Flexural Behavior of Concrete Beams Reinforced with Recycled Plastic Mesh

Abstract

The production of plastic material continues to increase around the world. Consequently, large amount of waste plastic is generated. This will lead to environmental concern due to its disposal. In order to reduce the environment effects and cost, waste plastic can be recycled and utilized in other applications including construction. This paper investigated the flexural behavior of non-structural concrete beams containing waste plastic meshes as a replacement of traditional steel reinforcement. To achieve this objective, beams with steel reinforcing bars and waste plastic sheets with different effective widths and patterns were prepared. After 28 days of curing, the beams were subjected to an increasing load until failure and the central deflection was measured at each load increment. Furthermore, a numerical analysis was performed on the specimens using ABAQUS software. This will allow the comparison between the experimental and numerical results. The experimental data indicated that using plastic sheets improved the flexural toughness and ductility of concrete beams. Additionally, correlations were carried out between the ultimate capacity of the beams, the flexural toughness and the effective width of the plastic meshes. As the effective mesh width increased, the flexural toughness and ultimate capacity of the concrete beams increased. The results of this investigation will allow greater utilization of waste plastic in construction activities.

1. Introduction

Concrete is widely used in the construction industry as it possesses numerous favorable properties such as excellent compressive strength, and other beneficial durability properties. Unfortunately, large amounts of natural resources are needed to produce concrete. Materials used in concrete production release significant amount of CO₂ into the atmosphere, thus replacing natural materials with waste and recycled materials such as waste glass powder, bottom ash, waste lathe scraps, waste lathe scraps and recycled steel wires is beneficial [1,2,3,4,5,6,7]. Also, plastic is widely considered as a very commonly used material in the industry [8]. In general, plastic can be classified into two types: thermoplastic and thermosetting. The first type “thermoplastic” is very sensitive to temperature change in that, it transforms to a liquid on heating and a solid on cooling [9]. It comes in various forms: polyethylene terephthalate (PET), high-density polyethylene (HDPE), polyvinyl chloride (PVC), low-density polyethylene/linear low density polyethylene (LDPE/LLDPE), etc. [10]. On the other side, the second type “thermosetting” becomes irreversibly rigid when heated. Examples of thermosetting include: Vulcanized rubber, Polyester resin, Silicone resin, etc. [11].

Because of the plastic various applications in modern life (packaging, construction, agriculture, automotive and other manufacturing industries [12]) and because of its favorable properties (extreme versatility to meet specific needs, lightweight, durability, resistance to chemicals and water, etc. [13]), its production has increased almost exponentially from around five million tons to nearly 381 million tons in 2021 [14]. This last number is expected to increase to 1100 million tons by 2050 [15]. This extremely fast production of plastic products leads to an increase in plastic waste generation. This brings challenges and raise concerns. Today, there is an increasing alarming trend toward single-use plastic products. For example, approximately, 36% of plastic generated are used in packaging [16]. This include single use plastic products such as beverage bottles that are discarded directly after single short use.

There are three methods to deal with waste plastic: landfilling, incineration and recycling [17]. Landfilling is not preferred because of space requirement and because plastic wastes are considered non-biodegradable [18]. This will ultimately lead to long term pollution problems [19]. Incineration is adopted in some countries because it eliminates huge amount of waste by about 90–95% [11]. However, there is a growing public resistance against incineration because of the release of some toxic fumes (CO₂, etc.) into the environment during the burning process and the generation of different types of ashes that requires as well proper disposal to avoid groundwater and soil pollution [20]. Recycling of waste plastic is therefore an effective method instead of land-filling and incineration. Benefits of recycling include reduction of environmental impact, waste disposal and global warming [21].

Among the different recycling techniques, the use of recycled plastic materials in the construction industry is regarded as the optimum method for discarding plastic waste. During the last two decades, the use of recycle plastic materials in mortar and concrete was extensively researched [22,23,24,25,26,27,28,29,30,31,32,33,34]. In those studies, plastic wastes were used in two forms: (a) plastic aggregate as an alternative or substitute of fine or coarse aggregate. As the volume of aggregate can be anywhere between 65 to 85%, partial or total replacement of aggregate by plastic waste is an attractive option for plastic waste consumption, and (b) plastic fibers (PF). PF are not expensive, low energy consuming and are highly resistant to corrosion [35]. Thus, they can be an alternative for steel fibers in concrete beams [36].

