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Behavior and Three-Dimensional Finite Element Modeling of Circular Concrete Columns Partially Wrapped with FRP Strips Junjie Zeng

ID

, Yongchang Guo *, Lijuan Li and Weipeng Chen

School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou 510006, China; [email protected] (J.Z.); [email protected] (L.L.); [email protected] (W.C.) * Correspondence: [email protected]; Tel.: +86-203-9322-538 Received: 21 January 2018; Accepted: 27 February 2018; Published: 1 March 2018

Abstract: Fiber-reinforced polymer (FRP) jacketing/wrapping has become an attractive strengthening technique for concrete columns. Wrapping an existing concrete column with continuous FRP jackets with the fiber in the jacket being oriented in the hoop direction is referred to as FRP full wrapping strengthening technique. In practice, however, strengthening concrete columns with vertically discontinuous FRP strips is also favored and this technique is referred to as FRP partial wrapping strengthening technique. Existing research has demonstrated that FRP partial wrapping strengthening technique is a promising and economical alternative to the FRP full wrapping strengthening technique. Although extensive experimental investigations have hitherto been conducted on partially FRP-confined concrete columns, the confinement mechanics of confined concrete in partially FRP-confined circular columns remains unclear. In this paper, an experimental program consisting of fifteen column specimens was conducted and the test results were presented. A reliable three-dimensional (3D) finite element (FE) approach for modeling of partially FRP-confined circular columns was established. In the proposed FE approach, an accurate plastic-damage model for concrete under multiaxial compression is employed. The accuracy of the proposed FE approach was verified by comparisons between the numerical results and the test results. Numerical results from the verified FE approach were then presented to gain an improved understanding of the behavior of confined concrete in partially FRP-confined concrete columns. Keywords: finite element (FE) analysis; plastic-damage model; circular column; FRP; partially FRP-confined concrete; confinement

1. Introduction Over the past two decades, fiber-reinforced polymer (FRP) has become a favorite material for the strengthening of existing concrete columns. The FRP strengthening technique for a concrete column is predominantly referred to as FRP full wrapping strengthening technique in which an existing deteriorated concrete column is fully wrapped with FRP jacket along the height of the column (Figure 1a). The resulting column of this strengthening technique is referred to as a fully FRP-confined concrete column. Existing research has demonstrated that the compressive strength and ductility of circular columns fully wrapped with FRP jackets are substantially enhanced [1–14]. Alternatively, partially FRP-confined concrete columns, usually wrapped with FRP strips, refer to FRP-confined concrete columns with discontinuous FRP jackets along their longitudinal axis (Figure 1b). Strengthening existing columns by FRP partial wrapping are hereafter referred to as FRP partial wrapping strengthening technique. Although most studies related to FRP-confined concrete columns are on fully FRP-confined concrete columns, partially FRP-confined concrete columns have also been demonstrated to possess adequate increase in strength and excellent increase in ductility compared Polymers 2018, 10, 253; doi:10.3390/polym10030253

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also been demonstrated to possess adequate increase in strength and excellent increase in ductility with its corresponding un-confined columns (e.g., [15]).(e.g., Under certain partially compared with its corresponding un-confined columns [15]). Undercircumstances, certain circumstances, FRP-confined concrete columns are comparatively favorable, especially for columns only requiring partially FRP-confined concrete columns are comparatively favorable, especially for columns only considerable increase inincrease axial deformation capacity. Additionally, less FRP materials arematerials required are for requiring considerable in axial deformation capacity. Additionally, less FRP partially FRP-confined concrete columns while FRP partial wrapping strengthening technique can required for partially FRP-confined concrete columns while FRP partial wrapping strengthening be appliedcan more and faster than FRP full than wrapping strengthening technique [16]. The interest technique be easily applied more easily and faster FRP full wrapping strengthening technique [16]. in understanding the behavior of partially FRP-confined concrete has led to several experimental The interest in understanding the behavior of partially FRP-confined concrete has led to several studies on partially FRP-confined columnsconcrete [15,17–25]. The research has demonstrated experimental studies on partiallyconcrete FRP-confined columns [15,17–25]. The research that has the FRP partial wrapping increases both strength and ductility of concrete. The existing test results demonstrated that the FRP partial wrapping increases both strength and ductility of concrete. The enable and available design guidelines for partially FRP-confined existingthe testverification results enable theassessment verificationofand assessment of available design guidelines for partially concrete columns [26,27] in which a longitudinal confinement effectiveness factor based on “arching FRP-confined concrete columns [26,27] in which a longitudinal confinement effectiveness factor action” [28,29] is suggested for partially FRP-confined concrete so that the partially FRP-confined based on “arching action” [28,29] is suggested for partially FRP-confined concrete so that the partially concrete columns can becolumns designed with appropriate accuracy. FRP-confined concrete can be designed with appropriate accuracy.

(a)

(b)

Figure 1. 1. Fully and partially partially FRP-confined FRP-confined concrete. concrete. (a) Partially Figure Fully and (a) Fully Fully FRP-confined FRP-confined concrete; concrete; (b) (b) Partially FRP-confined concrete. FRP-confined concrete.

In real application, however, the lateral confinement can be provided by many different In real application, however, the lateral confinement can be provided by many different approaches, including simple transverse steel reinforcement (e.g., [28–30]), steel cage (e.g., [31,32]), approaches, including simple transverse steel reinforcement (e.g., [28–30]), steel cage (e.g., [31,32]), steel tube (e.g., [33]), FRP (e.g., [20,34,35]), shape memory alloy (e.g., [36,37]), and active confinement steel tube (e.g., [33]), FRP (e.g., [20,34,35]), shape memory alloy (e.g., [36,37]), and active confinement techniques such as post-tensioned metal straps (e.g., [38,39]). In these structures, concrete receives techniques such as post-tensioned metal straps (e.g., [38,39]). In these structures, concrete either uniform or non-uniform confinement from its confining mechanism. In particular, the receives either uniform or non-uniform confinement from its confining mechanism. In particular, confinement to the confined-concrete in fully wrapped axial loaded circular columns is uniform. the confinement to the confined-concrete in fully wrapped axial loaded circular columns is uniform. However, concrete under non-uniform confinement is more commonly seen in practice, such as FRPHowever, concrete under non-uniform confinement is more commonly seen in practice, such as confined concrete in square columns or confined concrete subjected to eccentric compression [40]. As FRP-confined concrete in square columns or confined concrete subjected to eccentric compression [40]. for partially FRP-confined concrete in circular columns, the confinement is non-uniform along the As for partially FRP-confined concrete in circular columns, the confinement is non-uniform along the height due to the usage of discontinuous FRP strips [29]. The consequence of the usage of height due to the usage of discontinuous FRP strips [29]. The consequence of the usage of discontinuous discontinuous FRP strips is the less effective confinement between the two adjacent FRP strips, which FRP strips is the less effective confinement between the two adjacent FRP strips, which was assumed was assumed to arise from the “arching action” between two adjacent confining strips/hoops (Figure to the the “arching between adjacent confining strips/hoops (Figure is 2).believed As a result, 2).arise As afrom result, axial action” deformation of two partially FRP-confined concrete columns to the axial deformation of partially FRP-confined concrete columns is believed to concentrate at or near concentrate at or near the mid-plain of two adjacent FRP strips (Figure 3) where the confinement from the adjacent FRP strips (Figure 3) where the confinement from the FRP strips is weak. the mid-plain FRP stripsof is two weak.

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bf bf sf' sf sf' sf

FRP FRP

A A

D' D' D D (a) (a)

A A

D' =D- s'f' /2 D' =D- sf /2 D D Section A-A Section A-A(b) (b)

Figure 2. Effective confinement area in a circular column partially wrapped with FRP. (a) Arching Figure 2. 2. Effective Effective confinement confinement area area in in aa circular circular column column partially partially wrapped wrapped with with FRP. FRP. (a) (a) Arching Arching Figure action; (b) Effective Effective confinement confinement area area at at the thecenter centerlevel levelof ofaastrip. strip. action; (b) action; (b) Effective confinement area at the center level of a strip.

Mid-plain of Mid-plain of each FRP strip each FRP strip Mid-plain of two Mid-plain of two adjacent FRP strips adjacent FRP strips Mid-plain of Mid-plain of each FRP strip each FRP strip Mid-plain of two Mid-plain of two adjacent FRP strips adjacent FRP strips Mid-plain of Mid-plain of each FRP strip each FRP strip Figure 3. Illustration of the mid-plain of each FRP strip and the mid-plain of two adjacent FRP strips. Figure 3. 3. Illustration Figure Illustrationof ofthe themid-plain mid-plainof ofeach eachFRP FRP strip strip and and the the mid-plain mid-plain of of two two adjacent adjacent FRP FRP strips. strips.

