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Geogrid-confined pervious geopolymer concrete piles with FRP-PVC-confined concrete core: Analytical models
Structures 23 (2020) 731–738
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Geogrid-confined pervious geopolymer concrete piles with FRP-PVCconfined concrete core: Analytical models Haiqiu Zhang, Muhammad N.S. Hadi
T
⁎
School of Civil, Mining and Environmental Engineering, University of Wollongong, Australia
A R T I C LE I N FO
A B S T R A C T
Keywords: FRP PVC Geogrid Pervious geopolymer concrete Analytical model
The geogrid-confined pervious geopolymer concrete pile (GPGCP) with fibre reinforced polymer (FRP)-polyvinyl chloride (PVC)-confined concrete core (FPCC) is a new form of composite piles proposed in a previous study, which consists of a circular geogrid outer tube, a FPCC, and pervious geopolymer concrete (PGC) filled in between. For FPCC, the normal geopolymer concrete (NGC) was used to fill the FRP-PVC tubes. In this study, new analytical models are proposed to simulate the axial compressive behaviour of GPGCPs without and with FPCC. According to the characteristics of the mechanical behaviour of GPGCPs, analytical models are proposed which can predict the large axial strain behaviour. The unconfined concrete model proposed by the European Standards, and an existing popular FRP-confined concrete model are combined here. It was found that the analytical results are in good agreement with the experimental results. Based on the analytical models, the influences of different parameters on the axial compressive behaviour of GPGCPs have been investigated through parametric analyses.
1. Introduction In the past two decades, the use of FRP has been increasingly popular in civil engineering applications, due to its high strength-toweight ratio, high durability, and high anti-corrosion ability [1–7]. Especially in harsh marine environments, concrete columns and piles strengthened by FRP can significantly reduce the cost compared with steel reinforced concrete columns and piles [7–13]. The USA is reported to spend about two billion dollars annually to replace and repair reinforced concrete piers and more than $1 billion annually to maintain waterfront piling systems due to the corrosion of steel reinforcement. Using FRP materials are regarded as suitable alternatives to overcome this problem [10]. Some studies have investigated the properties of FRP-reinforced concrete piles. Ding et al. [14] conducted an experimental program to study the effectiveness of using Carbon Fibre Reinforced Polymer (CFRP) grid to confine precast concrete piles. The results showed that CFRP grid can effectively reinforce the precast concrete piles. Fam et al. [8] summarized the construction details and findings of laboratory and field tests of Glass Fibre Reinforced Polymer (GFRP) confined precast concrete piles. It was found that using GFRP tubes to reinforce piles for bridges is practical and feasible. Fakharifar and Chen [15] investigated the mechanical behaviour of FRP-confined, PVC-confined and FRP-
⁎
PVC-confined concrete. The results showed that the ultimate strength and ultimate strain of FRP-PVC-confined concrete specimens are larger than those of concrete columns confined by FRP alone or PVC alone. Recently, Zhang and Hadi [16] proposed a new concept of composite piles: geogrid-confined pervious geopolymer concrete piles (GPGCPs) with fibre reinforced polymer (FRP)-polyvinyl chloride (PVC)-confined concrete core (FPCC). Pervious geopolymer concrete (PGC) was used to fill between FPCC and geogrid tubes. Normal geopolymer concrete (NGC) was used to fill the FRP-PVC tube. This new form of composite piles combines the advantages of geopolymer concrete, pervious concrete, geogrid, FRP-PVC-confined concrete. Geopolymer concrete is a kind of green building material, which uses industrial by-products such as fly ash and slag to replace ordinary Portland Cement (OPC). Reducing the use of OPC can significantly decrease the amount of greenhouse gas emissions. Pervious concrete can increase the rate of consolidation and reduce the liquefaction potential caused by seismic and traffic loading [17–22]. Geogrid can sustain large strain and hold aggregates together [23]. The FRP-PVCconfined concrete have larger ultimate strength and ultimate strain than concrete columns confined by FRP alone or PVC alone [15]. However, only experiments have been carried out for GPGCPs without and with FPCC, but mathematical models need to be proposed to further understand the axial compressive behaviour of GPGCPs without
Corresponding authors. E-mail addresses: [email protected] (H. Zhang), [email protected] (M.N.S. Hadi).
https://doi.org/10.1016/j.istruc.2019.11.005 Received 31 July 2019; Received in revised form 7 November 2019; Accepted 17 November 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
Structures 23 (2020) 731–738
H. Zhang and M.N.S. Hadi
lateral confining pressure (fla,grid) is equal to the equivalent lateral confining force (Fle,grid) provided by the equivalent lateral confining pressure (fle,grid), which is shown as follows:
and with FPCC. The focus of the present study is to propose new analytical models to simulate the detailed axial stress-axial strain behaviour of GPGCPs without and with FPCC. The experimental details of the GPGCP specimens can be referred to at Zhang and Hadi [16].Through carefully interpreting the experimental results, the unconfined concrete model proposed by ENV1992-1–1 [24], and the FRP-confined model proposed by Teng et al. [25] are combined in these new analytical models here. According to the specific characteristics of the mechanical behaviour of GPGCPs, tailored analytical models are proposed which can predict the large axial strain behaviour. The analytical results have been found to be in good agreement with the experimental results. Based on the analytical models, the influences of different parameters on the axial compressive behaviour of GPGCPs have been investigated through parametric analyses. There is a need for this study as these developed models will help to apply the new proposed system of GPGCPs without and with FPCC.
Fla, grid = Fle, grid
(1)
The Fla,grid is the sum of forces provided by each transverse geogrid rib, which is given by
Fla, grid = 2n·Frib
(2)
where Frib is the force provided by one transverse geogrid rib; n is the number of transverse geogrid ribs for one GPGCP. The equivalent lateral confining force (Fle,grid) is expressed by:
Fle, grid = fle, grid ·H ·dp
(3)
where H is the height of the GPGCPs; dp is the diameter of the GPGCPs. Combining the Eq. (1), Eq. (2) and Eq. (3), the equivalent lateral confining pressure (fle,grid) is given by:
2. Details of GPGCP specimens
fle, grid = The experimental details of GPGCP specimens can be referred to at Zhang and Hadi [16]. A brief description of the specimens is described below to better understand the models. A total of 12 GPGCP specimens were cast and tested under axial compression. These specimens were divided into two groups. The six specimens of the first group did not have FPCC. The six specimens of the second group had FPCC. The inner diameter and outer diameter of PVC tubes were 76 mm and 84 mm, respectively. The height of PVC tubes was 325 mm. The inner diameter and outer diameter of FRP-PVC tubes were 76 mm and 86 mm, respectively. The height of FRP-PVC tubes was 325 mm. The average 28-day compressive strength of PGC for GPGCPs without FPCC was 22.1 MPa; that of GPGCPs with FPCC was 21.7 MPa. The average 28-day compressive strength of NGC for GPGCPs with FPCC was 49.2 MPa. The inner dimensions of square openings of geogrid are 25 mm × 25 mm. The widths of the transverse ribs and the longitudinal ribs are 10 mm and 6 mm, respectively. The average tensile ultimate load of geogrid ribs was 2.8 kN and the average ultimate tensile strain was 9.2%. The GFRP sheets were formed from bidirectional glass fibre and had a nominal thickness of 0.15 mm. The test results showed that the average tensile strength, elastic modulus and ultimate tensile strain were 621.5 MPa, 33.4 GPa and 1.86%, respectively. The commercial PVC pipes were used in this study, with an outside diameter of 84 mm and a thickness of 4 mm. The average tensile strength, fracture stress, elastic modulus and ultimate tensile strain were 51.2 MPa, 42.7 MPa, 1.58 GPa and 55.4%, respectively.
2n·Frib dp H
(4)
The next step is to calculate the lateral confinement modulus which is directly used in the analytical model. The lateral confinement modulus (Ele,grid) is defined as the ratio of the increment of the confining pressure and the increment of the hoop strain of concrete:
Ele, grid =
Δfle, grid Δεl
=
2n ΔFrib dp H Δεl
(5)
As the tensile force-strain relationship of geogrid is nearly linear, the value of ΔFrib can be calculated by: Δεl
Pgrid ΔFrib = Δεl εgrid, u
(6)
where the Pgrid is the average peak load of one geogrid rib; and ɛgrid,u is the corresponding tensile strain. For the PGC piles wrapped by two and three geogrid layers, their equivalent lateral confinement modulus is 2Ele,grid and 3Ele,grid, respectively. 3.2. Analytical model for GPGCPs without FPCC The test results of GPGCPs without FPCC [16] revealed that geogrid alone do not improve the compressive strength and the axial strain at the compressive strength of PGC. The axial stress–strain curves were divided into three branches. The first two branches are similar to the behaviour of unconfined concrete. Therefore, the equation used to simulate the behaviour of unconfined concrete was adopted to describe the first two branches of the axial stress–strain curves of GPGCPs without FPCC. In this study, the model presented by ENV1992-1–1 [24] was applied for the first two branches of the axial stress–strain curves:
3. Analytical model To better understand the axial compressive behaviour of GPGCPs, analytical models are proposed in this part. The research studies on the development of axial stress-axial strain models for predicting the axial compressive behaviour of geogrid confined concrete are very limited. Here, according to the characteristics of experimental behaviour of GPGCPs, tailored analytical models are proposed.