PET fibers that are recycled from waste bottles are currently used in concrete because they improve concrete desired properties [37]. Several researches studied the addition of PET fibers on the concrete mechanical strength. It was reported that adding PET to concrete did not enhance its compressive strength [38,39,40,41]. However, other works found that PET fibers control the propagation of cracks, mainly post cracking and increase toughness [42,43]. Another study showed that PET fibers are effective in resisting shock and impact force when used as reinforcement in concrete [44].

Many authors have studied the flexural behavior of concrete beams containing PF [45,46]. Alani et al. studied the effect of incorporated PET fibers on the ultra-high performance green concrete containing different amount of silica fume [SF] and palm oil fuel ash [POFA]. They concluded that the ductility of SF and POFA can be improved by the presence of PET fibers [47]. Another study investigated the flexural behavior of reinforced concrete beams using different ratio of shredded plastic waste as sand replacement and found that for structural application, 15% well graded PET waste can be safely added to the concrete mix [48]. It was shown that PET-FRP could be considered a strengthening material that can increase the structural performance of concrete beams and offered an alternative to FRP strengthening systems [49].

This current investigation throws a light on the flexural behavior of non-structural concrete beams (i.e., lintels, etc.) made of concrete containing different pattern of plastic meshes. Based on the literature conducted by the authors, there is hardly any investigation on the use of plastic mesh in non-structural elements. Therefore, the main objective of this investigation is to examine the flexural behavior of concrete beams having different pattern of plastic mesh. Conventional reinforced concrete beams were prepared in order to compare with those containing waste plastic meshes. The outcome of this research is expected to assist professionals in the construction industry to choose cheaper elements; thus reducing the cost of construction projects and contribute toward sustainable development. For this reason, flexural tests in the laboratory were conducted on eight concrete beams: one beam without reinforcement playing the role of a control sample, one beam reinforced with rebar and six beams containing six different patterns of plastic mesh. Ultimate load, deformation, flexural toughness, ductility index and the mode of failure were carefully evaluated. In addition, experimental results were compared with numerical ones.

2. Materials and Methods

2.1. Materials

2.1.1. Plastic Fibers

The plastic material used in this study was obtained from waste water plastic gallons. Before producing the plastic meshes to be used as replacement for reinforcement in concrete beams, the plastic properties need to be first determined. A linear wire of waste plastic of 150 mm length × 1 mm width × 1 mm depth, obtained using a shredder machine, was inserted into the tensile testing machine and tested according to ASTM D638 [50] as shown in Figure 1. From the tensile test results, it was shown that the yield strength and ultimate strength of plastic fiber were 27.2 and 68.4 MPa respectively. Other mechanical properties are shown in

Table 1. Mechanical properties of plastic wire.

Parameter	Unit	Symbol	Plastic Fibers
Modulus of elasticity	MPa	E1	313
Yield strength	MPa	fy	27.2
Ultimate strength	MPa	fu	68.4
Poisson’s ratio		ν	0.35
Water absorption	%		0.00
Density	KN/m3	ρ	9.45

.

2.1.2. Steel Bars

Steel bars of 6 mm diameter were used for the beam reinforcement. The tensile test was performed according to ASTM A615 [51]. The yield strength and the ultimate strength were found to be 240 and 300 MPA respectively. The mechanical properties are provided in

Table 2. Mechanical properties of steel bars.

Parameter	Unit	Symbol	Steel Bars
Modulus of elasticity	MPa	Et	200,000
Yield strength	MPa	fy	240
Ultimate strength	MPa	fu	300
Poisson’s ratio		ν	0.3
Density	KN/m3	ρ	78.5

.

2.1.3. Concrete

Ordinary Portland cement type I according to ASTM C150 [52] was used in the preparation of concrete mixes. The maximum size of fine and coarse aggregates used were 2 mm and 19 mm respectively. Sieve analysis was conducted and results were presented in Figure 2. As shown from the gradation curve, the particle size distribution of coarse and fine aggregate fell within the limits specified by ASTM C33 specifications [53]. Tap water was used with high water/cement ratio of 0.6 because no water reducing admixtures was added.