To obtain in-depth understanding of partially FRP-confined concrete, the strains and stresses obtain in-depth understanding of partially FRP-confined concrete, the stresses alongTothe generatrix (column height) need to be understood appropriately. Thestrains strainsand distribution along the generatrix (column height) need to be understood appropriately. The strains distribution

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To obtain in-depth understanding of partially FRP-confined concrete, the strains and stresses along the generatrix (column height) need to be understood appropriately. The strains distribution along the column height can be tackled by several strain gauges or particle image velocimetry (PIV) technique. However, laboratory tests were incapable of clarifying the distribution of stresses (axial stresses and confining pressures) along the column height, because of the limitations of laboratory measurements. To overcome the obstacles associated with laboratory studies as noted previously, a robust three-dimensional (3D) finite element (FE) approach based on improved concrete plastic-damage model (CDPM) [41] was employed. Compared with some other 3D FE models (e.g., [42,43]), this 3D FE model was shown to be more reasonable and accurate in modeling of concrete under non-uniform confinement from an FRP jacket owing to the improved CDPM constitutive model. The improvement of this CDPM model included three main aspects [41,44]: a yield criterion related to the third deviatoric stress invariant, a confinement-dependent hardening rule and a confined-dependent non-associated flow rule. This model was successfully implemented in ABAQUS for the FE analysis of FRP-confined circular/square concrete columns and hybrid FRP-concrete-steel double-skin tubular columns under concentric compression [41]. The model has subsequently been utilized by some other researchers (e.g., [40,45–47]) and it was found that this model is capable of providing reasonable stress-strain responses for FRP-confined concrete under both uniform and non-uniform confinement [40,48]. Against the above background, an experimental program was conducted to study axial compressive behavior of circular columns wrapped with CFRP strips. In total, 15 columns were fabricated and tested. The PIV technique was utilized to measure strains in the specimens. The test results of the experimental program were presented and discussed. The improved CDPM was employed for FE analysis of partially FRP-confined concrete columns. The accuracy of the proposed FE approach was verified by comparing the numerical results and the test results. The axial and confining pressure distributions based on numerical results were presented to verify the existing “arching action” and to illustrate the confinement mechanics of partially FRP-confined concrete. 2. Experimental Program 2.1. Test Specimens A total of 15 cylindrical column specimens were prepared and tested to investigate the behavior of partially FRP-confined circular columns. All specimens had a diameter of 150 mm and a height of 300 mm. The main column parameters investigated in present study are the FRP strip width, clear spacing of two adjacent FRP strips and FRP thickness. The column specimens were wrapped with different numbers of FRP strips (3, 4 and 5 strips) with different widths (i.e., 25, 30, and 35 mm) and thicknesses (1, 2 and 3 layers). The design of strip number and strip width led to nine different clear spacing ratios in present study (Table 1). Note that the ratio between the clear spacing of the two adjacent FRP strips and the center-to-center spacing of adjacent strips is referred to as clear spacing ratio (sf0 /sf ) (Figure 1). The details about the test columns (including the clear spacing of the two adjacent FRP strips, FRP volumetric ratio and FRP thickness) are given in Table 1. Each column was given a name (Table 1), which starts with the letter “S” to represent “Specimen”, followed by a number indicating the number of FRP layer/layers. This is then followed by a number presenting the total number of FRP strips and then followed by the width of FRP strips.

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Table 1. Key information of test columns and key test results. Specimen tf (mm) S-1-3-25 S-1-3-30 S-1-3-35 S-2-3-30 S-3-3-30 S-1-4-25 S-1-4-30 S-1-4-35 S-2-4-30 S-3-4-30 S-1-5-25 S-1-5-30 S-1-5-35 S-2-5-30 S-3-5-30

0.167 0.167 0.167 0.334 0.501 0.167 0.167 0.167 0.334 0.501 0.167 0.167 0.167 0.334 0.501

sf0

æf

0 fcc (MPa)

εcc

0 fcu (MPa)

fflcu

0 0 fcu /fco

112.5 110 97.5 110 110 66.67 60 53.33 60 60 43.75 37.5 31.25 37.5 37.5

0.0008 0.0010 0.0012 0.0021 0.0029 0.0012 0.0015 0.0018 0.0030 0.0045 0.0016 0.0020 0.0024 0.0040 0.0059

23.49 23.46 24.30 29.44 27.87 / / / / / / / / / /

0.0030 0.0033 0.0029 0.0049 0.0083 / / / / / / / / / /

22.0 21.8 23.0 26.7 25.4 24.5 27.1 30.5 33.2 41.0 29.8 33.5 36.7 42.4 41.0

0.0072 0.0110 0.0119 0.0158 0.0174 0.0103 0.0245 0.0169 0.0116 0.0328 0.0186 0.0197 0.0188 0.0247 0.0328

0.94 0.93 0.98 1.14 1.09 1.05 1.16 1.30 1.42 1.75 1.27 1.43 1.57 1.81 1.75

fflcu /fflco εh,rup 2.88 4.40 4.76 6.32 6.96 4.12 9.80 6.76 4.64 13.12 7.44 7.88 7.52 9.88 13.12

−0.0083 −0.0119 −0.0103 −0.0119 −0.0107 −0.0099 −0.0113 −0.0141 −0.0072 −0.0171 −0.0179 −0.0145 −0.0184 −0.0164 −0.0171

Note: tf —FRP thickness; sf0 —clear spacing of two adjacent FRP strips; ρf —FRP volumetric ratio.

2.2. Preparation of Specimens and Material Properties Normal concrete made of river sand and natural gravels was utilized to cast the column specimens. Standard cylinders were also cast with the same batch concrete to determine the mechanical properties of the unconfined concrete. After the concrete columns had been cured at room temperature for 28 days, columns were wrapped with carbon FRP (CFRP) strips using a wet layup process, with fibers oriented only in the hoop direction. A 150-mm-long overlapping zone between the starting end and the finishing end of each strip could ensure the fully-developed tensile strength of the FRP. Unidirectional high-tensile-strength carbon fiber sheets, with a nominal layer thickness of 0.167 mm, were utilized to form the FRP strips. FRP tensile tests were conducted to determine the material properties of FRP strips. In the tensile test, a unidirectional one-layer CFRP coupon was employed. The test procedure followed what is specified by the ASTM standard [49]. Five flat coupons were tested, and results were only based on coupons failed by FRP rupture at the middle. The average modulus of elasticity, tensile strength, and rupture strain of single-layer CFRP were found to be 249.1 GPa, 4477.6 MPa and 1.66%, respectively. The concrete mix proportioning is 1:0.71:2.02:3.59 (cement:water:fine aggregate:coarse aggregate). The properties of unconfined concrete were obtained from compression tests on three standard 0 and concrete cylinders in accordance with ASTM C469 [50] and the unconfined concrete strength f co 0 strain εco is determined by the compressive strength and strain of concrete cylinders (i.e., f c and εc ). The compressive strength, strain at compressive strength and Poisson’s ratio of concrete cylinders were found to be 23.5 MPa, 0.0025 and 0.2, respectively. 2.3. Optical Strain Measurement Particle image velocimetry (PIV) system is a novel digital correlation technique (hereafter this text will be abbreviated to PIV technique) that was originally developed in the field of experimental fluid mechanics by tracking the location of seed particles [51]. Based on the image-processing technique of normalized cross-correlation (i.e., principles of PIV), White et al. [52] implemented PIV in geotechnical tests (geoPIV) by tracking the texture (i.e., the spatial variation of brightness) of geoPIV test patches instead of seed particles. A displacement field can then be calculated from the correlation of a reference surface and a displaced or deformed surface. It is worth noting that validation experiments using the PIV code reported by White et al. [53] have demonstrated that the precision of this measurement technique is typically better than 1/10th of one pixel and the strain precision of the technique is a function of the size of the image, the resolution of the cameras used, and the chosen gauge length. Recently, some researchers [54–57] employed PIV technique to catch axial and hoop strain distribution in FRP jacket of FRP-confined concrete columns because this technique is capable of measuring strains in a patch with a certain area simultaneously.

