Flexural capacity prediction of composite RC members strengthened with UHPC based on existing design models

Structures 23 (2020) 44–55

Contents lists available at ScienceDirect

Structures journal homepage: www.elsevier.com/locate/structures

Flexural capacity prediction of composite RC members strengthened with UHPC based on existing design models

T

Kazutaka Shiraia, , Hor Yinb, Wee Teoc ⁎

a

Faculty of Engineering, Hokkaido University, Kita 13, Nishi 8, Sapporo 060-8628, Japan Graduate School of Engineering, Hokkaido University, Kita 13, Nishi 8, Sapporo 060-8628, Japan c School of Energy, Geoscience, Infrastructure and Society (EGIS), Heriot Watt University Malaysia, Jalan Venna P5/2, Precinct 5, 62200 Putrajaya, Malaysia b

ARTICLE INFO

ABSTRACT

Keywords: Ultra-high-performance concrete (UHPC) Flexural strength UHPC layer Reinforced concrete structure UHPC-concrete composite member Failure mode

Ultra-high-performance concrete (UHPC), a new generation of cementitious materials with very high strength, ductility, and durability, has been used for enhancing reinforced concrete (RC) structures as a strengthening material. The structural performance of RC members strengthened by UHPC or UHPC-concrete composite members is significantly improved. However, there are few methods for predicting the capacity of UHPC-concrete composite members. The present study proposes a simple method based on existing design models for the prediction of the flexural strength of composite RC members strengthened with UHPC at the tension zone. Rectangular stress block diagrams are used for the compression and tension zones of the conventional concrete and UHPC layers, respectively, in a composite section. The prediction results show good agreement with experimental results. The failure modes are predicted and compared with those observed in an actual test. Furthermore, a parametric study is carried out by varying some parameters, including the thickness of the UHPC layer and the compressive strength of UHPC. The results show that the proposed method can predict the flexural strength of UHPC-concrete composite members.

1. Introduction Ultra-high-performance concrete (UHPC), a cementitious concrete material initially developed by Richard and Cheyrezy (1995) [1], has been applied in construction, either cast in situ or applied in the form of prefabricated panels. UHPC is defined by its superior mechanical properties, including high strength (> 150 MPa in compression and > 8 MPa in tension), strain hardening, low permeability, and high energy absorption [2–4]. UHPC structural members have been experimentally and analytically investigated [5–8] and numerically simulated [9–12]. The overall performance of UHPC structures, including ultimate resistance strength, stiffness, and strain hardening, is significantly improved compared to that of conventional reinforced concrete (RC) elements. Several studies on composite RC members strengthened with a UHPC layer have been conducted [13–18]. According to Brühwiler and Denarié (2008) [13], UHPC has been applied to strengthen parts of RC structures in full-scale applications. They showed that UHPC has sufficiently matured to be used for strengthening RC structures. Many UHPC-concrete composite members have been experimentally tested [14–17]. The results confirmed that the UHPC layer enhances structural

⁎

performance. Studies have also applied finite element methods to evaluate the behaviour of UHPC-concrete members [16,19,20]. Although the structural performance of UHPC-concrete composite members is significantly enhanced by UHPC strengthening, analytical models of the flexural strength of such members are very limited [14,15,21–23]. The flexural strength has been computed based on moment-curvature relationships using a cross-sectional analysis; however, these methods require several analytical steps. For RC members or fibre-reinforced concrete (FRC) members, the flexural strength can be obtained from existing design models [24,25]. According to ACI Committee 318 (2008) [24], the moment resistance can be computed using a simplified stress block diagram. The tensile stress of normal-strength concrete (NSC) is generally neglected, whereas that of FRC or UHPC should be taken into account because FRC and UHPC have high tensile strength. There are no design models available for UHPC-concrete composite members. Therefore, the development of simpler analytical models for such composite members is needed. The modification of existing design models for non-composite RC or FRC members is desirable because they are simple and easy to use. The present study proposes a simple method based on a

Corresponding author. E-mail addresses: [email protected] (K. Shirai), [email protected] (H. Yin), [email protected] (W. Teo).

https://doi.org/10.1016/j.istruc.2019.09.017 Received 23 May 2019; Received in revised form 29 July 2019; Accepted 27 September 2019 2352-0124/ © 2019 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.

Structures 23 (2020) 44–55

K. Shirai, et al.

Fig. 2. For the non-composite specimens, NSC specimen RE-0 and UHPC specimen RE-100 showed shear and flexural failure, respectively. All specimens strengthened with UHPC in the RE series mainly failed in flexure, except specimen RE-20, which showed debonding and inclined shear cracks (Fig. 2(a)). For the OV series, all specimens failed in shear along with debonding of the UHPC overlays (Fig. 2(b)). Fig. 3(a) and (b) show the load-deflection curves of the RE series and OV series specimens, respectively. In addition to improvement in failure modes, the overall behaviour of the strengthened slab changed completely. For RE series, as shown in Fig. 3(a), all UHPC-concrete composite slabs (RE-20, RE-32, and RE-50) exhibited extensive deflection hardening and ductility in the post-cracking range. The lack of strength enhancement of the strengthened slabs compared with non-composite NSC specimen RE-0 offset by excellent energy absorption. The noncomposite UHPC RE-100 showed the highest ultimate load (Fig. 3(a)). In RE series, partial strengthening of the tension zone with UHPC created a weak bond interface between the UHPC layer and NSC substrate. The main reason that the composite slabs (RE-20, RE-32, and RE-50) failed at a lower loading than the non-composite specimen RE-0 would be due to the effect of this weak bond interface. For the OV series (Fig. 3(b)), owing to the strengthening effect, including an increase in the total height of the specimens, the UHPC layer enhanced the overall performance of UHPC-concrete composite specimens compared to that of specimen RE-0. In addition, composite specimen OV-50a, which was reinforced with five 10-mm-diameter hightensile-strength steels in its UHPC layer, did not differ from specimen OV-50, which lacked rebar, in terms of initial stiffness. However, the rebar in the UHPC layer increased the ultimate load of the specimen. A detailed discussion can be found in the original study [17].

