Confinement-concrete interaction in pre-tensioned partial steel-confined concrete

Structures 23 (2020) 751–765

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Confinement-concrete interaction in pre-tensioned partial steel-confined concrete

T

Chee-Loong China, Chin-Boon Onga, Jia-Yang Tana, Chau-Khun Maa,b, , Abdullah Zawawi Awanga, Wahid Omarc ⁎

a

School of Civil Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor Forensic Engineering Centre, Institute for Smart Infrastructure and Innovative Construction, School of Civil Engineering, Faculty of Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor c Office of Vice Chancellor, Universiti Teknologi Malaysia, 81310 Skudai, Johor b

ARTICLE INFO

ABSTRACT

Keywords: Pre-tensioned confinement Confined concrete Confinement-concrete interaction Steel confinement Confinement model

External confinement is an attraction technique to enhance strength and deformability of high strength concrete. Previous research revealed that pre-tensioned confinement is an approach to improve existing confinement techniques. However, limited experimental data are available especially for pre-tensioned steel-confined high strength concrete in square section. On the other hand, the stress distribution in confined square section and partial confinement is not clearly understood. This paper explores the compressive behaviour of pre-tensioned steel-confined high strength concrete. A new confinement-concrete interaction based on localised force and stress distribution in circular and square partial confined concrete is presented. By incorporating the confinement-concrete interaction, failure surface of confined concrete is calibrated with an experimental database. Confinement effect is then estimated based on the calibrated failure surface. This approach is shown to be more accurate than existing confinement models.

1. Introduction External confinement has been shown to be effective in improving the strength and deformability of concrete in the past decades. This has allowed strengthening and retrofitting of structurally deficient reinforced concrete structures to accommodate higher structural loads [1–4]. External confinement is also an attractive solution to solve the brittleness problem associated with high strength concrete (HSC) [5–7]. To date, extensive research has been conducted to experimentally investigate the behaviour of confined concrete [8–10]. Various closedform expressions [11–13] and advanced concrete constitutive models [14–16] have been developed to predict strength and stress–strain behaviour of confined concrete. Accurate prediction of these properties is crucial in design works of structural engineering. Recent research revealed that pre-tension can activate confinement earlier and further enhance the structural properties of confined concrete [17–21]. Among the advantages of pre-tension confinement includes higher elastic limits [22], higher toughness [17], and higher strength enhancement [23]. This turns out to enable less confinement

⁎

material to achieve similar structural performance. On the other hand, using partial confinement can also result in beneficial effect in strengthening columns [24–26]. Potential local buckling problem can also be avoided as the confinement hoops are not directly loaded [6,25]. Besides, partial confinement can be pre-tensioned to achieve better structural performance. Pre-tensioned metal straps or steel strapping tensioning technique (SSTT) is an example of pre-tensioned partial steel confinement technique [27,28]. This technique has been demonstrated by previous research to successfully strengthen structural elements such as columns [29], beams [30] and beam-column joint [31]. Confinement effect is less effective in square section compared to that in circular section. This is due to the non-uniform distribution of confining pressure which concentrated at the corners of square section [32]. An approach to distribute the concentrated confining pressure at corners is by rounding corners of the section [33,34]. Although it has been suggested that square section without rounded corner offers no confinement [35], previous experimental research has revealed otherwise [27,36,37]. Wang and Wu [36] reported that fiber-reinforced

Corresponding author. E-mail address: [email protected] (C.-K. Ma).

https://doi.org/10.1016/j.istruc.2019.12.006 Received 1 August 2019; Received in revised form 3 December 2019; Accepted 4 December 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.

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Nomenclature: A AAE D Ec Es fcc fco Fh fl fle fy ke ks MSE N p P q r R

