# Flexural Behavior of the Innovative CA-UHPC Slabs with High and Low Reinforcement Ratios

Authors: Yu Feng; Jianan Qi; Jingquan Wang; Jiaping Liu; Jianzhong Liu
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

This paper presents an experimental study on the flexural behavior of an innovative CA-UHPC (ultrahigh-performance concrete containing coarse aggregate) slab with high and low reinforcement ratios. A total of eighteen CA-UHPC slabs were tested to failure under the parameters of longitudinal reinforcement ratio, curing method, and maximum aggregate size. Test results indicated that sufficient longitudinal reinforcement should be embedded to prevent the brittle failure and disastrous damage. High ductile failure mode was observed for specimens with high reinforcement ratio compared with specimens with low reinforcement ratio. Instead of extensively crushing as normal strength concrete, delamination failure appeared in the compression zone of the CA-UHPC slabs owing to the fibers’ bridging effect, the yielding of longitudinal reinforcement, and the large expansion of flexural cracks which led to the final failure. The reinforced CA-UHPC slabs demonstrated excellent deformability, and ultimate ratio of deflection to span increased from 1/281 to 1/12 when the reinforcement ratio raised from 0% to 3.45%. Stiffness of the reinforced specimens at the flexural cracking state was about 88% and only approximately 6% at the ultimate state, but nearly 50% of the initial stiffness remained when the longitudinal reinforcements yielded, which indicated superior load resistance ability and excellent postcracking deformability. A new ductility index was proposed to evaluate the postcracking ductility of the CA-UHPC specimens. Finally, test results were compared with the flexural strength predictions of CECS 38-2004, ACI 544.4R, and BS EN 1992.


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## Body

## 1. Introduction

UHPC (ultrahigh-performance concrete) is a generic term for a class of advanced cementitious composite materials that reflects excellent strength, stiffness, ductility, and energy dissipation, and these allow more economic and long-life structures than the conventional concrete even without accounting for the increase in structural durability [1–4]. The tensile strength and ultimate tensile strain of UHPC could be as high as 8 MPa and 1% [5–8]. Due to these remarkable mechanical properties, applying of UHPC will decrease self-weight of structures and reduce the cracking risk effectively [9, 10]. Therefore, an increasing number of applications of UHPC in bridges, high-rise buildings, and infrastructure maintenances have been achieved during the past decades [11, 12].Because of the relatively high compressive strength and ultimate tensile strain of UHPC, which allows for increased strain of the embedded reinforcement and higher stress in the compressive zone, the design concept of UHPC is quite different from the normal strength concrete [13]. To utilize the superior mechanical properties of UHPC adequately, using high-strength steel bars and increasing the reinforcement ratio could be two alternative ways according to the force equilibrium condition [14–16]. Some researchers adopted the first method to achieve material mechanical performance matching. Sumpter et al. [17] compared the structural performance of beams with high-strength reinforcement and conventional reinforcement; test results demonstrated that shear capacity improved distinctly by using high-strength steel reinforcement. Munikrishna et al. [18] studied the shear behavior of RC beams with high-strength stirrups, and it was found that the required number of high-strength stirrups was less than that of conventional stirrups when the shear capacities were approximately equal. Qi et al. [13] tested eleven UHPC T-beams reinforced with high-strength steel (HSS) bars; results indicated that the HSS-UHPC beam kept nearly 50% of the initial stiffness at ultimate state.Influences of the reinforcement ratio on UHPC structures have been of great interest also. Yang et al. [19] investigated the flexural behavior of fourteen UHPC beams with six different rebar ratios ranging from 0 to 1.96%; results showed that the ductility improved with the increment of the rebar ratio, but UHPC specimens with a fiber volumetric ratio of 2% exhibited lower ductility compared with the nonfiber ones. Kamal et al. [20] evaluated the flexural behavior of twelve UHPC beams with and without web reinforcement; the promotion impact of reinforcement ratio on structural ductility was also confirmed. Kahanji et al. [21] conducted flexural test of eight UHPC beams with and without reinforcement rebar, and it was found that flexural moment capacity and stiffness increased with the fiber volume fraction. Flexural behaviors of four UHPC beams with different reinforcement ratios (0%∼1.71%) were experimentally and numerically investigated by Yoo et al. [22] also, and test results indicated that the postcracking stiffness and load carrying capacity increased with the reinforcement ratio, whereas the first cracking load decreased. Hasgul et al. [23] studied the flexural behavior of eight UHPC beams with low and high reinforcement ratios (0.9%, 1.9%, 2.8%, and 4.3%), and results demonstrated that the ductile flexural behavior could be achieved even at high reinforcement ratios because of its high compressive strength and deformation capacity.Although there are some research achievements about the influences of reinforcement ratio on structural performance of UHPC beams, most of the research studies concentrate on the low reinforcement ratio [24, 25]. As far as the authors are aware, less research existed on UHPC slabs with high reinforcement ratio and inadequacy of data samples may reduce the scope of the conclusions; comprehensive understanding is needed to obtain better structural performance and broaden the application of UHPC slabs in civil engineering.This paper mainly aims at the flexural behavior of the innovative CA-UHPC slabs with high and low longitudinal reinforcement ratio via an experimental program on eighteen CA-UHPC slabs. The effects of longitudinal reinforcement ratio, curing method, and maximum aggregate size are investigated, including failure mode, postcracking performance, ductility, and stiffness degradation of the CA-UHPC specimens. In addition, the applicability of CECS 38-2004, ACI 544.4R, and BS-EN 1992 is compared to evaluate flexural capacity of the innovative CA-UHPC slabs with high and low reinforcement ratios.


