Effect of Presence of Subsoil Voids on the Seismic Performance of Reinforced Concrete Buildings Considering Different Building Structural Systems

doi:10.21203/rs.3.rs-4928845/v1

The presence of underground voids beneath reinforced concrete structures causes many problems in settlement under the foundations, which may cause tilting problems and affect the building's stability, especially if these buildings are subjected to seismic loads. In this paper, three-dimensional seismic analyses of RC structures founded on soil containing voids were performed using the finite element method (FEM). Two buildings with the same slab area (20*20) m² were considered in the analysis. The first building is a six-stories building while the second building is a fifteen-stories building. The buildings were exposed to the ground acceleration for the El-Centro earthquake with a time interval of 0.02 sec. The buildings were rested on clay soil with two different critical locations of weak soil region (underground void) and one analysis on the soil without a void. Several factors that affect the seismic performance of structures, such as void locations, structural systems of the buildings, the effects of infill brick walls, foundation level, and the number of floors were considered. These factors were considered in the analysis to obtain a complete description of the seismic response of the structures constructed on soil with voids to be used in design processes. Based on the results, charts were developed for the seismic response of RC structures built on soil containing voids. These charts could be used in the prediction of the seismic response of structures built on soil with voids.

underground void

ANSYS

structural systems

void depth

void eccentricity

seismic load

Construction on foundation soils that contain weak regions or subterranean cavities creates problems with the stability and tilt of the superstructures. The extent of the danger of underground voids under structures varies depending on their sizes and locations from the building foundations. These voids form in the soil for various reasons, including the dynamic loads caused by mining and tunneling projects, old tubes, and poorly compacted trench backfill. Tunneling processes are one of the most common reasons for the formation of voids. Tunneling-induced soil defects significantly affect superstructures. Therefore, it's crucial to study the behavior of these buildings, the various effects on them resulting from the soil defect caused by the excavation process, the extent to which these effects affect their structural elements, and the building's future resistance to earthquakes.

Several researchers studied the stability of footings that are founded on soil and contain voids under static and dynamic loads. Many studies have also investigated the seismic behavior of footings above underground voids. The researchers examined footings resting on soils containing voids under static loading (Badie and Wang 1984; M. C. Wang and Badie 1985; M. C. Wang and Hsieh 1987; M. C. Wang et al. 1989; C. Hsieh 1991; Azam et al. 1991; C. W. Hsieh and Wang 1992; Kiyosumi et al. 2007; Sireesh et al. 2009; Moghaddas Tafreshi et al. 2011; Lee et al. 2014; Hussein 2014; Lee et al. 2015; Lavasan et al. 2016; Xiao et al. 2018; Zhou et al. 2018; Zhao et al. 2018; Lee and Kim 2019; Jayamohan et al. 2019; Wu et al. 2020; Anaswara and Shivashankar 2020; Mansouri et al. 2021; Mazouz et al. 2022).

Many researchers investigated the response of footings above underground voids to dynamic loads. Sahoo and Kumar (2012) investigated analytically the stability of a continuous, unsupported circular tunnel in a cohesive frictional soil type using finite element method. An experimental work of a foundation rested on unreinforced and geogrid-reinforced sand with a circular void that was subjected to both static and repetitive loads was carried out by Asakereh et al. (2013). Chakraborty and Kumar (2013) examined the stability of a long, unsupported circular tunnel in the presence of seismic body forces using the lower-bound finite element limit analysis. Chakraborty and Sawant (2017) used the lower bound theorem of limit analysis and the finite element method to estimate the bearing capacity of a strip foundation resting above an unlined, long circular tunnel in undrained clay soil that was exposed to pseudo-static horizontal seismic body forces. Using an AFELA program and the pseudo-static technique, Zhang et al. (2022) examined the seismic bearing capacity of strip footings over voids in pure cohesive clay. Es-haghi et al. (2021) used machine learning techniques to determine the seismic bearing capacity of a shallow strip foundation resting on an unsupported rectangular void in heterogeneous soil. Es-haghi et al. (2021) studied the undrained seismic bearing capacity and the failure mechanisms of a shallow strip foundation that is founded on homogeneous and heterogeneous cohesive soils on a single unsupported rectangular void using finite-element limit analysis.There are few researchers who have studied the responses of the underground tunnel-soil-surface structure interaction system. Jao and Wang (1998) used the finite element analysis method to investigate the interaction between strip foundations and continuous concrete-lined circular soft-ground tunnels located below the center of the strip foundations. Mroueh and Shahrour (2003) studied numerically the interaction between the tunneling and adjacent structures within soft soils. The numerical modeling was developed using a full three-dimensional simulation that considers the existence of the structure during tunneling. Boldini et al. (2018) conducted a parametric study of the response to tunneling of reinforced concrete-framed structures built on strip footings using the finite element method.