SD s t Vc Vs w α β γ εcc εco εcu εpre σ1 σxx σyy σzz τxy τxz τyz ρ

actual fcc/fco average absolute error diameter or edge length of concrete elastic modulus of concrete elastic modulus of steel peak stress of confined concrete unconfined concrete strength hoop tension force in steel strap confining pressure effective confining pressure yield stress of steel strap confinement effectiveness ratio for spacing confinement effectiveness ratio for shape mean squared error number of datasets effective hydrostatic pressure predicted fcc/fco von Mises equivalent stress concrete brittleness expression corner radius

standard deviation clear spacing between confinement hoops total confinement thickness volume of concrete volume of steel strap width of steel strap first material constant in Eq. (15) second material constant in Eq. (15) third material constant in Eq. (15) peak strain of confined concrete peak strain of unconfined concrete ultimate strain of confined concrete pre-tension strain maximum principal stress normal stress in x-direction normal stress in y-direction normal stress in z-direction shear stress in xy-plane shear stress in xz-plane shear stress in yz-plane confinement ratio

interaction. In the last part of this paper, the accuracy of the proposed model is assessed against the experimental test result and an experimental database assembled in this paper.

polymer (FRP) confinement can improve the deformability of concrete in sharp corners square section. However, very limited strength improvement has been reported in the same research. Conversely, Thermou et al. [37] reported about 40% increase in strength in sharp corners square section using steel reinforced grout confinement. The experiment work conducted by Suon et al. [38] revealed that both strength and deformability can be improved using basalt FRP in sharp corners square section. Frangou et al. [39] and Moghaddam et al. [27] revealed that the strength of concrete in sharp corners square section can be improved using SSTT confinement. Nonetheless, the experimental evidences of SSTT-confined concrete in square section were scarce and were limited to normal strength concrete (NSC) with unconfined compressive strength of less than 55 MPa. Existing confinement models for SSTT-confined concrete were calibrated based on experimental results [40–43]. Moghaddam et al. [40] proposed confinement model based on the experimental result of circular and square confined NSC conducted by Frangou et al. [39] and Moghaddam et al. [27]. Other confinement models used experimental results of circular confined HSC for model calibration [41–43]. Due to the lack of experimental data of square confined HSC, the calibration of these did not include square confined HSC. On top of that, these models used reduced confinement effectiveness concept to account for noncircular shape and spacing. Since this concept was developed based on empirical understanding, the actual stress distribution was not clearly understood. In view of this, this paper first explores the applicability of SSTT confinement on HSC in square section. Subsequently, a new confinement-concrete interaction based on localised force and stress distribution in SSTT-confined concrete is presented. Besides, a confinement model is proposed by incorporating the confinement-concrete

2. Experimental programme 2.1. Test specimens A total of 12 specimens with cross-section of 100 mm × 100 mm were prepared. Two specimens were not confined, and ten specimens were confined by SSTT confinement. Two identical pair of specimens were tested for each confinement configuration. The specimens casted in formworks with internal dimension of 100 mm × 100 mm × 205 mm. The specimens were removed from the formworks one day after casting and were placed in a curing water tank. The specimens were grounded to the desired height of 200 mm using a machine to ensure uniform surface prior to confining and testing. 2.2. Materials The concrete mix proportion used in this research and its average cubes strength are tabulated in Table 1. CEM I 52.5N cement, densified silica fume, tap water, graded sand, and 10-mm nominal size crushed gravel were used as the concrete constituents. Polycarboxylate etherbased high range water reducer were added as superplasticizer to attain workable mix. Six concrete cubes with 100 × 100 × 100 mm dimensions were prepared to identify the concrete strength on 28-day and on testing day. Steel straps used in packaging industry were used as the confining material in this research. The steel strap has a width and thickness of 16 mm and 0.5 mm, respectively. The tensile properties of

Table 1 Concrete constituents and mix details. Cement (kg/m3)

Silica fume (kg/m3)

Fine aggregate (kg/ m3)

Coarse aggregate (kg/ m3)

Water (kg/ m3)

Superplasticizer (L/m3)

Cube strength on 28day (MPa)

Cube strength on testing day (MPa)

460

37

608

1130

149

8.2

68

82

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captured by using 2 displacement transducers mounted on a holding rig. The holding rig was positioned at the mid height region and had gauge length of 70 mm. Axial loads applied onto the specimen were measured a load cell with rated capacity of 2000 kN. The specimens were carefully aligned with the center of spherical seating prior to loadings. If the axial deformations recorded from 2 displacement transducers were different at the beginning of loading, the specimens were unloaded, re-aligned and re-loaded. The detailed test setup is as shown in Fig. 3.

Table 2 Mechanical properties of steel straps. Strap No.