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gauge length. length. Recently, Recently, some some researchers researchers [54–57] [54–57] employed employed PIV PIV technique technique to to catch catch axial axial and and hoop hoop gauge strain distribution in FRP jacket of FRP-confined concrete columns because this technique is capable strain distribution in FRP jacket of FRP-confined concrete columns because this technique is capable Polymers 2018, 10,strains 253 6 of 29 of measuring measuring in aa patch patch with with aa certain certain area area simultaneously. simultaneously. of strains in To further further validate validate the the optical optical strain strain measurement measurement technique technique for for the the current current PIV PIV application, application, aa To standard concrete cylinder (150 mm in diameter and 300 mm in height) fully confined with aa oneonestandard concrete cylinder mmstrain in diameter and 300technique mm in height) fully confined with To further validate the(150 optical measurement for the current PIV application, layer CFRP CFRP jacket jacket was was tested tested under under axial axial compression. compression. In In the the test, test, both both PIV PIV technique technique and and layer a standard concrete cylinder (150 mm in diameter and 300 mm in height) fully confined with a one-layer conventional strain measurement technique were utilized to measure axial and hoop strains: four conventional strain measurement technique were In utilized to both measure and hoop strains: four CFRP jacket was tested under axial compression. the test, PIV axial technique and conventional strain gauges gauges were were installed installed on on the the FRP FRP jacket jacket at at the the mid-height: mid-height: two two at at 180 180 degrees degrees apart apart around around the the strain strain measurement technique were utilized to measure axial and hoop strains: four strain gauges circumference were were utilized to to measure hoop hoop strains strains and and the other other two two were were utilized utilized to to measure measure axial axial circumference were installed on theutilized FRP jacketmeasure at the mid-height: two at the 180 degrees apart around the circumference strains near the hoop strain gauges; two linear variable differential transformers (LVDTs) (TML, strains near the hoop strain twothe linear differential (TML, were utilized to measure hoopgauges; strains and othervariable two were utilized totransformers measure axial(LVDTs) strains near the Tokyo, Japan) Japan) with with aa gauge gauge length length of of 120-mm 120-mm at at 180 180 degrees degrees apart apart were were utilized utilized to to measure measure the the axial axial Tokyo, hoop strain gauges; two linear variable differential transformers (LVDTs) (TML, Tokyo, Japan) with a shortenings (Figure 4). 4). An overlap overlap length length of of 150 mm mm was was utilized utilized in in all all these these cylinders. cylinders. An An additional shortenings gauge length(Figure of 120-mmAn at 180 degrees apart150 were utilized to measure the axial shorteningsadditional (Figure 4). 25-mm-wide FRP strip was wrapped at each end of the cylinder to avoid premature local failure. The The 25-mm-wide FRP strip was wrapped at each of the cylinder An to avoid premature local failure. An overlap length of 150 mm was utilized in end all these cylinders. additional 25-mm-wide FRP strip unconfined concrete concrete strength and and the the axial axial strain strain at peak peak axial axial stress stress from from three three unconfined unconfined concrete concrete unconfined was wrapped at eachstrength end of the cylinder to avoidatpremature local failure. The unconfined concrete cylinder tests were 28.9 and 0.0025 MPa, respectively. The stress-strain curves of these CFRP-confined cylinder teststhe were 28.9 and 0.0025 The unconfined stress-strainconcrete curves of these CFRP-confined strength and axial strain at peakMPa, axialrespectively. stress from three cylinder tests were 28.9 concrete cylinders cylinders from from both both the the PIV PIV and and conventional conventional sources sources are are shown shown in in Figure Figure 5. 5. Note Note that that the the concrete MPa and 0.0025, respectively. The stress-strain curves of these CFRP-confined concrete cylinders from axial strain strain was was from the the LVDTs LVDTs and and the visual visual strain strain gauges gauges were were located located besides the the conventional conventional axial both the PIV andfrom conventional sourcesthe are shown in Figure 5. Note that the besides axial strain was from the foil strain gauges (Figure 4). It is clearly seen from Figure 5 that the strains from both sources are in in foil strain gauges (Figure 4). It is clearly seen from Figure 5 that the strains from both sources are LVDTs and the visual strain gauges were located besides the conventional foil strain gauges (Figure 4). close agreement, demonstrating a good reliability of the PIV technique. The technique was thus close agreement, demonstrating good reliability of sources the PIVare technique. The technique was thus It is clearly seen from Figure 5 thatathe strains from both in close agreement, demonstrating employed in this study to measure the hoop and axial strain distribution of partially FRP-confined employed in this of study to measure theThe hoop and axial strain partially FRP-confined a good reliability the PIV technique. technique was thus distribution employed inof this study to measure the concrete columns. columns. concrete hoop and axial strain distribution of partially FRP-confined concrete columns.

Figure 4. Location of of cameras, cameras, foil foil strain strain gauges LVDTs in Figure 4. Location Location of cameras, foil strain gauges and and LVDTs LVDTs in the the verification verification test. test. Figure in the verification test.

Figure 5. 5. Stress-strain Stress-strain curves curves of of FRP-confined FRP-confined concrete and foil foil gauges. gauges. concrete from Figure from visual visual and and foil gauges.

Figure 6 provides schematic diagrams showing the instrumentations for the column tests. Digital images with the field of view shown in Figure 6a were captured every three seconds during the loading, employing a Canon 5D-Mark II digital camera (Canon, Tokyo, Japan). The camera was

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Figure 6 provides schematic diagrams showing the instrumentations for the column tests. 7 of 29 Digital images with the field of view shown in Figure 6a were captured every three seconds during the loading, employing a Canon 5D-Mark II digital camera (Canon, Tokyo, Japan). The camera was electronically synchronized synchronizedby bycontrolling controllingthe theframe framerate rateusing usingaadigital digitalinput/output input/output channel channel which which electronically allowed the the load/strain load/strain data acquisition system to trigger the cameras cameras during during testing. testing. The The horizontal horizontal allowed line linking linking the the center center of of the the camera camera lens lens is is perpendicular perpendicular to to the the longitudinal longitudinal physical physical axis axis of of the the line specimenand andthe thelocation locationofof the camera is shown in Figure 6b. The system of acquisition PIV acquisition has specimen the camera is shown in Figure 6b. The system of PIV has been been carefully adjusted the formal testand starts any dislevelment and inclination not carefully adjusted before before the formal test starts anyand dislevelment and inclination were notwere allowed allowedthe during during tests. the tests.

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(a)

(b)

(c)

Figure 6. 6. Instrumentations. Instrumentations. (a) (a) Location Location of of cameras, cameras, foil foil strain strain gauges gauges and and LVDTs; LVDTs; (b) (b) The The system system of of Figure PIV image image acquisition; acquisition; (c) (c) Visual Visualgauges gaugesand andfoil foilgauges. gauges. PIV

For the strain measurement using particle image velocimetry, an image-processing algorithm For the strain measurement using particle image velocimetry, an image-processing algorithm which uses normalized cross-correlation was utilized to calculate virtual axial and hoop strains along which uses normalized cross-correlation was utilized to calculate virtual axial and hoop strains along a vertical line for each of the three camera views. The details of the image analysis are not within a vertical line for each of the three camera views. The details of the image analysis are not within scope of attention of current study, but essentially the technique defines regions of interest, called scope of attention of current study, but essentially the technique defines regions of interest, called patches, in the first image of each set, and then used a specialized algorithm to track the patches, in the first image of each set, and then used a specialized algorithm to track the displacements displacements of each patch in subsequent images. A high-contrast image texture is required to of each patch in subsequent images. A high-contrast image texture is required to ensure that each pixel ensure that each pixel patch contains sufficient pixel color variations for the algorithm to track patch contains sufficient pixel color variations for the algorithm to track successfully in subsequent images. The surfaces of these specimens were sprayed with black paint while the texture was formed

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successfully in subsequent images. The surfaces of these specimens were sprayed with black paint by white A schematic diagram showing of the particle texture in thedetails patch used strain while thepaint. texture was formed by white paint.details A schematic diagram showing of thefor particle measurements is given in Figure 7. texture in the patch used for strain measurements is given in Figure 7.

Figure 7. 7. Particle texture on on the the specimen. specimen. Figure Particle texture

2.4. Experimental Setup 2.4. Experimental Setup All specimens were tested under concentric compression using a loading machine (SHIJIN, All specimens were tested under concentric compression using a loading machine (SHIJIN, Jinan, Jinan, China) with a load-carrying capacity of 5000 kN (Figure 6b). Each of the column ends were China) with a load-carrying capacity of 5000 kN (Figure 6b). Each of the column ends were leveled leveled using high-strength gypsum mortar so that the axial load could be simultaneously applied using high-strength gypsum mortar so that the axial load could be simultaneously applied on the on the whole section. To ensure the centering of the specimen, each specimen was loaded to around whole section. To ensure the centering of the specimen, each specimen was loaded to around 30% of its 30% of its unconfined column strength to check the test alignment. Calibration was carried out by unconfined column strength to check the test alignment. Calibration was carried out by examining the examining the readings from the two vertical strain gauges. The specimen was unloaded, realigned, readings from the two vertical strain gauges. The specimen was unloaded, realigned, and loaded again and loaded again if the readings differ each other by 10% at the time the applied load reached about if the readings differ each other by 10% at the time the applied load reached about 30% of its unconfined 30% of its unconfined column strength. Column compression test was realized using displacement column strength. Column compression test was realized using displacement control with a rate of control with a rate of 0.4 mm/min was used. In addition to the cameras, four strain gauges (HYCSYQ, 0.4 mm/min was used. In addition to the cameras, four strain gauges (HYCSYQ, Taizhou, China) Taizhou, China) were adopted to obtain the strains in FRP. Two of them were utilized to measure the were adopted to obtain the strains in FRP. Two of them were utilized to measure the hoop strains hoop strains and the other two were employed to measure the axial strains, as is seen in Figure 6c. and the other two were employed to measure the axial strains, as is seen in Figure 6c. The full-height The full-height axial shortening was measured using the linear variable differential transformers axial shortening was measured using the linear variable differential transformers (LVDTs) mounted (LVDTs) mounted in the testing machine. All test data, including the loads, displacements, and in the testing machine. All test data, including the loads, displacements, and strains were recorded strains were recorded simultaneously by a data logger. simultaneously by a data logger. 3. Test Results and and Discussion Discussion 3. Test Results 3.1. Failure Modes

models of of the the partially partially FRP-confined FRP-confined concrete concrete specimens. specimens. As can be Figure 8 shows the failure models fromthe thefigure, figure, specimens generally failed byrupture the rupture of the FRP jackets. Some seen from allall thethe specimens generally failed by the of the FRP jackets. Some clicking clicking of sounds epoxy were rupture firstfollowed heard, followed by a explosive sudden explosive of FRP sounds epoxyofrupture firstwere heard, by a sudden sound ofsound FRP rupture. rupture. FRPoccurred rupture occurred or near mid-height andthe outside thezone, overlap zone, with crushing of FRP rupture at or nearatmid-height and outside overlap with crushing of concrete concrete simultaneously, resulting to a catastrophic failure with sudden loss of load capacity, which simultaneously, resulting to a catastrophic failure with sudden loss of load capacity, which is in is in accordance with the experimental observations frometZeng et al. [15]. This did failure did not take accordance with the experimental observations from Zeng al. [15]. This failure not take place at place at the column ends because of the existence of additional confinement from the additional the column ends because of the existence of additional confinement from the additional strip atstrip the at the column ends [48]. The initiated failure initiated while concrete adjacent stripswhen cracked, column ends [48]. The failure while concrete between between adjacent FRP stripsFRP cracked, the when the average stress approximately the unconfined concrete strength. Then average axial stressaxial approximately reached thereached unconfined concrete strength. Then the crack in the crack in the concrete grew and FRP rupture occurred, with crushing of concrete simultaneously. This concrete grew and FRP rupture occurred, with crushing of concrete simultaneously. This failure failuremarks pointthe marks the ultimate condition of the FRP-confined as wasadopted widely in adopted in point ultimate condition of the FRP-confined concrete,concrete, as was widely previous previous studyLikewise, [14,58]. Likewise, the concrete crushing wasevident more evident for specimens with larger study [14,58]. the concrete crushing was more for specimens with larger clear clear spacing of adjacent FRP strips, implying concentration of localized of concrete spacing of adjacent FRP strips, implying concentration of localized failure offailure concrete between between adjacent adjacent FRP strips the confinement FRP strips where thewhere confinement was low. was low.

