# Analysis of Bond Behavior of FRP-Confined Concrete Piles Based on Push-Out Test

Authors: Zheng-zhen Wang; Wei-ming Gong; Guo-liang Dai; Ling-feng Liu
Journal: Advances in Materials Science and Engineering
 (2020)

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## Abstract

Due to the significant differences in the properties (e.g., anisotropy, elasticity modulus, and surface roughness) of fibre-reinforced polymer (FRP) and traditional pile materials, research on bond behavior between FRP tube and concrete should be conducted to ensure that they can work together properly. Push-out tests on twenty-nine GFRP-confined concrete piles were performed, the influence of bond type, slenderness ratio of FRP tube, radius-thickness ratio of FRP tube, concrete stress and concrete type on bond behavior and distribution of axial strains were studied, and simplified bond-slip constitutive models based on test results were proposed. It was found that bond type was a critical factor influencing bond behavior. A smaller radius-thickness ratio, a higher concrete stress, and the use of expansive concrete were advantageous for achieving higher bond behavior, whereas the slenderness ratio had little influence on the bond behavior. The axial strain distribution of all FRP tubes demonstrated the following rules: the upper strain was greater than the middle strain, which was larger than the lower strain, but for normal concrete specimens, the strain was linearly distributed with height, while for expanded concrete specimens, the distribution curves were polylines.


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## Body

## 1. Introduction

Pile foundations have been widely used in bridge engineering and off-shore wind industry [1]. However, there are many problems associated with pile foundations made of traditional materials such as steel, concrete, and timber, especially when installed in corrosive and marine environments. For example, steel corrosion and concrete deterioration may reduce the bearing capacity of pile foundations and affect the safety of its superstructure [2, 3]. For the past decade, there has been a continuously increasing interest in the use of composite piles to replace traditional piles. FRP-confined concrete pile is a typical type of the composite piles, which are comprised of an outer FRP tube and concrete infill. The outer FRP tube can confine the concrete in compression, keep the concrete from severe environment effects, and act as a load-carrying partner. On the other hand, the concrete can prevent local buckling of FRP tube and increase the stiffness of piles [4, 5].Nevertheless, before FRP-confined concrete piles are widely accepted, research must be done on all aspects of their behavior. Bond between FRP tube and concrete is of great importance for the effectiveness of FRP-confined concrete pile because bond is the key for composite action of FRP tube and concrete [6].Many studies have been undertaken to understand the bond behavior between FRP and concrete. Based on their tests, Larralde and Silva-Rodriguez reported that the average bond stress at failure was greater for the steel bars than for the FRP bars under the same test condition, and this conclusion was confirmed by Hao et al. [7, 8]. Pellegrino et al. found that bond behavior between FRP and concrete depends on many factors including concrete stress, bar diameter, surface treatment, and the type of adhesive layer [9–12]. Chen and Chouw investigated the effect of the interface condition on the bond between FRP tube and concrete and found that mechanically bonded interface could highly enhance the bond [13]. Katz et al. concluded that fine roughness of rod surface had a positive effect on high bond, whereas high temperature and cyclic loading were detrimental to bond stress [14–16]. Li et al. studied the influence of concrete strength on bond stress of FRP tube–encased concrete columns and reported that the confinement efficiency and the interfacial bond stress were low for very high stress concrete [17]. Dai et al. analyzed the effect of moisture on the initial and long-term bond behavior of FRP sheets to concrete interfaces and concluded that the effect of the concrete substrate moisture content on short-term interfacial bond performance could be eliminated, but the interfacial bond stress degraded asymptotically with the time of being subjected to combined wet/dry and thermal cycling [18]. Zheng et al. investigated the fatigue bond performance of FRP laminate-concrete interface subjected to hygrothermal environment and found that the hygrothermal environment adversely affected the bond behavior of FRP laminate-concrete interface and the fatigue life of specimens under hygrothermal environment was significantly less than that of reference specimens without hygrothermal pretreatment [19]. Savoia et al. derived a nonlinear mode and a new bond-slip model in terms of CFRP-bonded length, CFRP-bonded width, and anchored system by the inverse analysis and the parametric study of bond-slip behavior [20, 21]. A simple but robust finite-element model and a mesoscale finite-element model using the K&C concrete damage model in LS-DYNA were proposed by Tao et al. and Li et al. separately to simulate the bond behavior of FRP-concrete [22, 23]. Neto et al. identified the role of the load misalignment in the bond behavior of GFRP-concrete by numerical simulation, and it was concluded that the bond behavior significantly decreased in the case of a misaligned load pointing outward the reinforced surface, and this effect was less relevant for thick laminates when compared with thin FRP sheets [24].It is noted that most research of FRP-concrete bond behavior is based on FRP bar or FRP sheet, and little work has previously been conducted on the bond behavior between FRP tube and concrete. Thus, in this paper, push-out tests of twenty-nine specimens were preformed to further identify the parameters that control the bond behavior between FRP tube and concrete, including bond type, slenderness ratio of FRP tube, radius-thickness ratio of FRP tube, concrete stress, and concrete type. Based on the test results, distribution and development law of axial strain of FRP tube were analysed, and simplified bond-slip constitutive models were proposed to describe the bond-slip curves of FRP-confined concrete piles.


### 1.1. Test Conditions

#### 1.1.1. Test Setup

Push-out test, which is a good way to assess the bond behavior between FRP tube and concrete infill, was performed on all the specimens [25–27]. The test setup is shown in Figure 1. All tests were conducted on a self-made load reaction frame, which was welded by Q235 steel in the laboratory and had sufficient stiffness to ensure ignorable deformation during all tests. A hand hydraulic jack with a capacity of 300 kN and a measuring range of 60 mm was used to apply vertical loads on loading plate. A 50 mm gap was reserved when pouring concrete inside a FRP tube. The loading plate was placed in contact with the top of the specimen where the gap was located to transfer pressure applied by the hydraulic jack on the FRP tube only, whereas the bottom of the specimen was in contact with a steel column whose diameter was less than the FRP tube leading to reaction force being applied only to the concrete.Figure 1
Test setup.


## 1.1. Test Conditions

### 1.1.1. Test Setup

Push-out test, which is a good way to assess the bond behavior between FRP tube and concrete infill, was performed on all the specimens [25–27]. The test setup is shown in Figure 1. All tests were conducted on a self-made load reaction frame, which was welded by Q235 steel in the laboratory and had sufficient stiffness to ensure ignorable deformation during all tests. A hand hydraulic jack with a capacity of 300 kN and a measuring range of 60 mm was used to apply vertical loads on loading plate. A 50 mm gap was reserved when pouring concrete inside a FRP tube. The loading plate was placed in contact with the top of the specimen where the gap was located to transfer pressure applied by the hydraulic jack on the FRP tube only, whereas the bottom of the specimen was in contact with a steel column whose diameter was less than the FRP tube leading to reaction force being applied only to the concrete.Figure 1
Test setup.


## 1.1.1. Test Setup

Push-out test, which is a good way to assess the bond behavior between FRP tube and concrete infill, was performed on all the specimens [25–27]. The test setup is shown in Figure 1. All tests were conducted on a self-made load reaction frame, which was welded by Q235 steel in the laboratory and had sufficient stiffness to ensure ignorable deformation during all tests. A hand hydraulic jack with a capacity of 300 kN and a measuring range of 60 mm was used to apply vertical loads on loading plate. A 50 mm gap was reserved when pouring concrete inside a FRP tube. The loading plate was placed in contact with the top of the specimen where the gap was located to transfer pressure applied by the hydraulic jack on the FRP tube only, whereas the bottom of the specimen was in contact with a steel column whose diameter was less than the FRP tube leading to reaction force being applied only to the concrete.Figure 1
Test setup.


## 2. Materials and Specimens

The parameters of the twenty-nine specimens fabricated for this study are provided in Table1; the test variables included bond type, slenderness ratio of FRP tube, radius-thickness ratio of FRP tube, concrete strength, and concrete type. All FRP tubes were made from glass fibre-reinforced polymer (GFRP), and the properties of the GFRP are shown in Table 2.Table 1
Parameters of specimens.
Code
Bond type
Outside diameter of FRP tubeD (mm)
Thickness of FRP tubet (mm)
Length of FRP tubeL (mm)
Slenderness ratio of FRP tube (L/D)
Radius-thickness ratio of FRP tube (D/t)
Concrete type
Concrete stress
1-1
Direct bond
200
11
100
0.5
18.2
Normal
C30
1-2
Internal threads
200
11
100
0.5
18.2
Normal
C30
1-3
Shear connectors
200
11
100
0.5
18.2
Normal
C30
2-1
Direct bond
200
11
200
1
18.2
Normal
C30
2-2
Internal threads
200
11
200
1
18.2
Normal
C30
2-3
Shear connectors
200
11
200
1
18.2
Normal
C30
3-1
Direct bond
200
11
400
2
18.2
Normal
C30
3-2
Internal threads
200
11
400
2
18.2
Normal
C30
3-3
Shear connectors
200
11
400
2
18.2
Normal
C30
4-1
Direct bond
400
13
800
2
30.8
Normal
C30
4-2
Internal threads
400
13
800
2
30.8
Normal
C30
4-3
Shear connectors
400
13
800
2
30.8
Normal
C30
5-1
Direct bond
400
13
400
1
30.8
Normal
C30
5-2
Internal threads
400
13
400
1
30.8
Normal
C30
5-3
Shear connectors
400
13
400
1
30.8
Normal
C30
6-1
Direct bond
400
13
200
0.5
30.8
Normal
C30
6-2
Internal threads
400
13
200
0.5
30.8
Normal
C30
6-3
Shear connectors
400
13
200
0.5
30.8
Normal
C30
7-1
Direct bond
200
15
200
1
13.3
Normal
C30
7-2
Internal threads
200
15
200
1
13.3
Normal
C30
7-3
Shear connectors
200
15
200
1
13.3
Normal
C30
8-1
Direct bond
400
17
400
1
23.5
Normal
C30
8-2
Internal threads
400
17
400
1
23.5
Normal
C30
8-3
Shear connectors
400
17
400
1
23.5
Normal
C30
9-1
Direct bond
200
11
200
1
18.2
Normal
C50
10-1
Direct bond
200
11
200
1
18.2
Normal
C60
P-1
Direct bond
200
11
400
2
18.2
Expansive
C30
P-2
Internal threads
200
11
400
2
18.2
Expansive
C30
P-3
Shear connectors
200
11
400
2
18.2
Expansive
C30Table 2
Properties of GFRP.
Material
Specific gravity
Tensile stress (GPa)
Elastic modulus (GPa)
Thermal expansion coefficient (10−6/°C)
Elongation (%)
Specific stress (GPa)
Specific modulus (GPa)
GFRP
2.65
3.4
52
5.1
4.7
1.41
32According to the bond type, there were three types of FRP tubes, the first type was normal FRP tube, whose inner surface is smooth (Figure2(a)); the second type was FRP tube with internal threads: the depth and spacing of internal threads were 2.5 mm and 10 mm separately and the internal threads were arranged along the entire inner surface of FRP tube (Figure 2(b)); the third type was FRP tube with shear connectors: shear connectors were made of steel nails with a length of 70 mm, and a diameter of 3 mm (Figure 2(c)); the number and position of shear connectors are shown in Figure 3.Figure 2
Different types of FRP tubes. (a) Normal FRP tubes. (b) FRP tube with internal threads. (c) FRP tube with shear connectors.
(a)
(b)
(c)Figure 3
Number and positions of shear connectors of specimens with different lengths. (a) 100 mm. (b) 200 mm. (c) 400 mm. (d) 800 mm.Two types of concrete (normal concrete and expansive concrete) and three different concrete strengths (C30, C50 and C60) were used in the tests, and the concrete was prepared in the laboratory. Calcium sulphoaluminate expansive agent was added into the expansive concrete, whose amount was 8% of cement weight. To measure the mechanical properties of concrete, three standard concrete test blocks of each kind of concrete strength were reserved, which would be cured for 28 days under the same condition of the specimens. The properties of concrete are demonstrated in Table3.Table 3
Properties of concrete.
Concrete stress
Mix proportion (cement : water : sand : stone)
Sand ratio (%)
Water-cement ratio
Mean cubic compressive stress (MPa)
C30
450 : 183 : 600 : 1192
33.5
0.41
31.2 (CV = 3.76%)
C50
510 : 178 : 545 : 1220
30.9
0.35
52.1 (CV = 1.65%)
C60
525 : 180 : 530 : 1250
29.8
0.34
59.1 (CV = 3.44%)