Abate and Massimino (2017) performed a parametric analysis using the finite element method: from a real case of the Catania (Italy) underground network, the tunnel depth, the location of the superstructure, and the seismic inputs were edited to examine their effects on the dynamic tunnel-soil-structure interaction. Wang et al. (2018) investigated the seismic response law of the system of the underground structure-soil-superstructure interaction. Pitilakis et al. (2014) presented and analyzed a series of numerical analyses that were conducted to investigate the dynamic response of shallow circular tunnels, taking into consideration the interaction effects of the nearby above-ground oscillating buildings. Abdel-Motaal et al. (2014) investigated the seismic interaction between tunnels and the surrounding granular, dry soil. Mirhabibi and Soroush (2012) investigated how surface buildings affect the ground settlement of twin tunneling by using field data from Shiraz Metro Line1 and the finite element software ABAQUS. Abdel-Nasser et al. (2023) performed a non-linear static analysis using the FE program (ANSYS). Three dimentional models of RC structures founded on soil containing a void in different locations and sizes were analyzed to estimate the critical void locations under structures depending on structure size and void case. Abdel-Nasser et al. (2024) performed a non-linear analysis to investigate the static response of RC structures founded on soil containing voids subjected to lateral loads equivalent to seismic loads.

Previous studies in the literature primarily examined the behavior of footings resting on soil with voids, ignoring the soil-structure interaction or the nonlinear behavior of the concrete structure. Research on three-dimensional, fully reinforced concrete structures constructed on soil containing voids is extremely lacking. Further research is necessary to understand how the various sizes and structural systems of real 3D reinforced concrete buildings affect how structures behave when resting on voids, especially under seismic load. The current study mainly focused on the seismic response of the structures that were found above soil containing voids. Several factors can affect the seismic performance of structures, such as void locations, structural systems of the buildings, the effects of infill brick walls, foundation level, and the number of floors. These factors were considered in this study to obtain a complete description of the seismic response of the structures founded on voids to use in design processes.

Thirty 3D models of two RC buildings with the same area and different numbers of floors (heights) were analyzed using ANSYS software. The structures were exposed to El-Centro (1940) ground acceleration, scaled down to a maximum acceleration of 0.15 g, to investigate the seismic response of structures built on soils with voids. Many factors were studied in this analysis, such as the structural system of floors, the effect of brick infill walls, the location of RC walls in the higher structure, and the presence of the basement. Two cases of void locations with the same diameter and depth were selected to represent the region of weak soil. These void cases were analyzed for all of the parameters mentioned above. A linear modal analysis was also performed for all structures to investigate the effect of the studied parameters on the fundamental natural frequency F and period T of the structure with and without voids.

2.1 Problem Defination

Figure 1a shows the dimensions of the two buildings with the same slab area (20*20) m². The first building's height above the foundation is 19 meters. It consists of five floors, 3 m high, and a ground floor, 4 m high. The second building has a height of 46 m from the foundation level and consists of 14 floors, 3 m high, and the ground floor, 4 m high. The buildings were exposed to the ground acceleration for the El-Centro earthquake (1940) with a time interval of 0.02 sec. (Vibration data, 1940). For the current analysis, the ground acceleration data were scaled down to acceleration amplitude = 0.15 g. The buildings were rested on clay soil with two different critical locations of weak soil region (underground void) and one analysis on the soil without a void. Figure 1b shows the three models that were performed for each structure in this analysis. Case 1: no-void condition; Case 2: a centric void location located below the foundation with a diameter D of 15 m at a depth y of 10 m from the foundation; and Case 3: an eccentric void location located below the foundation with a diameter D of 15 m at a depth y of 10 m from the foundation and at a horizontal distance equal to B/2 from the raft center.

2.2 Structure Description

The following sections will present details of the structural models and the factors studied for the two main structures: the low-rise structure (ST1) and the moderate-rise structure (ST2).

2.2.1 Low-rise structure (ST1)

The low-rise structure ST1 was analyzed using ANSYS software, considering the effects of the structural system of floors (beamed slabs and flat slabs) and the effect of brick infill walls in three different patterns. Table 1 lists the structural dimensions of the two structural floor systems.