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(a)

(b)

(c) Figure 8. 8. Failure withthree threeFRP FRPstrips; strips;(b) (b)Specimens Specimens wrapped with Figure Failuremodes. modes.(a) (a)Specimens Specimens wrapped wrapped with wrapped with four FRP strips; strips. four FRP strips;(c)(c)Specimens Specimenswrapped wrapped with with five FRP strips.

Specifically, the concrete cracking failure at mid-height of specimens wrapped with four FRP Specifically, the concrete cracking failure at mid-height of specimens wrapped with four FRP strips was more obvious than that of specimens wrapped with three and five FRP strips (Figure 8a,c). strips was more obvious than that of specimens wrapped with three and five FRP strips (Figure 8a,c). This is because the concrete at mid-height was not wrapped with any FRP strip for specimens This is because the concrete at mid-height was not wrapped with any FRP strip for specimens wrapped wrapped with four FRP strips. with four FRP strips. 3.2. Stress-Strain Responses and Ultimate Condition 3.2. Stress-Strain Responses and Ultimate Condition The stress-strain responses of the concrete in the test columns are shown in Figure 9. For stressThe stress-strain responses of the concrete in the test columns are shown in Figure 9. strain curves in present paper, the following sign convention is adopted: in concrete, compressive For stress-strain curves in present paper, the following sign convention is adopted: in concrete, stresses and strains are taken to be positive, while in FRP jackets, tensile stresses and strains are taken compressive stresses and stresses strains are taken towere be positive, while in FRP the jackets, stresses and to be negative. The axial of concrete calculated by dividing axial tensile load that it takes. strains are taken bePIV negative. Theisaxial stresses of were calculated by dividing the axial The strain basedtoon technique not discussed inconcrete the current section but it will be presented in load that it takes. The strain based on PIV technique is not discussed in the current section but will the section below. In Figure 9, the axial strains were obtained from readings of the two LVDTs at it the be presented in the section below. In Figure 9, the axial strains were obtained from readings of the two

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mid-height The axial strains strain gauges weregauges found were to be found much to smaller than those LVDTs at thesection. mid-height section. The from axial strains from strain be much smaller from LVDTs due to the local failure of FRP jackets and thus they were not utilized [59,60]. The hoop than those from LVDTs due to the local failure of FRP jackets and thus they were not utilized [59,60]. strains were averaged from the from two hoop strain outsideoutside the FRPthe overlap zone at the at midThe hoop strains were averaged the two hoopgauges strain gauges FRP overlap zone the height section. In this article, the experimental stress-strain curves are terminated at the point when mid-height section. In this article, the experimental stress-strain curves are terminated at the point FRP rupture occurred, unlessunless otherwise specified. when FRP rupture occurred, otherwise specified. 35 30

Axial stress (MPa)

25 20 15 s-1-3-25 s-1-3-30 s-1-3-35 s-3-3-30 s-2-3-30

10 5 0 -15

-10 -5 -3 Hoop strain(10 )

0

5 10 15 Axial strain(10-3)

20

(a) 45 40

Axial stress (MPa)

35 30 25 20 s-1-4-25 s-1-4-30 s-1-4-35 s-2-4-30 s-3-4-30

15 10 5 0 -20 -15 -10 -5 0 Hoop strain (10-3)

5

10 15 20 25 30 Axial strain (10-3)

35

40

(b) 50 45

Axial stress (MPa)

40 35 30 25 20

s-1-5-25 s-1-5-30 s-1-5-35 s-2-5-30 s-3-5-30

15 10 5 0 -25 -20 -15 -10 -5 -3 Hoop strain (10 )

0

5

10 15 20 25 30 35 40 -3 Axial strain (10 )

(c) Figure 9. Stress-strain curves. (a) Specimens wrapped with three strips; (b) Specimens wrapped with four strips; (c) Specimens wrapped with five strips.

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Figure 9 shows the stress-strain curves (i.e., axial stress-axial strain and axial stress-hoop strain curves) of concrete of the specimens. In each sub-figure of Figure 9, the number of FRP strips is identical, allowing direct comparisons between specimens with different FRP strip thicknesses and widths. It can be seen from Figure 9 that all the axial stress-axial strain curves of FRP-confined concrete in the test columns feature approximately a bilinear shape with two segments. The stress-strain curves show monotonic ascending, while the stress-strain curves of specimens in Figure 9a (specimens wrapped with three strips) show descending second-segment. The descending stress-strain behavior is resulted from the increase in clear spacing of adjacent FRP strips. It is seen from Figure 9 that the peak stress increases with the width of FRP strips while the slope of the second-segment seems to be independent of the width of FRP strips. This is because an increase of width of FRP strips leads to a decrease of clear spacing of adjacent FRP strips, which subsequently leads to an increase in the confinement stiffness. It is also found from Figure 9 that the ultimate axial strain of concrete and hoop rupture strain of FRP were independent of the clear spacing of adjacent FRP strips, which is in accordance with the findings by Zeng et al. [15]. This implies difference between partially FRP confined-concrete and fully FRP confined-concrete, as the ultimate axial strain was found to be highly dependent on the FRP volume ratio. The details of the ultimate conditions will be discussed in detail in the following section. It is interesting to find that the peak axial stress increases with the FRP strip thickness while the slope of the second-segment is nearly independent of the strip thickness. 0 ), axial strains at peak stresses (ε ), ultimate axial stresses ( f 0 ), ultimate The peak axial stresses ( f cc cc cu axial strains (εcu ) and FRP hoop rupture strains (ε h,rup ) (at the mid-height section) for the test columns 0 / f 0 ), normalized ultimate axial strains are listed in Table 1. The normalized ultimate axial stresses ( f cu co (εcu /εco ) are also given in Table 1. In Table 1, εh,rup refers to the average FRP hoop strain from the two hoop strain gauges which were outside the overlap. It is noteworthy that the ultimate axial stress is equal to the peak stress for the confined-concrete with sufficient FRP confinement (i.e., the stress-strain behavior is characterized by a monotonic ascending branch); in this case only ultimate axial stress and ultimate axial strain are given in Table 1. However, as for the confined concrete with insufficient FRP confinement (i.e., the stress-strain behavior is generally characterized by an ascending first branch and a second descending branch), the ultimate axial stress is smaller than the peak strength; in this case both the ultimate and peak axial stresses and corresponding strains are given. The average FRP hoop rupture strain εh,rup was found to be independent of the FRP strip layers and width, as given in Table 1. 0 / f 0 ) and normalized ultimate axial As shown in Table 1, the normalized ultimate axial stresses ( f cu co strains (εcu /εco ) varied in a considerable range with respect to the column parameters. It is found from Table 1 that the normalized axial stresses range from 0.93–1.81 and normalized ultimate axial strains are from 2.88–13.12, which demonstrates excellent strength and ductility of partially FRP-confined concrete. The normalized ultimate axial stresses of specimens that experienced descending stress-strain curves were less than one. This is believed to be due to the existence of a larger clear strip spacing of these specimens, which easily leads to localized crushing failure of concrete. 3.3. Axial and Hoop Strain Distribution Figures 10–12 show revolutionary insights into the distribution of hoop strains and axial strains along the height of the specimens at different axial strain levels, with the strains being drawn in the vertical axis and the distance to the bottom of the specimen being drawn in the horizontal axis. Note that in Figures 10–12, the number between two arrows indicates the location of FRP strip. The axial and hoop strain distributions were based on the PIV technique and the virtual strain gauges were located opposite to the center of the overlap layer (Figure 6). The gauge lengths of the virtual strain gauges were 20 mm for both hoop strain and axial strain measurement.


12 of 29 12 of 29 0.06

0.06

εc=0.002

εc=0.002

0.05

εc=0.004 εc=0.006

0.04

εc=0.008 εc=0.010

0.03

εc=0.004 εc=0.006

0.04

Axial strain

H oop strain

0.05

εc=0.011

0.02

εc=0.008 εc=0.010

0.03

εc=0.011

0.02 0.01

0.01

0.00

0.00 0

150 Distance to the bottom of the specimen (mm)

2

1

3

2

1

0

300

3


300

(a) S-1-3-30 0.04

0.08

ec=0.002 ec=0.004 ec=0.006 ec=0.008 ec=0.010 ec=0.012 ec=0.014

εc=0.002 εc=0.004

0.06

0.03

εc=0.006

Axial strain

Hoop strain

εc=0.008 εc=0.010

0.04

εc=0.012 εc=0.014

0.02

0.02

0.01

0.00

1 0

2

0.00

3


300

2

1 0

3


300

(b) S-2-3-30 0.06

0.08 ec=0.002 ec=0.004

A xial strain

H oop strain

0.06

ec=0.006 ec=0.008

0.04

ec=0.002 ec=0.004

ec=0.010

0.02

0.00

ec=0.006 ec=0.008 ec=0.010

0.04

0.02

0.00

1

0

2


1

3

300

0

2 150 Distance to the bottom of the specimen (mm)

(c) S-3-3-30 Figure 10. Strain distribution along the column height (specimens wrapped with three strips). Figure 10. Strain distribution along the column height (specimens wrapped with three strips).

