The Seismic Resistance Analysis of Frame Structures and Wall Structures Using Ferrocement and Expanded Metal

Abstract

This article presents a study of the use of ferrocement and expanded metal in the columns, beams, and walls of a reinforced concrete building structure to increase its seismic resistance. This study focused on a concrete building with three stories, located in Thailand. In the design of the reinforcement structure, a calculation and analysis of seismic resistance were conducted in a comparison of the original concrete building structure with the reinforced concrete building structure using the nonlinear static force method (pushover analysis method). The results showed that the seismic resistance of the reinforced concrete building structure was higher than the design value (DPT), with different seismic resistance values for the reinforced frames, columns, and walls of approximately 14%, 81%, and 19%. In particular, it had increased stiffness values for the frames, columns, and walls and increased ductility values for the walls. Moreover, the seismic resistance values originating from the reinforcement were significantly higher than those of the concrete building structure. Therefore, reinforcement should be applied to all concrete building structures with the implementation of the damage index, ensuring that it is reduced to the allowable level.

1. Introduction

As a result of seismic activity in Mae Lao District, Chiang Rai Province, in 2014, many columns were damaged due to shear. In addition, for partially walled structures with wide, open-spaced windows, the column may also be damaged because of the effect of shear loads on the short columns [1]. Therefore, these buildings require reinforcement. The ferrocement reinforcement technique is widely used due to its ease and safety in construction and low cost. Research results of shear strength testing of reinforced columns with ferrocement and expanded metal have shown that reinforced columns have increased ductility values when the reinforcing steel volume ratio of the ferrocement is increased. Furthermore, reinforcement with expanded metal leads to ductility values higher than those resulting from general reinforcing steel usage [2]. Studies have reported results on building frames reinforced with brick walls using ferrocement and expanded metal. The resistance strength of the reinforced building frame was higher than the original brick wall building frame [3]. Further research results based on the use of column reinforcement throughout the length of the column showed that reinforcement helps to prevent joint connecting failure in columns and beams and prevent brick wall corners from cracking. This application led to a reinforcement building frame with a resistance value higher than that of the original building frame [4]. On the other hand, the results of using a dowel bar, which underwent bond ferrocement with concrete, showed that L-shaped dowel bar usage leads to the best shear bonding when applying ferrocement with concrete, as compared with different shapes of dowel bars [5]. The results of a study on short columns subjected to shear strength reinforcement ferrocement and expanded metal showed that the shear strength of the column was higher when the volume ratio of expanded metal was increased using an efficiency multiplier of the steel grating to predict the shear strength value of the reinforced column [6].

In a study of the seismic-resistant behavior of a six-story-high building structure that was reinforced with the cover steel column cladding method, it was found that the reinforced structure had higher lateral strength and a higher toughness value. However, it was also found that structural irregularity can reduce a building’s seismic resistance [7]. In a study of the seismic-resistant behavior of a three-story building structure that was reinforced by the column cladding method with steel mesh and expanded metal, the results showed that the stiffness value and lateral force resistance value of the reinforced structure were higher. Otherwise, a structural model based on flexibility provided less improvement in terms of its effects than a structural model based on fixity [8].

In this study, we conducted a seismic resistance analysis of a three-story concrete building structure with columns, beams, and walls reinforced using ferrocement and the expanded metal technique. We used the nonlinear static analysis method (pushover analysis) to conduct comparisons of the results, comparing the seismic resistance strength of the reinforced columns, beams, and walls with that of the original building structure.

2. Materials and Methods

The materials used in this study included a computer, a computer design program, Microsoft office, and the Autocad program, applied in a seismic resistance analysis model of a three-story concrete building structure with its columns, beams, and walls reinforced using ferrocement and expanded metal, as shown in Figure 1, Figure 2 and Figure 3. We used the nonlinear static force method (pushover analysis method) in a comparison of the results of the reinforced columns, beams, and walls with those of the original building structure. This case study focused on a hypothetical building located in Wang Chin District, Phrase Province, Thailand. This location is a severe earthquake area and has a response spectral acceleration $S_s$ = 1.086, $S_1$ = 0.275 (DPT, Standard 1301/1302-61). The methods used in this study are shown in Figure 4.