2
2εc ⎛ εc ⎞ ⎤ σc, p = fco′ ⎡ ⎢ εco − εco ⎥ ⎝ ⎠⎦ ⎣ ⎜
⎟
(7)
where σc and ɛc are the axial stress and axial strain, respectively; fco′ is the compressive strength of concrete and ɛco is the axial strain at the peak stress of concrete. In the third branch, the axial stress–strain behaviour of GPGCPs without FPCC became more gradual, and finally became stable. This can be explained that after the significant reduction of axial stress, the lateral strain of concrete became larger and the confinement effect provided by the geogrid became higher [23]. This characteristic is different from the axial stress–strain behaviour of unconfined concrete, which lost all the load carrying capacity after drastic reduction in the axial load. Through carefully interpreting the test results, it is found that the transition axial strain point, where the axial stress–strain curves of GPGCPs without FPCC can be differentiated from that of
3.1. Equivalent confining pressure provided by geogrid For geogrid-confined concrete, only part of the pervious concrete surface was covered by geogrid ribs, which is different from FRP and PVC wrapped concrete [23]. In this study, the actual lateral confining pressure (fla,grid) is transferred into equivalent lateral confining pressure (fle,grid), which is assumed to uniformly cover all lateral surface of the PGC. The criterion to calculate the equivalent lateral confining pressure is that the actual lateral confining force (Fla,grid) provided by the actual 732
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unconfined PGC, is related to the equivalent elastic modulus of geogrid tubes. This transition axial strain point can be determined by Eq. (9):
GG1-1
GG1-2
Axial Stress (MPa)
20
Ele, grid ⎞ ⎛ εt , p = εco, p ⎜a − bf ′co, p ⎟ ⎝ ⎠
Prediction by Eq. (10) a=1.72 b=10 c=1.5 d=0.011 Eg,eq =11.8
15
10
5
⎡ 1 ⎛ Ele, grid ⎞ σc, p = fco′ , p ⎢ cεc + d ⎜ ⎟ f ⎢ εco, p ⎝ co, p ⎠ ⎣
0 0
0.04
0.08 Axial strain
0.12
0.16
GG2-1 GG2-2
Axial Stress (MPa)
20
Prediction by Eq. (10)
( )
a=1.72 b=10 c=1.5 d=0.011 Eg,eq =23.6 MPa
15
10
σc, p
εc ⎤ ⎥ εco, p ⎥ ⎦
(9) c and d were which are 1.5 combined tobehaviour of
2
⎧ f ′ ⎡ 2εc − εc ⎤ for 0 ⩽ εc ⩽ εt , p ε εco, p ⎥ ⎪ co, p ⎢ ⎣ co, p ⎦ ⎪ = 0.2 ⎨ Ele, grid ⎡ 1 ⎞ · εc ⎤ for εt , p ⩽ εc ⎪ f ′co, p ⎢ cεc + d ⎛ f ⎥ ⎝ co, p ⎠ εco, p ⎦ ⎪ εco, p ⎣ ⎩
(10)
The comparisons between the experimental results and analytical modelling results of GPGCPs without FPCC are shown in Fig. 1. It can be seen that the analytical modelling results matched well with the experimental results. In general, the analytical modelling results predicts the axial stress–strain curves of GPGCPs without FPCC with good agreement due to the appropriate mathematical models.
5
0 0
0.04
0.08 Axial strain
0.12
0.16 3.3. Analytical model for hollow FRP-PVC tubes
(b) GG2
Based on the regression analysis of test data of hollow FRP-PVC tubes under axial compression loading, it can be found that the following equation can effectively describe the compressive behaviour of them:
25 GG3-1 GG3-2
20 Axial Stress (MPa)
0.2
where, σc, p is the axial stress of PGC. The constants obtained based on the regression analysis of test results, and 0.011, respectively. For clarity of presentation, Eq. (7) and Eq. (9) are gether in Eq. (10) to simulate the axial stress–strain GPGCPs without FPCC:
(a) GG1 25
(8)
where εt , p is transition axial strain point of PGC; εco, p is the axial strain at the peak stress of PGC; fco′ , p is the compressive strength of PGC; the a and b are constants determined by the test results; and the Ele,grid is the confinement modulus of geogrid. The suggested values of a and b were obtained based on the regression analysis of test results, which are 1.72 and 10, respectively. Based on the regression analysis of the test data shown in Fig. 1, the following expression is proposed to describe the axial stress–strain curves of Geogrid-confined PGC piles:
Prediction by Eq (10) Fh =
a=1.72 b=10 c=1.5 d=0.011 Eg,eq =35.4 MPa
15
10
2 ⎧− Epvc ·Apvc ·m (εc − εhp ) + Fp
⎨ ⎩
s·Epvc·Apvc (εc )3
for 0 ⩽ εc ⩽ εhp for εhp ⩽εc
(11)
where, the Epvc is the elastic modulus of PVC materials; Apvc is the cross-sectional area of PVC tubes; Fp is the peak load of hollow FRP-PVC tubes; ɛhp is the axial strain at the peak load of hollow FRP-PVC tubes; m and s are constants. The comparison between the experimental results and the analytical modelling results of FRP-PVC tubes under compression loading are shown in Fig. 2. It can be seen that this analytical model prediction is in good agreement with experimental results.
5
0 0
0.04
0.08 Axial strain
0.12
0.16
3.4. Analytical model for FRP-PVC-confined geopolymer concrete (FPCC) In this section, the analytical model proposed by Teng et al. [25] is adopted. This analytical model is based on the following assumptions: (1) the axial stress–strain curve consists of two parts, one is the parabolic first branch and the other one is a linear second branch; (2) the slope of the parabola at zero axial strain is the same as the elastic modulus of unconfined concrete; (3) the nonlinear part of the first branch is affected to some degree by the confinement of the FRP jacket; (4) the parabolic first branch meets the linear second branch smoothly;
(c) GG3 Fig. 1. Comparisons between experimental results and model predictions for GPGCPs without FPCC.
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50
80
FP1 FP2 Prediction by Eq. (11)
FPCC2
Epvc = 1.58GMa Apvc = 1004.8mm2 Fp =45.1kN εhp = 0.045 m = 0.07 s = 0.005
30
20
Prediction by Eq. (11)+Eq. (12)
60
Axial Stress (MPa)
Axial Load (kN)
40
FPCC1
Efrp = 33.43GMa Dn = 76mm ε h,rup =0.0186 ε co,n = 0.0022 f = 49.2 MPa
40
20
10 0
0
0
0.04
0.08 Axial Strain
0.12
σc, n =
4f ′co, n
⎨ f′ + E2 ε c ⎩ co, n
εc 2
for
εcu, n = 1.75 + 12ρκ ρε1.45 εco
0 ⩽ εc, r ⩽ εt , n for
εt , n ⩽ εc, r
f ′cc, n − f ′co, n εcu, n
(14)
σtotal =
where, fcc′ , n is the confined compressive strength of NGC; fco′ , n is the unconfined compressive strength of NGC; εcu, n is the ultimate axial strain of confined NGC, which is shown in Eq. (18). The compressive strength equation takes the following equation:
1 + 3.5(ρκ − 0.01) ρε for ρκ ⩾ 0.01 fcc′ , n = ⎧ 1 for ρκ ⩾ 0.01 ⎨ ⎩
ρε =
2EFRP ·t (f ′co, n εco, n ) dp εh, ult εco, n
Fp + Fh + Fn (19)
Atotal
where Fp, Fh and Fn are the axial loads carried by the outer PGC, the hollow FRP-PVC tubes and the inner NGC, respectively. The Fh can be given by Eq. (11). The Fp and Fn can be calculated by the following expressions:
dp2 − dh 2 ⎞ Fp = σc, p × Ap = σc, p·π·⎜⎛ ⎟ 4 ⎠ ⎝
(15)
where the ρκ is the confinement stiffness ratio; the ρε is the strain ratio. The mathematical expressions of these two ratios are as follow:
ρκ =
(18)
The axial load carrying capacity can be calculated as the sum of axial loads carried by the outer pervious geopolymer concrete (PGC), the hollow FRP-PVC tubes and the inner normal geopolymer concrete (NGC):
(13)
The slope of the linear second branch E2 is expressed as:
E2 =
0.16
3.5. Analytical model for GPGCPs with FPCC
2f ′co, n Ec, n − E2
0.12
where, the ρκ is the confinement stiffness ratio, which is shown in Eq. (16); the ρε is the strain ratio, which is shown in Eq. (17). The axial load carrying capacity of FRP-PVC-confined NGC is the sum of axial loads provided by the hollow tube and the confined NGC. The comparison between the experimental results and the analytical modelling results of FRP-PVC-confined NGC under axial compression loading are shown in Fig. 3. It can be seen that the prediction of analytical model is in good agreement with the experimental results.