3 300


13 of 29 13 of 29 0.12

0.30

ec=0.002

0.25

ec=0.006 ec=0.010

0.15

ec=0.006 ec=0.008

0.08

ec=0.008

Axial strain

Hoop strain

0.20

ec=0.002 ec=0.004

0.10

ec=0.004

ec=0.012 0.10

0.06

ec=0.010 ec=0.012

0.04 0.02

0.05 0.00

1 0

2

4

3


0.00

300

3

2

1 0

4

150

300

Distance to the bottom of the specimen (mm)

(a) S-1-4-30 0.09

0.14

0.08

εc=0.002

0.07

εc=0.004 εc=0.006

0.10

εc=0.008

0.05

Axial strain

Hoop strain

0.06

ec=0.002 ec=0.004

0.12

0.04 0.03

ec=0.006 ec=0.008

0.08 0.06 0.04

0.02

0.02

0.01 0.00

0.00

2

1

0

4

3

150

1 0

300

4

3

2



300

(b) S-2-4-30 0.16

0.18 εc=0.003

0.12

εc=0.009

0.09

εc=0.015

εc=0.003

0.14

εc=0.006

εc=0.006

0.12

εc=0.012

A xial strain

H oop strain

0.15

0.06

εc=0.009

0.10

εc=0.012

0.08

εc=0.015

0.06 0.04

0.03

0.02

0.00 1 0

2

3


0.00

4 300

1 0

2

3


(c) S-3-4-30 Figure 11. Strain distribution along the column height (specimens wrapped with four strips). Figure 11. Strain distribution along the column height (specimens wrapped with four strips).

4 300


14 of 29 14 of 29

0.06

0.05

εc=0.002

εc=0.002

εc=0.004

0.05

εc=0.006

εc=0.008 εc=0.010

0.03

A xial strain

H oop strain

0.04

εc=0.004

0.04

εc=0.006

εc=0.012 εc=0.014

0.02

εc=0.008

0.03

εc=0.010 εc=0.012

0.02

εc=0.014

0.01

0.01 0.00

2

1 0

4

3

0.00

5


1 0

300

3

2

5

4


300

(a) S-1-5-30 0.16 0.14

εc=0.002

0.12

εc=0.004 εc=0.006

0.12

εc=0.010

εc=0.010 εc=0.012 εc=0.014

0.06

εc=0.014

0.06

εc=0.008

0.08

εc=0.012

0.08

εc=0.006

0.10

εc=0.008

0.10

εc=0.004

Axial strain

Hoop strain

0.14

εc=0.002

εc=0.016

εc=0.016

0.04

0.04

0.02

0.02 0.00

2

1 0

3

4

0.00

5

150

300


1

2

0

3

4

5

150


300

(b) S-2-5-30 0.06

0.16 0.14

0.05

εc=0.004

0.12

εc=0.006

0.10

εc=0.008 εc=0.010

0.08

εc=0.012

0.06

εc=0.004 εc=0.006

0.04 Axial strain

H oop strain

εc=0.002

εc=0.002

0.04

εc=0.008 εc=0.010

0.03

εc=0.012

0.02 0.01

0.02

0.00

0.00

1 0

4 3 150 Distance to the bottom of the specimen (mm) 2

1

5 300

0

2

3

4

150

5 300


(c) S-3-5-30 Figure 12. Strain distribution along the column height (specimens wrapped with five strips). Figure 12. Strain distribution along the column height (specimens wrapped with five strips).

The evolution of hoop strains appears to increase consistently at all displacement levels, The evolution of hoop strains appears to increase consistently at all displacement levels, providing providing additional credence to the optical strain measurement technique. It is interesting to find additional credence to the optical strain measurement technique. It is interesting to find that the axial that the axial strains and hoop strains are larger at the mid-plain of the two adjacent FRP strips than strains and hoop strains are larger at the mid-plain of the two adjacent FRP strips than those at the those at the mid-plain of each FRP strip. This is because the confining stress to concrete between the mid-plain of each FRP strip. This is because the confining stress to concrete between the FRP strips FRP strips is less effective than that of concrete in the FRP strips at a given axial strain, which leads is less effective than that of concrete in the FRP strips at a given axial strain, which leads to a larger to a larger axial strain in the concrete between the FRP strips. This serves as a reason why ultimate axial strain in the concrete between the FRP strips. This serves as a reason why ultimate axial strain of axial strain of partially FRP-confined concrete based on LVDTs is larger than that of fully FRPconfined concrete [15]. In most circumstance, hoop strains in FRP jacket remained small and uniform along the height until the average axial stress of concrete surpassed the unconfined concrete strength, after which the hoop strains increased rapidly as the confined concrete began to dilate, activating the

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partially FRP-confined concrete based on LVDTs is larger than that of fully FRP-confined concrete [15]. In most circumstance, hoop strains in FRP jacket remained small and uniform along the height until the average axial stress of concrete surpassed the unconfined concrete strength, after which the hoop strains increased rapidly as the confined concrete began to dilate, activating the FRP confinement. Figures 10–12 also clearly show that the hoop strain distribution is uniform along the height at strain levels below 0.004, while the hoop strains in FRP strips are substantially smaller than those in the concrete between adjacent strips when the axial strain was larger than 0.004. This is because the cracking of the concrete at/near the mid-plain of the two adjacent FRP strips leads to substantial increase of hoop strains. Considerable variation is observed in virtual axial strain readings over the height of specimens, although the upper half of the specimen are symmetrical to the bottom half. Additionally, the hoop strain distributions are not vertically symmetrical, although the column is symmetrical in the vertical direction. These hoop strain distributions also provide a striking explanation for the observed variation in hoop strain measurement which is implicit in essentially all previously published research on FRP-confined concrete. It also implies that it is not surprising that the maximum recorded hoop stains by conventional foil strain gauges at failure show strain efficiency values with substantial inconsistency. Nevertheless, the existing available test data of hoop strain on an FRP-confined concrete member is mainly depended on conventional foil strain gauges. It is, therefore, not at all surprising that the available model for predicting FRP-confined concrete’s ultimate axial strain are incapable of making predictions with an average absolute error of less than about 20% [61]. 4. Finite-Element Modeling of FRP-Confined Concrete 4.1. General An improved versatile constitutive concrete damage-plastic model (CDPM) which can produce accurate predictions for FRP-confined concrete under both uniform and non-uniform confinement was proposed and carefully validated by Yu et al. [41]. In this model, all the material parameters have been found from Teng et al.’s analysis model [62], which is for concrete under uniform FRP confinement. In Yu et al. [41]’s model, an effective confining pressure was defined and two methods of defining the flow rule were proposed for non-uniformly confined concrete. It was found that this model is capable of providing reasonable stress-strain responses for FRP-confined concrete in both uniform and non-uniform sections by subsequent investigations [40,41,44,63]. For ease of reference, Yu et al. [41] model is briefly summarized in the following sections. 4.2. FRP-Confined Concrete As explained earlier, the modified CDPM [41] has related the loading function F, the hardening function κ, the potential function G, and the damage parameter d to confinement-dependent variables. The loading function F adopts the yield function proposed by Lubliner et al. [64] and modified by Lee and Fenves [65]. As can be found in the ABAQUS theory manual, the mathematic expression for F is: 1 F= 1−A

q

3J 2 − AI 1 + B e εp h−σmin i − C h−σmin i − σcn e εpc = 0

with A=

f b0 0 −1 f co ; f0 2 f 0b − 1 co

0 ≤ A ≤ 0.5,

σcn e εpc (1 − A ) − (1 + A ), B= σtn e εpt

(1)

(2)

(3)

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C=

3(1 − K ) . 2K − 1

(4)

where, I 1 is the first invariant of the effective stress, J 2 is the second invariant of the effective stress, 0 is unconfined concrete cylinder strength, σ f b0 is the biaxial concrete strength, f co min is the minimum principal effective stress, e εp is the equivalent plastic strain, e εpc is the equivalent compressive plastic strain, e εpt is the equivalent tensile plastic strain, σcn is the effective compressive cohesive strength, σtn is the effective tensile cohesive strength, K is the ratio of biaxial concrete strength to triaxial compression strength and the Macauley bracket h·i is defined by h x i = (| x | + x )/2. The value 0.725 of K has been found by Yu et al. [44] using the empirical equation for the strength of concrete under biaxial compression and tri-axial compression [62]. Then other parameters need be 0 and the ratio of f 0 to f 0 which input for this loading function are the unconfined concrete strength f co co b has a default value 1.16 in the ABAQUS software. The strain hardening rule is defined in the function of σcn e εpc . The flow potential function G adopted in the CDMP model is the hyperbolic function as follows: G=

q

(3 σto tan ψ) + J 2 − I 1 tan ψ

(5)

where Ψ is the dilation angle; σto is the uniaxial tensile stress at failure; 3 is the eccentricity; when the eccentricity 3 is zero, Equation (5) degenerate to: G=

q

J 2 − I 1 tan ψ

(6)

