Experimental studies on the behavior of concrete-filled uPVC tubular columns under axial compression loads

Abstract The behavior of concrete-filled uPVC tubular columns under axial compression loads were studied experimentally by testing columns prepared from five different concrete strength classes. Accordingly, the unconfined, concrete-filled uPVC tube with and without wire-mesh reinforced mortar cover and reinforced concrete columns were evaluated. The main variables considered in this study are concrete strength , uPVC thickness to diameter ratio (2t/D) and aspect ratio (h/D). The effect of uPVC confinement on strength, ductility, energy absorption, and post-peak behavior was explored. Also, a model was developed to predict the peak strength. Results show that the uPVC confinement increased the strength, ductility, and energy absorption in between 1.28–2.35, 1.84–15.3, and 11–243 times the unconfined, respectively. The confinement performed well on increasing the strength, ductility, and energy absorption for lower concrete strength and higher 2t/D ratios. The post-peak behavior of the stress-strain curve was affected by 2t/D and h/D ratios; an abrupt drop in the stress-strain curve was observed in specimens with lower 2t/D and higher h/D ratio. For a given value of concrete strength , tensile strength , thickness (t), diameter (D), and height (h), the stress-strain model predicted the peak strength of axially loaded concrete-filled uPVC tube column with a mean absolute error of 2.7%.


PUBLIC INTEREST STATEMENT
Although uPVC tube is durable, ductile, low-cost, light, and resistant to the harsh environment, it is not used as concrete confining material. Very few studies have investigated the effect of uPVC tube confinement on the performance of concrete columns. To fill the gap, the effect of uPVC tube confinement on strength, ductility, energy absorption, and durability of concrete columns were evaluated. The results show that confining a concrete in a uPVC tube increased the strength, ductility, and energy absorption in between 1.28-2.35, 1.84-15.3 and 11-243 times the unconfined, respectively. Therefore, the uPVC tube can be used as a concrete confining material and stay-in -place formwork to improve the structural performance of concrete structures, reduces the duration of construction and avoid the cost incurred for timber and steel formwork.

