Slabs	16. cm
Columns	75.0 cm × 75.0 cm (20-story Building) 80.0 cm × 80.0 cm (30-story Building)
Material Properties (RC)
Elasticity modulus	$\mathrm{E}=3.522\times {10}^7 \mathrm{kN}/{\mathrm{m}}^2$
Compressive strength	${\mathrm{F}}_{\mathrm{c}}=56 \mathrm{MPa}$
Poisson’s ratio	$\mathsf{\upsilon }=0.2$
RC density	$\mathsf{\gamma }=25 \mathrm{kN}/{\mathrm{m}}^2$

.

Dead loads in gravity load design include the structure’s self-weight and a standard floor cover of $1.5 \mathrm{kN}/{\mathrm{m}}^2$, and the live load is taken as $2.0 \mathrm{kN}/{\mathrm{m}}^2$ because the building is considered residential.

4.2. Loading

A time history analysis is performed on 20 and 30-story RC moment-resisting frame towers considering scaled time histories of El-Centro, Northridge, Kobe, Chichi, Friuli, Kocaeli, and Loma earthquakes, as shown in Figure 6 and Figure 7. Geometric nonlinearity is taken into consideration during the analysis of the buildings. The Egyptian Code for Loads (ECP-201) [31] (New Mansoura Zone) was utilized to scale all earthquake recordings used in the investigation. The seismic characteristics of this zone are the same as the second seismic zone due to ECP-201, and the spectrum’s shape is type (2) with ground design acceleration, (${\mathrm{a}}_{\mathrm{g}}=0.125 \mathrm{g}$) connected with a code reference probability of exceeding 10% in 50 years (Figure 8). The tower is considered a residential building with an importance factor ($\mathsf{\gamma }=1$). The soil is classified as “C” with a soil factor of ($\mathrm{S}=1.15$).

For time history analyses, regarding ECP-201, the total model self-weight and floor cover plus 25% of the live load are considered as the seismic mass source.

5. Soil Modelling

A square RC raft with dimensions of 29 × 29 m and a depth of 2 m (20-stories) and 3 m (30-stories) supports the building, Figure 9 and Figure 10. This raft is resting on 15 m-long piles. The soil is assumed to have the same properties as [32] a single layer of sandy clay with the mechanical parameters (elasticity modulus, $\mathrm{E}=\mathrm{19,000} \mathrm{kN}/{\mathrm{m}}^2$; Poisson’s ratio, $\mathsf{\upsilon }=0.3$; unit weight, $\mathsf{\gamma }=19.0 \mathrm{kN}/{\mathrm{m}}^2$; cohesion coefficient, $\mathrm{C}=23.0 \mathrm{k}\mathrm{N}/{\mathrm{m}}^2$; frictional angle, $\mathsf{\varphi }={32}^{\circ }$; and dilatancy angle, $\mathsf{\psi }=2^{\circ }$). The Mohr–Coulomb model was used to describe soil nonlinearity. The Mohr–Coulomb model, which is a linear elastic–perfect plastic model, is the most commonly used constitutive model in soil medium modelling. The Mohr–Coulomb model is one of the most straightforward soil constitutive models, using only two strength factors to describe plastic behavior. Researchers showed that stress combinations generating failure in real soil samples accord well with the hexagonal shape of the failure contour established with the Mohr–Coulomb model [33].

6. Boundary Conditions

For the best soil dimensions, absorbing boundaries are introduced at an appropriate distance from the structure to simulate the radiation of energy. Gosh and Wilson [34] demonstrated that the distance from the center of the foundation to the soil horizontal limit should be 3–4 times the base radius, and the distance from the center of the foundation to the vertical boundary should be 2–3 times the foundation radius, to get negligible reflexive wave effects. Furthermore, Rayhani and El-Naggar [35] found that most of the increase in seismic activity occurs within the first 30 m of the soil profile, raising the soil boundary from five to ten times the breadth of the structure results in a 5% difference in output. Therefore, the soil dimensions were taken 225 m × 225 m × 60 m for more accuracy.

7. Cellular Raft

After the analysis of the full 3D model without or with the soil–structure interaction effect, another case is taken into consideration as a comparison, so the model is analyzed under three conditions:

(1)

No soil–structure interaction exists (NSSI), meaning that the tower base nodes are considered fixed supports.

(2)

Soil–structure interaction (SSI) is considered, and the raft is modelled as a solid raft.

(3)

Soil–structure interaction (SSI) is considered using a cellular raft.

For choosing the best gap dimensions in the cellular raft, different reduction percentages in raft volume are considered, which are (5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, and 50%) from the solid raft dimensions (29 m × 29 × 2 m), then all results are discussed and lead to:

• The maximum top floor sway decreased with increasing the reduction in the raft volume percentage from 5% to 45% and then started to increase, as shown in Figure 11.
• In addition, the maximum relative drift decreased with increasing the reduction percentage as the maximum relative sway of the top floor increased, as shown in Figure 12.
• The maximum stresses over the soil decreased with increasing the reduction percentage from 5% to 35% and then started to increase, as shown in Figure 13.
• The maximum stresses over the raft increased as the reduction percentage was increased until it decreased when 35% and 40% were used, then increased again, as shown in Figure 14.
• Due to the punching shear stress limits defined by ECP 203-2018 [31], the maximum reduction percentage that can be used until failure is 42.15%.