Yield stress (MPa)

Elastic modulus (GPa)

Tensile strength (MPa)

Ultimate strain

Strap 1 Strap 2 Strap 3 Average

812 868 873 851

192 204 205 200

923 937 915 925

0.01 0.009 0.01 0.01

2.5. Specimen labels

the steel straps obtained from uniaxial tensile test are summarised in Table 2.

The specimens were labelled based on the following nomenclature. The first number indicates the unconfined concrete strength. The second number indicates the number of steel strap layer used. The third number indicates the clear spacing between confinement. Suffix “a” and “b” were used to distinguish between identical specimens. For example, 70–3-10a refers to the specimen confined by 3 layers of steel straps with 10 mm clear spacing. For unconfined specimens, only the unconfined concrete strength and suffix were included in the specimen label.

2.3. Confining and pre-tensioning The specimens were confined with various layers of confinement and spacings between confinement. Prior to confining, alignment lines were drawn on the specimens to achieve the intended spacings. The spacings were reduced at both ends of each specimen to avoid unintended premature failure of specimen. The steel straps were cut into intended length and made into hoops and connections clips. Anchorage with length of 100 mm was provided for each hoop. In this research, it is proposed that anchorage to be positioned at corner and about half of the anchorage crossed the corner of the square specimens. Portions of steel with reduced area at connection clips were positioned away from the corners during pre-tensioning. The pre-tensioning process was done by using a pneumatic tensioner (Fig. 1a) to apply pre-tension force to the steel. The pre-tension force was controlled by setting a constant 4 bar pressure using a pressure gauge valve (Fig. 1b). A strain gauge was attached on the steel hoop to record the induced pre-tension strain. The pre-tension ends were anchored at the connection clip after pretensioning and before releasing the grips of tensioner. Steel wire were used to tie the anchor to the hoops. This process resulted in minor losses of pre-tension and the remaining pre-tension strain was 0.00218. The details of anchorage and confinement before the pre-tensioning and after the pre-tensioning are illustrated in Fig. 2(a) and Fig. 2(b), respectively.

3. Experimental result and discussion 3.1. Observation During compression test, cracks formed at near mid-height of unconfined specimens upon reaching peak stress. This was followed up by brittle concrete crushing failure associated with loud explosive sound. As for each of the confined specimens, hairline cracks formed at near mid-height of specimens within the spacing between confinement upon reaching the unconfined strength. The hairline cracks were first observed at the flat sides of the cross-section and eventually at the corners of the cross-section. Subsequent loading resulted in formation of cracks at the corners of the cross-section. The cracks were more obvious for specimens with larger spacing between confinement. This was followed up concrete crushing indicated by loud explosive sound and sudden loss of axial capacity. None of the steel strap ruptured throughout the compression test. This is similar to the failure of weakly confined concrete reported in previous research [44–47]. These suggest that failure of weakly confined concrete is initiated by the localised failure of concrete within the spacing between confinement.

2.4. Compression test setup and procedure The specimens were tested under monotonic axial compression with loading rate of 0.006 mm/ s. A closed-loop universal testing machine with 2000 kN rated capacity was used to test the specimens. A selfaligning spherical seating was used to ensure full contact between specimens and platens. Axial deformations of the specimens were

3.2. Axial stress–strain curves In this paper, axial stress was calculated by dividing the recorded load by the cross-sectional area. Axial strain was calculated by dividing

(a)

(b)

Fig. 1. Tensioning devices: (a) pneumatic tensioner; (b) pressure gauge valve.

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internal anchorage

pre-tension end

external anchorage connection clips

(b)

(a)

Fig. 2. Details of anchorage and confinement: (a) before pre-tensioning; and (b) after pre-tensioning.

Fig. 3. Schematic compression test setup.

the average recorded deformations by the gauge length. The stress–strain curves of the tested specimens in this research typically consists of two portions. The first portion is a linear elastic ascending branch with a gradient similar to the unconfined specimens. The second portion is either descending or ascending branch depending on the amount of confinement provided. Fig. 4 illustrates the typical stress–strain curves of the tested specimens.