3. Reinforcement of the Frames of the Concrete Building Structure

3.1. Reinforced Frames of the Concrete Model

The reinforced rigid frame model is shown in Figure 1A. The columns were reinforced using the ferrocement technique with expanded metal throughout the length of the columns, because shear strength will act on columns in buildings with open-space windows. The beams were reinforced by ferrocement with expanded metal over a length 2.5 times their depth. This was equal to the plastic hinge, which may occur at the end of beams and expanded metal grating, formed by welding with a steel angle bar, as shown in Figure 1B.

The reinforced column’s moment resistance (M_S) can be calculated from the sum of the original column’s moment resistance (M_c) and the ferrocement moment resistance (M_F), as follows:

$$M_S=M_C+M_F$$

(1)

The ferrocement moment resistance (M_F) can be calculated from the sum of the steel angle bar and expanded metal moment resistance, as follows:

$$M_F={\sum }_{i=1}^n(f_{\mathit{ys}}(S_s)i_i)+{\sum }_{i=1}^n(f_{\mathit{ye}}(S_e)i_i)$$

(2)

where

• fys and fye = yield strength of the steel angle bar and expanded metal;
• Ss and Se = cross-sectional modulus of the steel angle bar and expanded metal;
• V_BF = lateral load resistance of the reinforced rigid frame.

$$V_{\mathit{BF}}=\frac{2(M_{\mathit{pj}}+M_S)}{h}=\frac{2(M_{\mathit{pj}}+M_C+M_F)}{h}$$

(3)

where

M_pj = the joint connecting plastic moment, which is considered to include the smallest moment of the column M_pc plastic moment, the beam M_pb plastic moment, and the joint connecting moment of the column–beam. The shear strength of the column V_C is ½ times that of the V_BF:

$$V_C=(M_{\mathit{pj}}+M_S/h)$$

(4)

3.2. Reinforced Wall Frame Model

On top of the walls in some parts of the building frame, due to the fact that the entrance door is a wide, open space, as shown in Figure 2A, an analytical model of the brick wall frame was used with the equivalent compressive bracing frame method. Here, the width of the diagonal compressive strength of the brick wall is $W_1$. Moreover, the diagonal compressive strength of the brick wall is the lateral force resistance of the wall, which can be written in a graph expressing the relation of the lateral force to the displacement value, as shown in Figure 2B. When ${\mathrm{V}}_m^{+}$, ${\mathrm{V}}_y^{+}$, ${\Delta }_m^{+}$ and ${\Delta }_y^{+}$ are the maximum resistance, resistance at the yield point, maximum movement, and movement at the yield point in the direction of the acting force, $K_0$ and $K_{\mathit{sec}}$ are the initial stiffness value and cross-sectional stiffness value, respectively.

The maximum resistance of the compressive strength $V_m$ of the brick wall can be calculated as

$$V_m=F_1\mathit{cos}{\theta }_1=W_{1}t{f}_a\mathit{cos}{\theta }_1$$

(5)

where

• $F_a$ is the allowable compressive stress of the brick wall prism, $F_a=0.6Øf_m$,
• $f_m$ is the maximum compression of the brick wall prism
• Ø = 0.65, t = the thickness of the brick wall
• ${\theta }_1$ is the tilt angle of the diagonal compressive strength on the top of the brick wall.

In addition, the compressive strength of the reinforced brick wall $f_m$ is proportional to the specific surface area of the expanded metal $S_r$ and can be calculated from the relationship between $f_m$ and $S_r$ [9]. The width of the compressive strength $W_1$ is calculated from the touch surface length of the force unit, which can spread between the column and brick wall [10], as follows:

$$W_1=a_c\frac{l_m}{\sqrt{{h_1}^2+{l_m}^2}}=a_c{h}_1\mathit{cos}{\theta }_1$$

(6)

$$a_c=\frac{1}{h}\sqrt{\frac{2M_{\mathit{pj}}+2{\beta }_c{M}_{\mathit{pc}}}{{{\sigma }_c}^t}}$$

(7)

$${\sigma }_c=a_c\frac{f_m}{\sqrt{1+{3\mu }^2{r}^4}}$$

(8)

where

• $\mu$ is the friction coefficient between the building frame and brick wall;
• $r$ is the ratio between the height and width of the building frame $(r=h/l)$;
• ${\beta }_c$ is the reduction factor of the pole $({\beta }_c=0.2)$.