From the previous results, 35% was used in the final analysis as the best reduction percentage for more safety. Therefore, the cellular raft model is modelled as three layers. The upper and lower layers are solid with a thickness of 50 cm, and the middle layer is 1 m thick with 25 gaps (each gap is 4.7 m × 4.7 m × 1 m) for the 20-story building, as shown in Figure 15; moreover, the middle layer with a thickness of 1.5 m for the 30-story building, as shown in Figure 16.

8. Results and Discussion

8.1. Modal Analysis

The period of vibration for the considered buildings was calculated using MIDAS GTS NX. Figure 17 showed that the vibration period of the first mode increased from 1.7151 swhen not considering soil–structure interaction (NSSI) to 2.8943 s (SSI) in the 20-story building, while it increased from 2.6726 s (NSSI) to 4.266 s (SSI) in the 30-story building. Therefore, it is concluded that considering soil–structure interaction leads to lengthening the vibration period of the structures.

8.2. Time History Analysis

Time history analysis is performed due to the seven aforementioned earthquake records, then the average response is studied and presented in figures. The discussion of the results obtained is introduced as follows:

8.2.1. For the 20-Story Building

• Figure 18 and Figure 19 showed the average top velocity and acceleration under the two cases of analysis (NSSI and SSI with solid raft). The maximum velocity and acceleration increased by 122.24% (from 0.1718 m/s to 0.3818 m/s) and 16.32% (from 1.0136 m/s² to 1.179 m/s²), respectively, while the soil–structure interaction was considered. In addition, curves showed that the maximum velocity and acceleration decreased by 10.32% (from 0.3818 m/s to 0.3424 m/s) and 5.11% (from 1.179 m/s² to 1.1187 m/s²), respectively, while using the cellular raft.
  Figure 18. The average top floor velocity for the 20-story building.

  Figure 18. The average top floor velocity for the 20-story building.

  Figure 19. The average top floor acceleration for the 20-story building.

  Figure 19. The average top floor acceleration for the 20-story building.
• Table 5. Comparison between some output for the used seven seismic records and the average response (20-story building).

  Output Response	Analysis Case	El-Centro (USA)	Northridge (USA)	Kobe (Japan)	Chichi (Taiwan)	Friuli (Italy)	Kocaeli (Turkey)	Loma (USA)	Average Response
  Top Floor Max. Displacement (mm)	Fixed Base	121.83	128.7	118.76	120.44	128.59	122.42	131.59	36.38
  	Solid Raft	519.74	447.08	500.93	341.51	411.29	427.54	416.54	116.96
  	Cellular Raft	486.21	420.12	472.32	384.96	582.24	468.27	393.68	139.17
  Max. Base Shear (kN)	Fixed Base	14,029.4	13,787.9	15,881.3	16,698.9	12,504.3	14,253.2	13,315.1	4634.4
  	Solid Raft	29,541.87	22,757.6	1932.1	26,843.7	30,400	24,000	25,700	7644.5
  	Cellular Raft	28,126.8	22,757.6	18,399.7	16,430.4	16,400	18,000	17,300	6585.3

  shows the maximum top floor displacement and the maximum base shear due to the seven records and the average response. From the average response comparison; it is found that the maximum top floor displacement increased by 221.5% (from 36.38 mm to 116.96 mm) while considering SSI, and also it increased by 18.9% (from 116.96 mm to 139.17 mm) while using a cellular raft instead of a solid raft. Furthermore, the maximum base shear increased by 64.95% (from 4634.4 kN to 7644.5 kN) while considering SSI, although the period of vibration is increased because of considering the soil mass in the analysis [36,37]. Moreover, it was discovered that using a cellular raft reduces maximum base shear by 13.86% (from 7644.5 kN to 6585.3 kN).
• Figure 20 shows that the average maximum relative sway along the tower height is increased while applying the soil–structure interaction for each tower story. Therefore, as a result, the maximum relative drift through the SSI case is larger than the NSSI case. Additionally, the curves show that the maximum relative sway along the tower height is decreased while using a cellular raft for each tower story. In addition, the average maximum relative drift through a cellular raft is smaller than a solid raft by 15.38% (from 0.006506 to 0.00549), as shown in Figure 21.
  Figure 20. Maximum relative sway (20-story building, average).

  Figure 20. Maximum relative sway (20-story building, average).

  Figure 21. Maximum relative drift (20-story building, average).

  Figure 21. Maximum relative drift (20-story building, average).
• Figure 22 and Figure 23 show the normal stress distribution over the raft due to El-Centro as an example, which increased by 82.36% (from 1587.59 kN/m² to 2895.15 kN/m² in the x-direction) while using a cellular raft over the solid raft.
  Figure 22. Raft stress (S-xx) due to scaled El-Centro as an example, 20 stories, (solid raft).