For concrete under uniform confining pressure, the value of tan ψ can be obtained using the following equation: √ p p 3 dεc + 2dεl tan ψ = (7) p p 6 dεc − dεl p

where dεl is the plastic strain increment in the lateral direction. Yu et al. [41] used the following assumption to simplify the input of damage variable. The damage variable is set to be zero before the peak stress and it is selected so that the effective axial stress-strain curve yields a platen after peak stress. That means for concrete under uni-axial compression, the expression of the damage variable is: d = 1−

σc 0 f co

(8)

Meanwhile for concrete under constant confining pressure, the expression of the damage variable can be revised to: σc − 1+1C−+A2A σl (9) d = 1− 0∗ − 1+C +2A σ f cc l 1− A 0∗ is the peak stress of concrete under a constant confining pressure. where f cc Beside the above four components in Yu et al. [41], the following equation was employed to calculate the equivalent confining pressure:

σl,eff =

0 )(σ + 0.039 f 0 ) 2(σ2 + 0.039 f co 3 co 0 − 0.039 f co 0 σ2 + σ3 + 0.078 f co

(10)

where σl,eff is the equivalent confining pressure; σ2 , σ3 are confining pressure in vertical direction. These modifications were ultimately implemented in the ABAQUS software using the solution dependent field variable (SDFV) option. The inclusion of confinement-dependent features in FE models requires the use of an analysis-oriented stress-strain model for FRP-confined concrete to produce the necessary material parameters, as all the material parameters have been based on analysis-oriental

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stress-strain model for uniformly confined concrete and it was expected that the FE model has same accuracy as the adopted analysis-oriental stress-strain model [44]. The procedure of generating concrete input data provided by Yu et al. [41] was adopted to generate the concrete field-dependent input data Polymers 2018, 10, x FOR PEER REVIEW 17 of 29 in the ABAQUS.

4.3. 4.3. FRP FRP Jacket Jacket The modeled as as aa linear linear elastic elastic brittle brittle material. material. The The FRP FRP strip strip is is modeled The stiffness stiffness of of FRP FRP in in the the axial axial direction (i.e., the loading direction) is negligible as the fibers in the FRP jackets are all oriented direction (i.e., the loading direction) is negligible as the fibers in the FRP jackets are all oriented in in the the hoop direction. The definition of the elastic behavior of FRP jacket was based on the elastic lamina hoop direction. The definition of the elastic behavior of FRP jacket was based on the elastic lamina option model anan isotropic elastic material. As explained earlier, the option in in the theABAQUS ABAQUSwhich whichisisused usedtoto model isotropic elastic material. As explained earlier, negligibility of FRP axial stiffness was achieved by activated the “no compression” option of elastic the negligibility of FRP axial stiffness was achieved by activated the “no compression” option of elastic material of FRP FRP was was set set to to be be zero. zero. material in in the the ABAQUS. ABAQUS. The The Poisson’s Poisson’s ratio ratio of 4.4. Modeling Modeling of of Partially FRP-Confined Circular Columns For each of column being investigated by FE approach, a one-fourth column model was established due to the symmetrical features of the column. Figure Figure 13 shows shows the the FE FE model model of of partially partially FRP-confined FRP-confined circular circular column, column, taking specimen specimen S-1-3-30 S-1-3-30 as an example. The boundary condition condition of the FE boundary ofof thethe model of of a quarter of FE model model isisshown shownin inFigure Figure14, 14,based basedon onthe thesymmetrical symmetrical boundary model a quarter column. In the FE model, concrete waswas modeled using 8-node solidsolid elements (i.e., (i.e., C3D8R) and FRP of column. In the FE model, concrete modeled using 8-node elements C3D8R) and was modeled withwith 4-node shellshell elements (i.e.,(i.e., S4R). TheThe FRP was FRP was modeled 4-node elements S4R). FRP wastied tiedtotoconcrete concreteusing using of of the ABAQUS tie constraint constraint and and the FRP jacket was tied to the corresponding node on the outer surface of the concrete infill so that the two nodes were forced to experience experience the same translations. A local coordinate system was assigned to the FRP jacket and the the hoop hoop direction direction and the the axial axial direction direction were were adopted as the 1-principan and 2-principal material orientations, respectively (Figure (Figure 15a). 15a).

Figure Figure 13. 13. Symmetry Symmetry FE FE model model for for aa partially partially FRP-confined FRP-confined circular circular column. column.

Polymers 2018, 10, 253 Polymers2018, 2018,10, 10,xxFOR FORPEER PEERREVIEW REVIEW Polymers

18 of 29 18ofof29 29 18

Figure14. 14.Boundary Boundaryconditions conditionsand andloading loadingof ofthe thesimulated simulatedcolumn columnspecimens. specimens. Figure 14. Boundary conditions and loading of the simulated column specimens. Figure

(a)FRP FRP (a)

(b)Concrete Concrete (b) Figure15. 15. Meshingofofthe the FEmodel. model. Figure Figure 15.Meshing Meshing of theFE FE model.

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The modified concrete damage plasticity model [41], illustrated above, was adopted for the concrete. The unconfined concrete and corresponding unconfined concrete strain ε The modified concrete damagestrength plasticity model [41], illustrated above, was adopted for the were obtained from compression tests presented in the current study. For each specimen, only 0 concrete. The unconfined concrete strength f co and corresponding unconfined concrete strain εco werea quarter offrom it was created in the FEpresented model due symmetric Mesh convergence obtained compression tests in to theitscurrent study.nature. For each specimen, only astudies quarterwere of it conducted for the model until suitable mesh sizes (10 mm) were found (Figure 15b). This provided was created in the FE model due to its symmetric nature. Mesh convergence studies were conducted almost the same axial stress-strain curves thosewere fromfound the next level15b). of refinement. for the model until suitable mesh sizes (10asmm) (Figure This provided almost the same axial stress-strain curves as those from the next level of refinement. 4.5. Numerical Results 4.5. Numerical Results 4.5.1. Stress-Strain Curves 4.5.1. Stress-Strain Curves Figure 16 shows the comparisons between experimental stress-strain curves and predicted Figure 16 shows and predicted stress-strain curves by the the comparisons FE approach. between Note thatexperimental the predictedstress-strain curves werecurves terminated at a hoop stress-strain curves by the FE Notestrain that the predicted terminated at a hoop strain equal to the average FRPapproach. hoop rupture based on testcurves results.were The test results presented strain equal to thewere average FRPtohoop rupture based on test results. The test be results in in current paper utilized validate the strain accuracy of the FE approach. It can seen presented from Figure current paper were utilized to validate the accuracy of thethan FE approach. It can be seenspecifically, from Figureit16 16 that the predicted axial stress-strain curves are lower the test results. More is that thethat predicted stress-strain curves are lower than thethe testultimate results. axial Morestrain specifically, is shown the FEaxial approach is capable of closely predicting of the ittest shown that the FE approachconservative is capable of axial closely predicting the ultimate axial strain of the columns columns while it provides compressive strength. The error of the FE test approach in while it provides conservative compressive The error of the FE approach in predicting predicting ultimate axial stressaxial is within 20% for strength. most of the specimens, which is in accordance with ultimate axialgiven stressbyisYu within most of thebelieve specimens, which is in accordance with findings the findings et al.20% [41].for The authors that the errors may result from thethe utilization given by Yuconfining et al. [41].stress The authors believe that nonuniform the errors may result from which the utilization of effective of effective for concrete under confinement, was derived by Yu confining stress for under nonuniform confinement, which wasdecades derivedago. by Yu et al. [44] based et al. [44] based on concrete data from experimental programs conducted four Nevertheless, the FE data approach conservative results for thefour compressive strength of some specimens (e.g., Son from provides experimental programs conducted decades ago. Nevertheless, the FE approach 2-4-30, S-3-5-30). However, forfor the experimental curvesspecimens of these specimens (i.e., S-3-5-30). S-2-4-30, provides conservative results the compressivestress-strain strength of some (e.g., S-2-4-30, S-3-5-30), the of the second-segment seems to be of the(i.e., FRPS-2-4-30, strip thickness, which However, forslope the experimental stress-strain curves ofindependent these specimens S-3-5-30), the contradicts the commonly accepted observation by otherwhich researchers that a slope of theto second-segment seems to experimental be independent of the FRPreported strip thickness, contradicts higher FRP confinement leads observation to a higher slope of the second-segment. Thisaimplies it is to the commonly acceptedstiffness experimental reported by other researchers that higher FRP reasonable tostiffness believe that thetoerrors in predicting thesecond-segment. above two specimens have little confinement leads a higher slope of the This implies it isimplication reasonablefor to the comparison. believe that the errors in predicting the above two specimens have little implication for the comparison. 35

Axial stress (MPa)

30 25 20 15

S-1-3-30_FE S-1-3-30_Test S-2-3-30_FE S-2-3-30_Test S-3-3-30_FE S-3-3-30_Test

10 5 0 -15

-10 -5 -3 Hoop strain (10 )

0

5 10 15 -3 Axial strain (10 )

(a) Figure 16. Cont.