The balance of the lateral force $P$ is equal to sum of the resistance frame and compressive strength $f_1$:

$$P=V_{\mathit{BF}}+F_1\mathit{cos}{\theta }_1$$

(9)

$$P=V_{\mathit{BF}}+W_{1}t{f}_a\mathit{cos}{\theta }_1$$

(10)

4. Reinforcement of the Model Building

4.1. Sample Reinforcement of the Building

In this research, we selected a three-story concrete building structure with four spaces, following the standard model of the Department of Public Works and Town & Country Planning (DPT). This case study concerned a hypothetical building located in Wang Chin District, Phrase Province, Thailand. This location is a severe earthquake area and has a response spectral acceleration of $S_s$ = 1.086, $S_1$ = 0.275 (DPT. Standard 1301/1302-61) [11].

The building has a width of 4.00 m/bay, with four spaces, a height of 11.25 m, a general floor thickness of 0.10 m, and a live load of 3 kN/m². Moreover, the front of the building frame, as shown in Figure 1, consists of a brick wall, with the width of the entrance being equal to the column spacing and cross-sectional dimensions. The details of the reinforced steel bars of the columns and the beams are shown in

Table 1. The details of the reinforced steel bars.

Building	Size (mm.)	Main Reinforcement (mm.)	Stirrup Reinforcement (mm.)
C1	200 × 200	4DB16	RB6@150
B2	200 × 400	5DB16	RB6@150
RB	200 × 400	4RB16	RB6@150

. The compressive strength of the cylinder concrete is 24 MPa, and the tensile strength of the reinforced steel bars is 400 MPa.

4.2. Sample Building Reinforcement Method

The reinforced concrete building’s rigid frame was calculated and designed for seismic resistance [11]. We calculated the concrete building structure using a computer design program to identify the requirements for the seismic resistance of the building frame using the nonlinear static force method (pushover analysis) with response spectrum acceleration. The building was located in Wang Chin District, Phrae Province (DPT. Standard 1301/1302-61) [11]. The base shear of the concrete building’s rigid frame design was 702 kilonewtons. When creating the reinforced design for the rigid frame, with steel angle bars along the length of the columns, for the beams’ reinforcement, we used an expanded metal size of XS 63, with the steel angle bars spanning a length 2.5 times the beams’ depth. For the upper part of the brick wall, we used expanded metal of size 22 on both sides, fixed with bolts of 6 mm. We inserted the bolts into the brick wall at a distance of 30 cm and applied plaster onto the wall, as shown in Figure 5.

The moment resistance and shear resistance of the original column were compared with those of the reinforced column, which we were able to calculate using Equations (1), (2), and (4), as shown in

Table 2. Resistance of the column.

Parameter	Original Column	Reinforced Column
$M_C(kN-m)$	30.05	30.05
$M_F(kN-m)$	-	475.61
$M_S(kN-m)$	-	505.66
$M_{\mathit{pj}}(kN-m)$	23.65	23.65
$V_c\left(kN\right)$	11.19	110.27

. Here, $V_c$ is the value of resistance of a single column. The resistance of the reinforced walls of the building can be calculated using Equations (5)–(10), as shown in

Table 3. Resistance of the brick wall.

Parameter	Original Wall	Reinforced Wall
$a_c$	0.085	0.1176
$W_1\left(\mathit{mm}\right)$	89.81	124.26
$W_{1}tfa\mathit{cos}{\theta }_1\left(\mathit{kN}\right)$	17.99	37.76
$V_{\mathit{BF}}\left(\mathit{kN}\right)$	22.38	220.54
$P\left(\mathit{kN}\right)$	40.37	258.30
$\mathit{Design\; Strength}\left(\mathit{kN}\right)$	127.91	702.39

, where the p value is the resistance of a single span of the sample wall building, as shown in Figure 5A. The design strengths, which we also calculated for the three-story concrete building structure, were 127.91 kN and 702.39 kN for the original structure and reinforced structure, respectively.

