The Material characterization was completely described in the previous author's work [2], but it is briefly discussed here for clarification purpose. Ordinary Portland Cement (OPC) power plus 42.5N manufactured by Bamburi cement Ltd, Kenya conforming to the European Norm EN 197-1:2011 [23] and locally available natural sand from Masinga river (Kenya) and crushed stone obtained from Mlolongo (Kenya) were used throughout the experiment to prepare the concrete mix. The fine and coarse aggregate material characterization was done according to BS standard and the results are presented in Table 1. The sampling was done according to BS EN 932-1, 1997 [24]. Both the fine and coarse aggregate were graded through sieving and curve plotting according to BS EN 12620: 2013; BS EN 933-1:2012 [25] and BS EN 933-2, 1996 [26]. Un-plasticized polyvinyl chloride (uPVC) pipes produced by Elson plastics ltd. was used for this research. The tensile property of uPVC tube was obtained through a tensile test of dogbone coupon specimens as shown in Fig. (1). The test was done by applying a constant rate of 5mm/min according to ASTM D638 [27] and the results are presented in Table 2.

The concrete mix design and the fresh properties of concrete were completely described in the previous authors' work [2]. The mix designs were prepared based on BS EN 206: 20134 [30] and BS EN 8500-1/2:2012 [31], and are summarized in Table 3. Sampling, slump, density, and compaction factor tests were conducted in accordance with the procedures specified in BS EN 12350-1: 2009 [32], EN 12350-2: 2009 [33], BS EN 12350-6: 2009 [34], and BS 1881-103: 1993 [35] respectively. The results on the concrete mix and fresh properties of concrete are summarized in Tables 3 and 4.

Fig. (1). Dog-bone Coupon specimens prepared from the uPVC tube (based on ASTM D638) [2].

The instrumentation, test setup and loading program were completely described in the previous author's work [2], but are briefly discussed here for clarification purpose. After casting the specimens in water for 28 days, they were brought out from the water and the two sides of the specimens 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 as shown in Fig. (2b) and Fig. (4b). The test was performed using Compression Machine, which has a capacity of 2000kN and a testing frame with hydraulic loading jack connected to it as shown in Fig. (5). In addition, a load cell, transducers and strain gages connected to TDS-630 Datalogger were used to capture the measurements. First, the two strain gauges were placed on the surface of the specimen to measure the axial and radial strains. Then, 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. After carefully placing the specimen in the testing machine, 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. The data was recorded both from the compression machine (Load-time data, Max. Load & Max. Strength) and TDS-630 Datalogger (time, Load, axial strain, radial strain, & displacement).

Fig. (3). (a) Single Layer (b) Double Layer (double skin).

Fig. (4). (a) Before concrete pouring, (b) Double skin.

Fig. (5). Test set-up.

The failure modes of single and double skin concrete filled uPVC tube specimens are shown in Figs. (6, 7 and 8). In contrast to the un-confined ones , all the confined (single and double skin) specimens showed a ductile failure. The Concrete-Filled Single Skin uPVC Tubular (CFSUT) specimens experienced drum, shear and buckling type failure. Different types of failure progression were observed in Concrete-Filled Double Skin uPVC Tubular (CFDUT) specimens, which are outward expansion making a drum type failure with local buckling of internal uPVC tube. Fig. (6a) shows the drum and shear-type failure modes of single skin concrete filled uPVC tube specimens. Drum type failure mode is the most prevalent type of failure observed during the experiment. The drum type failure mode is due to the type 2 and 3 failure modes (ASTM C39/C39M − 15a) of the core concrete. The shear-type failure mode was a observed event. The diagonal cracks of the concrete due to type 4 failure (ASTM C39/C39M − 15a) created the shear-type failure. Further loading the specimen pushed the two halves in the opposite direction on the inclined plane, creating a bump like structure. Fig. (7) shows the failure mode of double skin concrete filled uPVC tube specimens. The specimen expanded outside similar to the single skin creating drum-type failure. The internal tube has undergone local buckling (Fig. 7). Buckling type failure mode was observed for higher aspect ratios for both single and double skin concrete filled uPVC tube specimens (Fig. 8).