Introduction
There is always a need to find alternative, sustainable material for building, highway structures, and bridges to overcome the drawbacks of conventional concrete and steel. Brittle failure of the concrete structure and its damage to life and property in Africa has been reported for a long period of time. At least 27 reinforced concrete buildings had collapsed in Kenya from 2006(Fernandez, 2014, 139 in Nigeria from 1978 to 2014 (Basirat et al., 2016) and 11 in Cameroon (Yaoundé & Douala) from 2010 to 2014 (Tchamba & Bikoko, 2015). Most of them are due to brittle failure of the columns causing overlapping of the floors and giving no time for people to scape. Reinforced concrete columns began to fail (collapse) from taking-off the concrete cover, leaving the reinforcement exposed. The exposed reinforcement starts buckling outward followed by concrete-reinforcement bonding fragmentation, which leads to a global collapse of the structures. Also, the waterfront peeling of the reinforced concrete structure has been a challenge to date for engineers. Countries like the U.S spends more than 1 USD billion per year for maintenance, especially for waterfront peeling (Fakharifar & Chen, 2016). Composite materials have been used extensively in the last three decades to improve the performance and avoid the brittle failure of the concrete structures. Extensive studies have been done on different types of confining materials such as steel tube, steel stirrups, FRP stirrups, FRP tubes, FRP rings, FRP shells, hybrid jackets, composite ropes, SMA warp, CFRP, and PVC for application on new structures as well as to strengthen the existing structures (Abdulla, 2017;Alves & Martins, 2009;Boersma & Breen, 2005;Fakharifar & Chen, 2016, 2017Folkman, 2014;Gathimba et al., 2015;Gupta, 2013;Gupta & Verma, 2014;Kurt, 1978;Lam et al., 2012;Oyawa et al., 2015Oyawa et al., , 2016Ranney & Parker, 1995;Shanmugam & Lakshmi, 2001;Woldemariam et al., 2020). Steel-concrete composite material has been one of the most widely used composite materials and has shown superior performance in increasing the load-carrying capacity, ductility, strength, and energy absorption (Lam et al., 2012;Shanmugam & Lakshmi, 2001). In concrete-filled steel tube columns, the concrete resists the vertical load and reduces potential buckling of the steel tube, and the steel tube confines the concrete and avoids sudden brittle failure of concrete (Kurt, 1978). However, the durability issues of steel, RC and steelconcrete composite structures under different environmental exposure have been a challenge. And also, the high cost of steel and the environmental issue (as manufacturing of steel emits a large percentage of carbon dioxide to the environment) has spurred to find alternative materials.
A recent development regarding the use of fiber-reinforced polymer (FRP) as a reinforcement and confinement in the concrete structure has shown a positive result. FRP confinement increased the strength of concrete and reduced the peeling of concrete cover, permeability, and protected the concrete from alkali attacks. However, the lack of material ductility delayed the use of FRP as a reinforcement. In the recent past, ductile failure of plastics (polyvinyl chloride) gained the attention of researchers to use it as a confining material in concrete. Plastics (uPVC tube) have the potential to increase strength, ductility, energy absorption and durability. However, the knowledge on the use of plastic tubes in construction is scattered and lacks information regarding how to design a concrete confined in a plastic tube (Abdulla, 2017;Alves & Martins, 2009). Unplasticized polyvinyl chloride uPVC) is the most commonly used polymer families for plumbing purposes. Unlike polyvinyl chloride (PVC), uPVC is strong, stiff, hard, and doesn't burn by itself (Abdulla, 2017;Fakharifar & Chen, 2016;Gathimba et al., 2015;Gupta, 2013;Gupta & Verma, 2014;Oyawa et al., 2015Oyawa et al., , 2016Woldemariam et al., 2019a). PVC/uPVC has remarkable mechanical properties. Tests were undertaken to evaluate the durability of the uPVC tube by exposing it into acid, alkaline, and organic compounds. The material performed well under all exposure conditions and has the potential to stay for more than 50 years without deterioration (Abdulla, 2017;Alves & Martins, 2009;Fakharifar & Chen, 2017;Gupta & Verma, 2014;Ranney & Parker, 1995). Experimental investigation on damage initiation, stress deterioration, crack initiation and growth, impact tests, burst, tensile and fatigue of PVC tube has exhibited a remarkable performance that its service life may extend beyond 100 years (Abdulla, 2017;Boersma & Breen, 2005;Breen, 2006;Burn et al., 2006;Folkman, 2014). Also, plastic (uPVC) has a lower thermal conductivity of about 0.45% of a steel tube, which makes it a suitable environment to cure a core concrete compared to steel tube (J. Wang & Yang, 2012;Wang & Yang, 2010).
Previous researches on concrete columns confined by plastic tube have shown a positive result, but the results on strength and ductility were very scattered from one research to another. Confining a concrete in plastic tube increased the strength and ductility of concrete (Fakharifar & Chen, 2016, 2017Gathimba et al., 2015;Jamaluddin et al., 2017;Oyawa et al., 2016;K. Wang & Young, 2013;Woldemariam et al., 2019b;Xue et al., 2016). Marzoucka and Sennah (2002) evaluated the effect of uPVC confinement on the axial strength of concrete columns by testing concrete-filled uPVC tubular columns under axial compression loads, and the result showed that the strength increased by 11-17% (Marzoucka & Sennah, 2002). In a similar study, the strength and strain of concrete confined by plastic tube increased in between 1.324 to 2.345 and 2.094 to 5.540 times the unconfined, respectively (J. Wang & Yang, 2012). Oyawa et al. (2016) reported a similar finding on the strength of axially loaded uPVC confined concrete stub columns with different uPVC tube diameter, concrete grade, and height to diameter ratio. The strength increased by 1.18 to 3.65 times the unconfined strength. In another study, the axial strength and strain of the PVC tube confined concrete column increased by168.8 and 147.3% times the unconfined, respectively (Saadoon, 2010). Similarly, an increase of over 40% was reported for axial strength and strain of confined concrete columns compared to the unconfined (Jamaluddin et al., 2017). In another study, confining a concrete stub column using a PVC tube has increased the strength by 71.8% (Kurt, 1978). Gupta (2013) evaluated the effect of uPVC diameter and core concrete strength on the strength, ductility, and energy absorption of uPVC tube confined concrete columns. The result showed that the strength, ductility, and energy absorption increased by 1.352 to 2.100, 1.30 to 2.65 and 1.55 to 3.52 times the unconfined, respectively (Gupta, 2013). Also, Gupta and Verma (2014) evaluated the durability of PVC confined RC columns by dipping the specimens into a salt solution, which was 20 times natural seawater. The result showed that the PVC had protected the column from salt-induced deterioration (Gupta & Verma, 2014).
The literature shows that the uPVC confinement improved the structural performance of concrete; however, the findings on strength and ductility are very scattered from one research to another and limited in the scope of the study. The effect of uPVC confinement on energy absorption, failure mode, stress-strain (elastic & inelastic), and post-peak behavior of uPVC confined concrete, and how the uPVC confined concrete undergoes straining for the applied load beyond the elastic state was not fully understood. Therefore, it is necessary to carry out an extensive experimental investigation on strength, ductility, energy absorption, stress-strain relation, and mode of failure. This research work is to investigate the performance of concrete-filled uPVC tubular columns under axial compression loads. It will give a full understanding of tensile properties of uPVC material, load-carrying capacity, strength, ductility, energy absorption, failure mode, stress-strain behavior, and post-peak behavior of uPVC confined concrete.