(12)
where σc,n is the axial stress of confined normal geopolymer concrete; ɛc is the axial strain of confined normal geopolymer concrete; Ec,n is the elastic modulus of unconfined NGC, which is taken to be Ecn = 4730 f co' (in MPa) according to ACI 318–11 [26]; fco′ , n is the unconfined compressive strength of NGC; E2 is the slope of the linear second branch; ɛt,n is the transition axial strain for NGC. In order to let the parabolic first branch meet the linear second branch with a smooth transition, the ɛt,n is given by:
εt , n =
0.08 Axial strain
the thickness of the FRP jacket; dp is the diameter of the GPGCPs; fco′ , n is the unconfined compressive strength of NGC; εco, n is the axial strain at the peak stress of NGC; εh, ult is the hoop ultimate tensile strain of the FRP jacket. Based on the test results of this study, the equation to calculate the ultimate axial strain of FRP-confined concrete (εcu, n ) proposed by Lam and Teng [27] was used:
(5) the linear second branch terminates at a point where both the compressive strength and the ultimate axial strain of confined concrete are reached; and (6) the linear second branch intercepts the axial stress axis at a stress value equal to the unconfined concrete strength. Based on these assumptions, the analytical model proposed by Teng et al. [25] is shown as follows: (Ec, n − E2 )
0.04
Fig. 3. Comparisons between experimental results and model predictions for FPCC.
Fig. 2. Comparisons between experimental results and model predictions for FRP-PVC tubes.
⎧ Ec, n εc −
0
0.16
Fn = σc, n × An = σc, n·π·
(16)
Atotal = π ×
dp 4
dn 4
(20)
2
(21)
2
(22)
where σc, p is the axial stress of PGC; σc, n is the axial stress of NGC; Ap is the cross-sectional area of PGC; Ap is the cross-sectional area of PGC; An is the cross-sectional area of NGC; Atotal is the cross-sectional area of
(17)
where EFRP is the elastic modulus of FRP in the hoop direction; t is 734
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30
the whole PGC piles; dp is the outer diameter of PGC; dh is the outer diameter of hollow FRP-PVC tubes; dn is the diameter of NGC. The comparison between the experimental results and the analytical modelling results of GPGCPs with FPCC under the compression loading are shown in Fig. 4. It can be seen that this analytical model predicts results that is in good agreement with the experimental ones.
GGC1-1 GGC1-2
25
Axial Stress (MPa)
Prediction by Eq. (19) 20
15
4. Parametric analyses
10
Parametric analyses have been conducted to study the effects of different parameters on the axial compression behaviour of GPGCPs. The effects of PGC compressive strength, the confinement modulus of geogrid tubes, NGC compressive strength, the number of plies of GFRP and the ultimate strain of GFRP have been investigated. Equation (11) has been used to calculate the axial load capacity of GPGCPs without FPCC. Equation (20) has been used to calculate the axial load capacity of GPGCPs with FPCC.
5
0 0
0.04
0.08 Axial strain
0.12
0.16
(a) GGC1 30
4.1. Parametric analyses of GPGCPs without FPCC
GGC2-1 GGC2-2
25
4.1.1. Effect of confinement modulus of geogrid tubes Four values of confinement modulus of geogrid tubes grades have been considered (20 MPa, 35 MPa, 50 MPa, and 65 MPa). Fig. 5 shows the axial stress-axial strain behaviour of GPGCPs without FPCC with different confinement modulus of geogrid tubes. It is evident that the increase in the confinement modulus of geogrid tubes does not enhance the peak stress of GPGCPs without FPCC, which were all close to the compressive strength of the unconfined PGC. However, it is found that stable axial stress level of the last branch increased significantly with the increase of confinement modulus of geogrid tubes.
Axial Stress (MPa)
Prediction by Eq. (19) 20
15 10 5
4.1.2. Effect of PGC compressive strength Four PGC compressive strength grades have been considered (10 MPa, 20 MPa, 30 MPa, and 40 MPa). Fig. 6 shows the axial stressaxial strain behaviour of GPGCPs without FPCC with different PGC compressive strengths. It is evident that the increase in the PGC compressive strength significantly enhance the peak strength. However, it is found that stable axial stress level of the last branch increased to some extent with the increase of PGC compressive strength.
0 0
0.04
0.08 Axial strain
0.12
0.16
(b) GGC2 30
GGC3-1 GGC3-2 Prediction by Eq. (19)
25
20
Eg,eq Ele,grid =20 MPa Eg,eq Ele,grid =35 MPa
15
20
10
Axial Stress (MPa)
Axial Stress (MPa)
25
5 0
0
0.04
0.08 Axial strain
0.12
0.16
Ele,grid =50 MPa Eg,eq Ele,grid =65 MPa Eg,eq
15
10
5
(c) GGC3 Fig. 4. Comparisons between experimental results and model predictions for GPGCPs with FPCC.
0
0
0.04
0.08 Axial Strain
0.12
0.16
Fig. 5. Axial compression behaviour of GPGCPs without FPCC for different confinement moduli of geogrid tubes. 735
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50
ffpgc 'co , p =10 MPa
45
ffpgc 'co , p =10 MPa
ffpgc 'co , p =20 MPa
40
ffpgc 'co , p =20 MPa
35
fffpgc ''coco,,pp =30 MPa
30
ffpgc ''coco,,pp =40 MPa
ffpgc 'co , p =30 MPa
40
Axial Stress (MPa)
Axial Stress (MPa)
ffpgc 'co , p =40 MPa
30
20
25 20 15 10
10
5 0
0 0
0.04
0.08 Axial Strain
0.12
0
0.16
0.04
0.08 Axial Strain
0.12
0.16
Fig. 6. Axial compression behaviour of GPGCPs without FPCC for different PGC compressive strength grades.
Fig. 8. Axial compression behaviour of GPGCPs with FPCC for different PGC compressive strength grades.
4.2. Parametric analyses of GPGCPs with FPCC
compressive strengths. It is evident that the increase in the PGC compressive strength significantly enhances the first peak axial stress. It is also found that the axial stress level of the last branch increased slightly with the increase of PGC compressive strength. However, the axial strains at the first peak axial stress and the second peak axial stress are not enhanced.
4.2.1. Effect of confinement modulus of geogrid tubes Four values of confinement modulus of geogrid tubes grades have been considered (20 MPa, 35 MPa, 50 MPa, and 65 MPa). Fig. 7 shows the axial stress-axial strain behaviour of GPGCPs with FPCC for different confinement moduli of geogrid tubes. It is evident that the increase in the confinement modulus of geogrid tubes strength does not enhance the first peak axial stress and axial strain at the first peak axial stress of GPGCPs with FPCC. However, the increase in confinement modulus of geogrid tubes insignificantly improve the second peak axial stress and axial strain at the second peak axial stress of GPGCPs with FPCC. It is also found that the axial stress level of the last branch increased to some extent with the increase of confinement modulus of geogrid tubes.
4.2.3. Effect of NGC compressive strength Four NGC compressive strength grades have been considered (40 MPa, 50 MPa, 60 MPa, and 70 MPa). Fig. 9 shows the axial stressaxial strain behaviour of GPGCPs with FPCC with different NGC compressive strengths. It is evident that the increase in the NGC compressive strength significantly enhances the first and second peak axial stress. However, it is found that stable axial stress level of the last branch decreased to a slight extent with the increase of NGC compressive strength. This is because the ultimate strain of GFRP became lower with the increase of NGC compressive strength. When the GFRP ruptures, the hoop strain and the confinement effect of PVC become lower with the increase of NGC compressive strength. Therefore, axial stress of GPGCPs with FPCC reduces more quickly with the increase of
4.2.2. Effect of PGC compressive strength Four PGC compressive strength grades have been considered (10 MPa, 20 MPa, 30 MPa, and 40 MPa). Fig. 8 shows the axial stressaxial strain behaviour of GPGCPs with FPCC with different PGC
30
35
EEg,eq le,grid =20 MPa EEg,eq le,grid =35 MPa
20
EEg,eq le,grid =50 MPa
f 'co , n =60 MPa fc,n
EEg,eq le,grid =65 MPa
ffc,n 'co , n =70 MPa
25
15 10 5 0
f 'co , n =50 MPa fc,n
30
Axial Stress (MPa)
Axial Stress (MPa)
25
f 'co , n =40 MPa fc,n
20 15 10 5
0
0.04
0.08 Axial Strain
0.12
0
0.16
Fig. 7. Axial compression behaviour of GPGCPs with FPCC for different confinement moduli of geogrid tubes.
0
0.04
0.08 Axial Strain
0.12
0.16
Fig. 9. Axial compression behaviour of GPGCPs with FPCC for different NGC compressive strength grades. 736
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40
n =3
35
n =5
25
strains of GFRP does not enhance the first peak strength and the axial strain at the first peak axial stress of GPGCPs with FPCC. However, the increase in the number of GFPR layers significantly enhance the second peak axial stress and the axial strain at the second peak axial stress of GPGCPs with FPCC. It is also found that the axial stress level of the last branch increased to some extent with the increase of confinement modulus of geogrid tubes.