modification of existing design models for calculating the flexural strength of UHPC-concrete composite members. The rest of this paper is organised as follows. Experimental data reported in a previous study [17], mainly used to verify the proposed method, are briefly described in Section 2. Section 3 reviews existing design models for non-composite RC or FRC members. The proposed method for calculating the flexural strength of UHPC-concrete composite members is presented in Section 4. Sections 5 and 6 present and discuss the flexural moment calculation results and predicted failure modes, respectively. Section 7 presents the results of the parametric study to assess the predicted structural capacity of UHPC-concrete composite members and to establish the applicability of the proposed calculation method. In addition, the present study expands on a previous study [26]. 2. Data description and results 2.1. Specimen details Nine slab specimens tested by Yin et al. (2017b) [17] were used to verify the proposed flexural strength calculation method. Two of them are non-composite specimens made of NSC and UHPC, namely, RE-0 and RE-100, respectively. The remaining seven specimens are composite RC specimens strengthened with various UHPC configurations in the tension zone, as shown in Fig. 1. The test system is illustrated in Fig. 1(a). All specimens were simply supported and subjected to the three-point loading. Each specimen had a total length of 1600 mm with a clear span of 1200 mm and carried a concentrated load at the midspan. The specimens without UHPC overlays had a shear span-to effective depth ratio of 8.11. The specimens were grouped into two series. The first series, denoted the RE series, consists of five specimens, and the second series, denoted the OV series, consists of four specimens, as shown in Fig. 1(b) and (c), respectively. For the RE series, the composite specimens were strengthened with UHPC as a patch material for the repair and rehabilitation of structural members. In practice, when RC structures deteriorate, the affected concrete is often removed and a repair material is applied to the concrete substrate. For the OV series, two additional UHPC overlays, with thicknesses of 25 and 50 mm, respectively, were applied to the tension zone of specimen RE-0. Two specimens were prepared for each UHPC thickness; one was not reinforced (i.e., OV-25 and OV-50), and the other was reinforced with five 10-mm-diameter high-tensile-strength steels (i.e., OV-25a and OV-50a). Details of the longitudinal steel arrangement and geometry of the specimens are shown in Fig. 1 and Table 1. The specimens for both RE and OV series were prepared as follows. First, the NSC was cast. After the NSC hardened, the top surface of the concrete was randomly roughened throughout the NSC substrate using chisel and hammer to create a good bond surface for UHPC layer. Then, the UHPC was cast onto the NSC substrate.

3. Review of existing design models for flexural members 3.1. Design code ACI 318 for RC members According to design code ACI 318 (2008) [24] for RC structures, the moment resistance capacity of rectangular RC members can be calculated using the simplified stress block diagram with the concrete tensile stress neglected, as shown in Fig. 4. In Fig. 4, εcu is the concrete strain, C is the compressive force of concrete, and Ts is the tensile force of the longitudinal rebar. Based on this diagram, the moment resistance of the members Mn can be expressed as

Mn = As fy d

a 2

(1)

where As is the area of the longitudinal rebar, fy is the yield strength of the longitudinal rebar, d is the effective depth, and a is the depth of the compressive stress block (Fig. 4). 3.2. Design code ACI 544 for FRC members

2.2. Material properties of specimens

The design guideline ACI 544 (1988) [25] for FRC members recommends that the moment resistance capacity be calculated based on simplified assumptions in stress and strain diagrams, as shown in Fig. 5. The tensile stress of the concrete of FRC members is accounted for in the design calculation, whereas that of NSC of RC members is generally neglected. In Fig. 5, Tfc is the tensile force of fibrous concrete and Trb is the tensile force of the longitudinal rebar. From Fig. 5, the moment resistance Mn can be expressed as

Table 2 shows the properties of NSC and UHPC materials. The compressive and flexural strength were tested at day 28. For NSC, ready-mixed concrete was used. UHPC was manually mixed. Steel fibres (length: 13 mm; diameter: 0.2 mm; tensile strength: 2300 MPa) were added to the UHPC mixtures. More details regarding UHPC can be found in the original study [17]. Table 3 shows the properties of the longitudinal rebar in the specimens. Rebar with diameters of 10 and 12 mm was used, denoted T10 and T12, respectively. The tensile yield strength of T10 and T12 rebar was experimentally obtained. The results are shown in Table 3.

Mn = As fy d

a + 2

t b w (h

e)

h e + 2 2

a 2

(2)

where bw is the web width, h is the total height, σt is the tensile stress in fibrous concrete, and e is the distance from the extreme compression fibre to the top of the tensile stress block of fibrous concrete (Fig. 5). The other variables are as defined for Eq. (1).

2.3. Brief description of test results The crack patterns of the specimens after tests are illustrated in 45

Structures 23 (2020) 44–55

K. Shirai, et al.

200

600

600

5T12@62

3R6@60

Loading

5T12@62

Support

200 NSC

5T10@62

Support UHPC

(a) 5T12@62 26 62

100

62

62

26 62

62 26 26 48 26

74

26 62

100

62

62

300

26 62

100

150

300

OV-50

300

74

62

62 26 74

100

50

62

62

62 26 50

62

62 26

50

300

125

50

5T10@62

RE-50

100

62

RE-32

74

26 62

62

74

26 62

100

300

OV-25a

100

32

62

105

62 26 68

62

62 26

25

5T10@62

74

26 62

62

74

26 62 62

62

100

20 300

UHPC

OV-25

62 26

RE-20

NSC

25

80

62

62 26

74

5T12@62

74

26 62

62

100

300

RE-0

62

300

OV-50a

62 26

100

[Unit: mm]

RE-100 (b)

(c)

Fig. 1. Test scheme and details of specimens [17]: a – Overall test scheme (specimen OV-50a); b – RE specimen series; c – OV specimen series. Table 1 Geometry of specimens (Yin et al. 2017b) [17].