Materials
Ordinary Portland cement (OPC) power plus 42.5 N conforming to European Norm EN 197-1:2011(European Standard, 2011, locally available natural sand and crushed stone were used throughout the experiment to prepare five different concrete mixes. The fine and coarse aggregate material characterization were done according to BS standard, and the results are presented in Table 1. The sampling was done according to BS EN 932-1, 1997(British Standard Institution, 1997. Both the fine and coarse aggregates were graded through sieving and curve plotting according to BS EN 12620: 2013;BS EN 933-1:2012(British Standard Institution, 2012b and BS EN 933-2, 1996(British Standard Institution, 1996. Un-plasticized polyvinyl chloride (uPVC) pipes produced by Elson plastics ltd. (a company based in Nairobi, Kenya) was used for this research. The tensile and compressive properties of uPVC are also the most important parameters and obtained through testing the specimens according to their respective standards. The tensile strength will be used to calculate the confining pressure and to relate the yield stress of material under multiaxial loading in von Mises stress equation (failure criterion). The specimens were prepared from two different uPVC pipes having a thickness of 3 and 2.5 mm, and designated as uPVC1 and uPVC2, respectively. The tensile property of uPVC material was obtained through a tensile test of dogbone coupon specimens as shown in Figure 1. The test was performed by applying a constant rate of 5 mm/min according to ASTM D638 (ASTM International, 2014); and an average ultimate tensile strength, Young's modulus of elasticity, poisons ratio, and the stress-strain graph are presented in Table 2 and Figure 2. The compressive strength of the empty uPVC tube was obtained by testing a hollow uPVC specimen under axial compression load. The load-carrying capacity or strength of uPVC pipe is required later to compare the sum of individual load-carrying capacity (concrete + uPVC) with that of uPVC confined concrete. The equivalent cylinder size specimen was prepared by cutting the uPVC into the required size as shown in Figure 3 and tested using a UTM machine at a rate of 0.2MPa/s.

Specimens preparation
The specimens were prepared according to the parameters considered under the study (see Figure 4 and Table 4). First, a total of 60 unconfined and 60 equivalent concrete-filled uPVC tube cylinders with five different concrete strength classes (cylinder/cube: C12/15, C16/20, C20/25, C25/30, & C28/ 35), five different thickness to diameter ratios (2t/D = 0, 0.043, 0.055, 0.067, & 0.079), and height to diameter ratio of two(h/D = 2) were prepared to investigate the effect of concrete strength and 2t/D ratio of uPVC on the behavior of concrete-filled uPVC tubular cylinders under axial compression    the behavior of concrete-filled uPVC tubular columns under axial compression loads. Third, a wiremesh reinforced mortar cover M3 (1:3) was used to cover the uPVC tube from direct exposure to fire. For that, a total of 6 concrete-filled uPVC tube columns having C25 concrete strength, uPVC diameter (D = 110), aspect ratio (h/D = 2 & 4), and outer wire-mesh reinforced mortar cover was prepared. Fourth, a total of 9 columns (3 plain concrete, 3 reinforced concrete, and 3 concrete-filled uPVC tubes) having C25 concrete strength and aspect ratio (h/D = 4) were prepared to study the effect of uPVC confinement and to compare with reinforced concrete.
The uPVC tubes were prepared by cutting a uPVC through varying the high to diameter ratio (h/ D = 2, 4, 6 & 8). The wet concrete mixes were prepared; and accordingly, concrete cubes (BS EN 12,390-2:2009), concrete cylinders (ASTM C39-12 & C496-11), uPVC confined and unconfined concrete columns were cast by filling the wet concrete mix in three layers and compacting till no bubbles were seen on the surface (BS EN 12,390-2:2009). After 24 hours, the specimens were de-molded, labeled, and cured in water for 28 days. -C1P1H1 means a confined concrete column having a concrete strength of C12/15, the uPVC diameter of 63mm, and an aspect ratio of two (h/D=2).