20
5. Conclusions
15
In this study, analytical models for the prediction of axial compression behaviour of GPGCPs without and with FPCC have been developed and validated with experimental results. Moreover, parametric analyses have been carried out to investigate the effects of different parameters on the axial compression behaviour of GPGCPs without and with FPCC. The following conclusions can be drawn:
n =7
Axial Stress (MPa)
30
n =9
10 5 0 0
0.04
0.08 Axial Strain
0.12
0.16
1. For the analytical model of GPGCPs without FPCC, the first two branches of axial stress-axial strain curves were simulated by using the unconfined concrete model proposed by European Standards. The third branch was simulated by a new equation. The predicted results are found to be in good agreement with the experimental results. 2. For the prediction of hollow FRP-PVC tubes, the model was proposed by carefully interpreting the experimental results. For the prediction of FRP-PVC-confined normal geopolymer concrete (NGC), the model proposed by Teng et al. (2009) was adopted to predict the first two branches of axial stress-axial strain curves and a new equation was proposed to predict the third branch. 3. For the analytical model of GPGCPs with FPCC, the axial load carrying capacity was calculated as the sum of axial loads carried by outer geogrid-confined pervious geopolymer concrete (PGC), hollow FRP-PVC tubes and inner FRP-PVC-confined normal geopolymer concrete (NGC). The predicted results are found to be in good agreement with the experimental results. 4. Through the parametric analyses of analytical model of GPGCPs without FPCC, it can be concluded that the increase of confinement modulus of geogrid tubes cannot enhance the peak axial stress of GPGCPs without FPCC but can increase stable axial stress level of the last branch. However, the increase of PGC compressive strength can significantly increase the peak axial stress of GPGCPs without FPCC and increase stable axial stress level of the last branch. 5. Through the parametric analyses of analytical model of GPGCPs with FPCC, it can be concluded that the first peak axial stress can be increased by the increase of PGC compressive strength and NGC compressive strength. The second peak axial stress can be significantly increased by the increase of NGC compressive strength, the number of GFRP layers, and ultimate strains of GFRP. The axial stress level of the last branch can be significantly enhanced by the increase of number of GFRP layers and ultimate strains of GFRP.
Fig. 10. Axial compression behaviour of GPGCPs with FPCC for different number of GFRP layers.
NGC compressive strength. This model can capture these characteristics of GPGCPs with FPCC. 4.2.4. Effect of number of GFRP layers Four different number of GFRP layers have been considered (3 layers, 5 layers, 7 layers and 9 layers). Fig. 10 shows the axial stressaxial strain behaviour of GPGCPs with FPCC with different PGC compressive strengths. It is evident that the increase in the number of GFPR layers significantly enhance the second peak axial stress and the axial strain at the second peak axial stress of GPGCPs with FPCC. However, the first peak axial stress and the axial strain at the first peak axial stress was not enhanced. It is also found that the axial stress level of the last branch increased significantly with the increase of confinement modulus of the geogrid tubes. 4.2.5. Effect of ultimate tensile strains of GFRP Four different ultimate tensile strains of GFRP have been considered (0.010, 0.015, 0.020 and 0.025). Fig. 11 shows the axial stress-axial strain behaviour of GPGCPs with FPCC with different ultimate tensile strains of GFRP. It is evident that the increase in the ultimate tensile
30
ε eh ,ult = 0.010
25
ε eh ,ult = 0.020
Axial Force (kN)
ε eh ,ult = 0.015 ε eh ,ult = 0.025
20
Finally, the proposed analytical models of GPGCPs without and with FPCC have proven to be effective in predicting their mechanical behaviour. The curves produced from the parametric study can be used for the design of GPGCPs without and with FPCC.
15 10
Declaration of Competing Interest
5
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.
0 0
0.04
0.08 Axial Strain
0.12
0.16 Acknowledgements
Fig. 11. Axial compression behaviour of GPGCPs with FPCC for different ultimate tensile strains of GFRP.
The authors gratefully acknowledge the contributions of Mr. Ritchie Mclean for his help in carrying out the experiments. The authors thank 737
Structures 23 (2020) 731–738
H. Zhang and M.N.S. Hadi
the Australasian Slag Association for providing GGBFS and Eraring power station for providing fly ash. The first author acknowledges the China Scholarship Council and the University of Wollongong, Australia for supporting his PhD scholarship.
[12] Kashi A, Ramezanianpour AA, Moodi F. Durability evaluation of retrofitted corroded reinforced concrete columns with FRP sheets in marine environmental conditions. Construct Build Mater 2017;151:520–33. [13] Micelli F, Mazzotta R, Leone M, Aiello M. Review study on the durability of FRPconfined concrete. J Compos Construct 2014;19(3):04014056. [14] Ding L, Seliem HM, Rizkalla SH, Wu G, Wu Z. Behavior of concrete piles confined with CFRP grid. ACI Special Publication 2011;1(275):189–205. [15] Fakharifar M, Chen G. Compressive behavior of FRP-confined concrete-filled PVC tubular columns. Compos Struct 2016;141:91–109. [16] Zhang H, Hadi MNS. Geogrid-confined pervious geopolymer concrete piles with FRP-PVC-confined concrete core: Concept and behaviour. Construct Build Mater 2019;211:12–25. [17] Hugher J, Withers N. Reinforcing of soft cohesive soils with stone columns. Ground Eng 1974:7(3). [18] Juran I, Guermazi A. Settlement response of soft soils reinforced by compacted sand columns. J Geotech Eng 1988;114(8):930–43. [19] Cimentada A, Da Costa A, Cañizal J, Sagaseta C. Laboratory study on radial consolidation and deformation in clay reinforced with stone columns. Canad Geotech J 2010;48(1):36–52. [20] Ashford S, Rollins K, Bradford VS, Weaver T, Baez J. Liquefaction mitigation using stone columns around deep foundations: Full-scale test results. Transport Res Record: J Transport Res Board 2000;1736:110–8. [21] Martin, J.B. and GR. Quantitative evaluation of stone column techniques for earthquake liquefaction mitigation. in Proceedings of the Tenth World Conference on Earthquake Engineering: 19-24 July 1992, Madrid, Spain. 1992. CRC Press. [22] Ashour S. The response of stone columns under the cyclic loading. University of Birmingham; 2016. [23] Wang W, Sheikh MN, Hadi MNS. Axial compressive behaviour of concrete confined with polymer grid. Mater Struct 2016;49(9):3893–908. [24] ENV1992-1-1, Eurocode 2: Design of Concrete Structures-Part 1: General Rules and Rules for Buildings, European Committee for Strandardization. 1991, Brussels. [25] Teng J, Jiang T, Lam L, Luo Y. Refinement of a design-oriented stress–strain model for FRP-confined concrete. J Compos Construct 2009;13(4):269–78. [26] ACI committee 318, Building code requirements for structural concrete (ACI 31811) and commentary. 2011, ACI 318R-11, Farmington Hills, MI. [27] Lam L, Teng J. Design-oriented stress–strain model for FRP-confined concrete. Construct Build Mater 2003;17(6–7):471–89.
References [1] Hadi MNS. Behaviour of FRP wrapped normal strength concrete columns under eccentric loading. Compos Struct 2006;72(4):503–11. [2] Hadi MNS, Khan QS, Sheikh MN. Axial and flexural behavior of unreinforced and FRP bar reinforced circular concrete filled FRP tube columns. Construct Build Mater 2016;122:43–53. [3] Csuka B, Kollár LP. FRP-confined circular concrete columns subjected to concentric loading. J Reinf Plastics Compos 2010;29(23):3504–20. [4] Mai AD, Sheikh MN, Hadi MNS. Investigation on the behaviour of partial wrapping in comparison with full wrapping of square RC columns under different loading conditions. Constr Build Mater 2018;168:153–68. [5] Cromwell J, Harries K, Shahrooz B. Environmental durability of externally bonded FRP materials intended for repair of concrete structures. Constr Build Mater 2011;25(5):2528–39. [6] Chen Y, Davalos JF, Ray I, Kim H-Y. Accelerated aging tests for evaluations of durability performance of FRP reinforcing bars for concrete structures. Compos Struct 2007;78(1):101–11. [7] Belarbi A, Bae S-W. An experimental study on the effect of environmental exposures and corrosion on RC columns with FRP composite jackets. Compos B Eng 2007;38(5–6):674–84. [8] Fam A, Pando M, Filz G, Rizkalla S. Precast piles for Route 40 bridge in Virginia using concrete filled FRP tubes. PCI J 2003;48(3):32–45. [9] Sen R, Mullins G. Application of FRP composites for underwater piles repair. Compos B Eng 2007;38(5–6):751–8. [10] Pando, M.A., Ealy, C.D., Filz, G.M., Lesko, J., and Hoppe, E., A laboratory and field study of composite piles for bridge substructures, United States. Federal Highway Administration. Office of Infrastructure Research and Development, 2006. [11] Guades E, Aravinthan T, Islam M, Manalo A. A review on the driving performance of FRP composite piles. Compos Struct 2012;94(6):1932–42.