### 2.1. Measuring Equipment and Test Method

To measure the relative slip between the FRP tube and concrete, four electronic displacement sensors and four dial gauges were installed at top surface and bottom surface of the FRP tube (each surface has two electronic displacement sensors and two dial gauges). The electronic displacement sensors were connected with the signal receiving apparatus, which could instantly display the load-displacement curves on a computer. The role of the dial gauges was to verify the correctness of test results recorded by the electronic displacement sensors.The axial strain distribution was obtained from strain gauges mounted on the outside surface of the FRP tube (Figure4). The BX120-4BB resistance strain gauges were used in the test, whose gauge resistance range was 120.1 ± 0.2 Ω and gauge factor was 2.08 ± 1%. The strain gauges’ data were collected by the DH3816 static strain test system.Figure 4
Number and position of strain gauges of specimens with different lengths. (a) 100 mm. (b) 200 mm. (c) 400 mm. (d) 800 mm.The slow speed load method was selected for all the tests, and each applied load was about one-tenth of estimated ultimate bearing capacity, which was obtained through preliminary tests on specimens with different bond types. Loading stopped when the slip remained stable or the concrete came into contact with the loading plate.Test results would be expressed by the following parameters:τ, average bond stress (kPa), which is a general designation of the interfacial bond stress between FRP tube and concrete, the anchoring force between internal threads and concrete and the anchoring force between shear connectors and concrete. τ could be calculated as follows:(1)τ=FπdLe,where F is the load applied by the hydraulic jack on FRP tube; d is inside diameter of FRP tube; and Le is bond length between concrete and FRP tube.It should be noted that actual bond stress between FRP tube and concrete is not constant, and there is an effective bond length of the interface [28]. Because this article is mainly concerned with the overall performance of bond stress rather than local bond stress, equation (1). is used here.τu, the maximum τ (kPa), which should be used for the design of FRP-confined concrete piles with shear connectors.τr, ultimate average bond stress (kPa), which is the constant value of bond stress at the end of τ−s curves and should be used for the design of direct bond FRP-confined concrete piles and FRP-confined concrete piles with internal threads.s, average slip between FRP tube and concrete (mm), which is the average displacement of top surface and bottom surface of the FRP tube measured by electronic displacement sensors, based on the assumption that the deformation of concrete and FRP tube is ignorable.su, average slip between FRP tube and concrete when τ reached τu (mm).sr, average slip between FRP tube and concrete when τ reached τr (mm).


## 2.1. Measuring Equipment and Test Method

To measure the relative slip between the FRP tube and concrete, four electronic displacement sensors and four dial gauges were installed at top surface and bottom surface of the FRP tube (each surface has two electronic displacement sensors and two dial gauges). The electronic displacement sensors were connected with the signal receiving apparatus, which could instantly display the load-displacement curves on a computer. The role of the dial gauges was to verify the correctness of test results recorded by the electronic displacement sensors.The axial strain distribution was obtained from strain gauges mounted on the outside surface of the FRP tube (Figure4). The BX120-4BB resistance strain gauges were used in the test, whose gauge resistance range was 120.1 ± 0.2 Ω and gauge factor was 2.08 ± 1%. The strain gauges’ data were collected by the DH3816 static strain test system.Figure 4
Number and position of strain gauges of specimens with different lengths. (a) 100 mm. (b) 200 mm. (c) 400 mm. (d) 800 mm.The slow speed load method was selected for all the tests, and each applied load was about one-tenth of estimated ultimate bearing capacity, which was obtained through preliminary tests on specimens with different bond types. Loading stopped when the slip remained stable or the concrete came into contact with the loading plate.Test results would be expressed by the following parameters:τ, average bond stress (kPa), which is a general designation of the interfacial bond stress between FRP tube and concrete, the anchoring force between internal threads and concrete and the anchoring force between shear connectors and concrete. τ could be calculated as follows:(1)τ=FπdLe,where F is the load applied by the hydraulic jack on FRP tube; d is inside diameter of FRP tube; and Le is bond length between concrete and FRP tube.It should be noted that actual bond stress between FRP tube and concrete is not constant, and there is an effective bond length of the interface [28]. Because this article is mainly concerned with the overall performance of bond stress rather than local bond stress, equation (1). is used here.τu, the maximum τ (kPa), which should be used for the design of FRP-confined concrete piles with shear connectors.τr, ultimate average bond stress (kPa), which is the constant value of bond stress at the end of τ−s curves and should be used for the design of direct bond FRP-confined concrete piles and FRP-confined concrete piles with internal threads.s, average slip between FRP tube and concrete (mm), which is the average displacement of top surface and bottom surface of the FRP tube measured by electronic displacement sensors, based on the assumption that the deformation of concrete and FRP tube is ignorable.su, average slip between FRP tube and concrete when τ reached τu (mm).sr, average slip between FRP tube and concrete when τ reached τr (mm).


## 3. Results and Discussion

Test results of 29 specimens are used to evaluate the bond behavior between FRP tube and concrete. Some important factors that influence bond behavior are examined in the following section.


### 3.1. Influence of the Bond Type on Bond Behavior

As mentioned earlier, all specimens were divided into three types according to bond type: direct bond specimens, specimens with internal threads, and specimens with shear connectors. Because direct bond specimens with normal concrete had low bond stress and limited test data were obtained, P-1, P-2 and P-3 with expansive concrete were selected to represent these three types of specimens to study the influence of bond type on bond behavior. All parameters of P-1, P-2, and P-3 were identical except the bond type, as shown in Table1. The test results of P-1, P-2, and P-3 are shown in Table 4 and Figure 5.Table 4
Test results of specimens P-1, P-2, and P-3.
Code
Bond type
τ
u (kPa)
s
u (mm)
τ
r (kPa)
P-1
Direct bond
59.46
3.56
57.22
P-2
Internal threads
418.45
1.87
307.58
P-3
Shear connectors
382.24
37.51
385.37Figure 5
τ
−
s curves of specimens P-1, P-2, and P-3.Obviously, bond type is a considerable factor affecting bond stress between FRP tube and concrete, and different bond types result in differentτ−s curves and failure modes. For P-1, τ increases with increasing s and remains stable after a small decrease and the specimen fails by shear failure of FRP tube-concrete interface, as shown in Figure 6(a). For P-2, the global behavior of τ−s curve is characterised by an initial increase in τ with little s, followed by softening once τu is attained and keeping stable after softening. This specimen fails by the deformation of internal threads. For P-3, τ shows a law of continuous growth and shear connectors are pulled out (Figure 6(b)). The maximum τu appears in P-2, which is 418.45 kPa, τu of P-3 is slightly lower than that of P-2, and P-1 exhibits the lowest τu, which is only 12% of P-2. However, it should be noted that su of both P-1 and P-2 are less than 4 mm, while su of P-3 is more than 35 mm. The reason for the above differences can be attributed to the different bearing mechanisms: direct bond specimens rely on interfacial friction and chemical adhesion between FRP tube and concrete to resist shear stress, whereas specimens with internal threads and specimens with shear connectors have anchoring force between internal threads and concrete and anchoring force between shear connectors and concrete, respectively, in addition to interfacial friction and chemical adhesion. For specimens with shear connectors, shear connectors still could provide anchoring force even if they are pulled into the FRP tube by concrete, leading to a relatively large su; however, anchorage force between internal threads and concrete and chemical adhesion would decrease dramatically after τ reaching τu, which is the reason for the softening stage of direct bond specimens and specimens with internal threads.Figure 6
Failure modes of specimens. (a) Shear failure of FRP tube-concrete interface. (b) Shear connectors were pulled out.
(a)
(b)


### 3.2. Influence of the Slenderness Ratio on Bond Behavior

As mentioned above, direct bond specimens with normal concrete have low bond stress, and limited test data were collected, so the following analysis of influencing factors mainly focuses on specimens with internal threads and specimens with shear connectors.