Fifteen structural models were examined using ANSYS software to study these effects on the behavior of the structure rested on soil with and without voids under seismic load. Figures 2 and 3 present the structural models investigated in this study for structure ST1. For each structure, three soil models were performed: the no-void condition (case 1), the central void location (case 2), and the eccentric void location (case 3), as illustrated in Figure 1b. These three models were analyzed for each of the following structures:

1. Structure with beamed slabs without considering the infill wall effect (The bare model), as shown in Figure 2a.

2. Structure with flat slabs without considering the infill wall effect (The bare model), as shown in Figure 2b.

3. Structure with beamed slabs, considering the effect of the infill walls at all structure bays (fully infilled model), as shown in Figure 3a.

4. Structure with beamed slabs, considering the effect of the infill walls at the external bays and some of the internal bays only, as shown in the Type 1 model in Figure 3b.

5. Structure with beamed slabs, considering the effect of the infill walls at the external bays and some of the internal bays only at all stories except for the ground floor, as shown in the Type 2 model in Figure 3c.

Table 1

Dimensions of the structure ST1.
Structure ST1	Slab with beams	Flat slab
Slabs Area (m²)	20 x 20	20*20
Slabs thickness (m)	0.15	0.2
Structure height H (m)	19	19
Number of floors	6	6
Raft Area (m²)	22.5 x 22.5	22.5*22.5
Raft depth t_f (m)	0.8	0.8
Beams (m²)	0.3x0.6	---
External columns dimension	0.4x0.8	0.4x0.8
Internal columns dimension	0.4x1.0	0.4x1.0

Figure 3 Models of structure (ST1) with brick infill walls; (a) the fully infilled model, (b) Type 1 model, and (c)Type 2 model

2.2.2 Moderate-rise structure (ST2)

A fifteen-story structure was designed with different RC walls’s locations. Table 2 lists all the structure dimensions for the two designs. The structure (ST2) was analyzed under seismic load, considering the effects of the following factors: the location of RC walls in the plan, the effect of the brick infill walls, and the presence of a basement.

Table 2

Dimensions of the structure ST2.
Structure ST2	RC walls (1)	RC walls (2)
Slabs Area (m²)	20 x 20	20 x 20
Slabs thickness (m)	0.15	0.15
Structure height H (m)	46	46
Number of floors	15	15
Raft Area (m²)	25 x 25	25 x 25
Raft depth t_f (m)	1.2	1.2
Beams (m²)	0.3x0.6	0.3x0.6
Corner columns dimension (m)	C₁ 0.5x0.5	-
Edge columns dimension (m)	C₂ 0.5 x 0.8	C₁ 0.5 x 0.6 C₂ 0.5 x 0.8
Internal columns dimension (m)	C₃ 0.5x0.7 C₄ 0.5*1.7	C₃ 0.5x1.7
RC walls (L shape) thickness (m)	0.3	0.3

Fifteen models of structure ST2 were performed by ANSYS software under seismic loading to study the effects of the previous factors on the seismic behavior of the structure above soil with and without a void. Figures 4 and 5 present the structural models investigated in this study for ST2. Three models were performed for each structure, including the no-void condition, the central void location (case 1), and the eccentric void location (case 2), as shown in Fig. 1b. The three models were analyzed for each of the following structures:

1. Structure with RC walls 1, where the walls are situated in the interior area of the structure without modeling the effect of the infill walls, as shown in Figure 4a.

2. Structure with RC walls 2, where the walls are positioned in the corners of the structure without modeling the effect of the infill walls, as shown in Figure 4a.

3. Structure with RC walls 1 with a basement without considering the effect of the infill walls, as shown in Figure 5b.

4. Structure with RC walls 1, considering the effect of the infill walls at all structure bays (fully infilled model), as shown in Figures 5c.

5. Structure with RC walls 1, considering the effect of the infill walls at the external bays and some of the internal bays only, as shown in the Type 1 model in Figure 5d.

2.3 Material Modeling

2.3.1 Soil modeling

The soil was modeled using the Mohr-Columb model in ANSYS software, which is characterized as an isotropic, linearly elastic-perfectly plastic model. Tolba et al. (2021) assumed that the soil modulus of elasticity increased linearly with depth. In the present research, the linear increase in modulus of elasticity has been converted into steps, as shown in Figure 6. A clay foundation soil for the structures was selected for this analysis, and the material properties of the two soil layers used in the present study were taken from Hsieh (1991). The soil depth in the analysis was modeled as 80 m from the foundation level; the first 40 m from the ground level was classified as a Kaolin soil layer with modulus of elasticity E_soil increasing with depth; and the second 40 m as a clayey sand soil layer. The properties of the soil layers used in the analysis are listed in Table 3.