2.2. Experimental Program

2.2.1. Preparation of Plastic Meshes

Large waste water plastic gallons of total height 40 cm and a squarish dimension of 15 cm, having a volume of 9.8 L were collected and cleaned. The gallons were then cut into flat sheets of dimension of 80 mm × 280 mm using a sharp cutter as shown in Figure 3. Afterward, the sheets were inserted into a laser-cutting machine, which is a computer numerical controlled equipment to produce the required mesh patterns as illustrated in Figure 4.

2.2.2. Characteristics of Specimens

Eight rectangular concrete beams (100 mm width × 100 mm depth × 500 mm length) were tested in this study to investigate the flexural behavior of concrete beams reinforced with plastic fiber sheets. The first beam is a plain concrete beam (PCB) with no reinforcement. The second beam is a reinforced concrete beam (RCB) which is reinforced with two bottom bars of Ø6 mm (mild steel) as a longitudinal reinforcement. The RCB is considered as a reference beam. The last six beams, referred to as “M10-S05” to “M20-S10”, are each composed of two layers of rectangular plastic mesh with dimensions of 280 mm length × 80 mm width × 1 mm thickness as described in Figure 5. In this notation, “M” stands for mesh, “10” to “20” indicates the void width in mm, “S” refers to strips, and “05” to “10” refers to the width of strips in mm, enclosing the void area.

2.2.3. Concrete Mix Design

The mix design information is shown in

Table 3. Concrete mix design.

Material	Cement	Sand	Gravel	Water
Amount (kg/m3)	300	650	1310	240

. Once the mix ingredients were weighted based on their proportions, they were placed into the concrete mixer in the following sequence. First, the gravel and sand were mixed together for about 3 min. Second, water was added to the drum and mixed together for nearly 30 s. Then, the cement was added to the mix. The mixing continued for around 3 min until the mix turned homogeneous. The mixer is then turned off for 3 min resting period followed by a final 2 min mixing period. Two replicate samples were cast for PCB, RCB and for each beam layered with plastic meshes.

To check concrete workability, the slump test was conducted and found to be equal to 15 cm indicating a highly workable mix. Following the slump test, concrete was poured into the molds. For the compressive strength (CS) test, standard steel cylinders of 150 × 300 mm were used according to ASTM C39 [54]. The CS of concrete was found to be 15 MPa at 28 days. For the flexural test, concrete was poured into the rectangular steel beams in the following order. For beams reinforced with plastic mesh, a layer of concrete of 1 cm thickness was placed at the mold base (Figure 6a). Then, the first plastic mesh was inserted on top of the concrete layer (Figure 6b). This was followed by laying down a second 1 cm layer of concrete. The second plastic mesh was then placed on top of the second concrete layer. A vibrator was used to remove entrapped air voids between the different layers of concrete and the perforated plastic meshes. Thus, full bonding was achieved between the plastic and concrete. This was followed by pouring concrete till the top of the mold (Figure 6c). Regarding RCB, similar steps were followed except that the beam was reinforced with 2Ø6 mm placed 1 cm above the mold base (Figure 6d). After 24 h, the specimens were demolded and placed in a lime saturated tank until the day of testing.

2.2.4. Test Setup

After 28 days of curing, the beams were subjected to a three-point loading in flexure, acting monotonically at the beam mid-span through a constant loading rate control (0.1 kN/sec) according to ASTM C293 [55]. The load cell range was between 1 and 10 kN. The shear span/effective depth (a_v/d) ratio is an important parameter that may affect concrete beams reaching their bending capacity [56]. In this study, this ratio was taken equal to 1.9 for all tested beams. The applied load was directly transferred to the beam by a steel roller placed at the top mid-span of the concrete beam. Figure 7 shows the dimensions and reinforcement details for the different specimens. Steel rods of 50 mm in diameter were put as roller supports with a clear spacing of 300 mm. The load produced single curvature bending in the beam. Two LVDTs were placed symmetrically on opposite sides of the beam, and the mid-span deflection was recorded as the average reading taken from the LDTVs outputs. The load and displacement data were recorded through a data acquisition system. Afterwards, the test was stopped as the load drops by 70~80% in order to avoid excessive overload that may break the machine.