#### 3.2.1. Specimens with Internal Threads

Test results of two groups of specimens (each group has three specimens) are used to demonstrate how slenderness ratio of the FRP tube influences on bond behavior of specimens with internal threads. The slenderness ratios vary from 0.5 to 2 in both groups, and the radius-thickness ratios are 18.2 in Group A-1 and 30.8 in Group A-2 separately. Test results of Group A-1 and A-2 are provided in Table5 and Figure 7.Table 5
Test results of specimens in Group A-1 and A-2.
Group
Code
Bond type
Radius-thickness ratio of FRP tube (D/t)
Slenderness ratio of FRP tube (L/D)
τ
u (kPa)
s
u (mm)
τ
r (kPa)
A-1
1-2
Internal threads
18.2
0.5
509.65
2.09
245.35
2-2
Internal threads
18.2
1
491.77
4.04
324.12
3-2
Internal threads
18.2
2
335.30
3.62
146.84
A-2
6-2
Internal threads
30.8
0.5
102.13
1.02
28.00
5-2
Internal threads
30.8
1
144.89
4.80
63.83
4-2
Internal threads
30.8
2
187.14
3.46
93.09Figure 7
τ
−
s curves of Group A-1 and A-2. (a) τ−s curves of Group A-1. (b) τ−s curves of Group A-2.
(a)
(b)As seen from Figure7, although the values of τu are significantly different, the development law of τ−s curves of six specimens is consistent, which could prove the correctness of the test results. For the three specimens in Group A-1, τu of 1-2 and 2-2 are nearly the same, which are 509.65 kPa and 491.77 kPa, respectively, while τu of 3-2 is 335.30 kPa, only 65.8% of 1-2. In terms of τr, the maximum value occurs in 2-2, followed by 1-2 and 3-2. Obviously, in Group A-1, there is no linear relation among τu, τr, and slenderness ratio of the FRP tube. However, for 6-2 in Group A-2, whose slenderness ratio is 0.5, τu, and τr are 102.13 kPa and 28 kPa, respectively. For 5-2, whose slenderness ratio is 1, τu and τr are 144.3 kPa and 63.83 kPa, and for 4-2, whose slenderness ratio is 2, τu and τr are 187.14 kPa and 93.09 kPa. It is obvious that τr increases with the increase of τu, and a linear relationship could be found between bond stress (τu or τr) and slenderness ratio in Group A-2. As to su, the smallest one in two groups appears in the specimens with slenderness ratio of 0.5, but the largest one appeared in the specimens with slenderness ratio of 1, implying that su does not have direct relation with the slenderness ratio.Different groups obtain different relationships between bond stress and slenderness ratio. In order to gain a deep understanding of this relationship, test results of specimens with shear connectors are shown below.


#### 3.2.2. Specimens with Shear Connectors

Test results of two other groups of specimens (each group has three specimens) are analysed to show the effect of slenderness ratio of FRP tube on bond behavior of specimens with shear connectors. The parameters of Groups A-3 and A-4 are identical to those of Groups A-1 and A-2 except bond type. Test results of Groups A-3 and A-4 are provided in Table6 and Figure 8.Table 6
Test results of specimens of Groups A-3 and A-4.
Group
Code
Bond type
Radius-thickness ratio of FRP tube (D/t)
Slenderness ratio of FRP tube (L/D)
τ
u (kPa)
s
u (mm)
τ
r (kPa)
A-3
1-3
Shear connectors
18.2
0.5
175.25
12.78
143.06
2-3
Shear connectors
18.2
1
259.30
12.36
257.51
3-3
Shear connectors
18.2
2
178.83
15.74
185.53
A-4
6-3
Shear connectors
30.8
0.5
93.62
8.65
102.98
5-3
Shear connectors
30.8
1
144.89
14.26
164.81
4-3
Shear connectors
30.8
2
126.78
11.99
135.83Figure 8
τ
−
s curves of Group A-3 and A-4. (a) τ−s curves of Group A-3. (b) τ−s curves of Group A-4.
(a)
(b)Similar to the test results of Group A-1 and A-2,τ−s curves of these six specimens in Group A-3 and A-4 also show a same development law. However, some common points could be found in test results of Group A-3 and A-4: firstly, both the maximum τu and the maximum τr appeared in specimens with slenderness ratio of 1, and both the minimum τu and the minimum τr appeared in specimens, whose slenderness ratio is 0.5; secondly, bond stress (τu or τr) does not increase or decrease with the increase of the slenderness ratio, and the relationship between bond stress and slenderness ratio is uncertain; thirdly, the minimum su appears in specimens with slenderness ratio of 0.5, while the maximum one appears in specimens with slenderness ratio of 1.Based on test results of specimens with internal threads and specimens with shear connectors, the following conclusion can be drawn: there is no obvious correlation between slenderness ratio and bond stress (andsu). This phenomenon can be explained by the following reasons: the resulting bond stress and su is a combined effect of various factors, not limited to those mentioned in this paper; slenderness ratio, as one of the many influencing factors, is the one with less influence; under the influence of other factors, τ−s curve is less sensitive to the change of slenderness ratio and exhibits irregularity.


### 3.3. Influence of the Radius-Thickness Ratio on Bond Behavior

#### 3.3.1. Specimens with Internal Threads

Test results of Groups B1 (7-2 and 2-2) and B2 (8-2 and 4-2) are used to study the influence of the radius-thickness ratio of FRP tubes on bond behavior of specimens with internal threads. Four specimens have the same slenderness ratio, concrete type and concrete stress, except radius-thickness ratio, which varies from 13.3 to 30.8, as shown in Table1. Test results are listed in Table 7, and τ−s curves of these four specimens are plotted in Figure 9.Table 7
Test results of specimens of Groups B-1 and B-2.
Group
Code
Bond type
Geometry size (D × L × t (mm))
Radius- thickness ratio (D/t)
τ
u (kPa)
S
u (mm)
τ
r (kPa)
B1
7-2
Internal threads
200 × 200 × 15
13.3
636.62
3.33
295.84
2-2
Internal threads
200 × 200 × 11
18.2
491.80
4.04
324.12
B2
8-2
Internal threads
400 × 400 × 17
23.5
197.40
5.26
97.62
4-2
Internal threads
400 × 400 × 13
30.8
144.89
4.80
63.83Figure 9
τ
−
s curves of Group B-1 and B-2. (a) τ−s curves of Group B-1. (b) τ−s curves of Group B-2.
(a)
(b)Figure9 clearly illustrates that in Group B-1, τu of specimen 7-2, whose radius-thickness ratio is 13.3, is 636.62 kPa, while τu of specimen 2-2, whose radius-thickness ratio is 18.2, is only 491.80 kPa, accounting for 77.25% of 7-2. The same phenomenon can also be found in Group B-2: compared with specimen 4-2, radius-thickness ratio of 8-2 is relatively small. But τu when the outer diameter changes, dryshrinkage during curing changes and lateral expansion under applied load of concrete is different. The reason why τu increases as radius-thickness decreases is, for specimens with internal threads, shear stress is completely offset by the interaction between concrete and the FRP tube. As the applied load increases, lateral expansion of concrete increases significantly, and the FRP tube starts to restrict the lateral deformation of the concrete. When outer diameters of specimens are the same, a larger thickness (a smaller radius-thickness ratio) means a smaller lateral deformation of the FRP tube, which can lead to a more powerful restriction of FRP tube on concrete [29]. So the bond stress of 7-2 and 8-2 is higher than 2-2 and 4-2, respectively. But when the outer diameter changes, dry shrinkage during curing changes and lateral expansion under applied load of concrete is different; although thickness of the FRP tube increases, its restriction effect may not be fully exerted, leading the bond stress of Group B-2 is smaller than Group B-1.


#### 3.3.2. Specimens with Shear Connectors

Test results of B3 (7-3 and 2-3) and B4 (8-3 and 4-3) are chosen to investigate the effect of the radius-thickness ratio of the FRP tube on the bond behavior of specimens with shear connectors, as summarized in Table8. τ−s curves of these four specimens are shown in Figure 10.Table 8
Test results of specimens of Groups B-3 and B-4.
Group
Code
Bond type
Geometry size (D × L × t (mm))
Radius-thickness ratio (D/t)
τ
u (kPa)
s
u (mm)
τ
r (kPa)
B3
7-3
Shear connectors
200 × 200 × 15
13.3
252.78
14.19
249.03
2-3
Shear connectors
200 × 200 × 11
18.2
259.30
12.36
268.24
B4
8-3
Shear connectors
400 × 400 × 17
23.5
147.85
12.71
171.33
5-3
Shear connectors
400 × 400 × 13
30.8
144.89
14.26
164.81Figure 10
τ
−
s curves of Group B-3 and B-4. (a) τ−s curves of Group B-3. (b) τ−s curves of Group B-4.
(a)
(b)It can be seen from Figure10 that τu of specimens with shear connectors does not increase as radius-thickness ratio decreases, which is completely different from the test results of specimens with internal threads: for Group B-4, radius-thickness ratio decreased by 23.7% (from 30.8 to 23.5), while τu increased only by 2.04% (from 144.89 kPa to 147.85 kPa); for Group B-3, τu does not increase but decreases by 2.5% (from 259.30 kPa to 252.78 kPa) when radius-thickness ratio decreases from 18.2 to 13.3. Different shear transfer methods between specimens with internal threads and specimens with shear connectors is the main reason for different influence of radius-thickness ratio on τu. Specimens with shear connectors relies mainly on anchoring force between shear connectors and concrete to resist the shear stress, and the interaction between concrete and FRP tube contributes only a small part of the shear resistance. The change of radius-thickness ratio has little effect on anchoring force between shear connectors and concrete; therefore, macroscopically, τu is not directly related to radius-thickness ratio.


### 3.4. Influence of the Concrete Strength on Bond Behavior

In order to demonstrate the influence of concrete strength on bond behavior, specimens 2-1, 9-1 and 10-1 are picked out. The only variable of these three specimens is concrete strength, which varies from C30 to C60. Test results are provided in Table9 and Figure 11.Table 9
Test results of specimens 2-1, 9-1, and 10-1.
Code
Concrete strength
τ
u (kPa)
s
u (mm)
τ
r (kPa)
2-1
C30
5.36
1.43
1.07
9-1
C50
7.87
1.00
0.54
10-1
C60
10.73
0.40
0.89Figure 11
τ
−
s curves of specimens 2-1, 9-1, and 10-1.Although dry shrinkage of concrete and smooth inner surface of FRP tube resulted in very low bond stress of the direct bond specimens with normal concrete and limited data were collected during test process, a conclusion that a higher concrete strength is advantageous not only to obtain a higherτu but also to control su could be got from Table 9 and Figure 11: for specimen 2-1, whose concrete strength is C30, τu is 5.36 kPa and suis 1.43 mm. When concrete strength increases to C50 and C60, τuof 9-1 and 10-1 develops rapidly to 7.87 kPa and 10.73 kPa and suis reduced to 1.00 mm and 0.40 mm, respectively. This is because the higher the concrete strength is, the higher the interfacial cohesion between the FRP tube and concrete [30]. Although with the increase of the concrete stress, dry shrinkage increases, leading to a tendency for the concrete to debond from the FRP tube, bond stress still increases with the increase of concrete strength. These results are in accordance with the conclusions of Li et al. [17]. Because a higher interfacial cohesion of concrete is also beneficial to anchoring force between threads and concrete and anchoring force between shear connectors and concrete, it is reasonable to extend this conclusion, which is obtained by the tests on directly bond specimens, to the other two types of specimens.