## 2. Experimental Program

### 2.1. Specimen Dimensions

A total of eighteen specimens were designed to research the bending performance of the innovative CA-UHPC slabs, and all the specimens were manufactured in pairs to control the discreteness of data (Table1). Due to the different reinforcement ratios of 0%, 1.41%, and 3.45%, test specimens are classified into Series R0, Series R1.13, and Series R3.45. All the slab specimens have the same external physical dimension of 1500 mm × 350 mm × 160 mm. Geometry dimensions and reinforcement diagram of the test specimens are shown in Figure 1.Table 1
Main parameters of the CA-UHPC slab specimens.
Specimen ID
a (mm)
b (mm)
d (mm)
h (mm)
l
s (mm)
l (mm)
ρ
s (%)
Mix type
Series R0
R0-S-8
400
350
/
160
1300
1500
0
A
R0-S-5
400
350
/
160
1300
1500
0
B
R0-N-8
400
350
/
160
1300
1500
0
C
Series R1.13
R1.13-S-8
400
350
114
160
1300
1500
1.13
A
R1.13-S-5
400
350
114
160
1300
1500
1.13
B
R1.13-N-8
400
350
114
160
1300
1500
1.13
C
Series R3.45
R3.45-S-8
400
350
130
160
1300
1500
3.45
A
R3.45-S-5
400
350
130
160
1300
1500
3.45
B
R3.45-N-8
400
350
130
160
1300
1500
3.45
C
S = steam curing; N = natural curing; 5/8 = 5 mm/8 mm aggregate size;a = length of pure bending zone; b = width of the web; d = effective depth; h = slab height; ls = span of the slab; l = length of the slab; ρs = longitudinal reinforcement ratio. Two specimens were precast in each ID, and subsequent researches are aimed at the average value of the two specimens.Figure 1
Dimensions and reinforcement diagram of test specimens. (a) R0-S/N-8/5. (b) R1.13-S/N-8/5. (c) R3.45-S/N-8/5.


### 2.2. Mix Properties and Specimen Preparation

#### 2.2.1. Raw Materials

The innovative CA-UHPC (ultrahigh-performance concrete containing coarse aggregate) which is budget saving and shrinkage inhabiting [26, 27] has been developed in this experimental program. Two kinds of clean medium coarse sands with the fineness modulus of 3.1 and 2.8 are adopted in the innovative UHPC system, which is obviously different from the UHPC material in general sense. The aggregates consisting of basalt and limestone are offered by four different domestic manufacturers, particle size of them ranges from 5 mm to 8 mm. Weight content of the main components of the innovative UHPC material is all illustrated in Figure 2, and the water-binder ratio (W/B) of the innovative CA-UHPC is 0.16.Figure 2
Weight per cubic meter of components of the innovative CA-UHPC material.High-strength straight steel fiber coated with a thin layer of copper is mixed in the matrix with the volume fraction of 2% to improve the tensile strength and ductility of UHPC matrix. Length and diameter of the steel fiber are 13 mm and 0.2 mm, respectively, and the yielding strength is 2900 MPa.