It is shown in Fig. 5 that deformability of the specimens depends largely on clear spacing between confinement. For instance, a decrease in clear spacing from 20 mm to 10 mm delayed the strain upon failure from about 0.004 to 0.007. It can be observed that the axial stress–strain curves of 70-3-30 series and 70 series were almost identical. This implies that the confinement provided was not sufficient and the confinement effect was near negligible. An increase in the number of steel

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Fig. 4. Typical stress–strain curve of specimens.

straps layers increased the peak stress. Increasing the number of steel straps also improved the inelastic portion of the stress–strain curve. 703-10 series and 70-4-10 series showed strain-hardening in the inelastic portion. As expected, the hardening modulus of 70-4-10 series was slightly higher. However, increasing the number of steel straps layers did not show much improvement to the deformability of specimens.

Moghaddam et al. [40] proposed Eq. (3) for fl in a partial steelconfined concrete:

fl =

Vc fco

=

ke = 1

(1)

ks = 1

where Vs is volume of steel strap; Vc is volume of concrete; fy is yield stress of steel strap; t is total confinement thickness; w is width of steel strap; s is clear spacing; and D is edge length of cross-section. Peak stress (fcc) and peak strain (εcc) refer to the axial stress and strain at the point with highest stress. Ultimate strain (εcu) refers to the axial strain at which the specimen experiences sharp drop in axial stress. For specimens with strain-softening behaviour, εcu refers to axial strain at which the axial stress drops 15% from fcc. Table 3 presents a summary of the experimental test results.

s 2D 2(D

2

(5)

2R)2 3D 2

(6)

where R is corner radius of square section. The predictions of fcc and εcc rely on fle and the type of confinement used. Richart et al. [49] suggested that fcc and εcc of actively confined concrete can be expressed as:

fcc fco cc co

4. Confinement models

= 1 + 4.1

=1+5

fle (7)

fco fcc fco

1

(8)

Eq. (7) was revealed to be one of the most accurate actively confined concrete model in a recent study [50]. Eq. (8) is also adopted by many researchers for both FRP-confined concrete [51,52] and steelconfined concrete [53]. As for SSTT-confined concrete, 5 existing confinement models are available in the literature [40–43,47]. These models were given in closed-formed expressions as summarised in Table 4. The axial stress–strain of confined concrete can be expressed by Eq. (9) proposed by Popovics [54]. This expression has been widely used by most confinement models [41,50,51,55].

4.1. Existing confinement models Confinement effect is typically modelled based on the confining pressure (fl) acting on concrete. For a steel-confined concrete, fl arises from the hoop tension (Fh) in steel. In a circular section, the compatibility between confinement hoops and concrete is as shown in Fig. 6. For steel-confined concrete, Fh can be evaluated as follows:

Fh = fy tw

(4)

where ke is confinement effectiveness ratio for spacing given by Eq. (5); and ks is confinement effectiveness ratio for shape given by Eq. (6).

4tf y

w fco D w + s

(3)

fle = ke ks fl

In this paper, unconfined concrete strength (fco) and peak strain of unconfined concrete (εco) were calculated from the average strengths of the unconfined concrete specimens and corresponding axial strain. Pretension strain (εpre) was recorded from the experimental programme. Confinement ratio, (ρ) was calculated using Eq. (1).

Vs fy

w w+s

D

To account for reduced confinement effect due to partial confinement and shape, effective confining pressure (fle) based on Sheikh and Uzumeri [48] can be adopted as:

3.3. Peak stress and strain enhancement

=

2tf y

(2)

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100 90 Axial stress (MPa)

80 70 60

70a 70-3-30a 70-3-20a 70-2-10a 70-3-10a 70-4-10a

50 40 30

20 10 0

0

0.001

0.002

0.003

0.004 0.005 Axial strain

0.006

0.007

0.008

(a) 100 90 Axial stress (MPa)

80 70 60

70b 70-3-30b 70-3-20b 70-2-10b 70-3-10b 70-4-10b

50 40 30 20 10 0

0

0.001

0.002

0.003

0.004 0.005 Axial strain

0.006

0.007

0.008

(b) Fig. 5. Axial stress–strain curves of specimens: (a) series a; (b) series b.

fc =

( )r 1+( ) cc

c

r

Ec = 4730 fco

c

fcc

cc

(9)

where r is a concrete brittleness expression given by Eq. (10) proposed by Carreira and Chu [56]. The elastic modulus of concrete (Ec) can be computed by using Eq. (11) proposed by Teng et al. [51].

r=

4.2. Proposed confinement-concrete interaction In this paper, a new confinement-concrete interaction is developed based on force distribution and localised stresses induced in concrete. This interaction is divided into two portions, i.e. interaction in crosssection and interaction in elevation.