### 3.5. Influence of the Concrete Type on Bond Behavior

Compared with normal concrete, expansive concrete is believed to have the ability to overcome concrete shrinkage and thus achieve in higher bond stress between concrete and FRP tube. In order to investigate this effect, three groups of specimens (Groups T-1, T-2, and T-3) are prepared, representing three types of bond type. Bond type, slenderness ratio, radius-thickness ratio, and concrete stress of each group are identical, except concrete type. Test results are listed in Table10, and τ−s curves of every group are shown in Figure 12.Table 10
Test results of the specimens in Groups T-1, T-2, and T-3.
Group
Code
Bond type
Concrete type
τ
u (kPa)
s
u (mm)
τ
r (kPa)
T-1
3-1
Direct bond
Normal
6.26
2.90
1.16
P-1
Direct bond
Expansive
59.46
1.56
57.22
T-2
3-2
Internal threads
Normal
335.30
3.62
146.64
P-2
Internal threads
Expansive
418.45
1.87
307.58
T-3
3-3
Shear connectors
Normal
178.83
41.22
185.53
P-3
Shear connectors
Expansive
382.24
37.51
385.37Figure 12
τ
−
s curves of specimens T-1, T-2, and T-3. (a) τ−s curves of Group T-1. (b) τ−s curves of Group T-2. (c) τ−s curves of Group T-3.
(a)
(b)
(c)Figure12 illustrates that τu and τr improve significantly after substituting expansive concrete for normal concrete in all three groups. In Group T-1, τu and τr of specimen 3-1 are only 6.26 kPa and 1.16 kPa, while for specimen P-1, τu and τr increase rapidly to 59.46 kPa and 57.22 kPa, respectively. In Group T-2, which represents specimens with internal threads, specimen P-2 with expansive concrete enhances τu and τr by 125% and 210% and reduces su by 48% than specimen 3-2 with normal concrete. In group T-3, τu reaches 382.24 kPa for specimen P-3, while for specimen 3-3, it is only 178.83 kPa; τr of specimen 3-3 is also only half of specimen P-3. It is clear that although both the improvement of concrete strength and the use of expansive concrete can increase the interaction between concrete and FRP tube, compared with the improvement of concrete strength, the use of expansive concrete is more efficient, and both τu and τr have a greater increase.


### 3.6. Distribution and Development Law of Axial Strain

The axial strain distribution and development law along the height of FRP tube are evaluated by strain gauges at different locations. Because the bond type and concrete type have a great influence on distribution and development law of axial strain, analysis is based on test results of specimens with different bond types and concrete types. The strain analyzed below is the average value of four strain gauges of the same cross section (see Figure4).


#### 3.6.1. Specimens with Internal Threads

4-2 and P-2 representing the specimens with normal concrete and expansive concrete are picked out to study the axial stains of specimens with internal threads. It can be seen from Figures13 and 14 that distribution and development law of axial strain of normal concrete specimens, and expansive concrete specimens are completely different.Figure 13
Strain-slip curves of specimens with internal threads. (a) 4-2. (b) P-2.
(a)
(b)Figure 14
Strain height of FRP tube curves of specimens with internal threads. (a) 4-2. (b) P-2.
(a)
(b)For specimen 4-2, development of strain at different heights is relatively balanced and consistent. All strain is maintained at a very small value when slip is less than 1 mm, but when slip exceeds 3 mm, strain increases markedly. Eventually, the upper strain is greater than the middle strain, which is larger than the lower strain, and an almost uniform strain distribution along the height of FRP tube is observed. The reason for this phenomenon may be that when the applied load is small, the load is resisted by elastic interlock between internal threads and concrete, and no deformation of FRP tube occurs. As the applied load increases, the internal threads distort gradually, leading to a small deformation of FRP tube. Finally, when the internal threads are completely broken, the strain of FRP tube suddenly increases.However, for P-2, strain of FRP tube develops gradually from top to bottom. The upper strain increases linearly from beginning to end, the middle strain begins to grow linearly after the slip reaches 0.25 mm, and the bottom strain begins to increase exponentially with a higher growth rate until the slip reaches 1 mm. The final strain distribution along the height of FRP tube is a polygonal line.The reason for the differences discussed above is considered to be the bond stress of expansive concrete specimens, which is larger than normal concrete specimens. For expansive concrete specimens, bond stress of upper part of specimen can offset the load completely under small load, and the load cannot be transferred to the lower part. As the load increases, the bond stress of the middle and lower parts gradually exerts. However, normal concrete specimens have a small bond stress, and the bond stress of the entire interface needs to be exerted under a small load. Therefore, the strains of the upper, middle, and lower parts are relatively close.


#### 3.6.2. Specimens with Shear Connectors

Figures15 and 16 show strain-slip curves and strain-height curves of specimens with shear connectors (4-3 and P-3 represent normal concrete specimens and expansive concrete specimens separately). By comparison, it can be found that there are many similarities between the two specimens: first, both strain-slip curves exhibit ductile behaviors: when slip is less than 7 mm, the strain increases with the increase of slip, and the strain remains stable after the slip exceeds 7 mm. Second, the upper strain is greater than the middle strain, which is greater than the lower strain. The second similarity is in line with the results of specimens with internal threads, but the difference between the upper stain and the lower strain is significantly larger, illustrating that the load transfer process from top to bottom is slower for specimens with shear connectors. The same conclusion can be drawn from the change of the slope in strain-height curves, which is shown in Figure 16.Figure 15
Strain-slip curves of specimens with shear connectors. (a) 4-3. (b) P-3.
(a)
(b)Figure 16
Strain height of FRP tube curves of specimens with shear connectors. (a) 4-3. (b) P-3.
(a)
(b)


#### 3.6.3. Direct Bond Specimens

For direct bond specimens, because the ultimate load of specimens with normal concrete is very small and axial strain obtained is limited, the strain of expansive concrete specimen (P-1) is analyzed only. In the case of P-1, an almost uniform strain distribution is observed for the initial loading levels. However, when load increases to 5 kN, the strain increases markedly in the upper strain gauge, as shown in Figures17 and 18. The final strain distribution along the height of FRP tube is also a polygonal line.Figure 17
Strain-slip curves of direct bond specimens.Figure 18
Strain-height curves of direct bond specimens.It is noted that the maximum strain of direct bond specimens is only about one-fifth of other two bond types, due to the poor bond stress between FRP tube and concrete. Because the bond stress is low, sliding failure would occur between FRP and concrete under a small load, leading to the stress and strain of FRP tube are very small. Therefore, direct bond type is not recommended in practical engineering.


### 3.7. Simplified Bond-Slip Constitutive Models

Different bond types result in differentτ−s curves, as discussed above. Because bond type is the most important factor, it is reasonable to establish the simplified bond-slip constitutive models according to bond type introduced in this paper.


#### 3.7.1. Direct Bond Specimens

As seen from the test results of direct bond specimens in this paper, a typicalτ−s curve for direct bond specimens is shown in Figure 19. As the load is applied, the ratio between τ and s is approximately linear at first, and the interfacial bond behaves almost as an elastic interface with virtually a full recovery of slip if the load is removed. As soon as the chemical adhesion breaks, the curve is no longer linear, and the maximum τ appears. After τu, τ decreased slightly and then remain constant as s increases to a value that may range from two to ten times than su.Figure 19
Simplified model of theτ−s curve of direct bond specimens.As mentioned before, for direct bond specimens, the applied load is transmitted by chemical adhesion and friction between FRP tube and concrete. Because chemical adhesion is very small, the typicalτ−s curve for direct bond specimens could be considered to be the transition from static friction to dynamic friction.Thus, equation (2) could be used to describe the bond-slip constitutive model of direct bond specimens.(2)τ=as2+bs,s≤su,τ=τr−τusr−sus−su+τu,su<s≤sr,τ=τr,s>sr,where a and b are coefficients, which should be generated by tests.It is easy to calculated that for P-1, representing direct bond specimens, whena = 15 and b = 5, good agreements can be reached between the test results and results of equation (2), as shown in Figure 20.Figure 20
Comparison between test result and theoretical result of P-1.


#### 3.7.2. Specimens with Internal Threads

The typicalτ−s curve of specimens with internal threads is shown in Figure 21. It is clear that the τ−s curve of specimens with internal threads, which can be divided into three sections by point A (τusu) and point B (τrsr), is approximately but not exactly the same as that of direct bond specimens.Figure 21
Simplified model for theτ−s curve of internal threads specimens.The biggest difference is in the first section (from pointO to point A). For direct bond specimens, the curve slope is gradually decreasing, while for specimens with internal threads, the curve slope is gradually increasing. This difference is thought to be a result of the developing law of anchoring forces between threads and concrete. Anchoring force between threads and concrete accounts for a large proportion of shear stress, and the ratio of anchoring forces to s increases as specimen approaches failure.Similarly, equation (3) is a relatively good expression form of the τ−s curve of specimens with internal threads.(3)
τ
=
γ
e
s
−
γ
,
s
≤
s
u
,
τ
=
τ
r
−
τ
u
s
r
−
s
u
s
−
s
u
+
τ
u
,
s
u
<
s
≤
s
r
,
τ
=
τ
r
,
s
>
s
r
.In equation (3), γ is the coefficient of the test parameters.Figure22 shows the comparison between test results and theoretical results of P-2, which represents specimens with internal threads. It is clear that although some errors exist between the results, relatively good agreements can be reached when γ = 75.Figure 22
Comparison between test result and theoretical result of P-2.


#### 3.7.3. Specimens with Shear Connectors

For all specimens with shear connectors tested, allτ−s curves obtained exhibit the same law: with the increase of s, τ becomes larger firstly and keeps steady after arriving at τu. Because of the persistence of anchoring force between shear connectors and concrete, the entire curve does not show a softening stage. Therefore, τ−s curves of specimens with shear connectors could be divided into two sections: an upward section and a steady section. A quadratic parabola and a straight line could be used to describe these two sections visually, and a simplified bond-slip constitutive model of specimens with shear connectors could be expressed as Figure 23 and equation (4).(4)τ=as2+bs,s≤su,τ=τu,s>su,where a and b are coefficients.Figure 23
Simplified model for theτ−s curve of specimens with shear connectors.As shown in Figure24, comparison between test results and theoretical results of P-3 illustrates that when a = -2 and b = 52, results of equation (4) are very close to the test results. Although ultimate bond stress of equation (4) is smaller than the test result, it is beneficial to ensure the safety of FRP-confined concrete piles.Figure 24
Comparison between test results and theoretical results of P-3.