Specimen labeling
-MC3P3H1 means a confined concrete column having a concrete strength of C20/25, the uPVC diameter of 100mm, the aspect ratio of two (h/D=2), and wire-mesh reinforced mortar cover.   -RC3H2 means RC columns having a concrete strength of C20/25, reinforcing steel, and an aspect ratio of two (h/D=4).

Instrumentation, test setup, and loading program
On day 28, the specimens were brought out from the water, and the two sides of the confined columns were smoothened using a concrete cutting machine to avoid a local buckling of the uPVC tube at the edge, and allowed to dry prior to testing. All the specimens (concrete cubes, concrete cylinders, uPVC confined concrete columns) were tested on the same day. The test was performed using a compression Machine (Servo-Plus Evolution Control Unit), which has a capacity of 2000KkN with a load rate control system and a testing frame with hydraulic loading jack (a load-controlled mechanism) (see Figure 5). Also, a load cell, transducers and strain gages connected to TDS-630 Datalogger were used to capture the measurements as shown in Figure 5. The instrumentation was done by placing two strain gauges on the specimens to measure axial and lateral strains. The specimen was placed in between the two flattens of the compression testing machine, and also in between the upper and lower beam of the testing frame. Two LVDTs (Linear variable differential transducers) were placed vertically pointing to the moving plate of the machine to measure the axial deformation. Then, the strain gauges, load cells, and LVDTs were connected to TDS-630 data logger. The load was applied to the specimen at the rate of 0.2MPa/s till failure.

Load-deformation
For unconfined concrete, the axial deformation was very small, accompanied by a brittle failure after reaching a peak load. The load-carrying capacity increased from a minimum of 12% to a maximum of 65 % for uPVC confined equivalent cylinder having an aspect ratio of two (h/ D = 2) and four different confinements to concrete ratio (2t/D). The confinement performed well for lower concrete strength, increasing the load-carrying capacity up to 65% as shown in Figure 6. The deformation for the tested specimens of uPVC confined concrete columns increased substantially compared to the unconfined columns. At a failure loading, the deformation increased from less than 1 mm for unconfined to a maximum of 28 mm for uPVC confined. Figure 7 shows a sample load-deformation curve of concrete-filled uPVC tube equivalent cylinder. For lower aspect ratios (h/ D = 2 & 4), the concrete-filled uPVC tube column undergone only axial deformation, whereas specimens with an aspect ratio (h/D = 6 & 8) undergone single and double curvature at a peak load as shown in Figure 9. The specimen with uPVC confinement had undergone high deformation after reaching the peak (maximum) load resulting in a ductile failure. The minimum deformation at a failure load registered was 4.7 mm which is by far more than the unconfined concrete (<1 mm). The deformations of all confined concrete cylinders from the peak to failure load were more than 53% of the total deformation, and whereas less than 19% for the unconfined concrete cylinder. When the unconfined concrete columns were loaded beyond the elastic limit, the crack propagated very fast, allowing the columns to undergo sudden and brittle failure. For confined concrete columns, the uPVC tube confinement restrained the crack propagation and the concrete from dilating laterally, allowing the concrete to carry additional loads and undergo ductile failure.

Failure modes and patterns
The failure modes observed for uPVC confined concrete columns under axial compression loads were a drum-type, shear-type (rarely observed), and buckling type failure, as shown in Figures 8  and 9. The hollow uPVC tube failed through local buckling inward and outward under axial compression loads. At a confined state, the uPVC was restrained by concrete from local buckling. Unlike steel, no local buckling of the uPVC tube was seen at an early stage of loading because of the lower Young's modulus elasticity of uPVC. For a uPVC confined concrete specimens, at about 90% to 100% of the peak load, the uPVC starts changing the color from grey to whitish-grey in the middle of the specimen and further developing bumps and strips on the surface. The color change was due to the yielding and elongation of the uPVC pipe. The change in color was dependent on the thickness of the uPVC pipe. The more the thick, the later the change in color or no change in color depending on the strength of the concrete. Failure modes observed were drum, shear and buckling type failure, which were dependent on the failure mode of the concrete core. The drum type failure occurred due to the expanding of the concrete core at the middle resulting from cone type failure, and the shear-type failure occurred due to shear failure of the concrete core. For specimen with a higher aspect ratio (h/D = 6 & 8) in Figure 9(a), a buckling failure with single and double curvature was observed. The uPVC along and around the crack of core concrete has undergone color change, which shows much elongation and plastic deformation of the uPVC tube around the cracked region. In addition to the color change, the specimen developed a pump along the direction of the crack. For a specimen with wire-mesh reinforced mortar Figure 9(b), the delamination of the cover started at about 70% of the peak load.