Table 2 Concrete properties of specimens (Yin et al. 2017b) [17].

Specimen

b (mm)

h (mm)

hU (mm)

ad (mm)

RE-0 RE-20 RE-32 RE-50 RE-100 OV-25 OV-25a OV-50 OV-50a

300 300 300 300 300 300 300 300 300

100 100 100 100 100 125 125 150 150

– 20 32 50 100 25 25 50 50

600 600 600 600 600 600 600 600 600

Material

Compressive strength (MPa)

Flexural strength (MPa)

Young’s modulus§ (GPa)

NSC UHPC

23 153

– 27.4

22.5 58.1

§ : calculated using Ec = 4700(f’c)0.5, where f’c is the compressive strength in MPa (ACI Committee 318 2008 [24]).

The distance e is given by

e = [ s (Fibres) + 0.003]

Note: b: width of specimen. h: height of specimen. hU: thickness of the UHPC layer. ad: distance between the loading point and support.

c 0.003

(3)

where εs(Fibres) is the tensile strain in the fibres and c is the depth of the neutral axis. The tensile stress σt (MPa) can be given by 46

Structures 23 (2020) 44–55

K. Shirai, et al.

• The NSC and UHPC parts of the composite members were assumed to fail simultaneously. • The assumed strain (ε ) corresponding to ultimate compressive stress was 0.003 for NSC. • The tensile stress, σ , used for FRC members (Fig. 5) was adopted for UHPC. • Because the UHPC layer at the tension chord is relatively thin, it was

Table 3 Longitudinal reinforcement properties of specimens (Yin et al. 2017b) [17].

t

Reinforcement

Diameter (mm)

Area (mm2)

Yield strength (MPa)

Young’s modulus (GPa)

T12 T10

12 10

113.1 78.5

502 475

200 200

l = 0.00772 d

f

c

t

Fbe

reasonably assumed that the distance h − e (Fig. 5) could be taken as the UHPC thickness (h − e = hU), as shown in Fig. 6. h is the total height of the section.

(4)

A tensile force for the UHPC, TUHPC, was then computed as the product of the stress, σt, obtained from Eq. (4), and the corresponding UHPC area AUHPC (=bw × hU). The bond behaviour of the interface between the NSC and UHPC remains a challenge in the development of accurate prediction methods. However, the present paper adopted a simple method, which did not consider the effect of actual bond mechanical interface for simplicity as an early study for predicting the flexural moment capacity, based on modification of the existing design codes.

where l is the fibre length, d is the effective depth, ρf is the percent by volume of steel fibres, and Fbe is the factor of bond efficiency of the fibre. The factor Fbe varies from 1.0 to 1.2 depending on fibre characteristics [25]. Because the fibre used for the specimens in the present study was smooth, straight, and short (13 mm long), Fbe of 1.0 was used in the present study. 4. Flexural strength of UHPC-concrete composite members 4.1. Overview

4.2. Equilibrium conditions

In the present study, the flexural moment of UHPC-concrete composite members was predicted based on the equilibrium with geometric compatibility in a section of the members. The assumed representation of stresses and strains in the UHPC-concrete composite sections is shown in Fig. 6. The following assumptions were made for the flexural moment calculation:

As widely accepted in current design models, in the present study, an equilibrium equation is derived from the compatibility condition, where the strain varies linearly along the cross-section, as shown in Fig. 6. At the equilibrium condition, the equations could be expressed as follows: For the RE series, except specimen RE-0,

Load

Load

Load

Load

Load

Load

Load

Load

(b)

Load

(a) Fig. 2. Experimentally obtained crack patterns [17]: a – RE specimen series; b – OV specimen series. 47

Structures 23 (2020) 44–55

K. Shirai, et al.

120

RE-0

120

100

RE-20

100

RE-32 RE-50

Load (kN)

Load (kN)

80

RE-100

60 40 20

RE-0 OV-25 OV-25a OV-50 OV-50a

80 60 40 20

0

0

10

20

30

40

50

60

70

80

0

90

0

10

20

30

40

Deflection (mm)

Deflection (mm)

(a)

(b)

50

60

70

Fig. 3. Load-deflection curves of test specimens [17]: a – RE specimen series; b – OV specimen series.

(5a)

Cc + Csc = Tst + TUHPC

d2 = distance from top-most concrete surface to centre of T10 rebar (Fig. 6(b)), dU = distance from top-most concrete surface to centre of UHPC layer (dU = hC + hU/2), hC = height of RC member, xn = distance between top-most surface and neutral axis. xn can be calculated using strain compatibility and equilibrium conditions, and checking the strain level in the reinforcement rebar, f′c = compressive strength of NSC, α = factor relating depth of equivalent rectangular compressive stress block to neutral axis depth, taken as 0.85 in the present study because f′c = 23 MPa (Fig. 7), A′s = area of top rebar (5 T12 = 565 mm2), As = area of bottom rebar (5 T12 = 565 mm2), AsU = area of longitudinal rebar in UHPC overlay (5 T10 = 393 mm2), AUHPC = area of UHPC layer (AUHPC = bw × hU), σ′s = stress in top rebar, σs = stress in bottom rebar, σsU = stress in longitudinal rebar in UHPC overlay.