20


20 of 29 20 of 29

50

Axial stress (MPa)

40

30

20


10

0 -25 -20 -15 -10 -5 -3 Hoop strain (10 )

0

5

10 15 20 25 30 35 40 Axial strain (10-3)

(b) 50

Axial stress (MPa)

40

30

20


10

0 -20 -15 -10 -5 0 Hoop strain (10-3)

5

10 15 20 25 -3 Axial strain (10 )

30

35

(c) Figure 16. 16. Stress-strain curves (experimental (experimental results results versus versus finite finite element element predictions). predictions). (a) (a) Specimens Specimens Figure Stress-strain curves wrapped with three strips; (b) Specimens wrapped with four strips; (c) Specimens wrapped withwith five wrapped with three strips; (b) Specimens wrapped with four strips; (c) Specimens wrapped strips. five strips.

4.5.2. Distribution of Axial Stresses and Radial Stresses 4.5.2. Distribution of Axial Stresses and Radial Stresses Figure 17 shows the FE axial stress and radial stress distributions in the shaft (axial-radial) Figure 17 shows the FE axial stress and radial stress distributions in the shaft (axial-radial) section section of S-2-3-30 (ε = 1.5%). This is served as an example of the axial stress and radial stress of S-2-3-30 (εh = 1.5%). This is served as an example of the axial stress and radial stress distributions in distributions in concrete in circular columns confined with FRP strips and the axial stress and radial concrete in circular columns confined with FRP strips and the axial stress and radial stress distributions stress distributions of specimens with different FRP strip thicknesses and widths are not given in the of specimens with different FRP strip thicknesses and widths are not given in the current paper current paper to limit the length of it. It is seen from Figure 17 that both the axial stress and radial to limit the length of it. It is seen from Figure 17 that both the axial stress and radial stress at the stress at the mid-plain of each FRP strip level are larger than those at the mid-plain level of the two mid-plain of each FRP strip level are larger than those at the mid-plain level of the two adjacent adjacent FRP strips. This suggests the plausibility of “arching action” between the levels of transverse FRP strips. This suggests the plausibility of “arching action” between the levels of transverse hoop hoop reinforcement [28,29]. It was believed that at the mid-plain of the two adjacent FRP strips reinforcement [28,29]. It was believed that at the mid-plain of the two adjacent FRP strips (Figure 3), (Figure 3), the area of ineffectively confined concrete will be largest and the area of effectively the area of ineffectively confined concrete will be largest and the area of effectively confined concrete confined concrete core will be smallest. The axial stress distribution shown in Figure 17 clearly core will be smallest. The axial stress distribution shown in Figure 17 clearly demonstrates the arching demonstrates the arching action in concrete confined with FRP strips. It should be noted that the action in concrete confined with FRP strips. It should be noted that the arching action is suggested for arching action is suggested for the FRP effective confinement pressure in the partially FRP-confined the FRP effective confinement pressure in the partially FRP-confined columns in the existing codes columns in the existing codes (e.g., [26,27]), in which it is assumed that the hoop confining pressure is only effective for concrete in the effective confinement area where the confining pressure has fully developed due to the arching action.

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(e.g., [26,27]), in which it is assumed that the hoop confining pressure is only effective for concrete in the of 29 the confining pressure has fully developed due to the arching 21 action.

Polymers 2018, 10, x FOR PEER effective confinement areaREVIEW where


(a)

21 of 29

(b)

Figure 17. Stress Stress distribution distribution in in shaft shaft section section (X-Z (X-Z section) section)of of S-2-3-30 S-2-3-30(ε (ε , 1.5%). (a) (a)Axial Axialstress; stress; Figure == 1.5%). (b) h,frp (a) (b) Radial Radial stress. stress. (b) Figure 17. Stress distribution in shaft section (X-Z section) of S-2-3-30 (ε (b) Radial stress. axial stress distribution over the section (a quarter of the

,

= 1.5%). (a) Axial stress;

The The axial stress distribution over the section (a quarter of the horizontal horizontal section) section) is is shown shown in in Figure 18. In the mid-plain of each FRP strip, the axial stress distribution along the radial direction is Figure 18.The In axial the mid-plain of each FRP strip, the axial stress distribution along the radial direction stress distribution over the section (a quarter of the horizontal section) is shown in more uniform than that inin the mid-plain ofofthe FRP indicating that of is more uniform than that the mid-plain thetwo twoadjacent adjacent FRPstrips, strips, indicating thatthe the area area Figure 18. In the mid-plain of each FRP strip, the axial stress distribution along the radial direction is of ineffectively confined concrete is largest and the area of effectively confined concrete core is smallest ineffectively confined concrete is largest and the area of effectively confined concrete core is smallest more uniform than that in the mid-plain of the two adjacent FRP strips, indicating that the area of at mid-plain adjacent FRP shows distributions of stress at the theineffectively mid-plain of of the the two two adjacent FRP strips. strips. Figure 19 shows the the distributions of axial axial stress and and confined concrete is largest and theFigure area of 19 effectively confined concrete core is smallest radial at edge along the (column height) at FRP hoop the mid-plain of the two adjacent strips. Figure 19 shows the distributions of axial stress andstrain radialatstress stress at the the section section edge along FRP the generatrix generatrix (column height) at three three given given FRP hoop strain levels (i.e., 0.5%, and specimens wrapped with two 30-mm the section edgefor along the generatrix (column height) at threeof given FRP FRP hoopstrips. strain It levelsradial (i.e., stress 0.5%,at1.0% 1.0% and 1.5%) 1.5%) for specimens wrapped with two layers layers of 30-mm FRP strips. It is is levels (i.e., 0.5%, 1.0% and 1.5%) for specimens wrapped with two layers of 30-mm FRP strips. It is obvious that at the mid-plain of each FRP strip, both the axial and radial stresses at the section edge obvious that at the mid-plain of each FRP strip, both the axial and radial stresses at the section edge obvious thatthose at theat mid-plain of each of FRP strip, the axial and radialThis stresses the section edge are than the two adjacent FRP strips. is with are largest largest than those at the mid-plain mid-plain of the the twoboth adjacent FRP strips. This is in inataccordance accordance with the the are largest than those at the mid-plain of the two adjacent FRP strips. This is in accordance with the in experimental observations. The deviation of radial stress of concrete increases with an increase experimental observations. The deviation of radial stress of concrete increases with an increase in FRP experimental observations. The deviation of radial stress of concrete increases with an increase in FRP strain. This indicates that the confining stress becomes muchnonuniform more nonuniform the hoophoop strain. This indicates that the confining stress becomes much more with thewith increase FRP hoop strain. This indicates that the confining stress becomes much more nonuniform with the increase of concrete expansion. of concrete expansion. increase of concrete expansion.

(a)

(a)

(b)

(b)

Figure Axialstress stressdistribution distribution ininthethe horizontal section (X-Y section) of specimen S-2-3-30 (ε S-2-3-30 Figure 18. 18. Axial horizontal section (X-Y section) of specimen , Figure 18. Axial stress distribution in the horizontal section (X-Y section) of specimen S-2-3-30 (ε , = 1.5%). (a) Mid-plain of each FRP strip; (b) Mid-plain of two adjacent FRP strips. (εh,frp = 1.5%). (a) Mid-plain of each FRP strip; (b) Mid-plain of two adjacent FRP strips. = 1.5%). (a) Mid-plain of each FRP strip; (b) Mid-plain of two adjacent FRP strips.

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22 of 29


22 of 29

(a)

(b)

(c)

(d)

(e)

(f)

Figure 19. Axial stress and radial stress distributions along the generatrix (column height). (a) Axial

Figure 19. Axial stress and radial stress distributions along the generatrix (column height). (a) Axial stress (S-2-3-30); (b) Radial stress (S-2-3-30); (c) Axial stress (S-2-4-30); (d) Radial stress (S-2-4-30); (e) stress (S-2-3-30); (b) Radial stress (S-2-3-30); (c) Axial stress (S-2-4-30); (d) Radial stress (S-2-4-30); Axial stress (S-2-5-30); (f) Radial stress (S-2-5-30). (e) Axial stress (S-2-5-30); (f) Radial stress (S-2-5-30).

To further validate the arching action, the axial stress distribution along the radial direction (X axis) is givenvalidate in Figurethe 20, arching with the action, axial stresses being drawn in the vertical axisthe andradial the radial To further the axial stress distribution along direction coordinate being drawn in the horizontal axis. It is also obvious that in the mid-plain of FRPradial (X axis) is given in Figure 20, with the axial stresses being drawn in the vertical axis each and the strip, the axial stress distribution along the radial direction is more uniform than that in the mid-plain

coordinate being drawn in the horizontal axis. It is also obvious that in the mid-plain of each FRP strip, the axial stress distribution along the radial direction is more uniform than that in the mid-plain of the two adjacent FRP strips. In Figure 20, a solid line was added to each figure to indicate the locations of ineffective and effective confinement areas. It is found that the axial stress experiences a quick drop


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ofPolymers the two adjacent FRP strips. In Figure 20, a solid line was added to each figure to indicate the 2018, 10, 253 23 of 29 locations of ineffective and effective confinement areas. It is found that the axial stress experiences a quick drop after the radial coordinate value approximately reach D − ⁄2 (Figure 20). This provides after the radial coordinate value approximately D − confinement sf0 /2 (Figure 20). This provides an evidence an evidence for the determination of diameter ofreach effective core, which is believed to be for the determination of diameter of effective confinement core, which is believed to be equal to the equal to the section dimension minus half of the clear spacing of the two adjacent FRP strips (Figure 2)section [28]. dimension minus half of the clear spacing of the two adjacent FRP strips (Figure 2) [28].