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Geogrid-confined pervious geopolymer concrete piles with FRP-PVCconfined concrete core: Analytical models Haiqiu Zhang, Muhammad N.S. Hadi
T
⁎
School of Civil, Mining and Environmental Engineering, University of Wollongong, Australia
A R T I C LE I N FO
A B S T R A C T
Keywords: FRP PVC Geogrid Pervious geopolymer concrete Analytical model
The geogrid-confined pervious geopolymer concrete pile (GPGCP) with fibre reinforced polymer (FRP)-polyvinyl chloride (PVC)-confined concrete core (FPCC) is a new form of composite piles proposed in a previous study, which consists of a circular geogrid outer tube, a FPCC, and pervious geopolymer concrete (PGC) filled in between. For FPCC, the normal geopolymer concrete (NGC) was used to fill the FRP-PVC tubes. In this study, new analytical models are proposed to simulate the axial compressive behaviour of GPGCPs without and with FPCC. According to the characteristics of the mechanical behaviour of GPGCPs, analytical models are proposed which can predict the large axial strain behaviour. The unconfined concrete model proposed by the European Standards, and an existing popular FRP-confined concrete model are combined here. It was found that the analytical results are in good agreement with the experimental results. Based on the analytical models, the influences of different parameters on the axial compressive behaviour of GPGCPs have been investigated through parametric analyses.
1. Introduction In the past two decades, the use of FRP has been increasingly popular in civil engineering applications, due to its high strength-toweight ratio, high durability, and high anti-corrosion ability [1–7]. Especially in harsh marine environments, concrete columns and piles strengthened by FRP can significantly reduce the cost compared with steel reinforced concrete columns and piles [7–13]. The USA is reported to spend about two billion dollars annually to replace and repair reinforced concrete piers and more than $1 billion annually to maintain waterfront piling systems due to the corrosion of steel reinforcement. Using FRP materials are regarded as suitable alternatives to overcome this problem [10]. Some studies have investigated the properties of FRP-reinforced concrete piles. Ding et al. [14] conducted an experimental program to study the effectiveness of using Carbon Fibre Reinforced Polymer (CFRP) grid to confine precast concrete piles. The results showed that CFRP grid can effectively reinforce the precast concrete piles. Fam et al. [8] summarized the construction details and findings of laboratory and field tests of Glass Fibre Reinforced Polymer (GFRP) confined precast concrete piles. It was found that using GFRP tubes to reinforce piles for bridges is practical and feasible. Fakharifar and Chen [15] investigated the mechanical behaviour of FRP-confined, PVC-confined and FRP-
⁎
PVC-confined concrete. The results showed that the ultimate strength and ultimate strain of FRP-PVC-confined concrete specimens are larger than those of concrete columns confined by FRP alone or PVC alone. Recently, Zhang and Hadi [16] proposed a new concept of composite piles: geogrid-confined pervious geopolymer concrete piles (GPGCPs) with fibre reinforced polymer (FRP)-polyvinyl chloride (PVC)-confined concrete core (FPCC). Pervious geopolymer concrete (PGC) was used to fill between FPCC and geogrid tubes. Normal geopolymer concrete (NGC) was used to fill the FRP-PVC tube. This new form of composite piles combines the advantages of geopolymer concrete, pervious concrete, geogrid, FRP-PVC-confined concrete. Geopolymer concrete is a kind of green building material, which uses industrial by-products such as fly ash and slag to replace ordinary Portland Cement (OPC). Reducing the use of OPC can significantly decrease the amount of greenhouse gas emissions. Pervious concrete can increase the rate of consolidation and reduce the liquefaction potential caused by seismic and traffic loading [17–22]. Geogrid can sustain large strain and hold aggregates together [23]. The FRP-PVCconfined concrete have larger ultimate strength and ultimate strain than concrete columns confined by FRP alone or PVC alone [15]. However, only experiments have been carried out for GPGCPs without and with FPCC, but mathematical models need to be proposed to further understand the axial compressive behaviour of GPGCPs without
Corresponding authors. E-mail addresses: [email protected] (H. Zhang), [email protected] (M.N.S. Hadi).
https://doi.org/10.1016/j.istruc.2019.11.005 Received 31 July 2019; Received in revised form 7 November 2019; Accepted 17 November 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
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H. Zhang and M.N.S. Hadi
lateral confining pressure (fla,grid) is equal to the equivalent lateral confining force (Fle,grid) provided by the equivalent lateral confining pressure (fle,grid), which is shown as follows:
and with FPCC. The focus of the present study is to propose new analytical models to simulate the detailed axial stress-axial strain behaviour of GPGCPs without and with FPCC. The experimental details of the GPGCP specimens can be referred to at Zhang and Hadi [16].Through carefully interpreting the experimental results, the unconfined concrete model proposed by ENV1992-1–1 [24], and the FRP-confined model proposed by Teng et al. [25] are combined in these new analytical models here. According to the specific characteristics of the mechanical behaviour of GPGCPs, tailored analytical models are proposed which can predict the large axial strain behaviour. The analytical results have been found to be in good agreement with the experimental results. Based on the analytical models, the influences of different parameters on the axial compressive behaviour of GPGCPs have been investigated through parametric analyses. There is a need for this study as these developed models will help to apply the new proposed system of GPGCPs without and with FPCC.
Fla, grid = Fle, grid
(1)
The Fla,grid is the sum of forces provided by each transverse geogrid rib, which is given by
Fla, grid = 2n·Frib
(2)
where Frib is the force provided by one transverse geogrid rib; n is the number of transverse geogrid ribs for one GPGCP. The equivalent lateral confining force (Fle,grid) is expressed by:
Fle, grid = fle, grid ·H ·dp
(3)
where H is the height of the GPGCPs; dp is the diameter of the GPGCPs. Combining the Eq. (1), Eq. (2) and Eq. (3), the equivalent lateral confining pressure (fle,grid) is given by:
2. Details of GPGCP specimens
fle, grid = The experimental details of GPGCP specimens can be referred to at Zhang and Hadi [16]. A brief description of the specimens is described below to better understand the models. A total of 12 GPGCP specimens were cast and tested under axial compression. These specimens were divided into two groups. The six specimens of the first group did not have FPCC. The six specimens of the second group had FPCC. The inner diameter and outer diameter of PVC tubes were 76 mm and 84 mm, respectively. The height of PVC tubes was 325 mm. The inner diameter and outer diameter of FRP-PVC tubes were 76 mm and 86 mm, respectively. The height of FRP-PVC tubes was 325 mm. The average 28-day compressive strength of PGC for GPGCPs without FPCC was 22.1 MPa; that of GPGCPs with FPCC was 21.7 MPa. The average 28-day compressive strength of NGC for GPGCPs with FPCC was 49.2 MPa. The inner dimensions of square openings of geogrid are 25 mm × 25 mm. The widths of the transverse ribs and the longitudinal ribs are 10 mm and 6 mm, respectively. The average tensile ultimate load of geogrid ribs was 2.8 kN and the average ultimate tensile strain was 9.2%. The GFRP sheets were formed from bidirectional glass fibre and had a nominal thickness of 0.15 mm. The test results showed that the average tensile strength, elastic modulus and ultimate tensile strain were 621.5 MPa, 33.4 GPa and 1.86%, respectively. The commercial PVC pipes were used in this study, with an outside diameter of 84 mm and a thickness of 4 mm. The average tensile strength, fracture stress, elastic modulus and ultimate tensile strain were 51.2 MPa, 42.7 MPa, 1.58 GPa and 55.4%, respectively.
2n·Frib dp H
(4)
The next step is to calculate the lateral confinement modulus which is directly used in the analytical model. The lateral confinement modulus (Ele,grid) is defined as the ratio of the increment of the confining pressure and the increment of the hoop strain of concrete:
Ele, grid =
Δfle, grid Δεl
=
2n ΔFrib dp H Δεl
(5)
As the tensile force-strain relationship of geogrid is nearly linear, the value of ΔFrib can be calculated by: Δεl
Pgrid ΔFrib = Δεl εgrid, u
(6)
where the Pgrid is the average peak load of one geogrid rib; and ɛgrid,u is the corresponding tensile strain. For the PGC piles wrapped by two and three geogrid layers, their equivalent lateral confinement modulus is 2Ele,grid and 3Ele,grid, respectively. 3.2. Analytical model for GPGCPs without FPCC The test results of GPGCPs without FPCC [16] revealed that geogrid alone do not improve the compressive strength and the axial strain at the compressive strength of PGC. The axial stress–strain curves were divided into three branches. The first two branches are similar to the behaviour of unconfined concrete. Therefore, the equation used to simulate the behaviour of unconfined concrete was adopted to describe the first two branches of the axial stress–strain curves of GPGCPs without FPCC. In this study, the model presented by ENV1992-1–1 [24] was applied for the first two branches of the axial stress–strain curves:
3. Analytical model To better understand the axial compressive behaviour of GPGCPs, analytical models are proposed in this part. The research studies on the development of axial stress-axial strain models for predicting the axial compressive behaviour of geogrid confined concrete are very limited. Here, according to the characteristics of experimental behaviour of GPGCPs, tailored analytical models are proposed.