For the OV series, (5b)

Cc + Csc = Tst + Tst , U + TUHPC where

Cc = 0.85fc xn b w

Csc = As

Tst = As

s

s

Tst , U = AsU

sU

TUHPC = AUHPC

t

The flexural moment capacity Mfle is then given by the following: For the RE series, except specimen RE-0,

Mfle = As

s

xn + AUHPC 2

d

t

dU

xn + As 2

s

xn 2

d

(6a)

For the OV series,

Mfle = As s

s

xn + AsU 2

d1 xn 2

d

sU

d2

xn + AUHPC 2

t

dU

In the analysis, the cases were classified as follows:

xn + As 2

• No reinforcement yielded (σ′ < f and σ < f ), where f is the rebar yield strength. • Tension reinforcement (bottom rebar) yielded and compression reinforcement (top rebar) did not yield (σ = f and σ′ < f ). • Both tension and compression reinforcement yielded (σ = f and s

(6b)

The notation in Eqs. (5) and (6) indicates as follows: d' = distance from top-most surface to centre of diameter of top rebar, d = assumed effective depth (Fig. 6(a)), d1 = distance from top-most concrete surface to centre of T12 rebar (Fig. 6(b)),

y

s

s

σ′s = fy).

y

y

y

s

y

s

y

It should be mentioned that the flexural moment of NSC specimen RE-0 (or B-0 described in Section 5) in this study was obtained based on

Fig. 4. Diagrams of stresses and strains in a section of RC members [24]. 48

Structures 23 (2020) 44–55

K. Shirai, et al.

Fig. 5. Diagrams of stresses and strains in a section of FRC members [25].

design code ACI Committee 318 (2008) [24]. For UHPC specimen RE100, the flexural moment was obtained using Eq. (6a), where the distance h − e (Fig. 5) and dU in Eq. (6a) were assumed to be 50 mm and 75 mm, respectively. In addition, the flexural strength calculation results for specimens RE-0, -32, -50, and -100 were taken from a previous study [26].

α 0.85 0.65 17

5. Prediction results and verification

28

56

f'c (MPa)

Fig. 7. Value of factor α according to ACI Committee 318 (2008) [24].

Table 4 shows the predicted flexural moment capacities for all specimens described in Section 2.1, and four additional specimens tested by Safdar et al. (2016) [16]. The four additional specimens, named B-0, BL-20, BL-40, and BL-60, had a length of 3000 mm and subjected to a four-point loading. Each specimen was simply supported on 2800 mm span, and the distance between the two concentrated loads was 800 mm. The cross-sectional

geometry of each specimen was 400 mm in height including UHPC layer by 250 mm in width. The specimen B-0 was an RC member, whereas the specimens BL-20, BL-40, and BL-60 were composite members of RC substrates repaired with UHPC layers in tension zones. The thickness of UHPC layers was 20, 40, and 60 mm for specimens BL20, BL-40, and BL-60, respectively. The compressive strength of the

(a)

(b) Fig. 6. Assumptions used for calculation of flexural strength of UHPC-concrete members: a – stresses and strains in a typical UHPC-concrete section for RE specimen series; b – stresses and strains in a typical UHPC-concrete section for OV specimen series. 49

Structures 23 (2020) 44–55

K. Shirai, et al.

Table 4 Comparison between predicted and experimental results. Authors

Yin et al. (2017b) (RE series) [17]

Safdar et al. (2016) [16]

Yin et al. (2017b) (OV series including RE-0) [17]

Specimen

RE-0 RE-20 RE-32 RE-50 RE-100 B-0 BL-20 BL-40 BL-60 Mean SD COV RE-0 OV-25 OV-25a OV-50 OV-50a Mean SD COV

Experimental results

Ratio of experimental to predicted flexural moments

Mu,exp (kNm)

Failure mode

Mu,exp/Mfle

18.32 17.15 13.10 16.61 33.88 59.45 59.45 72.65 78.15 – – – 18.32 22.07 23.39 23.39 28.52 – – –

Shear Flexure-shear Flexure Flexure Flexure Flexure-concrete crushing Flexure-concrete crushing Flexure-rebar fracture Flexure-rebar fracture – – – Shear Shear Shear Shear Shear – – –

1.18 1.07 0.80 1.00 0.99 1.11 1.04 1.21 1.24 1.07 0.14 12.7% 1.18 1.34 0.77 1.32 0.80 1.08 0.28 25.7%

Note: SD: standard deviation. COV: coefficient of variation.

concrete was 29.7 MPa and that of UHPC was 156.3 MPa. The longitudinal rebars were 2-D16 (SD345) for both the upper and lower sides. More details could be found in the original paper [16]. Because the volume fraction of steel fibres was not reported by Safdar et al. (2016) [16], it was set to be 3% as a main assumed case in the present study such that be consistent with those of the specimens RE and OV series. In Table 4, the predicted flexural moment, Mfle, was obtained using the proposed calculation approach (Section 4), and the ultimate moment, Mu,exp, was experimentally obtained as Mu,exp = Vn,exp × ad, where ad is the distance from the loading point to the support and Vn,exp is the shear force obtained as Vn,exp = Pu/2, with Pu being the experimental ultimate load. The ratio of the experimental to predicted moment capacities, Mu,exp/Mfle, was calculated. The results are given in Table 4. As can be seen in Table 4, the predicted moment capacities for specimens in the RE series and the specimens tested by Safdar et al. (2016) [16], which primarily failed in flexure, show good agreement with the experimental results, with mean Mu,exp/Mfle ratio and coefficient of variation (COV) of 1.07 and 12.7%, respectively. In the OV series, due to the occurrence of shear failure, the specimens might not have reached their maximum moment capacity. The flexural moment for the OV series was additionally calculated (see Table 4) for reference. The flexural moment for specimens in the OV series (including RE-0) showed a large variation, with a mean Mu,exp/Mfle ratio of 1.08 and a COV of 25.7%, compared to that for the series of specimens that mainly failed in flexure. The predicted values are plotted against the experimental results for specimens in the RE series and specimens tested by Safdar et al. (2016) [16], as shown in Figs. 8 and 9. Most of the data points of the flexural moment lie along the target line representing Mu,exp = Mfle (Fig. 8) and good agreement can be observed (Fig. 9). It should be noticed that for composite members, as the thickness of the UHPC layer increased, the calculated moment slightly increased. This result indicates that the contribution to flexural moment by tension fracture of the UHPC layer was not significant for the specimens used in this study. Among all specimens in the RE series, UHPC specimen RE-100 showed the highest calculated and measured flexural moment. This is mainly due to RE-100 being the only specimen to have UHPC in the compression zone; the high compressive strength of UHPC significantly