3. Results and Discussion

3.1. Experimental Test

3.1.1. Flexural Behavior

The main objective of this research is to examine the effect of plastic mesh on the flexural behavior of concrete beams. The load displacement curves are plotted in Figure 8. As shown, specimen PCB with no reinforcement exhibits a brittle behavior as the beam reaches the maximum capacity at 8.75 kN. Beyond that, the load drops directly without passing by the post-cracking phase due to the absence of reinforcement. The test was stopped right after the specimen has been fully crushed. On the other side, specimen RCB with 2Ø6 mm bottom reinforcement displays a ductile behavior. This is obvious due to the presence of steel reinforcement leading to a slight increase in the ultimate capacity (2%) to reach 8.90 kN. After that, the beam stiffness continues to decrease inducing propagation of wide cracks. The test was stopped while the specimen experienced large permanent displacement prior to failure. No slippage between the concrete layers was detected.

Similar to RCB, all specimens reinforced with plastic mesh display ductile behavior. The beams tend to withstand further deformations prior to failure. This is likely due to the ability of plastic mesh layers to stretch and limit the crack propagation before failure. Three main phases take place:

• An elastic zone describing the ascending part where the applied load and the displacement are linearly proportional up to the first hairline crack. The slope of the load displacement curve increases slightly as the ultimate capacity of the beam goes up.
• Beyond the first cracking point, the plastic zone starts. This zone involves the remaining part of the ascending branch where the applied load increases slightly as the deflection increases. At the end of this phase, the beam reaches the ultimate capacity through which cracks undergo further development.
• At the point the beam reaches the ultimate capacity, the damage zone starts indicating the stiffness degradation of the specimen. This phenomenon is well known as the post-cracking phase, in which the stiffness is reduced as the applied strain increases up to the rupture of the plastic sheets. This degradation is accompanied with large deformation induced by the bound between both the plastic meshes and concrete. In other words, the matrix is adhered well by concrete and fibers as a long softening zone remains. The bonding effect of the plastic converts the brittle behavior to a more ductile mode. Thus, the plastic mesh may play a role in controlling the propagation of cracks. At the end, the test was stopped as the deterioration became quite substantial (Figure 9).

To compare the flexure performance of concrete beams with different plastic mesh patterns, the parameter width ratio “W_r” is introduced. It is defined as the ratio of effective to the total mesh width. The effective width is the width of plastic mesh that resists the tension force resulting from the flexural load. As presented in

Table 4. Experimental test results.

Beam	Mesh Void Ratio, Vr	Mesh Effective Width (mm)	Mesh Width Ratio, Wr	Ultimate Capacity, Pu (KN)	Flexural Toughness, Tf (N.mm)	Yield Deflection (mm)	Ultimate Deflection (mm)	Ductility Index, Di
PCB	-	-		8.75	7169	0.52	0.60	1.15
RCB	-	-		8.90	19,076	0.35	0.60	1.71
M10-S05	0.38	30	0.38	7.25	16,089	0.35	0.55	1.57
M10-S10	0.26	40	0.50	7.64	19,708	0.22	0.40	1.80
M15-S05	0.52	20	0.25	6.37	12,186	0.37	0.45	1.22
M15-S10	0.33	35	0.44	7.21	17,355	0.31	0.50	1.61
M20-S05	0.59	20	0.25	6.25	11,408	0.34	0.43	1.26
M20-S10	0.32	40	0.50	7.43	19,202	0.25	0.43	1.72

, the beam M10-S10 with the highest width ratio (0.50), holds the highest ultimate load (7.64 kN) among the series layered with plastic mesh. This result is expected as upon increasing the mesh effective width, the flexural performance of beam goes up as well. Thereby, the use of plastic mesh with large effective width improves the behavior of the beam while acting as bridge across cracks and leads to postpone their fast propagation. Despite specimens M10-S10 and M20-S10 both have the highest width mesh ratio (W_r = 0.50), the ultimate capacity of the latter is slightly reduced by 3% in comparison with that of the former. This result may be attributed to the mesh void ratio of M20-S10 which is higher than that of M10-S10. This will be discussed further in the next section. On the other hand, the specimens with the lowest mesh ratio (0.25), M15-S05 and M20-S05, show as well the lowest ultimate capacity with a decrease of 38% and 42% respectively compared with M10-S10. This significant decrease is referred to the weak bonding between plastic mesh and concrete. The mesh effective width is no longer enough to withstand the stress applied.