2
2εc ⎛ εc ⎞ ⎤ σc, p = fco′ ⎡ ⎢ εco − εco ⎥ ⎝ ⎠⎦ ⎣ ⎜
⎟
(7)
where σc and ɛc are the axial stress and axial strain, respectively; fco′ is the compressive strength of concrete and ɛco is the axial strain at the peak stress of concrete. In the third branch, the axial stress–strain behaviour of GPGCPs without FPCC became more gradual, and finally became stable. This can be explained that after the significant reduction of axial stress, the lateral strain of concrete became larger and the confinement effect provided by the geogrid became higher [23]. This characteristic is different from the axial stress–strain behaviour of unconfined concrete, which lost all the load carrying capacity after drastic reduction in the axial load. Through carefully interpreting the test results, it is found that the transition axial strain point, where the axial stress–strain curves of GPGCPs without FPCC can be differentiated from that of
3.1. Equivalent confining pressure provided by geogrid For geogrid-confined concrete, only part of the pervious concrete surface was covered by geogrid ribs, which is different from FRP and PVC wrapped concrete [23]. In this study, the actual lateral confining pressure (fla,grid) is transferred into equivalent lateral confining pressure (fle,grid), which is assumed to uniformly cover all lateral surface of the PGC. The criterion to calculate the equivalent lateral confining pressure is that the actual lateral confining force (Fla,grid) provided by the actual 732
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25
unconfined PGC, is related to the equivalent elastic modulus of geogrid tubes. This transition axial strain point can be determined by Eq. (9):
GG1-1
GG1-2
Axial Stress (MPa)
20
Ele, grid ⎞ ⎛ εt , p = εco, p ⎜a − bf ′co, p ⎟ ⎝ ⎠
Prediction by Eq. (10) a=1.72 b=10 c=1.5 d=0.011 Eg,eq =11.8
15
10
5
⎡ 1 ⎛ Ele, grid ⎞ σc, p = fco′ , p ⎢ cεc + d ⎜ ⎟ f ⎢ εco, p ⎝ co, p ⎠ ⎣
0 0
0.04
0.08 Axial strain
0.12
0.16
GG2-1 GG2-2
Axial Stress (MPa)
20
Prediction by Eq. (10)
( )
a=1.72 b=10 c=1.5 d=0.011 Eg,eq =23.6 MPa
15
10
σc, p
εc ⎤ ⎥ εco, p ⎥ ⎦
(9) c and d were which are 1.5 combined tobehaviour of
2
⎧ f ′ ⎡ 2εc − εc ⎤ for 0 ⩽ εc ⩽ εt , p ε εco, p ⎥ ⎪ co, p ⎢ ⎣ co, p ⎦ ⎪ = 0.2 ⎨ Ele, grid ⎡ 1 ⎞ · εc ⎤ for εt , p ⩽ εc ⎪ f ′co, p ⎢ cεc + d ⎛ f ⎥ ⎝ co, p ⎠ εco, p ⎦ ⎪ εco, p ⎣ ⎩
(10)
The comparisons between the experimental results and analytical modelling results of GPGCPs without FPCC are shown in Fig. 1. It can be seen that the analytical modelling results matched well with the experimental results. In general, the analytical modelling results predicts the axial stress–strain curves of GPGCPs without FPCC with good agreement due to the appropriate mathematical models.
5
0 0
0.04
0.08 Axial strain
0.12
0.16 3.3. Analytical model for hollow FRP-PVC tubes
(b) GG2
Based on the regression analysis of test data of hollow FRP-PVC tubes under axial compression loading, it can be found that the following equation can effectively describe the compressive behaviour of them:
25 GG3-1 GG3-2
20 Axial Stress (MPa)
0.2
where, σc, p is the axial stress of PGC. The constants obtained based on the regression analysis of test results, and 0.011, respectively. For clarity of presentation, Eq. (7) and Eq. (9) are gether in Eq. (10) to simulate the axial stress–strain GPGCPs without FPCC:
(a) GG1 25
(8)
where εt , p is transition axial strain point of PGC; εco, p is the axial strain at the peak stress of PGC; fco′ , p is the compressive strength of PGC; the a and b are constants determined by the test results; and the Ele,grid is the confinement modulus of geogrid. The suggested values of a and b were obtained based on the regression analysis of test results, which are 1.72 and 10, respectively. Based on the regression analysis of the test data shown in Fig. 1, the following expression is proposed to describe the axial stress–strain curves of Geogrid-confined PGC piles:
Prediction by Eq (10) Fh =
a=1.72 b=10 c=1.5 d=0.011 Eg,eq =35.4 MPa
15
10
2 ⎧− Epvc ·Apvc ·m (εc − εhp ) + Fp
⎨ ⎩
s·Epvc·Apvc (εc )3
for 0 ⩽ εc ⩽ εhp for εhp ⩽εc
(11)
where, the Epvc is the elastic modulus of PVC materials; Apvc is the cross-sectional area of PVC tubes; Fp is the peak load of hollow FRP-PVC tubes; ɛhp is the axial strain at the peak load of hollow FRP-PVC tubes; m and s are constants. The comparison between the experimental results and the analytical modelling results of FRP-PVC tubes under compression loading are shown in Fig. 2. It can be seen that this analytical model prediction is in good agreement with experimental results.
5
0 0
0.04
0.08 Axial strain
0.12
0.16
3.4. Analytical model for FRP-PVC-confined geopolymer concrete (FPCC) In this section, the analytical model proposed by Teng et al. [25] is adopted. This analytical model is based on the following assumptions: (1) the axial stress–strain curve consists of two parts, one is the parabolic first branch and the other one is a linear second branch; (2) the slope of the parabola at zero axial strain is the same as the elastic modulus of unconfined concrete; (3) the nonlinear part of the first branch is affected to some degree by the confinement of the FRP jacket; (4) the parabolic first branch meets the linear second branch smoothly;
(c) GG3 Fig. 1. Comparisons between experimental results and model predictions for GPGCPs without FPCC.
733
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H. Zhang and M.N.S. Hadi
50
80
FP1 FP2 Prediction by Eq. (11)
FPCC2
Epvc = 1.58GMa Apvc = 1004.8mm2 Fp =45.1kN εhp = 0.045 m = 0.07 s = 0.005
30
20
Prediction by Eq. (11)+Eq. (12)
60
Axial Stress (MPa)
Axial Load (kN)
40
FPCC1
Efrp = 33.43GMa Dn = 76mm ε h,rup =0.0186 ε co,n = 0.0022 f = 49.2 MPa
40
20
10 0
0
0
0.04
0.08 Axial Strain
0.12
σc, n =
4f ′co, n
⎨ f′ + E2 ε c ⎩ co, n
εc 2
for
εcu, n = 1.75 + 12ρκ ρε1.45 εco
0 ⩽ εc, r ⩽ εt , n for
εt , n ⩽ εc, r
f ′cc, n − f ′co, n εcu, n
(14)
σtotal =
where, fcc′ , n is the confined compressive strength of NGC; fco′ , n is the unconfined compressive strength of NGC; εcu, n is the ultimate axial strain of confined NGC, which is shown in Eq. (18). The compressive strength equation takes the following equation:
1 + 3.5(ρκ − 0.01) ρε for ρκ ⩾ 0.01 fcc′ , n = ⎧ 1 for ρκ ⩾ 0.01 ⎨ ⎩
ρε =
2EFRP ·t (f ′co, n εco, n ) dp εh, ult εco, n
Fp + Fh + Fn (19)
Atotal
where Fp, Fh and Fn are the axial loads carried by the outer PGC, the hollow FRP-PVC tubes and the inner NGC, respectively. The Fh can be given by Eq. (11). The Fp and Fn can be calculated by the following expressions:
dp2 − dh 2 ⎞ Fp = σc, p × Ap = σc, p·π·⎜⎛ ⎟ 4 ⎠ ⎝
(15)
where the ρκ is the confinement stiffness ratio; the ρε is the strain ratio. The mathematical expressions of these two ratios are as follow:
ρκ =
(18)
The axial load carrying capacity can be calculated as the sum of axial loads carried by the outer pervious geopolymer concrete (PGC), the hollow FRP-PVC tubes and the inner normal geopolymer concrete (NGC):
(13)
The slope of the linear second branch E2 is expressed as:
E2 =
0.16
3.5. Analytical model for GPGCPs with FPCC
2f ′co, n Ec, n − E2
0.12
where, the ρκ is the confinement stiffness ratio, which is shown in Eq. (16); the ρε is the strain ratio, which is shown in Eq. (17). The axial load carrying capacity of FRP-PVC-confined NGC is the sum of axial loads provided by the hollow tube and the confined NGC. The comparison between the experimental results and the analytical modelling results of FRP-PVC-confined NGC under axial compression loading are shown in Fig. 3. It can be seen that the prediction of analytical model is in good agreement with the experimental results.
