NUMERICAL ANAL YSIS OF LIGHTWEIGHT CONCRETE WALL PANELS HAVING A VARIATION OF DIMENSIONS AND OPENINGS THAT WERE SUBJECTED TO STATIC LATERAL LOADS

Aisyah Nurjannah S., Saloma., Hanafia., Darin Putr N., Satria Albimanzur F. (2022) NUMERICAL ANAL YSIS OF LIGHTWEIGHT CONCRETE WALL PANELS HAVING A VARIATION OF DIMENSIONS AND OPENINGS THAT WERE SUBJECTED TO STATIC LATERAL LOADS, Journal of Applied Engineering Science, 20(1), 109 122, DOI:10.5937/ jaes0-31011 Saloma Civil Engineering Department, Faculty of Engineering, Universitas Sriwijaya, Indonesia Hanafia Civil Engineering Department, Faculty of Engineering, Universitas Sriwijaya, Indonesia


INTRODUCTION
Wall panels are commonly used for partitioning spaces in buildings [1]. The materials used for wall panels are made up of non-structural concrete that meet the strength of light mass requirements. One of the materials most appropriate to meet these requirements is foamed concrete. The mass of foamed concrete allows for the reduction of structural dimensions which results in buildings that are lighter than conventional ones [2,3], thus reducing the risk of damage under severe earthquake conditions, especially in high rise buildings [4]. The mass of foamed concrete ranges from 1200 to 1800 kg/m 3 and is included in the category of lightweight concrete. In this study, lightweight concrete was used as а material for wall panel models. The concrete consisted of Portland Composite Cement (PCC), expanded polystyrene (EPS), a foam agent, and water [5]. The use of EPS contributed to the hydrophobic qualities, as well as resistance to high thermal insulation and moisture, provided high durability and the ability to be formed in various sizes, along with recyclability [1,6,7,8]. Reinforced concrete panels with concrete compressive strengths of 38.0 up to 99.3 MPa can resist axial loads ranging from 191.3 to 1583.3 kN [9]. Although they are included in the non-structural system, reinforced concrete walls can affect the stiffness and strength of a building structure [1], especially when these contain openings for doors and windows [10]. A need remains for analyzing the behavior of lightweight wall panels under severe conditions, such as lateral loads due to earthquakes. Wall panels consist of partial non-structural components that form wall units and are widely used for lightweight construction. Compared to conventional brick walls, the thinner dimension of these wall panels provides a lesser load for buildings [11]. To investigate the performance of wall panels under lateral loads due to wind and severe earthquakes, experiments were conducted [12] using five types of wall panels with variations of frame materials and insulating concrete form (ICF) grids [13]. The concrete compressive strength of ICF wall panels is 17.24 MPa and is included in structural components. In this study, monotonically-increasing static lateral loads with initial loads of 0.89-1.33 kN were applied to each specimen. The maximum lateral drifts ranged from 19.30 mm to 22.60 mm and 41.66 mm to 67.56 mm for framed and ICF wall panels, respectively. The maximum lateral loads ranged from 17.81 kN to 20.25 kN and 124.06 kN to 152.33 kN for framed and ICF wall panels, respectively. These experiments showed that ICF wall panels could resist higher lateral loads than the various framed wall panels that were tested [13,14]. Reinforced concrete openings in wall panels with slenderness ratios of 30, 35, and 40 were tested under uniformly distributed axial loads in one-way and two-way directions. The wall panels were reinforced by wire mesh in the center of the cross-sections. Each opening corner was reinforced diagonally to prevent shear cracks. The one-way wall panels showed typical single-curvature bending failures in horizontal cracks, while the two-way wall panels showed typical double-curvature bending failures in diagonal cracks along the corners. The curves of load-deflection of the normal and high strength concrete wall panels were more non-linear and linear, respectively, than at the beginning of the loading history [9]. Six thin concrete wall panels with various aspect ratios (height/length) and concrete strengths were subjected to axial-eccentric uniformly-distributed loads in a two-way direction. The materials used in the experiments were normal and high-strength concrete, which consisted of Reactive Powder Concrete (RPC). The results of the experiments showed that an increase in aspect ratios decreased axial loads in normal concrete wall panels, while the opposite effect occurred in the RPC wall panels. The loads increased in the higher range of normal concrete strength, while the opposite effect occurred in the RPC wall panels. The deflections increased in the higher aspect ratios of the normal concrete wall panels, while the opposite effect occurred in the RPC wall panels [14]. Previous studies have used various dimensions of wall panels; these include concrete wall panels with lengths and heights of 1200 mm, 1400 mm, and 1600 mm and all having the same 40 mm thickness. Openings that served as windows and doors affected the main strength of the walls. Overall, the behavior of reinforced concrete walls with openings was effected by the geometry, supporting conditions, material properties, and dimensions, as well as the number of openings and their locations [15]. A previous study used wall panels made of lightweight concrete which were subjected to lateral loads. Some finite element models were used to predict specimen behavior; these showed close-crack patterns and load-deflection curves. Every two precast wall panels was connected with dowels, which indicated that having more dowel connections increased the resistance of the wall panels to lateral loads and reduced deformations [16]. Although non-structural lightweight concrete wall panels are widely used, their behavior under lateral loads still needs to be investigated, especially in highrisk earthquake zones. This study aims to determine the performance of lightweight concrete wall panel models that are subjected to static lateral loads until the ultimate condition, using a finite element method program by varying the dimensions, reinforcements, and openings. Efforts were made to assess the performance of these wall panel models under static lateral loads. By using an analysis of the correlation between load-deformation, stiffness, ductility, and deformation, information could be obtained about the behavior of these panel models under severe earthquake loads. In the past, researchers have conducted studies of wall panel behavior using the finite element method in numerical modelings. They reported that a prediction of the behavior of wall panel models in terms of correlation of load-deformation, stiffness, ductility, and temperature effects could be obtained by using numerical modelings [17,18]. The wall panel models were simulated as bearing elements. This information was taken into consideration when replacing the thick-er precast non-composite walls with thin-shell concrete sandwich panels [17]. Numerical modelings have also been used to predict the effect of insulation in resisting heat in the occurrence of fires. The results showed that the temperature-time curves of the numerical modeling were similar with the experimental specimens [18]. A previous study on the effect of sandwich panels in ballistic performance and energy absorption using numerical modelings has also been made. This study analyzed the correlation between residual velocity and the shape of the projectiles that impacted the panel models. The numerical results achieved were in good agreement with the literature [19].