Ec Ec

fcc cc

(11)

r

(10)

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Table 3 Summary of experimental test result. Specimen ID

fco (MPa)

εco (%)

εpre (%)

ρ

fcc (MPa)

εcc (%)

εcu(%)

fcc/fco

εcc/εco

εcu/εco

70a 70b 70-3-30a 70-3-30b 70-3-20a 70-3-20b 70-2-10a 70-2-10b 70-3-10a 70-3-10b 70-4-10a 70-4-10b

69.9 69.9 69.9 69.9 69.9 69.9 69.9 69.9 69.9 69.9 69.9 69.9

0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257 0.257

0.218 0.218 0.218 0.218 0.218 0.218 0.218 0.218 0.218 0.218

0.254 0.254 0.324 0.324 0.300 0.300 0.449 0.449 0.599 0.599

68.6 71.1 73.0 72.4 80.9 82.5 77.4 79.8 85.9 84.5 91.2 91.6

0.249 0.265 0.258 0.262 0.333 0.318 0.535 0.552 0.485 0.608 0.543 0.456

0.333* 0.340* 0.416* 0.385* 0.420 0.401 0.622 0.645 0.690 0.700 0.707 0.693

0.98 1.02 1.05 1.04 1.16 1.18 1.11 1.14 1.23 1.21 1.31 1.31

0.97 1.03 1.00 1.02 1.30 1.24 2.08 2.15 1.89 2.34 2.11 1.78

1.30 1.32 1.62 1.50 1.63 1.56 2.42 2.51 2.69 2.72 2.75 2.70

* Taken as axial strain at which axial stress drops 15 % from its peak. xy

4.2.1. Interaction in cross-section Consider a cross-section with arbitrary R and D, Fh and reaction from concrete can be visualised as in Fig. 7(a). As the corner radius region is essentially a quarter circle with radius equal to R, the reaction from concrete can be simplified into two perpendicular reactions acting on the center of the quarter circle as shown in Fig. 7(b). For static equilibrium, the magnitudes of the two reactions are equal to Fh. The confining actions acting on concrete induce normal stresses in x-direction (σxx) and y-direction (σyy) as shown in Fig. 7(c). Since the confining actions do not act on center of cross-section, shear stress in xy-plane (τxy) is induced. This is illustrated using an equivalent force system as shown in Fig. 8. Based on the geometrical properties, σxx, σyy and τxy can be calculated as follows:

=

yy

=

2Fh D (w + s )

2Fh (D 2R) D 2 (w + s )

(13)

4.2.2. Interaction in elevation For a partial confined concrete with arbitrary w and s, the elevation between center of steel strap and spacing between confinement is as shown in Fig. 9(a). Since only half of the steel strap is considered, the hoop tension force in a steel strap is halved to 0.5Fh. Therefore, two steel straps within the same elevation provide total hoop tension force of Fh. Considering the elevation in x-plane, the hoop tension force induces normal stress in x-direction (σxx) as shown in Fig. 9(b). Normal stress in z-direction (σzz) represents axial stress in concrete. Since the hoop tension force do not act on the center of elevation considered, shear stress in xz-plane ( xz) is induced. This is illustrated using an equivalent force system as shown in Fig. 10. Based on the equivalent force system, τxz can be calculated as follows:

Fig. 6. Compatibility between confinement hoop and concrete.

xx

=

xz

=

Fh (D 2 + R2 [

s 4]) w + s

(14)

Due to the symmetrical geometry, shear stress in yz-plane ( equal to xz.

yz)

4.3. Proposed confinement model Instead of relying on ke and ks to account for the reduced confinement effectiveness, a new confinement model is proposed by considering the stresses induced in concrete. All the stresses induced in concrete can be considered using the failure surface proposed by Lubliner et al. [57] given as:

(12)

Table 4 Existing models used in this research. Author(s) Moghaddam et al. [40]