5. Reinforced Building Concrete Frame Analysis

For the original concrete building frame, as shown in Figure 1, we created a model for structural analysis using the RUAUMOKO program, as shown in Figure 6 [12]. For the reinforced wall, we aimed to reinforce the columns, beams, and walls of the first story of the building with ferrocement and expanded metal. Moreover, the preparation of the model of the building walls for structural analysis is shown in Figure 7. The moment resistance of the columns and lateral force resistance of the walls were calculated, as shown in Equations (1)–(10).

For the bending strength of the columns and beams, we used the SINA model with a non-linear load to check the behavior of the columns and beams at the plastic joint connection, as shown in Figure 8A [13]. We also determined the moment resistance at the crack point in every cycle of round-trip force, as well as the stiffness reduction after the release of the force in each cycle. For the walls, we used an equivalent brace model, which is represented as a non-linear axial-load-bearing building based on the Wayne–Stewart model, as shown in Figure 8B [14]. The determination of the axial strength resistance at the crack point and the stiffness reduction in each cycle was carried out. Moreover, increased force and stiffness reduction caused weaknesses and increased the displacement value. This model’s results are comparable to the results of a brick wall frame reinforced by ferrocement in [4].

An analysis of the original concrete building structure and the reinforced concrete building structure using the non-linear static force method (pushover analysis method) was performed, calculating the target story drift value $({\delta }_t)$ with DPT. Standard 1301/1302-61 [11]. We used response spectrum acceleration for the building, located in Wang Chin District, Phrae Province. The target design story’s drift value was increased by 1.2 times $(1.2{\delta }_t)$ for the evaluation of the maximum resistance. The parameter calculation results of the target story’s drift value are shown in

Table 4. Parameters of the target design story’s drift value $(1.2{\delta }_t)$.

Structure	$C_0$	$C_1$	$C_2$	$T_{\mathrm{e}}$ (s)	$S_{\mathrm{a}}$ (g.)	${\delta }_{\mathrm{t}}$ (mm)	$1.2{\delta }_t$ (mm)
Original	1.3	1.03	1.01	1.04	0.32	114	137
Reinforce	1.3	1.25	1.03	0.36	0.94	39.9	48

[11].

The results obtained using the nonlinear static force method illustrate a relationship between the base shear force of the building with the displacement value of the original frame and reinforced frame, as shown in Figure 9. The results for the resistance of the original column were compared with those of the reinforced column, as shown in Figure 10, and the strength resistance of the original wall was compared with that of the reinforced wall, as shown in Figure 11. Finally, we combined all the details of the original building for a comparison with the reinforced building structure, as shown in Figure 12.

From Figure 9, we can see that the reinforced structure’s stiffness value is 26.15 kN/mm, and its strengthened value is 702.39 kN. By comparison, the original structure has a stiffness value of 2.29 kN/mm and a strengthened value of 127.91 kN. For the reinforced structure, the stiffness value and strengthened value are higher than those of the original structure. The strengthened value difference is approximately 14%.

When considering the original column in comparison with the reinforced column, the results of the reinforced column give a stiffness value of 21.07 kN/mm and a strengthened value of 551.35 kN. The reinforced column’s strengthened value is higher than that of the original column, as shown in Figure 10. The original column has a stiffness value of 1.07 kN/mm and a strengthened value of 55.95 kN.

When considering the original wall and reinforced wall, the results show a stiffness value of 6.56 kN/mm and a strengthened value of 151.04 kN, showing that the reinforced wall is strengthened to a higher degree than the original wall. The original wall has a stiffness value of 1.94 kN/mm and a strengthened value of 71.96 kN, as shown in Figure 11. Figure 9, Figure 10 and Figure 11 summarize the stiffness values, the strengthened values, and the ductility values of the three-story concrete building structures shown in

Table 5. Stiffness, seismic resistance, and ductility of the structures.

Structures	Stiffness (kN/mm)	Seismic Resistance (kN)	Ductility
The original frame	2.29	127.91	1.86
The reinforced frame	26.15	702.35	1.73
The original column	1.07	55.95	1.89
The reinforced column	21.07	551.35	1.64
The original wall	1.94	71.96	1.38
The reinforced wall	6.56	151.04	1.63

. The original wall has a natural frequency period of 1.04 s. The reinforced wall has an increased stiffness value that can lead to a decrease in the natural frequency period, which is 0.36 s. On the other hand, calculating the shear force requirement using the equivalent static force method (pushover analysis), we obtain $T=0.22$ s. Hence, the shear force required for the reinforced structure is the same.