MATERIALS AND METHODS
The material properties for modeling input in the ANSYS program used in this study referred to previous laboratory research results [5,20]. The materials used were foamed lightweight concrete with EPS and wire mesh, which are described in the following subchapter: Materials. It was necessary to use non-linear modeling to present the behavior of the materials that formed the wall panels.

Finite Element Method
The finite element method (FEM) is a numerical method that breaks down domains into several subdomains, or finite elements with systematic estimation, to build solutions. Three points need to be taken into consideration when using this method [21]: • Physical phenomena used to analyze the case and determine the deformation, critical areas, stress, and cracks. • Discretization to divide domains into smaller sub-domain (finite elements). Sub-domains are regions that are bounded by lines of elements which connect between nodes. • Assumption of linear functions for all sub-domain responses. The solution to the responses is obtained from iterations. The ANSYS program was used for the non-linear analysis. The concrete materials, wire mesh, and steel plates were modeled using Solid65 (8-node), Link180 (2-node), and Solid45 (8-node) elements, respectively. Solid65 was used to model the behaviour of concrete materials; i.e., brittle and unsuitable in resisting tensile forces. Link180 was used for modeling wire mesh with high ductility, while an analysis of the behavior of the steel plates was performed by Solid45 [22]. The ANSYS analysis was carried out in this study by subjecting the wall panel models to lateral loads. ANSYS uses the Newton-Raphson method to solve non-linear equation problems to obtain deformations through direct iterations. This process can be described in Equations (1) and (2) [21]: where [K], {u}, {F} are the stiffness matrix, the deformation vector, and the load vector, respectively; {u r+1 } is anapproximation of (r+1)-iteration. This will be convergent for an increased r when the values of {u r } are close to {u r+1 } with minimum deviation. The non-linear equilibrium was solved using the Newton-Raphson iteration method [23].

Materials
The materials of the wall panel used in this study consisted of lightweight foamed concrete and wire mesh. Table 1 shows the stress and strain properties of the lightweight foamed concrete using EPS. The material properties were: mass density, modulus elasticity, compressive strength, and the tensile strength of the foamed concrete, which were: 832.26 kg/m 3 , 4900 MPa, 5.224 MPa, and 0.2612 MPa, respectively [5]. The wall panel models were reinforced with wire mesh that was 4 mm in diameter with a spacing of 150 mm. Figure 1 shows the stress and strain relation of the wire mesh in an ascending curve. The modulus elasticity (E s ), yield strain (ε s ), yield strength (f y ), and ultimate strength (f u ) were: 177,570.19 MPa, 0.002562, 424.52 MPa, and 538.68 MPa, respectively [20].