## 3.1. Influence of the Bond Type on Bond Behavior

As mentioned earlier, all specimens were divided into three types according to bond type: direct bond specimens, specimens with internal threads, and specimens with shear connectors. Because direct bond specimens with normal concrete had low bond stress and limited test data were obtained, P-1, P-2 and P-3 with expansive concrete were selected to represent these three types of specimens to study the influence of bond type on bond behavior. All parameters of P-1, P-2, and P-3 were identical except the bond type, as shown in Table1. The test results of P-1, P-2, and P-3 are shown in Table 4 and Figure 5.Table 4
Test results of specimens P-1, P-2, and P-3.
Code
Bond type
τ
u (kPa)
s
u (mm)
τ
r (kPa)
P-1
Direct bond
59.46
3.56
57.22
P-2
Internal threads
418.45
1.87
307.58
P-3
Shear connectors
382.24
37.51
385.37Figure 5
τ
−
s curves of specimens P-1, P-2, and P-3.Obviously, bond type is a considerable factor affecting bond stress between FRP tube and concrete, and different bond types result in differentτ−s curves and failure modes. For P-1, τ increases with increasing s and remains stable after a small decrease and the specimen fails by shear failure of FRP tube-concrete interface, as shown in Figure 6(a). For P-2, the global behavior of τ−s curve is characterised by an initial increase in τ with little s, followed by softening once τu is attained and keeping stable after softening. This specimen fails by the deformation of internal threads. For P-3, τ shows a law of continuous growth and shear connectors are pulled out (Figure 6(b)). The maximum τu appears in P-2, which is 418.45 kPa, τu of P-3 is slightly lower than that of P-2, and P-1 exhibits the lowest τu, which is only 12% of P-2. However, it should be noted that su of both P-1 and P-2 are less than 4 mm, while su of P-3 is more than 35 mm. The reason for the above differences can be attributed to the different bearing mechanisms: direct bond specimens rely on interfacial friction and chemical adhesion between FRP tube and concrete to resist shear stress, whereas specimens with internal threads and specimens with shear connectors have anchoring force between internal threads and concrete and anchoring force between shear connectors and concrete, respectively, in addition to interfacial friction and chemical adhesion. For specimens with shear connectors, shear connectors still could provide anchoring force even if they are pulled into the FRP tube by concrete, leading to a relatively large su; however, anchorage force between internal threads and concrete and chemical adhesion would decrease dramatically after τ reaching τu, which is the reason for the softening stage of direct bond specimens and specimens with internal threads.Figure 6
Failure modes of specimens. (a) Shear failure of FRP tube-concrete interface. (b) Shear connectors were pulled out.
(a)
(b)


## 3.2. Influence of the Slenderness Ratio on Bond Behavior

As mentioned above, direct bond specimens with normal concrete have low bond stress, and limited test data were collected, so the following analysis of influencing factors mainly focuses on specimens with internal threads and specimens with shear connectors.


### 3.2.1. Specimens with Internal Threads

Test results of two groups of specimens (each group has three specimens) are used to demonstrate how slenderness ratio of the FRP tube influences on bond behavior of specimens with internal threads. The slenderness ratios vary from 0.5 to 2 in both groups, and the radius-thickness ratios are 18.2 in Group A-1 and 30.8 in Group A-2 separately. Test results of Group A-1 and A-2 are provided in Table5 and Figure 7.Table 5
Test results of specimens in Group A-1 and A-2.
Group
Code
Bond type
Radius-thickness ratio of FRP tube (D/t)
Slenderness ratio of FRP tube (L/D)
τ
u (kPa)
s
u (mm)
τ
r (kPa)
A-1
1-2
Internal threads
18.2
0.5
509.65
2.09
245.35
2-2
Internal threads
18.2
1
491.77
4.04
324.12
3-2
Internal threads
18.2
2
335.30
3.62
146.84
A-2
6-2
Internal threads
30.8
0.5
102.13
1.02
28.00
5-2
Internal threads
30.8
1
144.89
4.80
63.83
4-2
Internal threads
30.8
2
187.14
3.46
93.09Figure 7
τ
−
s curves of Group A-1 and A-2. (a) τ−s curves of Group A-1. (b) τ−s curves of Group A-2.
(a)
(b)As seen from Figure7, although the values of τu are significantly different, the development law of τ−s curves of six specimens is consistent, which could prove the correctness of the test results. For the three specimens in Group A-1, τu of 1-2 and 2-2 are nearly the same, which are 509.65 kPa and 491.77 kPa, respectively, while τu of 3-2 is 335.30 kPa, only 65.8% of 1-2. In terms of τr, the maximum value occurs in 2-2, followed by 1-2 and 3-2. Obviously, in Group A-1, there is no linear relation among τu, τr, and slenderness ratio of the FRP tube. However, for 6-2 in Group A-2, whose slenderness ratio is 0.5, τu, and τr are 102.13 kPa and 28 kPa, respectively. For 5-2, whose slenderness ratio is 1, τu and τr are 144.3 kPa and 63.83 kPa, and for 4-2, whose slenderness ratio is 2, τu and τr are 187.14 kPa and 93.09 kPa. It is obvious that τr increases with the increase of τu, and a linear relationship could be found between bond stress (τu or τr) and slenderness ratio in Group A-2. As to su, the smallest one in two groups appears in the specimens with slenderness ratio of 0.5, but the largest one appeared in the specimens with slenderness ratio of 1, implying that su does not have direct relation with the slenderness ratio.Different groups obtain different relationships between bond stress and slenderness ratio. In order to gain a deep understanding of this relationship, test results of specimens with shear connectors are shown below.


### 3.2.2. Specimens with Shear Connectors

Test results of two other groups of specimens (each group has three specimens) are analysed to show the effect of slenderness ratio of FRP tube on bond behavior of specimens with shear connectors. The parameters of Groups A-3 and A-4 are identical to those of Groups A-1 and A-2 except bond type. Test results of Groups A-3 and A-4 are provided in Table6 and Figure 8.Table 6
Test results of specimens of Groups A-3 and A-4.
Group
Code
Bond type
Radius-thickness ratio of FRP tube (D/t)
Slenderness ratio of FRP tube (L/D)
τ
u (kPa)
s
u (mm)
τ
r (kPa)
A-3
1-3
Shear connectors
18.2
0.5
175.25
12.78
143.06
2-3
Shear connectors
18.2
1
259.30
12.36
257.51
3-3
Shear connectors
18.2
2
178.83
15.74
185.53
A-4
6-3
Shear connectors
30.8
0.5
93.62
8.65
102.98
5-3
Shear connectors
30.8
1
144.89
14.26
164.81
4-3
Shear connectors
30.8
2
126.78
11.99
135.83Figure 8
τ
−
s curves of Group A-3 and A-4. (a) τ−s curves of Group A-3. (b) τ−s curves of Group A-4.
(a)
(b)Similar to the test results of Group A-1 and A-2,τ−s curves of these six specimens in Group A-3 and A-4 also show a same development law. However, some common points could be found in test results of Group A-3 and A-4: firstly, both the maximum τu and the maximum τr appeared in specimens with slenderness ratio of 1, and both the minimum τu and the minimum τr appeared in specimens, whose slenderness ratio is 0.5; secondly, bond stress (τu or τr) does not increase or decrease with the increase of the slenderness ratio, and the relationship between bond stress and slenderness ratio is uncertain; thirdly, the minimum su appears in specimens with slenderness ratio of 0.5, while the maximum one appears in specimens with slenderness ratio of 1.Based on test results of specimens with internal threads and specimens with shear connectors, the following conclusion can be drawn: there is no obvious correlation between slenderness ratio and bond stress (andsu). This phenomenon can be explained by the following reasons: the resulting bond stress and su is a combined effect of various factors, not limited to those mentioned in this paper; slenderness ratio, as one of the many influencing factors, is the one with less influence; under the influence of other factors, τ−s curve is less sensitive to the change of slenderness ratio and exhibits irregularity.


## 3.2.1. Specimens with Internal Threads

Test results of two groups of specimens (each group has three specimens) are used to demonstrate how slenderness ratio of the FRP tube influences on bond behavior of specimens with internal threads. The slenderness ratios vary from 0.5 to 2 in both groups, and the radius-thickness ratios are 18.2 in Group A-1 and 30.8 in Group A-2 separately. Test results of Group A-1 and A-2 are provided in Table5 and Figure 7.Table 5
Test results of specimens in Group A-1 and A-2.
Group
Code
Bond type
Radius-thickness ratio of FRP tube (D/t)
Slenderness ratio of FRP tube (L/D)
τ
u (kPa)
s
u (mm)
τ
r (kPa)
A-1
1-2
Internal threads
18.2
0.5
509.65
2.09
245.35
2-2
Internal threads
18.2
1
491.77
4.04
324.12
3-2
Internal threads
18.2
2
335.30
3.62
146.84
A-2
6-2
Internal threads
30.8
0.5
102.13
1.02
28.00
5-2
Internal threads
30.8
1
144.89
4.80
63.83
4-2
Internal threads
30.8
2
187.14
3.46
93.09Figure 7
τ
−
s curves of Group A-1 and A-2. (a) τ−s curves of Group A-1. (b) τ−s curves of Group A-2.
(a)
(b)As seen from Figure7, although the values of τu are significantly different, the development law of τ−s curves of six specimens is consistent, which could prove the correctness of the test results. For the three specimens in Group A-1, τu of 1-2 and 2-2 are nearly the same, which are 509.65 kPa and 491.77 kPa, respectively, while τu of 3-2 is 335.30 kPa, only 65.8% of 1-2. In terms of τr, the maximum value occurs in 2-2, followed by 1-2 and 3-2. Obviously, in Group A-1, there is no linear relation among τu, τr, and slenderness ratio of the FRP tube. However, for 6-2 in Group A-2, whose slenderness ratio is 0.5, τu, and τr are 102.13 kPa and 28 kPa, respectively. For 5-2, whose slenderness ratio is 1, τu and τr are 144.3 kPa and 63.83 kPa, and for 4-2, whose slenderness ratio is 2, τu and τr are 187.14 kPa and 93.09 kPa. It is obvious that τr increases with the increase of τu, and a linear relationship could be found between bond stress (τu or τr) and slenderness ratio in Group A-2. As to su, the smallest one in two groups appears in the specimens with slenderness ratio of 0.5, but the largest one appeared in the specimens with slenderness ratio of 1, implying that su does not have direct relation with the slenderness ratio.Different groups obtain different relationships between bond stress and slenderness ratio. In order to gain a deep understanding of this relationship, test results of specimens with shear connectors are shown below.