Based on the above, the effect of mesh width ratio on the ultimate load of the concrete beam is very dependent. Figure 10 displays the relationship between the beam ultimate capacity and the mesh width ratio. It appears clearly that this relationship is proportional with a high coefficient of determination (R² = 0.93). This indicates that as the width ratio increases, the load carrying capacity of the member goes up.

3.1.2. Flexural Toughness

Another aim of this research is to assess the effect of plastic mesh on the ability of the specimen to absorb high amount of energy with large deformations before fracture. This characteristic is referred to as the modulus of toughness “T_f” which is the total integral area of the load displacement curve. The results are presented in Figure 11.

Results demonstrate that the effect of plastic mesh on the flexural toughness is of high importance. The toughness capacity increases as the mesh effective width goes up. For example, specimens M15-S05 and M20-S05, with the lowest width ratio (0.25), yield the lowest toughness capacity. Accordingly, the % increase in toughness capacity is 41%, 52%, 68% and 73% for beams M10-S05 (0.38), M15-S10 (0.44), M20-S10 (0.50) and M10-S10 (0.50) respectively compared to beam M20-S05 with the lowest mesh width ratio (0.25). Furthermore, beams M10-S10 and M20-S10 with the highest width ratio (0.50) display the highest toughness among all beams. However, the toughness of the former beams are lightly enhanced by 1~3% in comparison with the reference RCB. On the other hand, compared with PCB, the improvement in toughness capacity of mesh layered beams is 124%, 175%, 70%, 142%, 59% and 168% for beams M10-S05, M10-S10, M15-S05, M15-S10, M20-S05 and M20-S10 respectively. The results shown above are attributed to the bond between the plastic mesh and concrete which delays the crack propagation as the specimens remain able to absorb more energy before failure. Therefore, the beams hold more deformation prior to the appearance of the first noticed crack. Contrarily, the beams with low mesh width ratio do not have the same energy absorption potential as those with larger effective width.

To further illustrate the importance of the effective width on the beam flexural capacity, the plastic mesh width ratio was plotted against the beam flexural toughness, and best fit was conducted using linear regression analysis. The coefficient of regression is 0.98 (i.e., almost all points lay on a straight line). This indicates a strong correlation between the variables. The proposed regression equation in Figure 12 allows the flexural toughness to be predicted based on mesh width ratio.

The consequence of increasing the area of voids in the plastic sheet on the flexural toughness of concrete beams is also a point of interest as this will affect the bonding strength between the concrete and the plastic mesh. Therefore, the mesh void ratio “V_r” is a parameter that can be defined as the area of openings in the plastic mesh to the total area of the plastic sheet. Results are shown in Table 4. As shown, the relation between the void ratio and the flexural toughness is inversely proportional. As the mesh void ratio increases, the flexural toughness decreases. For instance, beam M10-S10 with the lowest void ratio (0.26) holds the highest toughness capacity (19,706 N.mm). Beyond this limit, the toughness continues to decrease gradually. Moreover, beam M20-S05 with the highest void ratio (0.58) shows a drop in the measured toughness by 42% compared to M10-S10. This drop is expected as the plastic meshes is unable to sustain more stress prior to rupture. Figure 13 plots the correlation between the mesh void ratio and the predicted toughness capacity. Also the best fit line and equation are shown in the figure. The high value of the coefficient of determination (R² = 96%) indicates the strength and the almost linear relationship between the two variables.

3.1.3. Ductility Index

Ductility can be defined as the ability of a structural member to undergo large plastic deformations without significant loss of resistance. The ductility index is a parameter needed to characterize the structural behavior of flexural members. The ductility index “D_i” is the ratio between the deflection at ultimate load to the deflection at yielding load. The values of ductility indices for the different beams used are presented in Figure 14. As shown, the highest ductility index (1.8 and 1.72) is depicted in beams M10-S10 and M20-S10. It is interesting to mention that these two beams have both the highest width ratio and flexural toughness. In contrast, the results show a significant reduction in the ductility (1.22 and 1.26) of beams M15-S05 and M20-S05. Similarly, those specimens have the lowest width ratio (0.25 and 0.25) and flexural toughness (12,186 and 11,408 N.mm). Furthermore, unexpectedly, the ductility of Beam M10-S10 is 5% higher than the reference RCB. The performance of beam M10-S10 could be attributed to the high ductile nature of plastic mesh as it allows higher deformation before failure. This improvement in ductility index for beams reinforced with plastic meshes is a promoting finding that may be considered as a guidance for concrete beams subjected to flexural load where high ductility is required.