Methodology
In this research, lightweight concrete wall panel models were subjected to incremental static lateral loads until the ultimate condition. The wall panel models varied in dimension, reinforcement (wire mesh), and openings. The analysis was conducted using ANSYS as a finite element method program. The lateral static loads were applied on steel plates on the left and top of the panels and increased by 200 N until the panels collapsed. The analysis results were depicted in curves that showed a correlation between static lateral loads and lateral deflections in representing the performance of each wall panel model. Some assumptions were made in the modeling: 1. The wire mesh had fully bonded to the concrete. 2. Anchored wire mesh modeled as fixed-end restraints

Geometrical Data Model
As seen in Table 2 Table 3 shows the aspect ratio (H/L) and slenderness ratios (H/T) of each wall panel model. The loading setup of each wall panel model and the lateral load was based on the code in Figure 2 [28]. Wire mesh was anchored to the fixed base, and each panel was firmly bolted to the loading fixture. The height and width of each square opening was 200 mm. Figure 3 shows the dimension of wall panel models numbered 1 to 18 ( Table  2) with various thicknesses and reinforcements. Figure  4 shows the dimensions of the concrete panel models numbered 19 to 24 (Table 2) with double-square openings without and with reinforcements. There were three diagonal steel bars in the corner of each opening; these were 4 mm in diameter, with a length of 140 mm, the wire mesh in the wall panels having a 50 mm spacing.

RESULTS AND DISCUSSION
The incremental lateral static loads pushed against the wall panel models, which resulted in lateral deformation. The lateral deformation values varied and depended on the reinforcement, aspect ratio, slenderness, and number of openings.

Correlation Between Load and Deformation
The correlation between lateral loads and deformations in the wall panel models with various heights and thicknesses without wire mesh is shown in Figures 5 to 7. The thicker wall panel models showed higher resistance performance than other models of the same height and length. Wall panel models with thicknesses of 60 mm provided greater stiffness, yield, and ultimate loads than the thinner wall panel models. The wall panel model with a height of 2000 mm and a thickness of 60 mm showed a higher lateral deformation than other models with the same thickness.   without wire mesh. The wall panel models with wire mesh with a thickness of 60 mm showed higher stiffness, yield and ultimate load-carrying than other wall panel models with thicknesses of 40 and 50 mm. This behavior is similar to that of previous research results [29]. Wall panel models with a height of 1000 mm achieved the highest lateral loads results due to having greater stiffness than other wall panels. The largest lateral deformations were seen in the tallest wall panels, those of 2000 mm, due to having more flexible behavior than the other panels. The wall panel models with double-square openings performed the same as solid wall panel models, as seen in Figures 11 and 12. The thickest wall panel models, with or without wire mesh, carried higher lateral loads than other wall panel models. The use of wire mesh influenced their stiffness, ensuring that all reinforced wall panel models had less lateral deformation than the unreinforced panel models. Openings in wall panels will result in decreased resistance performance against lateral loads [30]. Three solid-wall and three wall panel models with double-square openings without wire mesh were compared when performing lateral load resistance, as shown in Figure  13. These six wall panel models were all 1500 mm in height and 1500 mm in length. The two-wall panel model thicknesses without wire mesh were 40 mm, 50 mm, and 60 mm. All wall panel models with double-square openings achieved longer deformations with lower lateral yield and ultimate loads due to having less stiffness than the solid panel models. Similar behavior was found in solid wall panel models and wall panel models with three double-square openings with wire mesh, as seen in Figure 14. The dimensions of all the wall panel models were 1500 mm in height and 1500 mm in length. 1500 mm in height and 1500 mm in length. The thicknesses of each two-wall panel model with wire mesh were: 40 mm, 50 mm, and 60 mm. All wall panel models with double-square openings had longer deformations and lower lateral yield and ultimate loads due to having less stiffness than the solid panel models. The deformations of all solid wall panel models with double-square openings and wire mesh were less than those without wire mesh due to their higher stiffness. The rate of lateral loads achieved by all of the wall panel models with wire mesh was higher than those without wire mesh because of their higher nominal moment.  Tables 4 and 5. All wire mesh wall panel models showed higher ultimate lateral loads than wall panels without wire mesh of the same thickness. The yield points were determined based on a code [31], while the ultimate points were in the maximum load and deformation conditions. The yield and ultimate lateral loads and the yield and ultimate lateral deformations increased as the thickness varied from 40 to 60 mm, both on unreinforced and wire mesh-enforced wall panel models. The openings reduced the stiffness of the wall panel models, thus increasing the deformation. The thickness, height, and openings influenced the lateral loads and deformations in yield and ultimate conditions. The thicker wall panels had greater resistance to deformation. The more ductile behavior of wall panel models with wire mesh made it possible to achieve longer deformation. Tables 6 and 7 show the percentages of load and deformation of each panel model compared to the panel models that had 60 mm thicknesses; these groups are divided according to height in yield and ultimate conditions, respectively.   Tables 8 and 9 show the stiffness and deformation ductility of each panel model, respectively. The yield and ultimate stiffnesses were influenced by the thickness and wire mesh reinforcement in the wall panel models. The thicker wall panel models achieved higher levels of stiffnesses. Stiffnesses were also higher in wall panel models with wire mesh as opposed to panels without wire mesh but with the same thicknesses. Lower ductility values were also achieved by the panel models with wire mesh. Table 8 also shows that the wall panel model with a height of 1000 mm, length of 1500 mm, and thickness of 60 mm with wire mesh (number 12) had the highest stiffness, which means this model also perfomed the best strength in resisting lateral loads. Based on all of the solid wall panel models (Nos. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], those with a height of 2000 mm and a thickness of 60 mm (Table 9, number 9) without wire mesh had the highest deformation ductili-ty; that of 36.59. Thus, it can be seen that the tallest and thickest panels had the best ductility. This behavior was also observed in previous research [32].