Awang [43] Lee et al. [42] Chin et al. [41] Yang et al. [47]

fcc Expression fcc fco fcc fco fcc fco fcc

fco fcc fco

=1+8

= 2.62 =1+

e

fle fco

εcc Expression

4

fle fco

0.4 where

e

1.2

= k e ks

f 5.57 le fco

= 1.124 +

= 1 + 3.35k e ks

=

cc co

= 11.6

cc co

f 1.02 le fco fl fco

cc co

0.48

fcc fco

cc co

–

=1+

Stress–strain Expression

1.1

fc =

fcc cc

2

fcr cc cr cc cr

c

2

+

1 cr

fcr

( ) cr cc

2

fcc 1

fcr cc cr cr cc

Adopted expression proposed by Popovics [54].

e

Adopted expression proposed by Popovics [54].

f 6.3 le fco

= 0.93 +

is

Adopted expression proposed by Popovics [54].

f 1.49 le fco

–

757

c where fcr

= 0.85fcc

cr

= 0.00031

fcr fco

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Fig. 7. Confinement-concrete interaction in cross-section: (a) forces acting on steel; (b) simplified forces acting on steel; (c) forces acting on concrete.

Fig. 10. Stresses induced within concrete elevation.

Fig. 8. Stresses induced in concrete cross-section.

fco =

1 1

(q

3 p+

1

1

)

(15)

q=

(

xx

yy

+(

yy

zz

)2

+(

zz

xx

)2

+ 6(

xy

2

+

yz

2

+

xz

+

yy

+

zz

(17)

3

Since confined concrete is predominantly in triaxial compression, Eq. (15) can be rewritten as follows:

where q is von Mises equivalent stress calculated based on Eq. (16); p is effective hydrostatic pressure calculated based on Eq. (17); σ1 is maximum principal stress; α, β and γ are material constant.

)2

xx

p=

fco =

2)

1 1

A

(q

3 p

1)

(18)

For uniformly confined concrete, the shear stresses in concrete are zero. In this case, xy = xz = yz = 0 and therefore xx = yy = 1. This enables simplification to Eq. (18) and ease of solving the relation

2 (16)

Fig. 9. Confinement-concrete interaction in elevation: (a) elevation considered; and (b) forces acting on concrete. 758

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Table 5 Summary of experimental database used. Author(s)

Shape

No. of datasets

D (mm)

Height (mm)

fco (MPa)

s (mm)

w (mm)

t (mm)

fl (MPa)

Frangou et al. [39] Moghaddam et al. [27] Awang [43] Zhang [58] Lee et al. [59] Lee et al. [28] Xia [60] Yang et al. [47] Chin et al. [61] Frangou et al. [39] Moghaddam et al. [27] This paper

Circular Circular Circular Circular Circular Circular Circular Circular Circular Square Square Square

12 11 36 16 1 2 18 16 4 14 20 10

100 100 100 200 100 150 300 400 100 100 100–150 100

200 200 200 500 200 300 750 1000 200 200 200–300 200

31 50 65–105 20–30 61 59 20–30 22–24 55 31 25–50 70

0–25.4 0–48 10–15 18.25–118.25 10 15 18.25–118.25 18.25–118.25 10 0–38.1 0–48 10–30

12.7 16–32 12.75 31.75 15.85 15.85 31.75 31.75 16 12.7 16–32 16

0.5 0.5–1 0.45–2.5 0.9–2.7 0.55 1.1–2.2 0.9–2.7 0.9–2.7 1.5 0.5 0.5–1 1–2

1.6–7.7 2.6–10.3 2.5–23.7 1.6–14.8 4.7 6.9–13.8 1.1–9.9 0.8–7.4 15.9 1.2–7.7 2.6–20.6 8.9–20.9

Total

Circular Square Both

116 44 160

100–400 100–150 100–400

200–1000 200–300 200–1000

20–105 25–70 20–105

0–118.25 0–48 0–118.25

12.7–32 12.7–32 12.7–32

0.45–2.7 0.5–2 0.45–2.7

0.8–23.7 1.2–20.9 0.8–23.7

Fig. 11. Failure surface of SSTT-confined concrete.

Fig. 12. Trends of experimental result in failure surface.