Table 3

The properties of the soil layers used in the analysis.
Soil layers	Kaolin soil (C. Hsieh 1991)	Clayey sand soil (C. Hsieh 1991)
Modulus of elasticity, E_soil	20 Mpa	50 Mpa
Poisson ratio, ν	0.39	0.32
Soil cohesion, C	158 kpa	9 kpa
Internal friction, φ	8°	31°
Dilation angle, ѱ	0	0
Dry unit weight of the soil	15.75 kN/m³	16.56 kN/m³

2.3.2 Reinforced concrete elements modeling

Reinforced concrete elements were modeled as a linear concrete material to reduce the time required for modeling. The effect of nonlinearity was assumed by reducing the stiffness of beams, columns, RC walls, and slab elements according to (ECP201 2008). Stiffness reduction was performed by reducing the modulus of elasticity of beams, columns, RC walls, and slabs to 0.5 E_c, 0.7 E_c, 0.7 E_c, and 0.25 E_c. Concrete material properties are as follows:

Modulus of elasticity, E_c	= 22000 Mpa
Poisson ratio ν	= 0.2
Density γ	= 2500 kg/m³

2.3.3 Brick infill walls modeling

A linear material model was used to represent the brick infill walls in the models that addressed the effects of the infill walls on the behavior of the structure, with a modulus of elasticity E = 5000 Mpa, a Poisson ratio ν of 0.2, and a unit weight of 18 kN/m³.

2.4 Structural Modeling

2.4.1 Soil modeling

The SOLID186 element was used to model the soil layers with boundary conditions at 80 m vertically under the structure and 3B horizontally from the foundation edges, B: the foundation length. The vertical and horizontal boundaries of the foundation soil model were chosen sufficiently far away to avoid any effects on the results obtained. The vertical boundaries were set to be free in the vertical direction only, and the bottom surface of the soil block has been fixed in all directions, as shown in Figure 7a. To achieve accuracy in the solution, the density of soil elements was increased in the area around the footing and the void locations. In the current analysis, the weak zone soil stiffness was totally neglected, and the elements filling the weak area were removed (presented as a void). Figure 7b shows the mesh elements for the half-part of the symmetric model of the two structures studied.

2.4.2 Reinforced concrete Modeling

The BEAM 188 element was used to model beam and column members, and the SHELL181 element was used to model floor slabs, RC walls, and basement walls. Raft foundation elements were modeled with SOLID 186.

2.4.3 Infill walls modeling

It is an established fact that brick infill walls have an important role in resisting the lateral load (or seismic load) to which concrete buildings are exposed. Therefore, to study the influence of the infill walls on the seismic response of RC structures with and without voids beneath, the two structures (ST1 and ST2) were analyzed with different distributions of brick infill walls. The equivalent method for modeling the wall effects as a diagonal strut element in the direction of loading was used. Diagonal strut elements were modeled in both directions for resisting compression forces that resulted from the applied accelerations, as shown in Fig. 8. LINK180 was selected to model the brick infill wall struts with a width w_e that was estimated according to the Mainstone equation (Mainstone 1974). The thickness of the infill walls is assumed to be 25 cm at the exterior panels and 12 cm at the internal panels. For all infill wall struts, LINK180 is modeled as a compression-only member to resist only the compression forces.

2.5 Verification of Numerical Model

Wang et al. (2018) experimentally investigated the seismic behavior of the tunnel-soil-surface structure interaction system using a shaking table test. Four cases were considered in Wang’s study as follows: free field (FF), soil-surface frame structure (SF), tunnel-soil (TS), and tunnel-soil-surface structure (TSF), as shown in Fig. 9a. The material of the soil, soil container, structure, and tunnel in the current study were used as the model test by Wang et al. (2018). The soil properties for the foundation soil used in the ANSYS model are: modulus of elasticity E_soil = 7 Mpa, Poisson ratio ν = 0.4, soil cohesion C = 2.8 Mpa, internal friction angle φ = 0, dry unit weight of the soil = 1190 kg/m³. Steel properties of the soil container used in the ANSYS model: modulus of elasticity E_s = 300,000 Mpa, Poisson ratio ν = 0.3, density = 7800 kg/m³. The properties of the material of the surface structure and tunnel used in the ANSYS model are: modulus of elasticity E = 2100 MPa, Poisson ratio ν = 0.3, density = 1180 kg/m³. The dimensions of the model are shown in Fig. 9b.