Predicted flexural moment, Mfle (kNm)

100 80

Target line Mu,exp = Mfle

60 40 20 0

0 20 40 60 80 100 Experimental ultimate moment, Mu,exp (kNm)

Fig. 8. Predicted flexural moments versus experimental results of RE specimen series tested by Yin et al. (2017b) [17] and specimens tested by Safdar et al. (2016) [16].

increased flexural capacity [26]. On the other hand, Bastien-Masse and Brühwiler (2016a) [22] have developed an analytical model based on a multilinear moment-curvature relation to predict the global bending behavior of the composite slabs of RC strengthened with ultra-high-performance fibre-reinforced cement-based composite layer. Moreover, Bastien-Masse and Brühwiler (2016b) [23] have also conducted calculation of the bending and shear resistance of 17 composite specimens and validated the analytical results with experimental data. The obtained mean and standard deviation (SD) of the ratios of the experimental to the predicted values were 1.02 and 0.10, respectively. Although the detail such as section geometry of composite specimens was different from the work by BastienMasse and Brühwiler (2016b) [23], the mean and SD of the ratios of the experimental to the predicted values of flexural moment capacity 50

Structures 23 (2020) 44–55

K. Shirai, et al.

Flexural moment (kNm)

90 80

Experimental ultimate moment (Mu,exp)

70

Predicted flexural moment (Mfle)

60 50 40 30 20 10 0

RE-0

RE-20

RE-32

RE-50

RE-100

B-0

BL-20

BL-40

BL-60

Fig. 9. Predictions and experimental results of flexural moment capacities for RE specimen series tested by Yin et al. (2017b) [17] and specimens tested by Safdar et al. (2016) [16].

obtained in the present study were 1.07 and 0.14, respectively, for the five specimens (RE series) [17] and the four specimens [16] as shown in Table 4. From this comparison, the present study showed a promising performance despite adopting the simpler and easier to use method based on application of modification of the existing codes. Moreover, as for the specimens BL-20, BL-40, and BL-60, in addition to the main assumed case of steel fibre volume (3%) as mentioned above, an additional calculation was conducted for several assumed cases (fibre volume of 1%, 2%, 4%, and 5%). The obtained results are listed in Table 5. From the calculation results, the predicted flexural moment gradually increases as volume fraction of steel fibres in UHPC increases.

with those (Vn,compos) obtained using the six methods adopted in the shear strength calculation by Yin et al. (2018b) [27]. In accordance with the methods proposed by Yin et al. (2018b) [27], the shear strength of UHPC-concrete composite members was calculated based on a modification of existing RC and/or FRC design codes. Three methods, named Methods A1, A2, and A3, are based on the conversion of the volume fraction of steel fibres to the equivalent longitudinal steel ratio. These Methods A1, A2, and A3 were respectively based on the current design codes for RC members ACI 318 (2008) [24], EN 1992-1-1 (2004) [28], and JSCE-2007 (2010) [29]. The other three methods, named Methods B1, B2, and B3, involve the computation of the sum of the independent contributions of the RC members and the UHPC layer to shear strength. In these Methods B1, B2, and B3, the RC contribution was obtained using the current design codes for RC members, ACI 318 (2008) [24], EN 1992-1-1 (2004) [28], and JSCE-2007 (2010) [29]. For the UHPC contribution, three design guidelines ACI 544 (1988) [25], MC 2010 (2010) [30], and JSCE (2006) [31] were respectively employed in Methods B1, B2, and B3. Details of the six methods can be found in the original study [27]. The failure mode was evaluated based on the ratio Vn,compos/Vfle. For Vn,compos/Vfle < 1, the failure mode is expected to be shear failure; otherwise, flexure failure is expected. As can be seen in Table 6, Method A2 gave the most accurate predictions of the failure mode, where the predicted modes for seven of the nine specimens agreed with the experimental failure mode.

6. Prediction of failure mode The predicted failure modes for all specimens described in Section 2.1 are shown in Table 6. The failure modes were predicted based on the proposed approach for flexural capacity and the computational results for shear strength presented by Yin et al. (2018b) [27]. In the present study, the failure mode prediction was conducted using the shear force Vfle given by the computed flexural moment Mfle described in Section 5, as Vfle = Mfle/ad, where ad is the distance between the loading point and support. This shear force Vfle was compared Table 5 Predicted flexural moments for different assumed volumes of steel fibres in UHPC for specimens tested by Safdar et al. (2016) [16]. Specimen

Experimental results

Assumed volume of steel fibres

Ratio of experimental to predicted flexural moments

Mu,exp (kNm)

(vol. %)