(12)
where σc,n is the axial stress of confined normal geopolymer concrete; ɛc is the axial strain of confined normal geopolymer concrete; Ec,n is the elastic modulus of unconfined NGC, which is taken to be Ecn = 4730 f co' (in MPa) according to ACI 318–11 [26]; fco′ , n is the unconfined compressive strength of NGC; E2 is the slope of the linear second branch; ɛt,n is the transition axial strain for NGC. In order to let the parabolic first branch meet the linear second branch with a smooth transition, the ɛt,n is given by:
εt , n =
0.08 Axial strain
the thickness of the FRP jacket; dp is the diameter of the GPGCPs; fco′ , n is the unconfined compressive strength of NGC; εco, n is the axial strain at the peak stress of NGC; εh, ult is the hoop ultimate tensile strain of the FRP jacket. Based on the test results of this study, the equation to calculate the ultimate axial strain of FRP-confined concrete (εcu, n ) proposed by Lam and Teng [27] was used:
(5) the linear second branch terminates at a point where both the compressive strength and the ultimate axial strain of confined concrete are reached; and (6) the linear second branch intercepts the axial stress axis at a stress value equal to the unconfined concrete strength. Based on these assumptions, the analytical model proposed by Teng et al. [25] is shown as follows: (Ec, n − E2 )
0.04
Fig. 3. Comparisons between experimental results and model predictions for FPCC.
Fig. 2. Comparisons between experimental results and model predictions for FRP-PVC tubes.
⎧ Ec, n εc −
0
0.16
Fn = σc, n × An = σc, n·π·
(16)
Atotal = π ×
dp 4
dn 4
(20)
2
(21)
2
(22)
where σc, p is the axial stress of PGC; σc, n is the axial stress of NGC; Ap is the cross-sectional area of PGC; Ap is the cross-sectional area of PGC; An is the cross-sectional area of NGC; Atotal is the cross-sectional area of
(17)
where EFRP is the elastic modulus of FRP in the hoop direction; t is 734
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H. Zhang and M.N.S. Hadi
30
the whole PGC piles; dp is the outer diameter of PGC; dh is the outer diameter of hollow FRP-PVC tubes; dn is the diameter of NGC. The comparison between the experimental results and the analytical modelling results of GPGCPs with FPCC under the compression loading are shown in Fig. 4. It can be seen that this analytical model predicts results that is in good agreement with the experimental ones.
GGC1-1 GGC1-2
25
Axial Stress (MPa)
Prediction by Eq. (19) 20
15
4. Parametric analyses
10
Parametric analyses have been conducted to study the effects of different parameters on the axial compression behaviour of GPGCPs. The effects of PGC compressive strength, the confinement modulus of geogrid tubes, NGC compressive strength, the number of plies of GFRP and the ultimate strain of GFRP have been investigated. Equation (11) has been used to calculate the axial load capacity of GPGCPs without FPCC. Equation (20) has been used to calculate the axial load capacity of GPGCPs with FPCC.
5
0 0
0.04
0.08 Axial strain
0.12
0.16
(a) GGC1 30
4.1. Parametric analyses of GPGCPs without FPCC
GGC2-1 GGC2-2
25
4.1.1. Effect of confinement modulus of geogrid tubes Four values of confinement modulus of geogrid tubes grades have been considered (20 MPa, 35 MPa, 50 MPa, and 65 MPa). Fig. 5 shows the axial stress-axial strain behaviour of GPGCPs without FPCC with different confinement modulus of geogrid tubes. It is evident that the increase in the confinement modulus of geogrid tubes does not enhance the peak stress of GPGCPs without FPCC, which were all close to the compressive strength of the unconfined PGC. However, it is found that stable axial stress level of the last branch increased significantly with the increase of confinement modulus of geogrid tubes.
Axial Stress (MPa)
Prediction by Eq. (19) 20
15 10 5
4.1.2. Effect of PGC compressive strength Four PGC compressive strength grades have been considered (10 MPa, 20 MPa, 30 MPa, and 40 MPa). Fig. 6 shows the axial stressaxial strain behaviour of GPGCPs without FPCC with different PGC compressive strengths. It is evident that the increase in the PGC compressive strength significantly enhance the peak strength. However, it is found that stable axial stress level of the last branch increased to some extent with the increase of PGC compressive strength.
0 0
0.04
0.08 Axial strain
0.12
0.16
(b) GGC2 30
GGC3-1 GGC3-2 Prediction by Eq. (19)
25
20
Eg,eq Ele,grid =20 MPa Eg,eq Ele,grid =35 MPa
15
20
10
Axial Stress (MPa)
Axial Stress (MPa)
25
5 0
0
0.04
0.08 Axial strain
0.12
0.16
Ele,grid =50 MPa Eg,eq Ele,grid =65 MPa Eg,eq
15
10
5
(c) GGC3 Fig. 4. Comparisons between experimental results and model predictions for GPGCPs with FPCC.
0
0
0.04
0.08 Axial Strain
0.12
0.16
Fig. 5. Axial compression behaviour of GPGCPs without FPCC for different confinement moduli of geogrid tubes. 735
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H. Zhang and M.N.S. Hadi
50
ffpgc 'co , p =10 MPa
45
ffpgc 'co , p =10 MPa
ffpgc 'co , p =20 MPa
40
ffpgc 'co , p =20 MPa
35
fffpgc ''coco,,pp =30 MPa
30
ffpgc ''coco,,pp =40 MPa
ffpgc 'co , p =30 MPa
40
Axial Stress (MPa)
Axial Stress (MPa)
ffpgc 'co , p =40 MPa
30
20
25 20 15 10
10
5 0
0 0
0.04
0.08 Axial Strain
0.12
0
0.16
0.04
0.08 Axial Strain
0.12
0.16
Fig. 6. Axial compression behaviour of GPGCPs without FPCC for different PGC compressive strength grades.
Fig. 8. Axial compression behaviour of GPGCPs with FPCC for different PGC compressive strength grades.
4.2. Parametric analyses of GPGCPs with FPCC
compressive strengths. It is evident that the increase in the PGC compressive strength significantly enhances the first peak axial stress. It is also found that the axial stress level of the last branch increased slightly with the increase of PGC compressive strength. However, the axial strains at the first peak axial stress and the second peak axial stress are not enhanced.
4.2.1. Effect of confinement modulus of geogrid tubes Four values of confinement modulus of geogrid tubes grades have been considered (20 MPa, 35 MPa, 50 MPa, and 65 MPa). Fig. 7 shows the axial stress-axial strain behaviour of GPGCPs with FPCC for different confinement moduli of geogrid tubes. It is evident that the increase in the confinement modulus of geogrid tubes strength does not enhance the first peak axial stress and axial strain at the first peak axial stress of GPGCPs with FPCC. However, the increase in confinement modulus of geogrid tubes insignificantly improve the second peak axial stress and axial strain at the second peak axial stress of GPGCPs with FPCC. It is also found that the axial stress level of the last branch increased to some extent with the increase of confinement modulus of geogrid tubes.
4.2.3. Effect of NGC compressive strength Four NGC compressive strength grades have been considered (40 MPa, 50 MPa, 60 MPa, and 70 MPa). Fig. 9 shows the axial stressaxial strain behaviour of GPGCPs with FPCC with different NGC compressive strengths. It is evident that the increase in the NGC compressive strength significantly enhances the first and second peak axial stress. However, it is found that stable axial stress level of the last branch decreased to a slight extent with the increase of NGC compressive strength. This is because the ultimate strain of GFRP became lower with the increase of NGC compressive strength. When the GFRP ruptures, the hoop strain and the confinement effect of PVC become lower with the increase of NGC compressive strength. Therefore, axial stress of GPGCPs with FPCC reduces more quickly with the increase of
4.2.2. Effect of PGC compressive strength Four PGC compressive strength grades have been considered (10 MPa, 20 MPa, 30 MPa, and 40 MPa). Fig. 8 shows the axial stressaxial strain behaviour of GPGCPs with FPCC with different PGC
30
35
EEg,eq le,grid =20 MPa EEg,eq le,grid =35 MPa
20
EEg,eq le,grid =50 MPa
f 'co , n =60 MPa fc,n
EEg,eq le,grid =65 MPa
ffc,n 'co , n =70 MPa
25
15 10 5 0
f 'co , n =50 MPa fc,n
30
Axial Stress (MPa)
Axial Stress (MPa)
25
f 'co , n =40 MPa fc,n
20 15 10 5
0
0.04
0.08 Axial Strain
0.12
0
0.16
Fig. 7. Axial compression behaviour of GPGCPs with FPCC for different confinement moduli of geogrid tubes.
0
0.04
0.08 Axial Strain
0.12
0.16
Fig. 9. Axial compression behaviour of GPGCPs with FPCC for different NGC compressive strength grades. 736
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40
n =3
35
n =5
25
strains of GFRP does not enhance the first peak strength and the axial strain at the first peak axial stress of GPGCPs with FPCC. However, the increase in the number of GFPR layers significantly enhance the second peak axial stress and the axial strain at the second peak axial stress of GPGCPs with FPCC. It is also found that the axial stress level of the last branch increased to some extent with the increase of confinement modulus of geogrid tubes.