The accelerations and displacements that occurred in the tunnel, structure, and soil were measured under different input accelerations. Two of these cases were selected to validate the model in ANSYS. The peak horizontal acceleration response of the surface structure under the El-Centro input waveform (acceleration amplitude = 0.03 g) of SF and TSF cases was analyzed using ANSYS and compared with the test results obtained by Wang et al. (2018). Results showed that the natural frequencies of the surface structure are 8 Hz in the current ANSYS model and 7.91 Hz for the experimental model obtained by Wang et al. (2018). The horizontal acceleration peak values at the floor levels of the frame structure model under the "El-Centro" input waveform, as shown in Fig. 10, show good agreement between the ANSYS FE model and the experimental results tested by Wang et al. (2018). This means that the adopted ANSYS FE model can investigate the seismic response of the surface structures, considering the soil-structure interaction with or without a tunnel.

The following sections present the results of the non-linear analysis of the structures exposed to accelerations in the El Centro earthquake time history, as well as the results of the linear modal analysis for all structures. The linear-modal analysis yielded the results of the natural frequency (F) and the natural period (T) of the structures. In the non-linear analysis, the following results were presented: lateral displacement at floor levels, inter-story drift, maximum acceleration at floor levels, base shear force during time at foundation level, settlement values under the foundation at maximum lateral displacement, and maximum differential settlement.

3.1.1 Lateral displacements and inter-story drift

Figure 11 shows the lateral displacement at floor levels and inter-story drift of structure (ST1) of different structural systems, including the floor structural system, and the effect of the infill walls with and without the presence of an underground void. In the three soil conditions, the structure with flat slabs exhibits larger lateral displacement values at floor levels compared to the structure with beamed slabs. The structure with a flat slab had the highest floor displacement, increasing by 15% compared to the structure with beamed slabs. In three soil conditions, the inter-story drift values for the structure with a flat slab increased compared to the structure with beams. Inter-story drift values were estimated for floor levels in the direction of the presence of underground voids. . The effect of the presence of voids on inter-story drift values is limited, regardless of the structural system of slabs, when comparing the same system with the presence of voids.

The figure shows that when considering the effect of infilled brick walls in the model, the lateral displacement at the foundation level gives a higher value compared to the bare model. The lateral displacements at the foundation level in the fully infilled structure model are equal to 2.7, 2.4, and 2.14 times the lateral displacements of the bare model for soil cases 1, 2, and 3, respectively. In the Type 1 model, lateral displacements at foundation levels are 2.6, 2.6, and 2.1 times those in the bare model in soil cases 1, 2, and 3, respectively. In the Type 2 model, lateral displacements at foundation levels are 2.4, 2.3, and 1.8 times those in the bare model in soil cases 1, 2, and 3, respectively. The earthquake's significant increase in base shear, as depicted in Figure 16, leads to larger lateral displacements in the models that incorporate infill wall effects compared to the bare model. This is a consequence of the significant increase in structural stiffness. The high base shear force of the models, which accounted for the effects of infill walls compared to the bare model, resulted in the first floor's inter-story drift value being the highest compared to the rest of the floors, whereas the bare model's largest value was on the third floor. The absence of infill wall effects on the ground floor in the Type 2 model leads to an increase in the lateral displacement at the foundation level as well as on the first floor, resulting in greater lateral displacement at all floor levels compared to other models. The results indicate that designing a structure resting on soil with voids exposed to seismic load in low-rise buildings requires greater attention to the effect of infill walls in modeling, as it significantly influences the lateral displacements and inter-story drifts of the superstructures.

Figure 12 shows the maximum lateral displacements at floor levels and inter-story drifts that occurred for the different models of structure ST2. It was noted that the location of RC walls has no noticeable effect on lateral displacements or inter-story drifts. That is because the two systems have the same stiffness. The lateral displacements decrease when considering the effect of brick walls. The lateral displacement of the highest floor in the fully infilled model decreases by 48, 40, and 25% compared to the bare model for soil cases 1, 2, and 3, respectively. For the Type 1 model, the lateral displacement of the highest floor decreases by 36, 28, and 16% compared to the bare model for soil cases 1, 2, and 3, respectively. The effect of walls decreases as the soil contains a void beneath the structure. In the case of the model with a basement, the lateral displacements at the highest floor in the model with a basement decreased by 10, 8, and 14% compared to the model without a basement in soil cases 1, 2, and 3, respectively.