It is clear from the analysis of Figure 14 that there exists a relation between the ductility index and the flexural toughness. Therefore, a regression analysis was conducted. Results obtained in Figure 15 indicate a strong positive correlation between the variables with a coefficient of determination equal to 0.97. As ductility index increases, the flexural toughness increases as well.

3.2. Finite Element Model

3.2.1. Methodology

As indicated earlier, the experimental program was followed by a numerical analysis. A three dimensional finite element model was developed using ABAQUS software. The concrete body was modeled using the linear brick element C3D8R with an 8-node hexahedral shape and reduced integration, whereas steel bars were modeled using the 2-node linear displacement truss element T3D2 [57,58]. On the other hand, plastic meshes were represented using the 4-node doubly curved shell with reduced regression and finite membrane strains S4R [58]. Three different types of mesh global sizes of 10 mm, 20 mm and 25 mm were used to determine the optimum size which provide the highest accuracy results and least convergence problem. Based on the output of the analysis, the model with 10 mm mesh size gave more accurate results. Thus, this mesh size (i.e., 10 mm) was selected for concrete (Figure 16), steel and plastic mesh reinforcement as well, with maximum deviation factor of 0.1.

The boundary conditions of the model were assigned conformably to the real conditions of the experimental work. A rigid body constrain was set between the top mid-span crossline of the model and a reference point, which is appropriate to avoid any stress concentration or singularities upon loading. Similarly, an embedment constrain type was assigned to steel bars and/or plastic sheet layers reinforced in the host concrete element. This last step was necessary to create full bonding between steel/plastic and concrete. The both opposite extremities of the beam were constrained as well against lateral translation. Static/Risk analysis method was used to model the beams. Accordingly, a uniformly increasing axial displacement of 6 mm was imposed. The relevant reactions were then recorded and noted.

The built-in Concrete Damaged Plasticity method (CDP) was used to define the nonlinear behavior of concrete. This method was introduced first by Lubliner, and developed later on by Lee and Fenves [59,60]. Vertical deflection, cracking and inelastic strains patterns and distribution, yield and ultimate capacities, as well as stiffness degradation were the main parameters output of the finite element model. According to CDP method provided in ABAQUS, the concrete behavior in compression and tension is shown in Figure 17 [57].

The parameter ${\epsilon }^{in}$ shown in Figure 17a is defined as the inelastic strain in compression, while the parameter ${\epsilon }^{ck}$ represents the cracking strain in tension. These parameters are computed by Equations (1) and (2) [57,58,61,62]:

$${\epsilon }^{in}={\epsilon }_c-\frac{{\sigma }_c}{E_0}$$

(1)

$${\epsilon }^{ck}={\epsilon }_t-\frac{{\sigma }_t}{E_0}$$

(2)

where: “σ_c” and “σ_t” are respectively the compressive and tensile stresses in concrete, and “E₀” is the initial modulus of elasticity.

Moreover, two isotropic damage parameters “d_c” and “d_t” are defined accordingly to describe the stiffness degradation of concrete in compression and in tension respectively. Depending on the severity of the damage, these parameters float between zero (undamaged) and one (full damage). Equations (3) and (4) compute these parameters as follows [57]:

$$d_c=1-\frac{{\sigma }_c}{E_0\left({\epsilon }_c-{\epsilon }_c^{pl}\right)}$$

(3)

$$d_t=1-\frac{{\sigma }_t}{E_0\left({\epsilon }_t-{\epsilon }_t^{pl}\right)}$$

(4)

Based on both damage parameters, the inelastic and crack strains are then converted respectively into plastic strains at compression “${\epsilon }_c^{pl}$” and tension “${\epsilon }_t^{pl}$” as per Equations (5) and (6) [57]:

$${\epsilon }_c^{pl}={\epsilon }^{in}-\left(\frac{d_c}{1-d_c}\right)\left(\frac{{\sigma }_c}{E_0}\right)$$

(5)

$${\epsilon }_t^{pl}={\epsilon }^{ck}-\left(\frac{d_t}{1-d_t}\right)\left(\frac{{\sigma }_t}{E_0}\right)$$

(6)

The mechanical properties of concrete used in the numerical study are presented in

Table 5. Mechanical properties of concrete.