Figs. (9 and 10) show the strength and strain enhancement ratio of unconfined concrete and single and double skin concrete-filled uPVC tube specimens. For both single and double skin specimens, the strength increased by more than 30% compared to the unconfined specimens. Similar researches that were done on single skin concrete-filled uPVC tube equivalent cylinders by Woldemariam et al. [2] showed that the strength enhancement ratio ranged was between 1.28 and 2.35 for different concrete strength and pipe size. Fig. (10a) shows the strain enhancement ratio of single skin and double skin concrete filled uPVC tube specimens at the peak load. For single and double skin specimens, the strain at peak load increased by more than 3 times compared to the unconfined specimen. Fig. (10b) shows the strain enhancement ratio of single and double skin at the failure load. It was observed that the strain at failure load increased by more than 9 times compared to the unconfined specimens.

Fig. (6). Failure modes of single skin concrete filled uPVC tube specimens: (a) drum type, (b) shear.

Fig. (7). Failure modes of double skin concrete filled uPVC tube specimens (outward expansion and inner tube local buckling.

Fig. (8). Failure modes of single and double skin concrete filled uPVC tube specimens for higher aspect ratios.

Fig. (9). Strength enhancement ratio .

The recorded axial strength of concrete filled double skin uPVC tubular (CFDUT) specimens is presented in Table 7, Figs. (11 and 12). The axial strength of (CFDUT) was obtained by testing the specimen under axial compression and compared with concrete filled single skin uPVC tubular (CFSUT) specimens. Figs. (11 and 12) show the relationship between the strength of single and double skin concrete-filled uPVC tube. For single skin, two types of uPVC tube size with a thickness of 3mm and a diameter of 110 and 140mm were used to prepare the specimens. The strength of (CFSUT) specimens were 26.99 and 24.57MPa. The strength decreased as the 2t/D ratio increased. The double skin specimen (CFDUT) was prepared from two uPVC tubes of the same height and different diameter where concrete is sandwiched in between the two tubes, as shown in Fig. (3b). To study the effect of hollow ratios on the axial strength, two different diameters of outer tubes (110 and 140mm) and inner (63 and 75mm) were used to prepare the specimens. The strength of the specimens decreased as the hollow ratio (d/D) increased.

Fig. (10). Strain enhancement ratio at (a) peak strength , (b) at failure .

Fig. (11). Effect of hollow ratio on the strength.

Fig. (12). Effect of overall thickness on the strength.

Fig. (13). Effect of aspect ratio (h/D) on strength.

Woldemariam et al. [2] have developed an analytical expression for concrete-filled single skin uPVC tube equivalent cylinders that relates the concrete strength, tensile strength, diameter, and thickness of the confining material as shown in Eq. (1):

(1)

An expression for double skin concrete-filled uPVC tube equivalent cylinder was developed based on Figs. (11 and 12) and Eq. 1. The results on two different 2t/D and three d/D ratios are used to define the relation in Eq. 2 and 3.

(2)

(3)

From the above two equations (Eq. 2 and 3), the two constants are equal to the peak strength of (p=90 &110mm) concrete filled single skin uPVC tubular specimens with h/D =2 and can be calculated by the expression in Eq. 1. The coefficients (coef 1 = -4.0003 & coef 2 = -9.1117) are dependent on 2t/D.

Thus, the strength of double skin concrete-filled uPVC tube specimen can be calculated by the expression in Eq. 4.

(4)

Fig. (13) shows the effect of aspect ratio (h/D) on strength. The strength decreased as the aspect ratio increased. An expression to predict the strength of double skin concrete filled uPVC tube specimens for different aspect ratios is developed. As the aspect ratio (h/D) increased from 2 to 6, the peak strength decreased, as shown in Fig. (13) and Table 7. The results of two different 2t/D and three h/D ratios are used to define the relation shown in Eq 5.

(5)

(6)

From the above equation (Eq. 5 and 6), the two constants are equal to the peak strength of (p=90 &110mm) double skin concrete-filled uPVC tube with h/D =2 in Eq. 4. The coefficients (coef 1= -1.2661 & coef 2= -0.9755) are dependent on 2t/D. Hence, .