20
5. Conclusions
15
In this study, analytical models for the prediction of axial compression behaviour of GPGCPs without and with FPCC have been developed and validated with experimental results. Moreover, parametric analyses have been carried out to investigate the effects of different parameters on the axial compression behaviour of GPGCPs without and with FPCC. The following conclusions can be drawn:
n =7
Axial Stress (MPa)
30
n =9
10 5 0 0
0.04
0.08 Axial Strain
0.12
0.16
1. For the analytical model of GPGCPs without FPCC, the first two branches of axial stress-axial strain curves were simulated by using the unconfined concrete model proposed by European Standards. The third branch was simulated by a new equation. The predicted results are found to be in good agreement with the experimental results. 2. For the prediction of hollow FRP-PVC tubes, the model was proposed by carefully interpreting the experimental results. For the prediction of FRP-PVC-confined normal geopolymer concrete (NGC), the model proposed by Teng et al. (2009) was adopted to predict the first two branches of axial stress-axial strain curves and a new equation was proposed to predict the third branch. 3. For the analytical model of GPGCPs with FPCC, the axial load carrying capacity was calculated as the sum of axial loads carried by outer geogrid-confined pervious geopolymer concrete (PGC), hollow FRP-PVC tubes and inner FRP-PVC-confined normal geopolymer concrete (NGC). The predicted results are found to be in good agreement with the experimental results. 4. Through the parametric analyses of analytical model of GPGCPs without FPCC, it can be concluded that the increase of confinement modulus of geogrid tubes cannot enhance the peak axial stress of GPGCPs without FPCC but can increase stable axial stress level of the last branch. However, the increase of PGC compressive strength can significantly increase the peak axial stress of GPGCPs without FPCC and increase stable axial stress level of the last branch. 5. Through the parametric analyses of analytical model of GPGCPs with FPCC, it can be concluded that the first peak axial stress can be increased by the increase of PGC compressive strength and NGC compressive strength. The second peak axial stress can be significantly increased by the increase of NGC compressive strength, the number of GFRP layers, and ultimate strains of GFRP. The axial stress level of the last branch can be significantly enhanced by the increase of number of GFRP layers and ultimate strains of GFRP.
Fig. 10. Axial compression behaviour of GPGCPs with FPCC for different number of GFRP layers.
NGC compressive strength. This model can capture these characteristics of GPGCPs with FPCC. 4.2.4. Effect of number of GFRP layers Four different number of GFRP layers have been considered (3 layers, 5 layers, 7 layers and 9 layers). Fig. 10 shows the axial stressaxial strain behaviour of GPGCPs with FPCC with different PGC compressive strengths. It is evident that the increase in the number of GFPR layers significantly enhance the second peak axial stress and the axial strain at the second peak axial stress of GPGCPs with FPCC. However, the first peak axial stress and the axial strain at the first peak axial stress was not enhanced. It is also found that the axial stress level of the last branch increased significantly with the increase of confinement modulus of the geogrid tubes. 4.2.5. Effect of ultimate tensile strains of GFRP Four different ultimate tensile strains of GFRP have been considered (0.010, 0.015, 0.020 and 0.025). Fig. 11 shows the axial stress-axial strain behaviour of GPGCPs with FPCC with different ultimate tensile strains of GFRP. It is evident that the increase in the ultimate tensile
30
ε eh ,ult = 0.010
25
ε eh ,ult = 0.020
Axial Force (kN)
ε eh ,ult = 0.015 ε eh ,ult = 0.025
20
Finally, the proposed analytical models of GPGCPs without and with FPCC have proven to be effective in predicting their mechanical behaviour. The curves produced from the parametric study can be used for the design of GPGCPs without and with FPCC.
15 10
Declaration of Competing Interest
5
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.
0 0
0.04
0.08 Axial Strain
0.12
0.16 Acknowledgements
Fig. 11. Axial compression behaviour of GPGCPs with FPCC for different ultimate tensile strains of GFRP.
The authors gratefully acknowledge the contributions of Mr. Ritchie Mclean for his help in carrying out the experiments. The authors thank 737
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the Australasian Slag Association for providing GGBFS and Eraring power station for providing fly ash. The first author acknowledges the China Scholarship Council and the University of Wollongong, Australia for supporting his PhD scholarship.
[12] Kashi A, Ramezanianpour AA, Moodi F. Durability evaluation of retrofitted corroded reinforced concrete columns with FRP sheets in marine environmental conditions. Construct Build Mater 2017;151:520–33. [13] Micelli F, Mazzotta R, Leone M, Aiello M. Review study on the durability of FRPconfined concrete. J Compos Construct 2014;19(3):04014056. [14] Ding L, Seliem HM, Rizkalla SH, Wu G, Wu Z. Behavior of concrete piles confined with CFRP grid. ACI Special Publication 2011;1(275):189–205. [15] Fakharifar M, Chen G. Compressive behavior of FRP-confined concrete-filled PVC tubular columns. Compos Struct 2016;141:91–109. [16] Zhang H, Hadi MNS. Geogrid-confined pervious geopolymer concrete piles with FRP-PVC-confined concrete core: Concept and behaviour. Construct Build Mater 2019;211:12–25. [17] Hugher J, Withers N. Reinforcing of soft cohesive soils with stone columns. Ground Eng 1974:7(3). [18] Juran I, Guermazi A. Settlement response of soft soils reinforced by compacted sand columns. J Geotech Eng 1988;114(8):930–43. [19] Cimentada A, Da Costa A, Cañizal J, Sagaseta C. Laboratory study on radial consolidation and deformation in clay reinforced with stone columns. Canad Geotech J 2010;48(1):36–52. [20] Ashford S, Rollins K, Bradford VS, Weaver T, Baez J. Liquefaction mitigation using stone columns around deep foundations: Full-scale test results. Transport Res Record: J Transport Res Board 2000;1736:110–8. [21] Martin, J.B. and GR. Quantitative evaluation of stone column techniques for earthquake liquefaction mitigation. in Proceedings of the Tenth World Conference on Earthquake Engineering: 19-24 July 1992, Madrid, Spain. 1992. CRC Press. [22] Ashour S. The response of stone columns under the cyclic loading. University of Birmingham; 2016. [23] Wang W, Sheikh MN, Hadi MNS. Axial compressive behaviour of concrete confined with polymer grid. Mater Struct 2016;49(9):3893–908. [24] ENV1992-1-1, Eurocode 2: Design of Concrete Structures-Part 1: General Rules and Rules for Buildings, European Committee for Strandardization. 1991, Brussels. [25] Teng J, Jiang T, Lam L, Luo Y. Refinement of a design-oriented stress–strain model for FRP-confined concrete. J Compos Construct 2009;13(4):269–78. [26] ACI committee 318, Building code requirements for structural concrete (ACI 31811) and commentary. 2011, ACI 318R-11, Farmington Hills, MI. [27] Lam L, Teng J. Design-oriented stress–strain model for FRP-confined concrete. Construct Build Mater 2003;17(6–7):471–89.
References [1] Hadi MNS. Behaviour of FRP wrapped normal strength concrete columns under eccentric loading. Compos Struct 2006;72(4):503–11. [2] Hadi MNS, Khan QS, Sheikh MN. Axial and flexural behavior of unreinforced and FRP bar reinforced circular concrete filled FRP tube columns. Construct Build Mater 2016;122:43–53. [3] Csuka B, Kollár LP. FRP-confined circular concrete columns subjected to concentric loading. J Reinf Plastics Compos 2010;29(23):3504–20. [4] Mai AD, Sheikh MN, Hadi MNS. Investigation on the behaviour of partial wrapping in comparison with full wrapping of square RC columns under different loading conditions. Constr Build Mater 2018;168:153–68. [5] Cromwell J, Harries K, Shahrooz B. Environmental durability of externally bonded FRP materials intended for repair of concrete structures. Constr Build Mater 2011;25(5):2528–39. [6] Chen Y, Davalos JF, Ray I, Kim H-Y. Accelerated aging tests for evaluations of durability performance of FRP reinforcing bars for concrete structures. Compos Struct 2007;78(1):101–11. [7] Belarbi A, Bae S-W. An experimental study on the effect of environmental exposures and corrosion on RC columns with FRP composite jackets. Compos B Eng 2007;38(5–6):674–84. [8] Fam A, Pando M, Filz G, Rizkalla S. Precast piles for Route 40 bridge in Virginia using concrete filled FRP tubes. PCI J 2003;48(3):32–45. [9] Sen R, Mullins G. Application of FRP composites for underwater piles repair. Compos B Eng 2007;38(5–6):751–8. [10] Pando, M.A., Ealy, C.D., Filz, G.M., Lesko, J., and Hoppe, E., A laboratory and field study of composite piles for bridge substructures, United States. Federal Highway Administration. Office of Infrastructure Research and Development, 2006. [11] Guades E, Aravinthan T, Islam M, Manalo A. A review on the driving performance of FRP composite piles. Compos Struct 2012;94(6):1932–42.
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