Confinement effectiveness
The confinement effectiveness is the measure of how the uPVC pipe confines the concrete. It is the ratio of uPVC confined concrete strength to the unconfined concrete strength f cc =f co ð Þ . The effectiveness increased as the 2t/D ratio increases and decreased as the concrete strength increases, as shown in Table 5 and Figure 10. For different 2t/D ratio of the equivalent cylinder (h/D = 2), the confinement effectiveness decreased from a maximum of 2.35 to a minimum of 1.28 as the core concrete strength increased from C15 to C35. Similar researches made by Oyawa et al. (2016) showed that the confinement effectiveness ranged between 1.18 & 3.65 for different concrete strength and pipe sizes.

Effect of Core concrete strength, 2t/D and h/D
As shown in Figures 11 and 13, the strength of uPVC confined concrete increased as 2t/D ratio increased and decreased linearly as the aspect ratio (h/D) increased. The uPVC confinement increased the strength for all five classes of concrete used in this research; however, it showed a decreasing rate as the core concrete strength increased, as shown in Figure 12

Concrete-filled uPVC tubular columns with wire-mesh reinforced mortar cover
The wire-mesh reinforced mortar cover was provided to avoid the uPVC from direct exposure to fire. In Figure 14, the result on peak strength of unconfined and uPVC tube confined with and  without wire-mesh reinforced mortar were presented. The wire-mesh reinforced mortar does not contribute to strength; the strength remains dependent on 2t/D and h/D. For the specimen with wire-mesh reinforced mortar, at about 70 to 85 % of the peak load, the delamination or peeling of the cover started and continued till failure (see Figure 15). After the load reaches the peak, the specimens with aspect ratio less than or equal to four (h/D ≤ 4) have started undergoing drum and shear-type failure and whereas the specimens with aspect ratio above four (h/D > 4) have started undergoing buckling and shear-type failure. The durum and buckling type failure were the most prevalent mode of failure, and whereas shear type failure was a rarely seen failure mode.

Comparison of plain concrete, RC and confined strength
Plain concrete, concrete-filled uPVC tube, and Reinforced concrete circular column were prepared and tested to compare the strength. The concrete strength and reinforcement used to prepare the specimens were C20 concrete, 5ϕ10 mm longitudinal steel, and stirrup of ϕ6 mm @ 130 mm spacing, as shown in Figure 4. The results in Figure 16 shows, RC and concrete-filled uPVC columns have similar strength, but high ductility was observed on concrete-filled uPVC tube columns.

Stress-strain behavior
The stress-strain behavior of unconfined and confined concrete columns are presented in Figures 17, 18, 19, 20 and 21. For unconfined specimen, a brittle failure was observed; the maximum strain recorded at failure load is 0.00376. The strain measured from the peak to the failure load was less than 19% of the total strain. The concrete crack propagated very fast when the unconfined concrete columns were loaded beyond the elastic limit, which caused the columns to undergo sudden and brittle failure. For specimens confined in a uPVC tube, no brittle failure was observed; the specimens underwent high deformation compared to the unconfined. The uPVC tube confinement restrained the crack propagation and the concrete from dilating laterally, allowing the concrete to carry additional loads and undergo ductile failure. Also, the peak strength decreased as the aspect ratio (h/D) increased, which was due to the slenderness effect. For lower aspect ratio (h/d = 2) of concrete-filled uPVC tubular columns, high deformation was observed; the strain measured from the peak to failure load was more than 53%. The aspect ratio significantly affected the post-peak behavior; a gradual drop in the stress-strain curve was observed for lower aspect ratio (see Figure 18). For higher aspect ratios (h/D ≥ 4), an abrupt drop in the stress-strain curve was observed (see Figures 19, 20 and 21).  Figure 15. Behavior of concrete-filled uPVC tube with wire-mesh reinforced mortar cover.