Mu,exp/Mfle

B-0 BL-20

59.45 59.45

BL-40

72.65

BL-60

78.15

0 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

1.11 1.09 1.06 1.04 1.02 1.00 1.30 1.25 1.21 1.16 1.12 1.38 1.31 1.24 1.17 1.12

7. Parametric study of flexural and shear strength calculation 7.1. Methodology This section reports carrying out a parametric study for the methods used to compute the structural capacity of the UHPC-concrete members by varying some influential parameters. An OV series specimen (OV-50) was used to study the effects of parameters, including ratios of the longitudinal reinforcement of the UHPC layer, volume fraction of steel fibres used in UHPC, UHPC thickness, and UHPC compressive and tensile strengths. The material properties and geometry shown in Tables 1–3 were used as the basic parameters in the computations. This parametric study was conducted for the proposed method for predicting flexural strength and the methods for predicting shear strength proposed by Yin et al. (2018b) [27]. The performance trends of the calculation methods are shown in Figs. 10–19. The experimental results of the respective specimens (OV-50, OV-50a, or OV-25a) are also shown in these figures for reference. Although the predicted flexural strength Vfle is not plotted in Figs. 11, 13, 15, 17, and 19, the values of Vfle were 51

RE-0 RE-20 RE-32 RE-50 RE-100 OV-25 OV-25a OV-50 OV-50a

Specimen

18.32 17.15 13.10 16.61 33.88 22.07 23.39 23.39 28.52

Mu,exp (kNm)

Experimental results

Shear Flexure-shear Flexure Flexure Flexure Shear Shear Shear Shear

Failure mode 1.18 1.07 0.80 1.00 0.99 1.34 0.77 1.32 0.80

Mu,exp/Mfle

Shear force, Vn,compos (kN)

Mfle (kNm)

25.85 26.78 27.19 27.59 56.91 27.44 50.73 29.48 59.57

Vfle (kN)

Predicted flexural strength

Note: Vfle: shear force obtained at the calculated flexural moment Mfle. Vn,compos: predicted shear force based on work done by Yin et al. (2018b) [27].

OV series

RE series

Series

Table 6 Predicted failure mode based on predicted flexural strength and previously computed shear strength.

Shear (0.75) Shear (0.94) Shear (0.89) Shear (0.83) Shear (0.81) Flexure (1.16) Shear (0.68) Flexure (1.29) Shear (0.69)

Method A1 Shear (0.77) Shear (0.98) Shear (0.91) Shear (0.80) Flexure (1.63) Flexure (1.13) Shear (0.66) Flexure (1.25) Shear (0.62)

Method A3

Shear force, Vn,compos (kN)

Shear (0.80) Flexure (1.02) Flexure (1.02) Flexure (1.00) Flexure (1.18) Flexure (1.18) Shear (0.72) Flexure (1.32) Shear (0.72)

Method A2

Predicted failure mode (Vn,compos/Vfle)

Predicted failure mode and shear strength ratio

Shear (0.75) Shear (0.94) Shear (0.70) Shear (0.94) Shear (0.81) Flexure (1.01) Shear (0.54) Flexure (1.31) Shear (0.65)

Method B1

Shear (0.77) Flexure (1.39) Flexure (1.09) Flexure (1.93) Flexure (1.63) Flexure (1.56) Shear (0.84) Flexure (2.24) Flexure (1.11)

Method B3

Mfle (kNm)

Shear (0.80) Shear (0.72) Shear (0.91) Flexure (1.59) Flexure (1.18) Shear (0.75) Shear (0.78) Shear (0.70) Shear (0.85)

Method B2

K. Shirai, et al.

Structures 23 (2020) 44–55

50 40

52

50

20

20

0

30

0

0

1

OV-50a

20

10

OV-50

0 0 Rebar ratio, ρs,UHPC (%)

2

OV-50

2

0 1

60

2

3

4

4

2

4

6

6

20

3 4

5

6

8

Fig. 10. Effect of longitudinal rebar ratio of UHPC layer, ρs,UHPC, on predicted flexural moment capacity.

70

60 Experiment Experiment

OV-50a Method A1 ACI318

Method A2 EC2

40

Method A3 JSCE (2007)

Method B1 ACI544

30 Method B2 MC2010

JSCE (2006) Method B3

8 10

5

OV-50a

50

40

30

7

12

Rebar ratio, ρs,UHPC (%)

Fig. 11. Effect of longitudinal rebar ratio of UHPC layer, ρs,UHPC, on predicted shear strength capacity.

50

40

30

OV-50a

10

Volume of steel fibres (vol.%) 6

Fig. 12. Effect of volume of steel fibres in UHPC on predicted flexural moment capacity.

70

Experiment Experiment

Method A1 ACI318

Method A2 EC2

JSCE (2007) Method A3

ACI544 Method B1

MC2010 Method B2

JSCE (2006) Method B3

Volume of steel fibres (vol.%)

8

9

Fig. 13. Effect of volume of steel fibres in UHPC on predicted shear strength capacity.

Structures 23 (2020) 44–55

50

50

40

40 Mfle (kNm)

Mfle (kNm)

K. Shirai, et al.

30 OV-50a

20

OV-25a

0

0

0

50

100

150

2

5

8

11

14

17

20

UHPC tensile strength, fct (MPa)

UHPC thickness, hU (mm) Fig. 14. Effect of UHPC thickness, hU, on predicted flexural moment capacity.

Fig. 18. Effect of tensile strength of UHPC, fct, on predicted flexural moment capacity.