#### 2.2.2. Site Casting and Curing Regime

High-quality wood formworks are adopted for the site pouring of the specimens, as shown in Figure3. Field mixing of the innovative CA-UHPC was conducted by the shaft mixer which provided 0.3 m3 concrete once, and the mixing processes are as follows. Cementitious materials and aggregates need to be dry-mixed for one minute first, and then water and additives were added to stir for four minutes. The high-strength steel fiber was put in terminally and continued stirring for three minutes. Matrix of the CA-UHPC were poured out for the forming of specimens after mixing evenly, and this operation should run parallel to the casting of samples for material properties test.Figure 3
Pouring and curing process of the innovative CA-UHPC. (a) Formwork. (b) Site casting. (c) Vibration. (d) Stream curing.
(a)
(b)
(c)
(d)Curing regime of the experiment consists of the natural curing and steam curing method. For the natural curing, test specimens need to be demolded immediately after casting for 24 h and maintained in the standard curing room at the temperature of 20 ± 2°C. The relative humidity needs to be no less than 95%, and the surface of the specimens should keep wet and not be flushed directly by water, as suggested by the Chinese code of test method for mechanical properties of ordinary concrete (GB/T 50081-2002). For the steam curing, heat maintenance starts after 24 h of casting also. Firstly, heating the curing box (Figure3) to 90°C in a rate of 10°C/h and keeping the temperature (90 ± 2°C) for 48 h, and then cooling down at the same rate until the difference between temperature of specimen surface and ambient temperature is no more than 20°C.


### 2.3. Material Properties

According to the Chinese code of reactive powder concrete (GB/T 31387-2015), all the specimens for material property experiment were tested after 28 d curing age, in which, three groups of cube specimens with dimensions of 100 mm × 100 mm × 100 mm were prepared for the compressive strength test, while six prism specimens with dimensions of 100 mm × 100 mm × 300 mm were utilized to determine the elastic modulus and Poisson ratio. The test method of bending toughness and initial cracking strength are based on the Chinese technical specification for fiber reinforced concrete structures (CECS 38-2004), and prism specimens with the size of 100 mm × 100 mm × 400 mm were utilized after maintenance for 28 d. Material properties of the innovative CA-UHPC are summarized in Table2.Table 2
Material properties of CA-UHPC.
Mix type
Curing method
Aggregate size (mm)
E
c (GPa)
ν
f
cu (MPa)
f
MOR (MPa)
f
MOR
† (MPa)
G
f (kJ·m−2)
A
Steam curing
8
50.4
0.20
165.7
13.59
19.91
24.58
B
Steam curing
5
49.5
0.20
168.5
13.92
20.16
21.52
C
Natural curing
8
49.3
0.21
146.7
12.66
17.13
24.11
E
c = elasticity modulus; ν = Poisson’s ratio; fcu = cubic compressive strength; fMOR = flexural strength at cracking state; fMOR† = flexural strength at ultimate state; Gf = fracture energy.Longitudinal and transverse reinforcement of the slab specimens consists of two types of steel bars with the diameter of 20 mm and 12 mm, while the yielding strength is 350.5 MPa and 446.6 MPa, respectively. In particular, layout of the reinforcement in slabs of Series R1.13 and Series R3.45 is reserved. It should be noted that no stirrups and bend-up bars were set in all the specimens. Material properties of reinforcement bars are presented in Table3.Table 3
Material properties of reinforcement bars in Series R3.45.
Steel type
d
s (mm)
A
s (mm2)
F
y (kN)
f
y (MPa)
F
u (kN)
f
u (MPa)
E
s (GPa)
Longitudinal reinforcement
20
314.2
110.1
350.5
183.0
582.5
200
Transverse reinforcement
12
113.1
50.5
446.6
64.1
566.3
200
Reinforcement layout of specimens in series R1.13 is contrary to that in series R3.45, which means diameter of the longitudinal reinforcement in series R1.13 is 12 mm and diameter of the transverse reinforcement is 20 mm.


### 2.4. Test Setup and Loading Mechanism

As shown in Figure4, static performance tests of the slabs are conducted through the four-point bending experiments. Simply supported boundary condition is applied, span of the slabs is 1300 mm, and length of the pure bending zone is 400 mm. Electrohydraulic servo actuator with the maximal measuring range of 1000 kN is chosen to apply the monotonic load, while extra force sensor is installed to ensure the accuracy of load data. Three groups of LVDT are set on midspan and bearings to monitor the displacement of specimens during each load stage, and strain gauges are arranged at the middle of the bottom of longitudinal reinforcements uniformly.Figure 4
Loading mechanical scheme.In order to inspect the loading system and eliminate inelastic deformation, all the slabs were loaded and unloaded repeatedly according to 40% of the predicted cracking load before officially loading. Preloading will not stop until deformation and strain are kept stable approximately, and the specific test processes are as follows. Firstly, loading to 80% of the predicted cracking load in the speed of 10∼20 kN per step and recording the deflection and strain. Then, reducing the load step to find out the actual cracking load of the specimen cautiously; displacement control is recommended once visible cracks are found. Finally, unloading the actuator slowly when the ultimate load is reached, and the cracks are too large for the sake of safety.