## 3.2.2. Specimens with Shear Connectors

Test results of two other groups of specimens (each group has three specimens) are analysed to show the effect of slenderness ratio of FRP tube on bond behavior of specimens with shear connectors. The parameters of Groups A-3 and A-4 are identical to those of Groups A-1 and A-2 except bond type. Test results of Groups A-3 and A-4 are provided in Table6 and Figure 8.Table 6
Test results of specimens of Groups A-3 and A-4.
Group
Code
Bond type
Radius-thickness ratio of FRP tube (D/t)
Slenderness ratio of FRP tube (L/D)
τ
u (kPa)
s
u (mm)
τ
r (kPa)
A-3
1-3
Shear connectors
18.2
0.5
175.25
12.78
143.06
2-3
Shear connectors
18.2
1
259.30
12.36
257.51
3-3
Shear connectors
18.2
2
178.83
15.74
185.53
A-4
6-3
Shear connectors
30.8
0.5
93.62
8.65
102.98
5-3
Shear connectors
30.8
1
144.89
14.26
164.81
4-3
Shear connectors
30.8
2
126.78
11.99
135.83Figure 8
τ
−
s curves of Group A-3 and A-4. (a) τ−s curves of Group A-3. (b) τ−s curves of Group A-4.
(a)
(b)Similar to the test results of Group A-1 and A-2,τ−s curves of these six specimens in Group A-3 and A-4 also show a same development law. However, some common points could be found in test results of Group A-3 and A-4: firstly, both the maximum τu and the maximum τr appeared in specimens with slenderness ratio of 1, and both the minimum τu and the minimum τr appeared in specimens, whose slenderness ratio is 0.5; secondly, bond stress (τu or τr) does not increase or decrease with the increase of the slenderness ratio, and the relationship between bond stress and slenderness ratio is uncertain; thirdly, the minimum su appears in specimens with slenderness ratio of 0.5, while the maximum one appears in specimens with slenderness ratio of 1.Based on test results of specimens with internal threads and specimens with shear connectors, the following conclusion can be drawn: there is no obvious correlation between slenderness ratio and bond stress (andsu). This phenomenon can be explained by the following reasons: the resulting bond stress and su is a combined effect of various factors, not limited to those mentioned in this paper; slenderness ratio, as one of the many influencing factors, is the one with less influence; under the influence of other factors, τ−s curve is less sensitive to the change of slenderness ratio and exhibits irregularity.


## 3.3. Influence of the Radius-Thickness Ratio on Bond Behavior

### 3.3.1. Specimens with Internal Threads

Test results of Groups B1 (7-2 and 2-2) and B2 (8-2 and 4-2) are used to study the influence of the radius-thickness ratio of FRP tubes on bond behavior of specimens with internal threads. Four specimens have the same slenderness ratio, concrete type and concrete stress, except radius-thickness ratio, which varies from 13.3 to 30.8, as shown in Table1. Test results are listed in Table 7, and τ−s curves of these four specimens are plotted in Figure 9.Table 7
Test results of specimens of Groups B-1 and B-2.
Group
Code
Bond type
Geometry size (D × L × t (mm))
Radius- thickness ratio (D/t)
τ
u (kPa)
S
u (mm)
τ
r (kPa)
B1
7-2
Internal threads
200 × 200 × 15
13.3
636.62
3.33
295.84
2-2
Internal threads
200 × 200 × 11
18.2
491.80
4.04
324.12
B2
8-2
Internal threads
400 × 400 × 17
23.5
197.40
5.26
97.62
4-2
Internal threads
400 × 400 × 13
30.8
144.89
4.80
63.83Figure 9
τ
−
s curves of Group B-1 and B-2. (a) τ−s curves of Group B-1. (b) τ−s curves of Group B-2.
(a)
(b)Figure9 clearly illustrates that in Group B-1, τu of specimen 7-2, whose radius-thickness ratio is 13.3, is 636.62 kPa, while τu of specimen 2-2, whose radius-thickness ratio is 18.2, is only 491.80 kPa, accounting for 77.25% of 7-2. The same phenomenon can also be found in Group B-2: compared with specimen 4-2, radius-thickness ratio of 8-2 is relatively small. But τu when the outer diameter changes, dryshrinkage during curing changes and lateral expansion under applied load of concrete is different. The reason why τu increases as radius-thickness decreases is, for specimens with internal threads, shear stress is completely offset by the interaction between concrete and the FRP tube. As the applied load increases, lateral expansion of concrete increases significantly, and the FRP tube starts to restrict the lateral deformation of the concrete. When outer diameters of specimens are the same, a larger thickness (a smaller radius-thickness ratio) means a smaller lateral deformation of the FRP tube, which can lead to a more powerful restriction of FRP tube on concrete [29]. So the bond stress of 7-2 and 8-2 is higher than 2-2 and 4-2, respectively. But when the outer diameter changes, dry shrinkage during curing changes and lateral expansion under applied load of concrete is different; although thickness of the FRP tube increases, its restriction effect may not be fully exerted, leading the bond stress of Group B-2 is smaller than Group B-1.


### 3.3.2. Specimens with Shear Connectors

Test results of B3 (7-3 and 2-3) and B4 (8-3 and 4-3) are chosen to investigate the effect of the radius-thickness ratio of the FRP tube on the bond behavior of specimens with shear connectors, as summarized in Table8. τ−s curves of these four specimens are shown in Figure 10.Table 8
Test results of specimens of Groups B-3 and B-4.
Group
Code
Bond type
Geometry size (D × L × t (mm))
Radius-thickness ratio (D/t)
τ
u (kPa)
s
u (mm)
τ
r (kPa)
B3
7-3
Shear connectors
200 × 200 × 15
13.3
252.78
14.19
249.03
2-3
Shear connectors
200 × 200 × 11
18.2
259.30
12.36
268.24
B4
8-3
Shear connectors
400 × 400 × 17
23.5
147.85
12.71
171.33
5-3
Shear connectors
400 × 400 × 13
30.8
144.89
14.26
164.81Figure 10
τ
−
s curves of Group B-3 and B-4. (a) τ−s curves of Group B-3. (b) τ−s curves of Group B-4.
(a)
(b)It can be seen from Figure10 that τu of specimens with shear connectors does not increase as radius-thickness ratio decreases, which is completely different from the test results of specimens with internal threads: for Group B-4, radius-thickness ratio decreased by 23.7% (from 30.8 to 23.5), while τu increased only by 2.04% (from 144.89 kPa to 147.85 kPa); for Group B-3, τu does not increase but decreases by 2.5% (from 259.30 kPa to 252.78 kPa) when radius-thickness ratio decreases from 18.2 to 13.3. Different shear transfer methods between specimens with internal threads and specimens with shear connectors is the main reason for different influence of radius-thickness ratio on τu. Specimens with shear connectors relies mainly on anchoring force between shear connectors and concrete to resist the shear stress, and the interaction between concrete and FRP tube contributes only a small part of the shear resistance. The change of radius-thickness ratio has little effect on anchoring force between shear connectors and concrete; therefore, macroscopically, τu is not directly related to radius-thickness ratio.


## 3.3.1. Specimens with Internal Threads

Test results of Groups B1 (7-2 and 2-2) and B2 (8-2 and 4-2) are used to study the influence of the radius-thickness ratio of FRP tubes on bond behavior of specimens with internal threads. Four specimens have the same slenderness ratio, concrete type and concrete stress, except radius-thickness ratio, which varies from 13.3 to 30.8, as shown in Table1. Test results are listed in Table 7, and τ−s curves of these four specimens are plotted in Figure 9.Table 7
Test results of specimens of Groups B-1 and B-2.
Group
Code
Bond type
Geometry size (D × L × t (mm))
Radius- thickness ratio (D/t)
τ
u (kPa)
S
u (mm)
τ
r (kPa)
B1
7-2
Internal threads
200 × 200 × 15
13.3
636.62
3.33
295.84
2-2
Internal threads
200 × 200 × 11
18.2
491.80
4.04
324.12
B2
8-2
Internal threads
400 × 400 × 17
23.5
197.40
5.26
97.62
4-2
Internal threads
400 × 400 × 13
30.8
144.89
4.80
63.83Figure 9
τ
−
s curves of Group B-1 and B-2. (a) τ−s curves of Group B-1. (b) τ−s curves of Group B-2.
(a)
(b)Figure9 clearly illustrates that in Group B-1, τu of specimen 7-2, whose radius-thickness ratio is 13.3, is 636.62 kPa, while τu of specimen 2-2, whose radius-thickness ratio is 18.2, is only 491.80 kPa, accounting for 77.25% of 7-2. The same phenomenon can also be found in Group B-2: compared with specimen 4-2, radius-thickness ratio of 8-2 is relatively small. But τu when the outer diameter changes, dryshrinkage during curing changes and lateral expansion under applied load of concrete is different. The reason why τu increases as radius-thickness decreases is, for specimens with internal threads, shear stress is completely offset by the interaction between concrete and the FRP tube. As the applied load increases, lateral expansion of concrete increases significantly, and the FRP tube starts to restrict the lateral deformation of the concrete. When outer diameters of specimens are the same, a larger thickness (a smaller radius-thickness ratio) means a smaller lateral deformation of the FRP tube, which can lead to a more powerful restriction of FRP tube on concrete [29]. So the bond stress of 7-2 and 8-2 is higher than 2-2 and 4-2, respectively. But when the outer diameter changes, dry shrinkage during curing changes and lateral expansion under applied load of concrete is different; although thickness of the FRP tube increases, its restriction effect may not be fully exerted, leading the bond stress of Group B-2 is smaller than Group B-1.


## 3.3.2. Specimens with Shear Connectors

Test results of B3 (7-3 and 2-3) and B4 (8-3 and 4-3) are chosen to investigate the effect of the radius-thickness ratio of the FRP tube on the bond behavior of specimens with shear connectors, as summarized in Table8. τ−s curves of these four specimens are shown in Figure 10.Table 8
Test results of specimens of Groups B-3 and B-4.
Group
Code
Bond type
Geometry size (D × L × t (mm))
Radius-thickness ratio (D/t)
τ
u (kPa)
s
u (mm)
τ
r (kPa)
B3
7-3
Shear connectors
200 × 200 × 15
13.3
252.78
14.19
249.03
2-3
Shear connectors
200 × 200 × 11
18.2
259.30
12.36
268.24
B4
8-3
Shear connectors
400 × 400 × 17
23.5
147.85
12.71
171.33
5-3
Shear connectors
400 × 400 × 13
30.8
144.89
14.26
164.81Figure 10
τ
−
s curves of Group B-3 and B-4. (a) τ−s curves of Group B-3. (b) τ−s curves of Group B-4.
(a)
(b)It can be seen from Figure10 that τu of specimens with shear connectors does not increase as radius-thickness ratio decreases, which is completely different from the test results of specimens with internal threads: for Group B-4, radius-thickness ratio decreased by 23.7% (from 30.8 to 23.5), while τu increased only by 2.04% (from 144.89 kPa to 147.85 kPa); for Group B-3, τu does not increase but decreases by 2.5% (from 259.30 kPa to 252.78 kPa) when radius-thickness ratio decreases from 18.2 to 13.3. Different shear transfer methods between specimens with internal threads and specimens with shear connectors is the main reason for different influence of radius-thickness ratio on τu. Specimens with shear connectors relies mainly on anchoring force between shear connectors and concrete to resist the shear stress, and the interaction between concrete and FRP tube contributes only a small part of the shear resistance. The change of radius-thickness ratio has little effect on anchoring force between shear connectors and concrete; therefore, macroscopically, τu is not directly related to radius-thickness ratio.