120 Experiment Experiment

100

ACI318 Method A1 OV-50a

80

EC2 Method A2 JSCE (2007) Method A3

OV-25a

60

ACI544 Method B1 MC2010 Method B2

40 20

Shear force, Vn,compos, (kN)

Shear force, Vn,compos (kN)

OV-50a

20 10

10

JSCE (2006) Method B3

0

50

100

150

200

UHPC thickness, hU (mm)

Mfle (kNm)

40 30 20

OV-50a

Method A2 EC2 OV-50a

60

Method A3 JSCE (2007) Method B1 ACI544 MC2010 Method B2

40

JSCE (2006) Method B3

20

2

7

12

17

22

27

7.2. Effect of longitudinal rebar ratio of UHPC layer

100

150

200

Figs. 10 and 11 show the effect of the reinforcement ratio of the UHPC layer, ρs,UHPC, on the flexural moment and shear force capacity, respectively. ρs,UHPC was calculated as ρs,UHPC = AsU/(bwhU). In Fig. 10, it can be clearly seen that the flexural moment increases with increasing longitudinal rebar ratio. In Fig. 11, the shear force obtained using Methods A1, A2, and B2 also increases with increasing reinforcement ratio of the UHPC layer. For Methods B1 and B3, the reinforcement ratio is not used in the calculation of the UHPC contribution to shear strength [27]. This ratio thus has no effect on the computed shear strength, as shown in Fig. 11. Moreover, although Method A3 considers the effect of the reinforcement ratio of the UHPC layer, the trend in Fig. 11 does not show this effect. This is due to a constraint on the term of the longitudinal reinforcement ratio in the formula [27].

250

UHPC compressive strength, f'c (MPa) Fig. 16. Effect of compressive strength of UHPC, f'c, on predicted flexural moment capacity.

80 Experiment Experiment

70 OV-50a

60

Method A1 ACI318 Method A2 EC2 Method A3 JSCE (2007)

50

7.3. Effect of volume steel fibres

Method B1 ACI544

40

Method B2 MC2010

30

The effect of the volume fraction of steel fibres on the flexural and shear strength of UHPC-concrete composite members is shown in Figs. 12 and 13, respectively. Fig. 12 shows that the trend of the flexural moment gradually increases with increasing volume fraction of steel fibres. In Fig. 13, the shear force obtained using Methods A1, A2, and A3 also increases with increasing volume fraction of steel fibres in UHPC. However, due to a constraint term in the computation for Method A3, a portion of the curve was steady. In addition, in the shear force calculation, the volume fraction of steel fibres is not considered for Methods B1, B2, and B3, and thus no effect was observed (Fig. 13).

Method B3 JSCE (2006)

100

Method A1 ACI318

29.48, 59.57, and 50.73 kN for the specimens OV-50, OV-50a, and OV25a, respectively, as shown in Table 6.

10

20

Experiment Experiment

80

Fig. 19. Effect of tensile strength of UHPC, fct, on predicted shear strength capacity.

50

0

100

UHPC tensile strength, fct (MPa)

Fig. 15. Effect of UHPC thickness, hU, on predicted shear strength capacity.

Shear force, Vn,compos (kN)

30

150

200

250

300

UHPC compressive strength, f'c (MPa) Fig. 17. Effect of compressive strength of UHPC, f'c, on predicted shear strength capacity.

53

Structures 23 (2020) 44–55

K. Shirai, et al.

7.4. Effect of UHPC thickness

with various sectional geometries such as reported in Ref. [23], and comparison of predicted results with other methods presented in past studies [15,22,23].

The effect of the thickness of the UHPC strengthening layer, hU, is shown in Figs. 14 and 15. The flexural moment obtained using the proposed method and the shear force obtained using Methods A1–3 and B1–3 both increase with increasing UHPC thickness.

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.

7.5. Effect of UHPC compressive strength Figs. 16 and 17 show the effect of UHPC compressive strength, f'c, on the flexural moment and shear force, respectively. Because the UHPC layer was located at the tension chord of the members, the compressive strength was not used in the flexural strength calculation, and thus it had no effect on the flexural moment, as shown in Fig. 16. However, the shear force increased with increasing UHPC compressive strength for all computation methods, except Method A3 (due to a constraint on a term in its formula).