Reinforcement resulted in an increase in the structure’s strength by 4.23 times. The reinforced column had a strength increase of 5.54 times, and the reinforced wall had a strength increase of 2.10 times. However, the total strengths of the reinforced column and reinforced wall are 81% and 19% of that of the entire three-story concrete building structure, respectively.

When comparing the ductility of the reinforced frame structure, which has a ductility value of 1.73, we found that it was decreased compared to the original frame structure, which has a ductility value of 1.86. In addition, the reinforced column structure has a ductility value of 1.64, showing a decrease from the original column structure, which has a ductility value of 1.89. In contrast, the wall reinforced by ferrocement and expanded metal has a ductility value of 1.63, which is increased compared to the ductility value of the original wall structure. The original wall has a ductility value of 1.38.

The damage levels of the original structure and the reinforced structure were determined using the damage index, as follows in Equation (11) [15].

$$\mathit{DI}=\frac{S_m}{S_u}+\mathsf{\beta }\frac{E_h}{F_y{S}_u}$$

(11)

where

• $S_m$ is the maximum deflection value of the system due to seismic force;
• $S_u$ is the maximum deflection value under monotonic loading;
• $F_y$ is the yield point of the structural system;
• $E_h$ is the hysteretic energy value of the structural system;
• $\mathsf{\beta }$ is a constant which indicates the scale of damage by the response modal shape.

The damage index values of the original building structure and reinforced building structure are shown in Figure 13 and Figure 14 and were obtained using criteria for measuring the degree of structural damage, defined based on the total damage index (DI) of the structural parts at the plastic hinge, which is the sum of the damage derived from the story drift structural value and the hysteretic energy value in response to the seismic forces. The definitions used to measure the results are as follows: a damage index DI which has a value less than 0.4 indicates a low-damage level, a DI value between 0.4 and 0.6 indicates repairable damage, a DI value more than 0.6 but not over 1.0 indicates severe damage which cannot be repaired, and a DI value more than 1.0 indicates the erosion of the structure. The analysis results showed that the original building structure had lower-level damage at both ends of the column and erosion, with a DI value over 1.0, when it was reinforced. Moreover, the damage level was decreased to a level not exceeding 0.6, which indicated a repairable level of damage.

6. Conclusions

This article presents a study on the reinforcement of columns, beams, and walls using ferrocement and expanded metal. A reinforced three-story concrete building structure was analyzed using the nonlinear static force method. The results of the calculated seismic resistances can be summarized as follows:

(A)

The seismic resistance of the reinforced frame is 702.39 kN, higher than that of the original frame, which is 127.91 kN, with a difference in seismic resistance of approximately 14%. The seismic resistance value of the reinforced frame is 4.23 times higher than that of the original frame. The results of the reinforced columns, beams, and walls were obtained by splitting the column into parts. The column has a seismic resistance value that is increased by 5.54 times, and the walls have a seismic resistance value increased by 2.1 times. The seismic resistances of the reinforced columns and reinforced walls are 81% and 19% of the whole three-story concrete building structure, respectively.

(B)

The reinforced building structure’s frames have a higher stiffness value, increased by 11.42 times in comparison with the original building structure. The results of the reinforced columns show a stiffness value increase of 19.69 times. Additionally, the walls’ stiffness value is increased by 3.38 times. Therefore, the results show that the reinforcement of the frames, columns, and walls increased the stiffness values with respect to the concrete building structure.

(C)

The reinforced building structure’s frames have a ductility value of 1.73, which shows a decrease from the value of the original building structure, whose ductility value is 1.86. Furthermore, the reinforced columns’ ductility value is 1.64, a decrease from the value of the original building structure’s columns, whose ductility value is 1.89. On the contrary, the reinforced walls show an increase in their ductility value of 1.63, while the original walls’ ductility value is 1.38 times lower.

(D)

Reinforcement with the technique described in this paper can improve the performance of the original building structure by reducing the damage index to a safe level.