Ductility
Ductility is the ability of the material to undergo inelastic deformation before failure. It is determined by the ratio of the strain at fracture (or strain at the inelastic yield strength demand) to strain at maximum elastic strength (Cui & Sheikh, 2010;Najdanović & Milosavljević, 2014;Wu, 2004;Zhang et al., 2012). Both the unconfined and confined ductility factors were calculated using the expression given in Equation (1) and stress-strain response parameters in Figure 22. The ductility factor was used to study the deformation of the tested specimens, and the results were presented in Tables 5 and 6. The unconfined concrete column suddenly ruptured after reaching the peak load, but the brittle failure was compensated by uPVC confinement. The ductility index was much affected by 2t/D and h/D ratio's; the specimens with higher 2t/D and lower h/D had higher ductility factor. For a confined specimen with h/D = 2, the ductility factor increased by 1.84-15.3 times the unconfined. Apart from the ductility factor, an increase of peak strain from uPVC confinement was observed due to the delay of core concrete cracking and lateral expansion. For  uPVC confined concrete, a brittle failure was not observed; the confinement helped the specimen to undergo ductile deformation and stay for a prolonged period of time.

Energy absorption capacity
Energy absorption is the toughness of the material measured from the stress-strain data. It is the area under a stress-strain curve and measured using the expression given in Equation (2). Energy absorption was reported in different ways depending on the strain value chosen to end the integration (Cui & Sheikh, 2010;Karabinis & Rousakis, 2002;Wang, 2014;Wu, 2004;Zhang et al., 2012). In this study, the energy absorption per volume at 100% strain (ultimate toughness) was calculated for both confined and unconfined specimens, as shown in Tables 5 and 6. OriginPro data analysis software was used to calculate the area under the stress-strain graph, as shown in Figure  23. The uPVC confinement increased energy absorption capacity. For an aspect ratio of h/D = 2, the ratio of confined to unconfined energy absorption per volume E C =E U ð Þincreased from 10.968 to 243.145 times the unconfined.

Work index
The work index is the material capability to undergo straining for the applied load beyond the elastic state. The work index is evaluated by the ratio of the total area under the stress-strain curve until failure to the area of the stress-strain curve under the elastic region, Equation (3). For confined specimens of aspect ratio two (h/D = 2), the calculated work index value ranged from 10.97 to 48.599 and whereas 2.65 to 2.884 for unconfined specimens as shown in Tables 5 and 6. The confinement effect of delaying the core concrete cracking and lateral expansion of the post-elastic region improved the inelastic resistance of concrete-filled uPVC tube column.

Analytical equations on peak strength and strain
The analytical expression for confined concrete that relates the tensile strength and thickness of the confining material, core concrete strength, and the diameter in Equation (4) was developed for the first time in 1928 (Richart et al., 1928). This expression was later modified by many researchers for different types of confining material. The peak strength of concrete-filled uPVC tube columns were dependent on the uPVC thickness to diameter ratio (see Figure 26), core concrete strength (see Figure 26), and aspect ratio (h/D) (see Figure 25). For a circular cross-section, the lateral confining pressure is uniformly distributed on the perimeter.
DÀ2t ð Þ ; f l is lateral confining pressure; f y is tensile strength of uPVC tube; k 1 is the confinement coefficient; D is the diameter of a confined cylinder; t is the thickness of the uPVC tube as shown in Figure 24.
For concrete confined by steel, Richart et al. (1928) assumed a constant value of 4.1 for k 1 in Equation (4). This value was later modified by many researchers for different types of confining material. Balmer (1949) found k 1 value varied between 4.5 and 7 and suggested to use the average value of 5.6 (Balmer, 1949). Although many researchers came up with their own k 1 values and models, it is found that the models are unable to predict the ultimate strength of concrete confined by different materials (Toutanji & Saafi, 2002). In this research, the value of k 1 for each specimen was calculated by using Equation (4) for f co and f cc values obtained from the experiment Figure 22. Stress-strain response parameters used to calculate the ductility factor.  and the lateral confinenig pressure (f l ) calculated for each specimen using the equilibrium conditions. As it is shown in Table 5, Figures 27 and 28, it is found that the value of k 1 decreased as the core concrete strength increased; and increased as the 2t/D ratio decreased. k 1 is dependent on both the concrete strength f co ð Þ and 2t/D ratio.Thus, a regression analysis was done by fitting f co vs k 1 and 2t/D vs k 1 where k 1 was defined as a function of f co and 2t/D. The expressions from the regression analysis were combined to give an expression for k 1 in Equation (5).
Substituting Equation (5) to Equation (4), the strength of uPVC tube confined concrete with an aspect ratio of two (h/D = 2) can be expressed in Equation (6) f cc ¼ f co þ 2:7f l f co ð Þ 0:394 2t=D ð Þ 0:453 As the aspect ratio (h/D) increases from 2 to 8, the peak strength decreased (see Figure 25 and Table 6). The results on two different 2t/D and four h/D ratios used to define the relation of uPVC confined concrete. The strength for specimens with an aspect ratio of two (h/D = 2) can be calculated by Equation (6). for concrete class (C25) confined by 90 and 110 mm uPVC pipe, and the strength calculated by Equation (6) were equivalent to 28.5 and 27 MPa, respectively. A regression analysis was done by fitting h D À 2 À Á vs f cc data where an expression for f cc in Equation (7) and Equation (8)   The general equation in Equation (9) was developed by combining Equation (6), Equation (7), and Equation (8).
The peak strength model was used to predict the peak strength and the values were compared with the experimental test results (see Figure 29). The predicted values were in good agreement Figure 30. Relationship between f l /f cc and ε cc -ε co. with the experimental test results. The model is capable of predicting the peak strength at a mean absolute error (MAE) of 2.7%, Equation (11).