Acknowledgment The authors are grateful for the financial support of this work by a Toda Scholarship Foundation 2017 research grant. References [1] Richard P, Cheyrezy M. Composition of reactive powder concretes. Cem Concr Res 1995;25(7):1501–11. [2] Wille K, El-Tawil S, Naaman A. Properties of strain hardening ultra high performance fiber reinforced concrete (UHP-FRC) under direct tensile loading. Cem Concr Compos 2014;48:53–66. [3] Graybeal BA, Baby F. Development of direct tension test method for ultra-highperformance fiber-reinforced concrete. ACI Mater J 2013;110(2):177–86. [4] Alkaysi M, El-Tawil S, Liu Z, Hansen W. Effects of silica powder and cement type on durability of ultra high performance concrete (UHPC). Cem Concr Compos 2016;66:47–56. [5] Graybeal BA. Flexural behavior of an ultrahigh-performance concrete I-girder. J Bridge Eng 2008;13(6):602–10. [6] Voo YL, Poon WK, Foster SJ. Shear strength of steel fiber-reinforced ultrahighperformance concrete beams without stirrups. J Struct Eng 2010;136(11):1393–400. [7] Yang IH, Joh C, Kim BS. Structural behavior of ultra high performance concrete beams subjected to bending. Eng Struct 2010;32(11):3478–87. [8] Yoo DY, Yoon YS. Structural performance of ultra-high-performance concrete beams with different steel fibers. Eng Struct 2015;102:409–23. [9] Magallanes JM, Wu Y, Morrill KB, Crawford JE. 2010. Feasibility studies of a plasticity-based constitutive model for ultra-high performance fiber-reinforced concrete. In: Int Symp: Military Aspects of Blast and Shock. Jerusalem, Israel. [10] Singh M, Sheikh AH, Ali MM, Visintin P, Griffith MC. Experimental and numerical study of the flexural behaviour of ultra-high performance fibre reinforced concrete beams. Constr Build Mater 2017;138:12–25. [11] Yin H, Shirai K, Teo W. Numerical assessment of ultra-high performance concrete material. IOP Conf Series: Mater Sci Eng 2017;241(1):012004. [12] Yin H, Shirai K, Teo W. Finite element modelling to predict the flexural behaviour of ultra-high performance concrete members. Eng Struct 2019;183:741–55. [13] Brühwiler E, Denarié E. Rehabilitation of concrete structures using ultra-high performance fibre reinforced concrete. Proceedings of the UHPC-2008: the second international symposium on ultra high performance concrete. 2008. p. 05–7. [14] Habel K, Denarié E, Brühwiler E. Structural response of elements combining ultrahigh-performance fiber-reinforced concretes and reinforced concrete. J Struct Eng 2006;132(11):1793–800. [15] Noshiravani T, Brühwiler E. Analytical model for predicting response and flexureshear resistance of composite beams combining reinforced ultrahigh performance fiber-reinforced concrete and reinforced concrete. J Struct Eng 2013;140(6). [16] Safdar M, Matsumoto T, Kakuma K. Flexural behavior of reinforced concrete beams repaired with ultra-high performance fiber reinforced concrete (UHPFRC). Compos Struct 2016;157:448–60. [17] Yin H, Teo W, Shirai K. Experimental investigation on the behaviour of reinforced concrete slabs strengthened with ultra-high performance concrete. Constr Build Mater 2017;155:463–74. [18] Yin H, Shirai K, Teo W. Shear capacity prediction of reinforced concrete members strengthened with ultra-high performance concrete overlay. Proc Japan Concr Inst 2018;40(2):1243–8. [19] Al-Osta MA, Isa MN, Baluch MH, Rahman MK. Flexural behavior of reinforced concrete beams strengthened with ultra-high performance fiber reinforced concrete. Constr Build Mater 2017;134:279–96. [20] Yin H, Shirai K, Teo W. Numerical model for predicting the structural response of composite UHPC–concrete members considering the bond strength at the interface. Compos Struct 2019;215:185–97. [21] Alaee FJ, Karihaloo BL. Retrofitting of reinforced concrete beams with CARDIFRC. J Compos Constr 2003;7:174–86. [22] Bastien-Masse M, Brühwiler E. Composite model for predicting the punching resistance of R-UHPFRC-RC composite slabs. Eng Struct 2016;117:603–16. [23] Bastien-Masse M, Brühwiler E. Contribution of R-UHPFRC strengthening layers to the shear resistance of RC elements. Struct Eng Int 2016;26(4):365–74. [24] ACI Committee 318. Building code requirements for structural concrete (ACI 318) and commentary. American Concrete Institute; 2008. [25] ACI Committee 544. Design considerations for steel fiber reinforced concrete. ACI Struct J 1988;85(5):563–79.

7.6. Effect of UHPC tensile strength As shown in Fig. 18, the flexural moment was not affected by the tensile strength, fct, of UHPC because in the present computation, the tensile stress of UHPC provided by ACI 544 (Eq. (4)) was adopted, in which the tensile strength is not considered. For the shear force, as shown in Fig. 19, as the tensile strength of UHPC increased, the shear force increased for all computational methods, except Methods A3 and B2 because the former does not include the tensile strength of UHPC in its formula and the latter adopts a constant characteristic tensile strength ratio of 0.62 [27]. 8. Conclusions A method for predicting the flexural strength of UHPC-concrete composite members based on existing design models was proposed. The test results of 13 specimens were used for verification. The following conclusions can be drawn. 1. The proposed method is able to predict the ultimate flexural moment in good agreement with the experimental results for UHPCconcrete composite members. As clearly shown for specimens that developed main cracks in flexure, the moment capacity was predicted with mean Mu,exp/Mfle ratio and COV of 1.07 and 12.7%, respectively. 2. In the OV series, due to the occurrence of shear failure, the specimens might not have reached their maximum moment capacity. The computed flexural moment showed a large COV of 25.7%, compared to that for specimens exhibiting flexural failure (COV = 12.7%). 3. The failure modes obtained from the ratio of the predicted shear force obtained by the previously proposed methods to the shear force obtained at the predicted flexural moment were presented. The failure modes predicted using Method A2 were found to be the most accurate. 4. A parametric study of the influential parameters on the flexural moment and shear force capacity was conducted. An OV series specimen (OV-50) was used to investigate the effects of the longitudinal rebar ratios in UHPC, volume fraction of steel fibres in UHPC, UHPC thickness, and UHPC compressive and tensile strengths. The results showed that flexural moment capacity increases with increasing the longitudinal rebar ratio, volume of steel fibres, and thickness of the UHPC layer. Although the predicted flexural strength was in reasonable agreement with the experimental results, further studies should be conducted to improve the proposed method. Future research tasks include consideration of the mechanical bond effect at the UHPC-NSC interface, further validation using much experimental data of composite members 54

Structures 23 (2020) 44–55

K. Shirai, et al. [26] Shirai K, Yin H, Teo W. Flexural strength calculation of the RC members rehabilitated with UHPC. Proc Japan Concr Inst 2018;40(2):1237–42. [27] Yin H, Shirai K, Teo W. Prediction of shear capacity of UHPC-concrete composite structural members based on existing codes. J Civil Eng Manage 2018;24(8):607–18. [28] EN 1992-1-1. (2004). Design of concrete structures: Part 1-1: General rules and rules for buildings. British Standards Institution.

[29] JSCE-2007. (2010). Standard specifications for concrete structures – 2007 “Design”. Guidelines for Concrete, No. 15. Japan Society of Civil Engineers (JSCE). [30] CEB-FIB Model Code (MC 2010). (2010). The first draft of the fib Model Code for Concrete Structures. International Federation for Structural Concrete (fib). [31] JSCE Concrete Committee. (2006). Recommendation for design and construction of ultra high strength fiber reinforced concrete structures (Draft). Guidelines for Concrete, No. 9. Japan Society of Civil Engineers (JSCE).

55