The values of the inter-story drift decrease significantly with considering the effect of the infill walls in the three soil conditions. In the case of the model with a basement, for the no-void case, the inter-story drift values in the model with the basement decrease by 49, 22, and 12% compared to the model without a basement at the first, second, and third floors, respectively. For the central void case, the inter-story drift values in the model with the basement decreased by 62, 25, and 13% compared to the model without a basement on the first, second, and third floors, respectively. For the eccentric void case, the inter-story drift values in the model with the basement decreased by 48, 27, and 18% compared to the model without a basement at the first, second, and third floors, respectively. It was noted that the eccentric void case is the most affected by the presence of the basement in lateral displacements and inter-story drifts.

3.1.2 Base shear force ratio

Figure 13a-c shows the base shear force ratios of structure ST1 at the foundation level during the applied acceleration history for the three soil cases. The base shear force ratio was estimated by dividing the base shear force by the total applied vertical load. The maximum base shear force of the flat slab structure decreases by 17, 14.5, and 13.3% of the base shear of the beamed slab structure in the cases of no-void, centric void location, and eccentric void location, respectively, as shown in Figure 13d. It was observed that the existence of the subsurface void reduced the difference in the base shear ratio for the two slab structural systems. The values of the base shear ratios of structure ST1 increased significantly in the models, which considered the effect of infill walls, compared to the bare model at all acceleration time steps. The significant increase in base shear force ratios for the infill wall models occurred due to the higher rigidity of these models compared to the bare model, which leads to higher base shear forces resulting from the seismic load. As shown in Figure 14a-c, the difference in the base shear force ratios between the two models with different locations of RC walls can be neglected. It was observed that the maximum base shear forces decreased in the fully infilled model by almost 21% compared to the bare model in all three soil cases, as shown in Figure 14d. The maximum base shear forces decrease in the Type 1 model by almost 15% compared to the bare model in the three soil cases, in contrast to structure ST1, in which the presence of infill walls in the model increases the base shear force caused by the earthquake. Structure ST2 has natural periods that are between 2 and 2.5 seconds for both the bare model and the models with infill walls. In the elastic response spectrum curve for the El-Centro earthquake, as mentioned in Sallam (2016), the acceleration value increases as the natural period increases within this interval. This explains why the base shear force value decreases in models that consider infill effects compared to the bare model in structure ST2. The model without the basement shows greater values of base shear force during the time domain than the model with the basement. The maximum shear force in the model with the basement decreases by 24% compared to the model without the basement in all soil cases.

3.1.3 Settlements under foundations

Figure 15a-c shows the settlement distribution under the foundation of structure ST1 for the different structural systems at the time of the maximum lateral displacement that occurred on the structure. The settlement distribution in the flat slab structure shows more flexibility than the beamed slab structure because of its low stiffness compared to the beamed slab structure. The maximum settlement under the foundation in the flat slab structure decreases by 4.9, 3.8, and 5.6% compared to the beamed slab structure. The maximum settlement under the foundation of the fully infilled model increases by 25, 14.6, and 31.1% compared to those of the bare model for soil cases 1, 2, and 3, respectively. The maximum settlements under the footing of the Type 1 model increase by 11, 9, and 27% compared to those in the bare model for soil cases 1, 2, and 3, respectively. The maximum settlements under the footing of the Type 2 model increase by 13, 11, and 28% compared to those in the bare model for soil cases 1, 2, and 3, respectively. The maximum settlement increases significantly in the case of eccentric void (soil case 3) when considering the effect of infill walls in the model compared to the bare model. It was noted that, considering the effect of the infill walls in the model, they have a noticeable influence on the settlement values under the footing, especially in the eccentric void case. The presence of voids and their location from the foundation most significantly influence the differential settlement under footings, as shown in Figure 15d. Differential footing settlement at maximum lateral displacement was calculated for each case. The differential footing settlements for the flat slab structure decreased by 44, 42.3, and 20.5% for soil cases 1, 2, and 3, respectively, compared to the structure with beams. The flat slab structure exhibits a decrease in differential settlements compared to the structure with beams due to the decrease in the base shear force caused by the earthquake, which is attributed to its lower stiffness. The differential settlement values of the fully infilled model increase by 2.6, 2.5, and 1.8 times those in the bare model for soil cases 1, 2, and 3, respectively. The increase in differential settlements in the fully infilled model compared to the bare model in low-rise structures is a result of the increase in the base shear force caused by the earthquake due to the high stiffness of the structure with fully infilled walls. Differential settlements in the two models (Type 1 and Type 2) are approximately 1.75 times that in the bare model, approximately in the three soil cases.