(a)

(c)

(e)

(b)

(d)

(f)

Figure stress distribution along thethe radial direction (X axis). (a) Mid-plain of each Figure20. 20.Axial Axial stress distribution along radial direction (X axis). (a) Mid-plain ofFRP eachstrip FRP (S-2-3-30); (b) Mid-plain of two adjacent FRP strips (S-2-3-30); (c) Mid-plain of each FRP strip (S-2-4strip (S-2-3-30); (b) Mid-plain of two adjacent FRP strips (S-2-3-30); (c) Mid-plain of each FRP strip 30); (d) Mid-plain of two of adjacent FRP strips (S-2-4-30); (e) Mid-plain of each FRP strip (S-2-5-30); (f) (S-2-4-30); (d) Mid-plain two adjacent FRP strips (S-2-4-30); (e) Mid-plain of each FRP strip (S-2-5-30); Mid-plain of two adjacent FRP strips (S-2-5-30). (f) Mid-plain of two adjacent FRP strips (S-2-5-30).


24 of 29 24 of 29

4.5.3.Distribution DistributionofofAxial AxialStrains Strainsand andHoop HoopStrains Strains 4.5.3. Figure21 21 shows the distributions of concrete confined withwith FRP FRP stripsstrips along Figure the axial axialand andhoop hoopstrain strain distributions of concrete confined the generatrix (column height) of theofspecimens. The following threethree findings can be from along the generatrix (column height) the specimens. The following findings canobserved be observed Figure 21: (1) of axial strain and hoop strain distributions provided by the approach are in from Figure 21:the (1)trend the trend of axial strain and hoop strain distributions provided byFE the FE approach accordance with the experimental observations: the axialthe strain and hoopand strain at the mid-plain of the are in accordance with the experimental observations: axial strain hoop strain at the midtwo adjacent FRP strips are larger than the mid-plain of each FRP strip; (2) the plain of the two adjacent FRP strips arethose largeratthan those at the mid-plain of each FRPpredicted strip; (2) axial the strains and hoop strains the FRP strips are FRP in reasonable with test results while is seen predicted axial strains andinhoop strains in the strips are agreement in reasonable agreement with testitresults that the between FRP strips deviate substantially the test results. findings from while it isstrains seen that the strains between FRP strips deviate from substantially from theAbove test results. Above the numerical results indicate a confinement mechanics difference between partially FRP-confined findings from the numerical results indicate a confinement mechanics difference between partially concrete and fully FRP-confined concrete. FRP-confined concrete and fully FRP-confined concrete. Forthe thefirst firstfinding, finding,ititisisnot notsurprising surprisingthat thatboth boththe theaxial axialstrain strainand andhoop hoopstrain strainatatthe themid-plain mid-plain For thetwo twoadjacent adjacentFRP FRPstrips stripsare arelarger largerthan thanthose thoseatatthe themid-plain mid-plainofofeach eachFRP FRPstrip stripasasthe theconcrete concrete ofofthe betweenFRP FRPstrips stripsisiseasier easiertotoexperience experiencecrushing crushingfailure. failure.This Thisclearly clearlydemonstrates demonstratesan anexperimental experimental between observationthat thatthe theultimate ultimateaxial axialstrain strainininpartially partiallyFRP-confined FRP-confinedconcrete concreteisislarger largerthan thanthat thatininfully fully observation FRP-confinedconcrete concreteififthe theaxial axial strain strain isis averaged averaged from from mid-height mid-height axial axial shortening. shortening. This Thisalso also FRP-confined impliesthe theultimate ultimateaxial axialstrain strainofofpartially partiallyFRP-confined FRP-confinedconcrete concretewill willbe beunderestimated underestimatedby bythe the implies analysis-oriented model [62] which is based on fully FRP-confined concrete while this phenomenon analysis-oriented model [62] which is based on fully FRP-confined concrete while this phenomenon needsfurther furtherexperimental experimentaland andtheoretical theoreticalverifications. verifications.For Forthe thesecond secondfinding, finding,the themeasured measuredstrains strains needs concretebecome becomeunreliable unreliablewhen whenthe theconcrete concretespalling spallingoccurred. occurred.This Thisexplains explainswhy whythe thepredicted predicted ininconcrete axialstrains strainsand andhoop hoopstrains strainsbetween betweenFRP FRPstrips stripsdeviate deviatesubstantially substantiallyfrom fromthe thetest testresults. results. axial Parametric studies on FRP-confined concrete basedbased on theon FE the approach can be conducted Parametric onpartially partially FRP-confined concrete FE approach can be to gain in-depth on the confinement mechanics. mechanics. Further research on research confinement conducted to gainunderstandings in-depth understandings on the confinement Further on mechanics ofmechanics partially FRP-confined wrapped with continuous FRP strip spirals isFRP necessary. confinement of partially concrete FRP-confined concrete wrapped with continuous strip To validate the FE approach, pressure technique (e.g., [63]) istechnique favored to(e.g., measure spirals is necessary. To validate the FEmeasurement approach, pressure measurement [63]) the is stress distribution FRP-confined concrete.FRP-confined concrete. favored to measurein thepartially stress distribution in partially

(b)

(a) Figure 21. Cont.


(c)

(e)

25 of 29 25 of 29

(d)

(f)

Figure Figure21. 21.Axial Axialstrain strainand andradial radialstrain straindistribution distributionalong alongthe thegeneratrix generatrix(column (columnheight). height).(a) (a)Hoop Hoop strain (S-2-3-30); (b) Axial strain (S-2-3-30); (c) Hoop strain (S-2-4-30); (d) Axial strain (S-2-4-30); (e) strain (S-2-3-30); (b) Axial strain (S-2-3-30); (c) Hoop strain (S-2-4-30); (d) Axial strain (S-2-4-30); Hoop strain (S-2-5-30); (f) Axial strain (S-2-5-30). (e) Hoop strain (S-2-5-30); (f) Axial strain (S-2-5-30).

5. Conclusions 5. Conclusions Test results based on the 15 FRP-strengthened cylindrical concrete column partially wrapped Test results based on the 15 FRP-strengthened cylindrical concrete column partially wrapped with FRP strips have been presented in this paper. Novel PIV technique was adopted to measure with FRP strips have been presented in this paper. Novel PIV technique was adopted to measure axial axial and hoop strains in the specimens. Never-seen axial and hoop strain variations along the and hoop strains in the specimens. Never-seen axial and hoop strain variations along the columns columns were presented. A finite element model based on concrete damage plasticity model was were presented. A finite element model based on concrete damage plasticity model was established established and validated by the test results. The confinement mechanics of partially FRP-confined and validated by the test results. The confinement mechanics of partially FRP-confined concrete was concrete was then investigated by the FE approach. Based on the combined test results and numerical then investigated by the FE approach. Based on the combined test results and numerical results, results, the following conclusions were drawn: the following conclusions were drawn: (1) The peak stress of confined concrete increases with an increase in width of FRP strip. The (1) The peak stress of confined concrete increases with an increase in width of FRP strip. The ultimate ultimate axial strain of concrete, the FRP hoop rupture strain and the slope of the secondaxial strain of concrete, the FRP hoop rupture strain and the slope of the second-segment are segment are independent of the clear spacing of adjacent FRP strips. The compressive strength independent of the clear spacing of adjacent FRP strips. The compressive strength increases with increases with an increase in the FRP strip thickness while the slope of the second-segment is an increase in the FRP strip thickness while the slope of the second-segment is independent of independent of the strip layer. the strip layer. (2) Based on digital image correlation technique, it is found that both the axial strains and hoop (2) strains Based are on larger digitalatimage correlation it is found that both axial and hoop the mid-plain of technique, the two adjacent FRP strips thanthe those at strains the mid-plain of strains are larger at the mid-plain of the two adjacent FRP strips than those at the mid-plain of each FRP strip. FRP strip. model based on modified concrete damage plasticity model was utilized to (3) Aeach finite element simulate the partially FRP-confined concrete. it is found that the FE approach is capable of

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(3)

(4)

(5)

(6)

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A finite element model based on modified concrete damage plasticity model was utilized to simulate the partially FRP-confined concrete. it is found that the FE approach is capable of closely predicting the ultimate axial strain and providing conservative axial compressive strength. Both the axial stress and radial stress at the section edge in the mid-plain of each FRP strip level are larger than those at the mid-plain level of the two adjacent FRP strips. In the mid-plain of each FRP strip, the axial stress distribution along the radial direction is more uniform than that in the mid-plain of the two adjacent FRP strips, indicating that the area of ineffectively confined concrete is largest and the area of effectively confined concrete core is smallest at the mid-plain of the two adjacent FRP strips. This also suggests that the plausibility of the arching action assumption. Both the axial and radial stresses in the mid-plain of each FRP strip are larger than those in the mid-plain of each FRP strip. The deviation of radial stress of concrete increases with an increase in FRP hoop strain. This indicates that the confining stress becomes much more nonuniform with the increase of concrete expansion. The trend of axial strain and hoop strain distributions provided by the FE approach are in accordance with the experimental observations: the axial strain and hoop strain at the mid-plain of the two adjacent FRP strips are larger than those at the mid-plain of each FRP strip.

Acknowledgments: The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (No. 11602060 and No. 11672076), the Science and Technology Planning Project of Guangdong Province (Nos. 2017A010103030 and 2014A020216053), the Science and Technology Planning Project of Guangzhou City (Nos. 201510010096 and 201510010042). Author Contributions: Yongchang Guo and Weipeng Chen conceived and designed the experiments; Weipeng Chen performed the experiments; Junjie Zeng and Yongchang Guo analyzed the data; Lijuan Li contributed reagents/materials/analysis tools; Junjie Zeng wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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