Conclusion
Based on the experiments carried out and the results on strength, ductility, energy absorption, failure mode, and post-peak behavior, the following conclusions are drawn: • The uPVC tube in a concrete-filled uPVC tube column added a substantial contribution to the axial load carrying capacity for specimens prepared from lower concrete strength. For column, with an aspect ratio of two (h/D=2), the load-carrying capacity at a confined state was 1.12-1.65 times the sum of individual capacity at an unconfined state. The confinement coped the concrete dilation; serving the concrete to undergo ductile failure.
• The main failure modes observed were drum, shear and buckling type failure. For lower aspect ratios of the specimens (h/D =2 & 4), drum and shear-type failure modes were observed. The failure modes of uPVC confined columns were much influenced by the type of core concrete failure. The drum type failure occurred due to the expanding of core concrete at the middle from cone type failure whereas the shear-type failure occurred due to shear failure of the core concrete. For higher aspect ratios of the tested specimen (h/D=6 & 8), buckling (single and double curvature) and shear failure occurred. The wire-mesh reinforced mortar cover did not contribute to the strength; the delamination of wire-mesh reinforced mortar cover started around 70-100% of the peak load.
• For an aspect ratio of two, the uPVC tube in a uPVC confined concrete column increased the strength by 1.28 −2.35 times the unconfined column. The effectiveness of the confinement was dependent on the core concrete strength and 2t/D ratio. The effectiveness increased as the core concrete strength decreased, and the 2t/D ratio increased. Also, the confinement performed well for higher aspect ratios as the unconfined column resistance to load reduces abruptly with the increase in aspect ratio (h/D). Figure 31. Relationship between f l /f co and f l /f cc.
• The post-peak stress-strain behavior of uPVC confined concrete proved to be affected by 2t/D ratio and h/D. The absolute value of the slope decreased as the 2t/D ratio increased. The aspect ratio significantly affected the post-peak behavior; a gradual drop in the stress-strain curve was observed for lower aspect ratio whereas an abrupt drop in the stress-strain curve was observed for a higher aspect ratio's (h/D≥4).
• The uPVC confinement increased the ductility and energy absorption of the columns. For h/D ratio of two, the ductility and energy absorption increased by 1.84-15.3 and 11-243 times the unconfined concrete column respectively. The confinement effect of delaying the core concrete cracking and lateral expansion improved the ductility; serving the concrete column to undergo straining beyond the elastic state without failure for a prolonged period of time compared to the unconfined column.
• The stress-strain model predicted the peak strength of the axially loaded concrete-filled uPVC tube column with a mean absolute error of 2.7%.
A ductile failure and high elongation capacity of the uPVC tube is a prominent behavior that attracted the attention to use as a confining material. However, more work is required on the performance of a uPVC confined concrete column.