Figure 16a-c shows the settlement distributions of the different models of structure ST2 for the three soil cases. It was observed that the settlement profiles are almost similar between the two models of different RC wall locations. The presence of the basement resulted in a decrease in the value of the settlements beneath the foundation. The maximum settlement in the model with the basement decreases by 19% compared to the model without the basement in soil cases 1 and 2, while it decreases by 23% in soil case 3. Figure 16d shows the differences between the models of structure ST2 in the values of the differential settlements.

3.1.4 Accelerations on floor levels

Figure 17 shows the maximum lateral accelerations on each floor level during the time of acceleration to which the buildings are exposed for the different models of structure ST1. The maximum acceleration on the second floor of the structure in the case of the flat slab system decreases by 25% compared to slabs and beams in the three conditions of the soil. It was noted that the maximum acceleration values at the foundation level and the sixth floor in the fully infilled model were 30% higher than in the bare model for the three types of soil cases. The maximum accelerations at the foundation level increase by 30 and 10% in the Type 1 and Type 2 models for the three soil cases, respectively, compared to the bare model.

Figure 18 shows the maximum accelerations on floor levels of the different models of structure ST2 for the three soil cases. It was noted that there is no difference between the two models of different RC wall locations. There was a change in the maximum acceleration values between the models considered the infill walls and the bare model in the first four floors only, while the other floors had the same values. The acceleration values in the model (with the basement) increase from the fourth to the tenth floors compared to the model without the basement, then decrease in the upper five floors. The maximum acceleration values occurred on the ninth floor; the acceleration value in the model with the basement increased by approximately 22% compared to the model without the basement for the three cases of soil.

3.1.5 Fundamental natural frequency and natural period

Fundamental natural frequencies F and periods T of structure ST1 of different models for the three different soil cases are shown in Figure 19a. The natural frequencies of the flat slab structure decreased by 20% compared to the structure with beams for the three soil cases. Natural frequencies of the fully infilled structure increase by 43, 42, and 38% compared to the bare structure for soil cases 1, 2, and 3, respectively. The natural frequencies of the Type 1 model increase by 38, 37, and 34% compared to the bare structure for soil cases 1, 2, and 3, respectively. The natural frequencies of the Type 2 model increase by 27, 27, and 25% compared to the bare structure for soil cases 1, 2, and 3, respectively. It was found that the presence of voids leads to a decrease the natural frequency of the structure. Figure 19b shows the fundamental natural frequencies and natural periods of the different models of structure ST2 for the three soil cases. It was noted that the natural frequency in the RC walls 2 model decreased by a slight value compared to the RC walls 1 model for all soil cases. The frequencies of the fully infilled model increase by 25, 24, and 23% compared to the bare model for soil cases 1, 2, and 3, respectively, while the frequencies of the Type 1 model increase by 21, 20, and 19% compared to the bare model for soil case 1, 2, and 3, respectively. It was noted that the effect of the infill walls on increasing the values of natural frequencies decreases when the soil contains voids beneath the structure. It was observed that the natural frequencies of the model with a basement increased by 14% compared to the model without a basement for all three soil cases.

3.2 The Effects of Void Location on Seismic Response of the Structures

Figures 20 and 21 show comparisons of the seismic response of the structures ST1 and ST2, respectively, for the three soil cases. This comparison includes all of the modeling parameters studied. Lateral displacement ratios at the highest floor, maximum settlement ratios, and differential settlement ratios were estimated, and this ratio was calculated by dividing the value in the presence of void by the no-void condition. It was observed from Figure 20 that the design with flat slabs for structure ST1 is affected by the presence of voids below it more than slabs and beams. The differential settlement ratios for designs with beams are equal to 1.07 and 1.87 for the centric void and the eccentric void locations, respectively, while the differential settlement ratios for designs with flat slabs are equal to 1.1 and 2.66 for the centric void and the eccentric void location, respectively. The presence of voids below the flat slab design has a greater effect than that of slabs and beams in differential settlements, particularly in eccentric voids. To predict the actual seismic response of the superstructures, modeling must take into account the effects of infill walls. Figure 20 clearly shows that the infill wall model influences the lateral displacement ratios at the highest floor. This suggests that considering the actual bays of infill walls significantly influences the lateral displacement values when voids are present. The fully infilled model is the least affected by the presence and location of the void compared to the bare model, Type 1, and Type 2 models. While Type 1 is the model most affected by the presence and location of the void, the lateral displacement at the highest floor significantly increases in the case of the eccentric void.