## 3.4. Influence of the Concrete Strength on Bond Behavior

In order to demonstrate the influence of concrete strength on bond behavior, specimens 2-1, 9-1 and 10-1 are picked out. The only variable of these three specimens is concrete strength, which varies from C30 to C60. Test results are provided in Table9 and Figure 11.Table 9
Test results of specimens 2-1, 9-1, and 10-1.
Code
Concrete strength
τ
u (kPa)
s
u (mm)
τ
r (kPa)
2-1
C30
5.36
1.43
1.07
9-1
C50
7.87
1.00
0.54
10-1
C60
10.73
0.40
0.89Figure 11
τ
−
s curves of specimens 2-1, 9-1, and 10-1.Although dry shrinkage of concrete and smooth inner surface of FRP tube resulted in very low bond stress of the direct bond specimens with normal concrete and limited data were collected during test process, a conclusion that a higher concrete strength is advantageous not only to obtain a higherτu but also to control su could be got from Table 9 and Figure 11: for specimen 2-1, whose concrete strength is C30, τu is 5.36 kPa and suis 1.43 mm. When concrete strength increases to C50 and C60, τuof 9-1 and 10-1 develops rapidly to 7.87 kPa and 10.73 kPa and suis reduced to 1.00 mm and 0.40 mm, respectively. This is because the higher the concrete strength is, the higher the interfacial cohesion between the FRP tube and concrete [30]. Although with the increase of the concrete stress, dry shrinkage increases, leading to a tendency for the concrete to debond from the FRP tube, bond stress still increases with the increase of concrete strength. These results are in accordance with the conclusions of Li et al. [17]. Because a higher interfacial cohesion of concrete is also beneficial to anchoring force between threads and concrete and anchoring force between shear connectors and concrete, it is reasonable to extend this conclusion, which is obtained by the tests on directly bond specimens, to the other two types of specimens.


## 3.5. Influence of the Concrete Type on Bond Behavior

Compared with normal concrete, expansive concrete is believed to have the ability to overcome concrete shrinkage and thus achieve in higher bond stress between concrete and FRP tube. In order to investigate this effect, three groups of specimens (Groups T-1, T-2, and T-3) are prepared, representing three types of bond type. Bond type, slenderness ratio, radius-thickness ratio, and concrete stress of each group are identical, except concrete type. Test results are listed in Table10, and τ−s curves of every group are shown in Figure 12.Table 10
Test results of the specimens in Groups T-1, T-2, and T-3.
Group
Code
Bond type
Concrete type
τ
u (kPa)
s
u (mm)
τ
r (kPa)
T-1
3-1
Direct bond
Normal
6.26
2.90
1.16
P-1
Direct bond
Expansive
59.46
1.56
57.22
T-2
3-2
Internal threads
Normal
335.30
3.62
146.64
P-2
Internal threads
Expansive
418.45
1.87
307.58
T-3
3-3
Shear connectors
Normal
178.83
41.22
185.53
P-3
Shear connectors
Expansive
382.24
37.51
385.37Figure 12
τ
−
s curves of specimens T-1, T-2, and T-3. (a) τ−s curves of Group T-1. (b) τ−s curves of Group T-2. (c) τ−s curves of Group T-3.
(a)
(b)
(c)Figure12 illustrates that τu and τr improve significantly after substituting expansive concrete for normal concrete in all three groups. In Group T-1, τu and τr of specimen 3-1 are only 6.26 kPa and 1.16 kPa, while for specimen P-1, τu and τr increase rapidly to 59.46 kPa and 57.22 kPa, respectively. In Group T-2, which represents specimens with internal threads, specimen P-2 with expansive concrete enhances τu and τr by 125% and 210% and reduces su by 48% than specimen 3-2 with normal concrete. In group T-3, τu reaches 382.24 kPa for specimen P-3, while for specimen 3-3, it is only 178.83 kPa; τr of specimen 3-3 is also only half of specimen P-3. It is clear that although both the improvement of concrete strength and the use of expansive concrete can increase the interaction between concrete and FRP tube, compared with the improvement of concrete strength, the use of expansive concrete is more efficient, and both τu and τr have a greater increase.


## 3.6. Distribution and Development Law of Axial Strain

The axial strain distribution and development law along the height of FRP tube are evaluated by strain gauges at different locations. Because the bond type and concrete type have a great influence on distribution and development law of axial strain, analysis is based on test results of specimens with different bond types and concrete types. The strain analyzed below is the average value of four strain gauges of the same cross section (see Figure4).


### 3.6.1. Specimens with Internal Threads

4-2 and P-2 representing the specimens with normal concrete and expansive concrete are picked out to study the axial stains of specimens with internal threads. It can be seen from Figures13 and 14 that distribution and development law of axial strain of normal concrete specimens, and expansive concrete specimens are completely different.Figure 13
Strain-slip curves of specimens with internal threads. (a) 4-2. (b) P-2.
(a)
(b)Figure 14
Strain height of FRP tube curves of specimens with internal threads. (a) 4-2. (b) P-2.
(a)
(b)For specimen 4-2, development of strain at different heights is relatively balanced and consistent. All strain is maintained at a very small value when slip is less than 1 mm, but when slip exceeds 3 mm, strain increases markedly. Eventually, the upper strain is greater than the middle strain, which is larger than the lower strain, and an almost uniform strain distribution along the height of FRP tube is observed. The reason for this phenomenon may be that when the applied load is small, the load is resisted by elastic interlock between internal threads and concrete, and no deformation of FRP tube occurs. As the applied load increases, the internal threads distort gradually, leading to a small deformation of FRP tube. Finally, when the internal threads are completely broken, the strain of FRP tube suddenly increases.However, for P-2, strain of FRP tube develops gradually from top to bottom. The upper strain increases linearly from beginning to end, the middle strain begins to grow linearly after the slip reaches 0.25 mm, and the bottom strain begins to increase exponentially with a higher growth rate until the slip reaches 1 mm. The final strain distribution along the height of FRP tube is a polygonal line.The reason for the differences discussed above is considered to be the bond stress of expansive concrete specimens, which is larger than normal concrete specimens. For expansive concrete specimens, bond stress of upper part of specimen can offset the load completely under small load, and the load cannot be transferred to the lower part. As the load increases, the bond stress of the middle and lower parts gradually exerts. However, normal concrete specimens have a small bond stress, and the bond stress of the entire interface needs to be exerted under a small load. Therefore, the strains of the upper, middle, and lower parts are relatively close.


### 3.6.2. Specimens with Shear Connectors

Figures15 and 16 show strain-slip curves and strain-height curves of specimens with shear connectors (4-3 and P-3 represent normal concrete specimens and expansive concrete specimens separately). By comparison, it can be found that there are many similarities between the two specimens: first, both strain-slip curves exhibit ductile behaviors: when slip is less than 7 mm, the strain increases with the increase of slip, and the strain remains stable after the slip exceeds 7 mm. Second, the upper strain is greater than the middle strain, which is greater than the lower strain. The second similarity is in line with the results of specimens with internal threads, but the difference between the upper stain and the lower strain is significantly larger, illustrating that the load transfer process from top to bottom is slower for specimens with shear connectors. The same conclusion can be drawn from the change of the slope in strain-height curves, which is shown in Figure 16.Figure 15
Strain-slip curves of specimens with shear connectors. (a) 4-3. (b) P-3.
(a)
(b)Figure 16
Strain height of FRP tube curves of specimens with shear connectors. (a) 4-3. (b) P-3.
(a)
(b)


### 3.6.3. Direct Bond Specimens

For direct bond specimens, because the ultimate load of specimens with normal concrete is very small and axial strain obtained is limited, the strain of expansive concrete specimen (P-1) is analyzed only. In the case of P-1, an almost uniform strain distribution is observed for the initial loading levels. However, when load increases to 5 kN, the strain increases markedly in the upper strain gauge, as shown in Figures17 and 18. The final strain distribution along the height of FRP tube is also a polygonal line.Figure 17
Strain-slip curves of direct bond specimens.Figure 18
Strain-height curves of direct bond specimens.It is noted that the maximum strain of direct bond specimens is only about one-fifth of other two bond types, due to the poor bond stress between FRP tube and concrete. Because the bond stress is low, sliding failure would occur between FRP and concrete under a small load, leading to the stress and strain of FRP tube are very small. Therefore, direct bond type is not recommended in practical engineering.


## 3.6.1. Specimens with Internal Threads

4-2 and P-2 representing the specimens with normal concrete and expansive concrete are picked out to study the axial stains of specimens with internal threads. It can be seen from Figures13 and 14 that distribution and development law of axial strain of normal concrete specimens, and expansive concrete specimens are completely different.Figure 13
Strain-slip curves of specimens with internal threads. (a) 4-2. (b) P-2.
(a)
(b)Figure 14
Strain height of FRP tube curves of specimens with internal threads. (a) 4-2. (b) P-2.
(a)
(b)For specimen 4-2, development of strain at different heights is relatively balanced and consistent. All strain is maintained at a very small value when slip is less than 1 mm, but when slip exceeds 3 mm, strain increases markedly. Eventually, the upper strain is greater than the middle strain, which is larger than the lower strain, and an almost uniform strain distribution along the height of FRP tube is observed. The reason for this phenomenon may be that when the applied load is small, the load is resisted by elastic interlock between internal threads and concrete, and no deformation of FRP tube occurs. As the applied load increases, the internal threads distort gradually, leading to a small deformation of FRP tube. Finally, when the internal threads are completely broken, the strain of FRP tube suddenly increases.However, for P-2, strain of FRP tube develops gradually from top to bottom. The upper strain increases linearly from beginning to end, the middle strain begins to grow linearly after the slip reaches 0.25 mm, and the bottom strain begins to increase exponentially with a higher growth rate until the slip reaches 1 mm. The final strain distribution along the height of FRP tube is a polygonal line.The reason for the differences discussed above is considered to be the bond stress of expansive concrete specimens, which is larger than normal concrete specimens. For expansive concrete specimens, bond stress of upper part of specimen can offset the load completely under small load, and the load cannot be transferred to the lower part. As the load increases, the bond stress of the middle and lower parts gradually exerts. However, normal concrete specimens have a small bond stress, and the bond stress of the entire interface needs to be exerted under a small load. Therefore, the strains of the upper, middle, and lower parts are relatively close.