  Figure 22. Raft stress (S-xx) due to scaled El-Centro as an example, 20 stories, (solid raft).

  Figure 23. Raft stress (S-xx) due to scaled El-Centro as an example, 20 stories, (cellular raft).

  Figure 23. Raft stress (S-xx) due to scaled El-Centro as an example, 20 stories, (cellular raft).

8.2.2. For the 30-Story Building

• Figure 24 and Figure 25 show the average top velocity and acceleration under the two cases of analysis (NSSI and SSI with solid raft). Curves show that the maximum velocity and acceleration decreased by 9.92% (from 0.1845 m/s to 0.1662 m/s), and 18.05% (from 0.8231 m/s² to 0.6745 m/s²) due to the foundation flexibility in case of considering SSI. In addition, curves show that the maximum velocity increased by 1.2% (from 0.1662 m/s to 0.1682 m/s), while the maximum acceleration decreased by 3.44% (from 0.6286 m/s² to 0.607 m/s²), respectively, while using cellular raft.
  Figure 24. The average top floor velocity for the 30-story building.

  Figure 24. The average top floor velocity for the 30-story building.

  Figure 25. The average top floor acceleration for the 30-story building.

  Figure 25. The average top floor acceleration for the 30-story building.
• Table 6. Comparison between some output for the used seven seismic records and the average response (30-story building).

  Output Response	Analysis Case	El-Centro (USA)	Northridge (USA)	Kobe (Japan)	Chichi (Taiwan)	Friuli (Italy)	Kocaeli (Turkey)	Loma (USA)	Average Response
  Top Floor Max. Displacement (mm)	Fixed Base	152.22	149.97	138.49	175	188.36	147.15	135.23	76.19
  	Solid Raft	416.71	341.43	332.95	244.44	451.97	604.17	328.28	123.98
  	Cellular Raft	399.71	287.88	346.53	253.82	448.76	598.82	277.49	130.37
  Max. Base Shear (kN)	Fixed Base	11,232.5	12,028.1	8515.8	11,724.5	13,520.5	11,464.6	13,069.6	4219.53
  	Solid Raft	22,464.6	15,992.2	12,102.4	12,293.9	14,100	17,400	19,600	3648.9
  	Cellular Raft	21,920.7	14,884.9	13,784.8	13,425.1	13,700	17,600	17,900	3541.2

  shows the maximum top floor displacement and maximum base shear as a result of the seven records and average reaction. According to the average response comparison, the maximum top floor displacement increased by 62.72% (from 76.19 mm to 123.98 mm) when SSI was included and increased by 5.15% (from 123.98 mm to 130.37 mm) with a cellular raft. Furthermore, when SSI was taken into account, the maximum base shear decreased by 13.52% (from 4219.53 kN to 3648.9 kN). Furthermore, the use of a cellular raft reduces maximum base shear by 2.95% (from 3648.9 kN to 3541.2 kN).
• Figure 26 shows that the average maximum relative sway along the tower height is increased while applying the soil–structure interaction. Furthermore, the maximum relative drift through the SSI case is larger than the NSSI case. It also shows that the maximum relative sway along the tower height is decreased while using a cellular raft. In addition, the average maximum relative drift through a cellular raft is larger than a solid raft by 3.03% (from 0.0033 to 0.0034), as shown in Figure 27.
• Figure 28 and Figure 29, show the normal stresses distribution over the raft due to El-Centro as an example, which increases by 44.753% (from 1004.59 kN/m² to 1454.14 kN/m² in the x-direction) while using a cellular raft over the solid raft.

9. Conclusions

This study is focused on the effect of using cellular rafts in high-rise buildings’ seismic analysis for seven earthquake records matched to the ECP-201 response spectrum. Full 3D models are considered for all cases in Midas GTS NX. Based on the results and discussion, it is possible to deduce that:

• Soil–structure interaction has a significant impact on the dynamic response of tall buildings. Considering SSI increases the dynamic response of 20- and 30-story moment-resisting frames.
• Base shear increased by 64.95% for the 20-story building and decreased by 13.52% for the 30-story building while considering the soil–structure interaction. Therefore, the SSI effect on shear demand is not the same for all structures, as it depends on the characteristics of the structure and the ground motions.
• A cellular raft generally leads to a slight decrease in the dynamic response of high-rise buildings. Moreover, using a cellular raft reduces the amount of concrete used in the building foundation. That leads to achieving sustainability based on material requirements.
• Base shear decreased by 13.86% and 2.95% for the 20- and 30-story buildings, respectively, while using a cellular raft instead of using a solid raft with the same dimensions.
• Using a cellular raft is a more economical design because it decreases the number of piles used in the foundation according to the weight of the reduced gaps that form the cellular raft.
• The reliable volume for cellular raft gaps can range from 35% to 42% of the solid raft volume.
• For future work, the building’s material nonlinearity will be considered, as this study took only geometric nonlinearity (p-delta effect), in addition to applying the study to other statical systems, such as diagrid and twisting towers.