Parameter	Unit	Symbol	Value
Compressive strength	MPa	f’c	15
Tensile strength	MPa	ft	2.40
Modulus of elasticity	MPa	Ec	18,203
Poisson’s ratio		ν	0.2
Density	KN/m3	ρ	24
Dilation angle	°	ψ	30
Eccentricity		ɛ	0.1
Bi-axial to uni-axial strength ratio		fb0/ft0	1.16
Second stress invariant ratio		K	0.667
Viscosity parameter		μ	0.00001

. Besides, the steel bars were modeled as per the elastoplastic behavior.

To simulate the behavior of plastic fiber mesh in concrete structures, the Hashin Failure criteria method was used [58]. This criteria define four modes of failure: tensile fiber failure, compressive fiber failure, tensile matrix failure, and compressive matrix failure as shown in

Table 6. Hashin Failure Criteria [58].

Failure Mode	Equation
Tensile fiber failure	$F_f^t={\left(\frac{{\sigma }_{11}}{X^T}\right)}^2+{\left(\frac{{\tau }_{12}}{S^L}\right)}^2$
Compressive fiber failure	$F_f^c={\left(\frac{{\sigma }_{11}}{X^C}\right)}^2$
Tensile matrix failure	$F_m^t={\left(\frac{{\sigma }_{22}}{Y^T}\right)}^2+{\left(\frac{{\tau }_{12}}{S^L}\right)}^2$
Compressive matrix failure	$F_m^c={\left(\frac{{\sigma }_{22}}{2S^T}\right)}^2+\left[{\left(\frac{Y^C}{2S^T}\right)}^2-1\right]\frac{{\sigma }_{22}}{Y^C}+{\left(\frac{{\tau }_{12}}{S^L}\right)}^2$

.

where σ₁₁ and σ₂₂ are the effective stress in directions 1 and 2 respectively, X^T and X^C are the tensile and compressive strength in the direction of fiber, Y^T and Y^C are the tensile and compressive strength in the direction of matrix, S^L and S^T are the shear strength of longitudinal and transverse direction, respectively.

3.2.2. Results and Discussion

Table 7. FE Model results.

Model	Ultimate Capacity, Pu (KN)			Flexural Toughness, Tf (N.mm)			Ductility Index, Di
	Exp. Test	FE Model	% of Error	Exp. Test	FE Model	% of Error	Exp. Test	FE Model	% of Error
PCB	8.75	9.10	4%	7169	8775	22%	1.15	1.24	7%
RCB	8.90	9.43	6%	19,076	20,184	6%	1.71	1.81	6%
M10-S05	7.25	7.51	4%	16,089	16,502	3%	1.57	1.63	3%
M10-S10	7.64	7.86	3%	19,708	19,907	1%	1.80	1.83	2%
M15-S05	6.37	6.62	4%	12,186	12,884	6%	1.22	1.30	7%
M15-S10	7.21	7.57	5%	17,355	17,362	0%	1.61	1.66	3%
M20-S05	6.25	6.53	5%	11,408	12,254	7%	1.26	1.33	5%
M20-S10	7.43	7.71	4%	19,202	19,681	2%	1.72	1.76	2%

shows a comparison between the numerical and experimental outcomes. The results demonstrate a very good agreement with approximately 6% discrepancy. Thus, the finite element model calibrates and verifies the experimental work. This work is a proof of the efficiency of using plastic meshes on the behavior of concrete beams subjected to flexural load. Similar to the experimental results, the curves outline a considerable increase in the ultimate capacity as the mesh effective width increases. Figure 18 represents the experimental and numerical works of the mid-span deflection for the different cases considered. It is well noted that the constitutive law of materials using CDP model proves the accuracy of simulation of beams layered with plastic meshes under the 3-point loading test. As shown in Figure 18, beams with plastic meshes display similar characteristic patterns. Accordingly, all models, except “PCB”, exhibit ductile failure modes. Conforming to the experimental results, upon increasing the mesh effective width, the energy absorption of the model increases significantly, which in turn raises the flexural toughness capacity of the concrete beams.