## 3.6.2. Specimens with Shear Connectors

Figures15 and 16 show strain-slip curves and strain-height curves of specimens with shear connectors (4-3 and P-3 represent normal concrete specimens and expansive concrete specimens separately). By comparison, it can be found that there are many similarities between the two specimens: first, both strain-slip curves exhibit ductile behaviors: when slip is less than 7 mm, the strain increases with the increase of slip, and the strain remains stable after the slip exceeds 7 mm. Second, the upper strain is greater than the middle strain, which is greater than the lower strain. The second similarity is in line with the results of specimens with internal threads, but the difference between the upper stain and the lower strain is significantly larger, illustrating that the load transfer process from top to bottom is slower for specimens with shear connectors. The same conclusion can be drawn from the change of the slope in strain-height curves, which is shown in Figure 16.Figure 15
Strain-slip curves of specimens with shear connectors. (a) 4-3. (b) P-3.
(a)
(b)Figure 16
Strain height of FRP tube curves of specimens with shear connectors. (a) 4-3. (b) P-3.
(a)
(b)


## 3.6.3. Direct Bond Specimens

For direct bond specimens, because the ultimate load of specimens with normal concrete is very small and axial strain obtained is limited, the strain of expansive concrete specimen (P-1) is analyzed only. In the case of P-1, an almost uniform strain distribution is observed for the initial loading levels. However, when load increases to 5 kN, the strain increases markedly in the upper strain gauge, as shown in Figures17 and 18. The final strain distribution along the height of FRP tube is also a polygonal line.Figure 17
Strain-slip curves of direct bond specimens.Figure 18
Strain-height curves of direct bond specimens.It is noted that the maximum strain of direct bond specimens is only about one-fifth of other two bond types, due to the poor bond stress between FRP tube and concrete. Because the bond stress is low, sliding failure would occur between FRP and concrete under a small load, leading to the stress and strain of FRP tube are very small. Therefore, direct bond type is not recommended in practical engineering.


## 3.7. Simplified Bond-Slip Constitutive Models

Different bond types result in differentτ−s curves, as discussed above. Because bond type is the most important factor, it is reasonable to establish the simplified bond-slip constitutive models according to bond type introduced in this paper.


### 3.7.1. Direct Bond Specimens

As seen from the test results of direct bond specimens in this paper, a typicalτ−s curve for direct bond specimens is shown in Figure 19. As the load is applied, the ratio between τ and s is approximately linear at first, and the interfacial bond behaves almost as an elastic interface with virtually a full recovery of slip if the load is removed. As soon as the chemical adhesion breaks, the curve is no longer linear, and the maximum τ appears. After τu, τ decreased slightly and then remain constant as s increases to a value that may range from two to ten times than su.Figure 19
Simplified model of theτ−s curve of direct bond specimens.As mentioned before, for direct bond specimens, the applied load is transmitted by chemical adhesion and friction between FRP tube and concrete. Because chemical adhesion is very small, the typicalτ−s curve for direct bond specimens could be considered to be the transition from static friction to dynamic friction.Thus, equation (2) could be used to describe the bond-slip constitutive model of direct bond specimens.(2)τ=as2+bs,s≤su,τ=τr−τusr−sus−su+τu,su<s≤sr,τ=τr,s>sr,where a and b are coefficients, which should be generated by tests.It is easy to calculated that for P-1, representing direct bond specimens, whena = 15 and b = 5, good agreements can be reached between the test results and results of equation (2), as shown in Figure 20.Figure 20
Comparison between test result and theoretical result of P-1.


### 3.7.2. Specimens with Internal Threads

The typicalτ−s curve of specimens with internal threads is shown in Figure 21. It is clear that the τ−s curve of specimens with internal threads, which can be divided into three sections by point A (τusu) and point B (τrsr), is approximately but not exactly the same as that of direct bond specimens.Figure 21
Simplified model for theτ−s curve of internal threads specimens.The biggest difference is in the first section (from pointO to point A). For direct bond specimens, the curve slope is gradually decreasing, while for specimens with internal threads, the curve slope is gradually increasing. This difference is thought to be a result of the developing law of anchoring forces between threads and concrete. Anchoring force between threads and concrete accounts for a large proportion of shear stress, and the ratio of anchoring forces to s increases as specimen approaches failure.Similarly, equation (3) is a relatively good expression form of the τ−s curve of specimens with internal threads.(3)
τ
=
γ
e
s
−
γ
,
s
≤
s
u
,
τ
=
τ
r
−
τ
u
s
r
−
s
u
s
−
s
u
+
τ
u
,
s
u
<
s
≤
s
r
,
τ
=
τ
r
,
s
>
s
r
.In equation (3), γ is the coefficient of the test parameters.Figure22 shows the comparison between test results and theoretical results of P-2, which represents specimens with internal threads. It is clear that although some errors exist between the results, relatively good agreements can be reached when γ = 75.Figure 22
Comparison between test result and theoretical result of P-2.


### 3.7.3. Specimens with Shear Connectors

For all specimens with shear connectors tested, allτ−s curves obtained exhibit the same law: with the increase of s, τ becomes larger firstly and keeps steady after arriving at τu. Because of the persistence of anchoring force between shear connectors and concrete, the entire curve does not show a softening stage. Therefore, τ−s curves of specimens with shear connectors could be divided into two sections: an upward section and a steady section. A quadratic parabola and a straight line could be used to describe these two sections visually, and a simplified bond-slip constitutive model of specimens with shear connectors could be expressed as Figure 23 and equation (4).(4)τ=as2+bs,s≤su,τ=τu,s>su,where a and b are coefficients.Figure 23
Simplified model for theτ−s curve of specimens with shear connectors.As shown in Figure24, comparison between test results and theoretical results of P-3 illustrates that when a = -2 and b = 52, results of equation (4) are very close to the test results. Although ultimate bond stress of equation (4) is smaller than the test result, it is beneficial to ensure the safety of FRP-confined concrete piles.Figure 24
Comparison between test results and theoretical results of P-3.


## 3.7.1. Direct Bond Specimens

As seen from the test results of direct bond specimens in this paper, a typicalτ−s curve for direct bond specimens is shown in Figure 19. As the load is applied, the ratio between τ and s is approximately linear at first, and the interfacial bond behaves almost as an elastic interface with virtually a full recovery of slip if the load is removed. As soon as the chemical adhesion breaks, the curve is no longer linear, and the maximum τ appears. After τu, τ decreased slightly and then remain constant as s increases to a value that may range from two to ten times than su.Figure 19
Simplified model of theτ−s curve of direct bond specimens.As mentioned before, for direct bond specimens, the applied load is transmitted by chemical adhesion and friction between FRP tube and concrete. Because chemical adhesion is very small, the typicalτ−s curve for direct bond specimens could be considered to be the transition from static friction to dynamic friction.Thus, equation (2) could be used to describe the bond-slip constitutive model of direct bond specimens.(2)τ=as2+bs,s≤su,τ=τr−τusr−sus−su+τu,su<s≤sr,τ=τr,s>sr,where a and b are coefficients, which should be generated by tests.It is easy to calculated that for P-1, representing direct bond specimens, whena = 15 and b = 5, good agreements can be reached between the test results and results of equation (2), as shown in Figure 20.Figure 20
Comparison between test result and theoretical result of P-1.


## 3.7.2. Specimens with Internal Threads

The typicalτ−s curve of specimens with internal threads is shown in Figure 21. It is clear that the τ−s curve of specimens with internal threads, which can be divided into three sections by point A (τusu) and point B (τrsr), is approximately but not exactly the same as that of direct bond specimens.Figure 21
Simplified model for theτ−s curve of internal threads specimens.The biggest difference is in the first section (from pointO to point A). For direct bond specimens, the curve slope is gradually decreasing, while for specimens with internal threads, the curve slope is gradually increasing. This difference is thought to be a result of the developing law of anchoring forces between threads and concrete. Anchoring force between threads and concrete accounts for a large proportion of shear stress, and the ratio of anchoring forces to s increases as specimen approaches failure.Similarly, equation (3) is a relatively good expression form of the τ−s curve of specimens with internal threads.(3)
τ
=
γ
e
s
−
γ
,
s
≤
s
u
,
τ
=
τ
r
−
τ
u
s
r
−
s
u
s
−
s
u
+
τ
u
,
s
u
<
s
≤
s
r
,
τ
=
τ
r
,
s
>
s
r
.In equation (3), γ is the coefficient of the test parameters.Figure22 shows the comparison between test results and theoretical results of P-2, which represents specimens with internal threads. It is clear that although some errors exist between the results, relatively good agreements can be reached when γ = 75.Figure 22
Comparison between test result and theoretical result of P-2.


## 3.7.3. Specimens with Shear Connectors

For all specimens with shear connectors tested, allτ−s curves obtained exhibit the same law: with the increase of s, τ becomes larger firstly and keeps steady after arriving at τu. Because of the persistence of anchoring force between shear connectors and concrete, the entire curve does not show a softening stage. Therefore, τ−s curves of specimens with shear connectors could be divided into two sections: an upward section and a steady section. A quadratic parabola and a straight line could be used to describe these two sections visually, and a simplified bond-slip constitutive model of specimens with shear connectors could be expressed as Figure 23 and equation (4).(4)τ=as2+bs,s≤su,τ=τu,s>su,where a and b are coefficients.Figure 23
Simplified model for theτ−s curve of specimens with shear connectors.As shown in Figure24, comparison between test results and theoretical results of P-3 illustrates that when a = -2 and b = 52, results of equation (4) are very close to the test results. Although ultimate bond stress of equation (4) is smaller than the test result, it is beneficial to ensure the safety of FRP-confined concrete piles.Figure 24
Comparison between test results and theoretical results of P-3.


## 4. Conclusions and Recommendations

The following conclusions could be drawn based on push-out tests of twenty-nine specimens and the analysis of axial strain and simplified bond-slip constitutive models of concrete-filled FRP-composite piles:The bond type, which determines theτ−s curve and failure model, is the most important factor influencing bond behavior between the FRP tube and concrete.The slenderness ratio of FRP tube has little effect on bond behavior of all tests, leading to no obvious correlation between bond stress and slenderness ratio, which could be observed.Bond stress of specimens with internal threads increases monotonically with decrease in the radius-thickness ratio because a smaller radius-thickness ratio could provide a better hoop constraint, while for specimens with shear connectors, bond stress is not directly related to radius-thickness ratio.High-strength concrete is advantageous for bond behavior because a higher concrete strength results in an interfacial cohesion between FRP tube and concrete.Bond behavior improves significantly after substituting expansive concrete for normal concrete for all specimens; compared with the improvement of concrete strength, the use of expansive concrete is more efficient and the bond stress has a greater increase.The axial strain distribution of all FRP tubes demonstrated the following rules: the upper strain is greater than the middle strain, which is larger than the lower strain; but for normal concrete specimens, the strains are linearly distributed with height, while for expansive concrete specimens, the distribution curves are polygonal lines.The simplified bond-slip constitutive models based on test results are simpler and more practical; however, their coefficients should be generated by tests.



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*Source: 3186832-2020-02-26.xml*