The general equation in Eq 7. was developed by combining Eq. 4, Eq. 5, and Eq. 6.

(7)

The model in Eq. 7 was used to predict the peak strength, compared with the experimental result (Fig. 14). The accuracy of the model was evaluated by using an Average Absolute Error (AAE), as defined in Eq. 8. The proposed model predicted the peak strength reasonably well with an AAE of 2.13%.

(8)

Fig. (15) shows the stress-strain behavior of unconfined concrete equivalent cylinders. The unconfined specimen has undergone a brittle failure after reaching the peak strength whereas both the single and double skin specimens have undergone a ductile failure without a sudden strength loss. Figs. (16 and 17) show the stress-strain curve of single and double skin concrete-filled uPVC tube specimens under axial compression load. The result shows that both single and double skin have exhibited similar behavior. When the h/D ratio was increased from 2 to 6, the specimens exhibited a post-peak displacement softening with a strength loss, as shown in Fig. (17e, f).

Fig. (14). Performance of the model in predicting the peak strength.

Fig. (15). Stress-Strain curve of the unconfined concrete cylinder of C25.

Fig. (16). Stress-strain curve for single skin concrete-filled uPVC specimen with a diameter of (a) 110mm, (b) 140mm.

Fig. (17). Stress-strain curve for double skin concrete-filled uPVC specimen.

3.5.1. Ductility and Energy Absorption

Fig. (18) shows the parameters used to calculate the ductility factor and energy absorption. The ductility factor is the ratio of strain at fracture strength to strain at maximum elastic strength [36-39] and it was calculated by the expression given in Eq. 9. Fig. (19) and Table 8 demonstrates the results on the ductility factor of unconfined concrete, single skin and double skin concrete-filled uPVC tube specimens. For single and double skin specimens, the ductility factor increased by 3.7 to 23.45 times compared to the unconfined concrete specimens.

Fig. (18). Stress-strain response parameters used to calculate the ductility factor and energy absorption.

Fig. (19). Ductility factor for unconfined, single and double skin specimens.

Table 8. Average maximum strength, strain, strength enhancement, energy absorption, and ductility Factor.

Label	fco	fcc	εco	εcc	ε1	εcr	fcc/fco	εcc/εco	μcr	E
C3	16.89		0.0029		0.0017	0.0033			1.89	0.038
C3P3H1		26.99		0.0098	0.0033	0.0515	1.60	3.43	15.85	1.14
C3P4H1		24.57		0.0094	0.0050	0.0650	1.45	3.32	13.00	1.11
C3P3H2		24.59		0.0331	0.0060	0.10000	1.02	10.18	16.67	1.99
C3P3H3		23.15		0.0175	0.0060	0.06580	0.96	5.40	30.54	1.18
C3P3H4		20.98		0.0187	0.0055	0.08600	0.87	5.76	16.23	1.29
C3D1H1		22.27		0.0130	0.0065	0.0458	1.32	4.56	7.05	0.79
C3D2H1		22.29		0.0090	0.0020	0.0314	1.32	3.16	15.69	0.59
C3D3H1		23.49		0.0130	0.0020	0.0891	1.39	4.56	44.56	1.73
C3D1H2		20.14		0.0045	0.0015	0.0234	1.19	1.56	15.61	0.29
C3D1H3		18.37		0.0124	0.0044	0.0151	1.09	4.35	3.43	0.21
C3D3H2		20.71		0.0084	0.0040	0.0247	1.23	2.95	6.17	0.39
C3D3H3		18.43		0.0255	0.0130	0.0340	1.09	8.94	2.62	0.47

Fig. (20). Energy absorption for unconfined, single and double skin specimens.

The energy absorption is the area under the stress-strain curve [36, 38-41] and it was obtained by integrating the stress-strain curve (see Eq.10). Fig. (20) and Table 8 shows the results on the energy absorption capacity of unconfined concrete, single and double skin concrete-filled uPVC tube specimens under axial compression loads. The energy absorption capacity of single and double skin specimens increased by 14.75 to 43.25 times compared to the unconfined concrete specimens.

(9)

(10)