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Fig. 13. Comparison with experimental result.

between p and q. However, such simplification is not valid for nonuniform confined concrete as the shear stresses in concrete are not zero. In this case, solving for the relation between p and q in Eq. (18) becomes tedious. In this paper, the relation between p and q was calibrated directly from an experimental database assembled from experimental results of previous research. To ensure consistency of the experimental database, only the experimental results satisfying the following restrictions were added:

1. 2. 3. 4.

Specimen height to D ratio ≤ 3 fco > 10 MPa No internal reinforcement Tested under monotonic uniaxial compression

A summary of the experimental database is tabulated in Table 5. For each of the dataset, Eqs. (12)–(14) were used to evaluate the stresses in concrete; Eqs. (16) and (17) were used to calculate q and p, respectively; and σzz was taken as -fcc.

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Fig. 11 shows the trends of failure surfaces based on the experimental database. It is evidenced that failure surface for circular section is different from that of square section. This is attributed to the fact that xy is significantly higher than xz and yz for square section. The higher shear stresses in square section resulted in smaller magnitude of σ1 as compared to that in circular section. Hence, q for square section is less than q for circular section at a given p. To offset such difference, Eq. (19) is proposed based on regression analysis to represent the failure surface of SSTT-confined concrete.

q p 2R = 1.65 + 0.3 + 0.15 fco fco D

(19)

To demonstrate the influence of relevant parameter on the failure surface, the experimental test results presented in Section 3 were plotted in the p-q plane as shown in Fig. 12. It is evidenced that higher ρ

Fig. 14. Comparison with experimental test result. Fig. 15. Comparison with experimental database. 761

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gives higher p/fco and q/fco. Besides, the value of q/fco increased with higher 2R/D. By using this failure surface, the estimation of fcc can be done by solving for σzz in Eq. (19). 5. Assessment of model 5.1. Comparison with experimental result The performances of the proposed model and existing confinement models discussed in Section 4.1 were compared with the experimental test result presented in Section 3. For this purpose, Eq. (8) was used to estimate εcc/εco of the confined specimens by using fcc/fco obtained from the proposed model. From Fig. 13(a), it can be observed that the proposed model was accurate in estimating fcc/fco. Model proposed by Richart et al. [49] also provided close estimation with the experimental test result. Models proposed by Yang et al. [47] and Lee et al. [42] had tendency to overestimate fcc/fco of the tested specimens. Fig. 13(b) shows the performance of each models in estimating εcc/εco. From the figure, it is noticed that most the models were not consistent and had tendency to underestimate the εcc/εco of the test specimens. The proposed model and Richart et al. [49] model had tendency to overestimate the εcc/εco of the tested specimens. The proposed model was used to estimate the stress–strain behaviour of the confined specimens tested in this paper. For this purpose, Eqs. (9)–(11) were used to generate the stress–strain curve of the confined specimens. Fig. 14 shows comparison between the estimated stress–strain curves and actual stress–strain curves for each tested specimen. The tendency to overestimate εcc/εco was the most obvious in Fig. 14(e). Nonetheless, the stress–strain curves estimated using the proposed model were still in good agreement with the experimental test result. 5.2. Comparison with experimental database Each model was used to estimate fcc/fco of each dataset in the experimental database assembled in this paper. Fig. 15 shows comparisons between each model with the experimental database. It is shown that the proposed model can provide the most consistent and accurate estimation among the models compared. While the trendline of Moghaddam et al. [40] model rivalled with the proposed model, it was less consistent as represented by the larger scattered plots. Additionally, the accuracy of each model was quantified using average absolute error (AAE) and mean squared error (MSE) given in Eq. (20) and Eq. (21), respectively. The reliability of each model was indicated by using standard deviation (SD) calculated by Eq. (22).

AAE =

MSE =

SD =

1 N 1 N

N

Pi

Ai Ai

i=1

(20)

N

(Pi

Ai )2

i=1

N i=1

Pi Ai

N

2 N i = 1 (Pi ) N i = 1 (Ai )

1

(21)

(22)

where N is the number of datasets; P is the predicted fcc/fco; and A is the actual fcc/fco. As illustrated in Fig. 16, the proposed model had the highest performance represented by the least AAE, MSE and SD among the models. Notwithstanding the above, the accuracy and reliability of the proposed model is strictly limited to the ranges each parameter in Table 5. This is because the proposed model was empirically calibrated based on these ranges of parameter.