There is an increase in settlements and differential settlements when designing RC walls in the corner compared to their location in the central area of the plan, but it isn’t a large percentage because the location of RC walls in the central area gives the structure greater rigidity compared to the location in the corners. The infill wall in the model has a clear effect on the seismic response of superstructures in the presence of underground voids. In cases where underground voids are present, the ratios of lateral displacements, maximum settlement, and differential settlement increase more than the bare model, as shown in Figure 21. For the fully infilled model, the differential settlement ratios are 1.25 and 2.26 for the centric void and the eccentric void location, respectively. For the Type 1 model, the differential settlement ratios are 1.2 and 2.24 for the centric void and the eccentric void location, respectively. The presence of a basement doesn’t have any obvious effect on the seismic behavior compared to the model without a basement in the case of voids beneath foundations. There is only an increase in the differential settlement ratio in the case of the centric void between the models with and without a basement, while the differential settlement ratios are 1.24 and 1.1 in the models with and without a basement, respectively.

Figure 22 shows a comparison of the seismic response of structures ST1 and ST2 in the three soil cases for the bare model, the fully infilled model, and the Type 1 model. Modeling the effect of infill walls has a significant effect on the lateral displacements and differential settlement of the structures. There is a clear difference in the ratios of lateral displacements and differential settlements between ST1 and ST2 in the case of modeling the fully infilled and Type 1 models with the presence of underground voids, especially in eccentric void locations.

In the current study, a non-linear analysis of two RC structures of the same area and different numbers of floors (heights) was performed using ANSYS software. The structures were exposed to El-Centro earthquake time history to investigate the seismic response of structures above voids. In each structure, many factors were studied, such as the effect of infill walls, slab systems, reinforced concrete wall systems, and the presence of basements. Two cases of void locations with the same diameter and depth were selected to represent the region of weak soil. These void cases were analyzed for all of the parameters mentioned above. The following are some specific conclusions drawn based on the results obtained from the models and structural analyses:

A good agreement was found between the current model and earlier experimental and analytical investigations found in the literature.
When dealing with underground voids, it is preferable to design slabs and beams instead of flat slabs to reduce the percentage of differential settlement. This is because the rigidity of a flat slab structure is less than that of a structure with beams, which leads to increased settlements beneath the structure and differential settlement in the case of eccentric voids.
It is crucial to consider the impact of the actual bays of infill walls in the model, as they significantly influence the lateral displacement values when voids are present. The void location away from the structure influences the behavior of the superstructure, depending on the model considering the infill wall effects.
The presence of a basement does not significantly alter seismic behavior when compared to surface footing construction in cases of voids beneath foundations.
Charts were provided for engineers to evaluate the response of RC structures resting on soils that contain voids subjected to seismic loads. A wide range of factors were taken into consideration when developing charts to assess the behavior of the structures above the soil with voids.

Author contribution: Methodology: Emad Y. Abdel-Galil, and Aya G. Abdel-Nasser; Validation: Ezzaat A. Sallam, and Aya G. Abdel-Nasser; Formal analysis: Ezzaat A. Sallam, and Aya G. Abdel-Nasser; Data curation: Emad Y. Abdel-Galil, and Aya G. Abdel-Nasser; Writing original draft: Aya G. Abdel-Nasser; Writing-review and editing: Emad Y. Abdel-Galil, and Ezzaat A. Sallam; Visualization: Emad Y. Abdel-Galil, and Ezzaat A. Sallam; Investigation: Ezzaat A. Sallam, and Aya G. Abdel-Nasser; Supervision: Emad Y. Abdel-Galil, and Ezzaat A. Sallam; All authors have read and agreed to the published version of the manuscript.

Competing interests: The authors declare there are no competing interests.

Funding: The authors declare no specific funding for this work.

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No competing interests reported.

Effect of Presence of Subsoil Voids on the Seismic Performance of Reinforced Concrete Buildings Considering Different Building Structural Systems

Status:

Version 1

Abstract

Figures

1. Introduction

2. Materials and Methods