Figure 18d shows that the experimental and numerical results of load displacement curve of model M10-S10 are quite similar with 3% error. Thus, this model with the largest mesh effective width (40 mm) is selected to describe the flexural behavior of concrete beams. Three main stages occur:

4.

The first phase starts with the beginning of the simulation up to a load of 6.85 kN. At this limit, the initial crack occurs at the flexural mid-span zone under loading point. This phase represents the elastic part of the curve. The deformation is directly proportional to the load applied. Similarly, the exerting stress is directly proportional to the strain. The yield deflection is observed at 0.29 mm.

5.

Beyond the linearity limit, the model exhibits plastic behavior as the stress is not anymore linearly proportional to the strain. This phase illustrates the remaining part of the ascending branch up to a pick of 7.86 kN with an ultimate deflection of 0.53 mm. It can be seen that the load increment rate is smaller than the first phase. Simultaneously, newer cracks develop as older cracks propagate wider and deeper in the bottom flexure zone, and then tend to propagate upward. Likewise, the axial stress S11 in the fiber sheets is early created in the middle third of the beam prior to propagate towards the both ends (Figure 19b). It should be noted that ABAQUS denotes the x, y and z axis as 1, 2 and 3 respectively. Besides, positive values correspond to tensile stresses and forces, while negative ones are for compression.

6.

Afterwards, the post-cracking phase of the model indicates excessive stiffness degradation of the beam. The curve undergoes a nonlinear sharp downward trend. The red volumes seen in Figure 19a represent the crushed concrete volumes. Meanwhile, the beam continues to deform plastically in a long softening way induced by the bond between the fiber and concrete. Consequently, the fiber mesh strongly contributes in enhancing the flexural toughness while restricting the propagation of damaged volumes. The plastic sheets might substitute the role of steel bars in regards. At the end, the model becomes substantially damaged although the FE simulation stops at a large controlled displacement of 6 mm.

4. Conclusions and Recommendations

This research investigates the flexural behavior of non-structural concrete beams reinforced with plastic mesh layers. Both experimental and numerical programs were performed on eight specimens subjected to flexural loads. The main variables examined were the mesh effective width and the mesh void ratio. The findings delivered herein would be a step forward towards using waste plastic material as a replacement of reinforcement in concrete beams.

7.

The experimental testing of concrete beams proves the failure mode of the specimens. As expected, all specimens reinforced with plastic fiber mesh exhibited ductile behavior. This is likely to be due to the presence of plastic meshes which may control the extent of cracks. The good bonding between concrete and fibers converts the brittle behavior to a more ductile mode.

8.

The effect of mesh effective width on the ultimate load of the beam is very dependent. The load carrying capacity of the member goes up as the mesh effective width is larger. Therefore, the use of plastic meshes improves the behavior of the beam while acting as bridge across cracks and leads to delay cracks fast propagation. Accordingly, a simplified linear correlation with high accuracy (R² = 0.93), was developed between the mesh width ratio and the beam ultimate capacity.

9.

The correlation between the mesh effective width and the flexural toughness shows a positive correlation with R² value equal to 0.98. The higher the mesh width ratio is, the higher the flexural toughness is. Contrarily, beams with low width ratio do not have the same energy absorption potential as those of higher ratio.

10.

There exists a high correlation between the void ratio and the flexural toughness (R² = 0.96). The relationship is inversely proportional. As the mesh void ratio increases, the flexural toughness decreases. This drop in flexural toughness is expected as the plastic meshes remain unable to sustain more stress prior to collapse.

11.

Concrete beams with large plastic mesh effective width display high ductility indices. A linear regression was developed between the mesh width ratio and the ductility index. It was found that the relation is proportional with a coefficient of regression R² equal to 97%. The improvement in ductility index for beams layered with plastic meshes is a promoting finding that may be considered as a guidance for concrete beams subjected to flexural load where high ductility is required.

12.

The comparison between the experimental and numerical results demonstrated the accuracy of CDP model to simulate the flexural behavior of beams with plastic meshes under the 3-point loading test. The average error in the simulation was less than 6%.

13.

The results obtained are based on the dimensions of the beams used in this investigation. Future research should examine the behavior of full scale beams containing waste plastic mesh. Different void ratios and mesh configurations should be attempted in order to obtain the optimal performance. Also, using waste plastic fibers in conjunction with plastic mesh should form part of a future work.