Fig. 15. (continued)

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Fig. 16. Accuracy of existing and proposed models: (a) AAE; (b) MSE; and (c) SD. 763

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6. Conclusion

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This paper has presented experimental test results of 2 plain HSC specimens and 10 SSTT confined HSC specimens in square section. A new confinement-concrete interaction is developed based on force distribution and localised stresses induced in concrete. Based on the stresses induced, the failure surface of SSTT-confined concrete is used to estimate the stress–strain behaviour of SSTT confined HSC. Additionally, the accuracy of the proposed model is compared with existing confinement models by using an experimental database. Based on the findings presented, the following conclusions were made: 1) Strength and deformability of HSC have shown to be enhanced using SSTT confinement even for sharp corners square section. As expected, the enhancements in strength and deformability were shown to be dependent on the amount of confinement provided. 2) Localised shear stresses are induced within the concrete in case of confinement in non-circular section and partial confinement. The induced shear stresses resulted in a change in stress state of concrete. 3) By incorporating the induced shear stresses, the strength of SSTTconfined concrete can be estimated based on its failure surface. This approach is shown to be more accurate than existing approach using reduced confinement effectiveness ratios. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was funded by Fundamental Research Grant Scheme [R.J130000.7851.5F176], GUP Tier 1 [Q.J130000.2522.19H16] and GUP Tier 2 [Q.J130000.2501.16J31] from Ministry of Higher Education, Malaysia. The authors are grateful to Nova Standard (Johor) Sdn. Bhd. for sponsoring the concrete admixtures used in this research. The scholarship support from Zamalah UTM is highly appreciated. References [1] Ma C-K, Apandi NM, Sofrie CSY, Ng JH, Lo WH, Awang AZ, et al. Repair and rehabilitation of concrete structures using confinement: A review. Constr Build Mater 2017;133:502–15. https://doi.org/10.1016/j.conbuildmat.2016.12.100. [2] Li P, Sui L, Xing F, Li M, Zhou Y, Wu Y-F. Stress-Strain Relation of FRP-Confined Predamaged Concrete Prisms with Square Sections of Different Corner Radii Subjected to Monotonic Axial Compression. J Compos Constr 2019;23(2):04019001. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000921. [3] Saljoughian A, Mostofinejad D, Hosseini SM. CFRP confinement in retrofitted RC columns via CSB technique under reversed lateral cyclic loading. Mater Struct 2019;52(4):67. https://doi.org/10.1617/s11527-019-1373-6. [4] Rajput AS, Sharma UK. Seismic behavior of under confined square reinforced concrete columns. Structures 2018;13:26–35. https://doi.org/10.1016/j.istruc. 2017.10.005. [5] Xiong M-X, Xiong D-X, Liew JYR. Axial performance of short concrete filled steel tubes with high- and ultra-high- strength materials. Eng Struct 2017;136:494–510. https://doi.org/10.1016/j.engstruct.2017.01.037. [6] Liu J, Teng Y, Zhang Y, Wang X, Chen YF. Axial stress-strain behavior of highstrength concrete confined by circular thin-walled steel tubes. Constr Build Mater 2018;177:366–77. https://doi.org/10.1016/j.conbuildmat.2018.05.021. [7] Vincent T, Ozbakkaloglu T. Influence of overlap configuration on compressive behavior of CFRP-confined normal- and high-strength concrete. Mater Struct 2016;49(4):1245–68. https://doi.org/10.1617/s11527-015-0574-x. [8] Chin C-L, Ma C-K, Tan J-Y, Ong C-B, Awang AZ, Omar W. Review on development of external steel-confined concrete. Constr Build Mater 2019;211:919–31. https://doi. org/10.1016/j.conbuildmat.2019.03.295. [9] Ozbakkaloglu T, Lim JC. Axial compressive behavior of FRP-confined concrete: Experimental test database and a new design-oriented model. Compos B Eng 2013;55:607–34. https://doi.org/10.1016/j.compositesb.2013.07.025. [10] Han L-H, Li W, Bjorhovde R. Developments and advanced applications of concretefilled steel tubular (CFST) structures: Members. J Constr Steel Res 2014;100:211–28. https://doi.org/10.1016/j.jcsr.2014.04.016.

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