Stiffness and Deformation Ductility
The inclusion of wire mesh significantly reduced deformation ductility in the wall panel models (Nos. 10 to 18) compared to models of the same dimension without wire mesh [26]. However, models with openings showed the opposite behavior (Nos. [19][20][21][22][23][24]. The best ductility among wall panels with openings was achieved by the thinnest panel models without wire mesh (1500H.40T.O). This also reveals that openings influence the behavior of wall panel models under lateral loads when compared to solid panel models without openings. Table 9 shows that in all the solid models without wire mesh (numbers 1-9), the tallest model, with height of 2000 mm, length of 1500 mm, and thickness of 60 mm (number 9), achieved the best ductility due to having the largest ultimate deformation. In all solid models with wire mesh (numbers 10-18),  [19][20][21] and with wire mesh (numbers [22][23][24], the models with heights of 1500, lengths of 1500 mm, and thicknesses of 40 mm achieved the best ductility. These results show that thickness and reinforcement with wire mesh influence ductility.

Deformation
The highest deformation ranges among all the solid wall panel models are at the top, as depicted in red. The red area depicts lightweight concrete and steel plate materials. Steel plates prevented wall panels from deforming out of the plane [12]. Wall panel models without wire mesh showed much greater deformations than wall panel models with wire mesh. These greater deformations were located around halfway the height of the panel on the lefthand side. The distribution and magnitude focused deformations appeared on the lefthand sides of the wall panels without wire mesh, which are represented in dark blue ( Figure 15). All panel models, with or without wire mesh, showed that the taller wall panel models had a greater number of maximum lateral deformations. This is because the points observed were at the top of the wall panel models. Models with the same dimensions showed that wire mesh significantly reduced lateral deformation due to having greater stiffness ( Figure 16). Comparing wall panel models of the same height and length showed that the dimension of thickness resulted in fewer maximum deformations.  Wall panel models with openings and without wire mesh had negative deformations halfway the height on the lefthand side. This indicates bending in the tensile areas which changed the shape of the wall panel models. The middle and righthand sides were more dominated by positive deformations due to compressive conditions. The wall panels reinforced with wire mesh showed an evenly distributed spread of negative deformations in the panels nearest the fixed supports. In contrast, positive deformations were dominant in the middle and upper parts of the panels ( Figure 17). All of the wall panel models without wire mesh achieved greater minimum and maximum deformations due to having less stiffness. The thinner panels had larger deformations around the openings, while the thicker panels showed increased deformations. The minimum and maximum deformations of the wall panels are shown in Table 10.

CONCLUSIONS
This study investigated the behavior of non-structural lightweight concrete wall panel models made of EPS foamed concrete and reinforced with wire mesh. A finite element method-based program was used to obtain a non-linear analysis of 24 wall panel models subjected to lateral static loads. The results showed that the dimensions, reinforcement, and openings influence how wall panels behave in the scope of deformation, strength, stiffness, and ductility. Optimum ultimate strength and stiffness were achieved by a solid wall panel with wire mesh, having a length of 1500 mm, a height of 1000 mm, and 60 mm thickness. Evidence for this is shown in both Tables 5 and 8. The wall panel models with openings, without wire mesh, and with a height, length, and thickness of 1500 mm, 1500 mm, and 40 mm, respectively, achieved the highest ductility. Evidence for this is shown in Table 9. As this study was based on the finite element method, further validation using experimental work is still needed.
Wall panel models with openings and without wire mesh had negative deformations halfway the height on the lefthand side. This indicates bending in the tensile areas which changed the shape of the wall panel models. The middle and righthand sides were more dominated by positive deformations due to compressive conditions. The wall panels reinforced with wire mesh showed an evenly distributed spread of negative deformations in the panels nearest the fixed supports. In contrast, positive deformations were dominant in the middle and upper parts of the panels ( Figure 17). All of the wall panel models without wire mesh achieved greater minimum and maximum deformations due to having less stiffness.
The thinner panels had larger deformations around the openings, while the thicker panels showed increased deformations. The minimum and maximum deformations of the wall panels are shown in Table 10.