## 2.1. Specimen Dimensions

A total of eighteen specimens were designed to research the bending performance of the innovative CA-UHPC slabs, and all the specimens were manufactured in pairs to control the discreteness of data (Table1). Due to the different reinforcement ratios of 0%, 1.41%, and 3.45%, test specimens are classified into Series R0, Series R1.13, and Series R3.45. All the slab specimens have the same external physical dimension of 1500 mm × 350 mm × 160 mm. Geometry dimensions and reinforcement diagram of the test specimens are shown in Figure 1.Table 1
Main parameters of the CA-UHPC slab specimens.
Specimen ID
a (mm)
b (mm)
d (mm)
h (mm)
l
s (mm)
l (mm)
ρ
s (%)
Mix type
Series R0
R0-S-8
400
350
/
160
1300
1500
0
A
R0-S-5
400
350
/
160
1300
1500
0
B
R0-N-8
400
350
/
160
1300
1500
0
C
Series R1.13
R1.13-S-8
400
350
114
160
1300
1500
1.13
A
R1.13-S-5
400
350
114
160
1300
1500
1.13
B
R1.13-N-8
400
350
114
160
1300
1500
1.13
C
Series R3.45
R3.45-S-8
400
350
130
160
1300
1500
3.45
A
R3.45-S-5
400
350
130
160
1300
1500
3.45
B
R3.45-N-8
400
350
130
160
1300
1500
3.45
C
S = steam curing; N = natural curing; 5/8 = 5 mm/8 mm aggregate size;a = length of pure bending zone; b = width of the web; d = effective depth; h = slab height; ls = span of the slab; l = length of the slab; ρs = longitudinal reinforcement ratio. Two specimens were precast in each ID, and subsequent researches are aimed at the average value of the two specimens.Figure 1
Dimensions and reinforcement diagram of test specimens. (a) R0-S/N-8/5. (b) R1.13-S/N-8/5. (c) R3.45-S/N-8/5.


## 2.2. Mix Properties and Specimen Preparation

### 2.2.1. Raw Materials

The innovative CA-UHPC (ultrahigh-performance concrete containing coarse aggregate) which is budget saving and shrinkage inhabiting [26, 27] has been developed in this experimental program. Two kinds of clean medium coarse sands with the fineness modulus of 3.1 and 2.8 are adopted in the innovative UHPC system, which is obviously different from the UHPC material in general sense. The aggregates consisting of basalt and limestone are offered by four different domestic manufacturers, particle size of them ranges from 5 mm to 8 mm. Weight content of the main components of the innovative UHPC material is all illustrated in Figure 2, and the water-binder ratio (W/B) of the innovative CA-UHPC is 0.16.Figure 2
Weight per cubic meter of components of the innovative CA-UHPC material.High-strength straight steel fiber coated with a thin layer of copper is mixed in the matrix with the volume fraction of 2% to improve the tensile strength and ductility of UHPC matrix. Length and diameter of the steel fiber are 13 mm and 0.2 mm, respectively, and the yielding strength is 2900 MPa.


### 2.2.2. Site Casting and Curing Regime

High-quality wood formworks are adopted for the site pouring of the specimens, as shown in Figure3. Field mixing of the innovative CA-UHPC was conducted by the shaft mixer which provided 0.3 m3 concrete once, and the mixing processes are as follows. Cementitious materials and aggregates need to be dry-mixed for one minute first, and then water and additives were added to stir for four minutes. The high-strength steel fiber was put in terminally and continued stirring for three minutes. Matrix of the CA-UHPC were poured out for the forming of specimens after mixing evenly, and this operation should run parallel to the casting of samples for material properties test.Figure 3
Pouring and curing process of the innovative CA-UHPC. (a) Formwork. (b) Site casting. (c) Vibration. (d) Stream curing.
(a)
(b)
(c)
(d)Curing regime of the experiment consists of the natural curing and steam curing method. For the natural curing, test specimens need to be demolded immediately after casting for 24 h and maintained in the standard curing room at the temperature of 20 ± 2°C. The relative humidity needs to be no less than 95%, and the surface of the specimens should keep wet and not be flushed directly by water, as suggested by the Chinese code of test method for mechanical properties of ordinary concrete (GB/T 50081-2002). For the steam curing, heat maintenance starts after 24 h of casting also. Firstly, heating the curing box (Figure3) to 90°C in a rate of 10°C/h and keeping the temperature (90 ± 2°C) for 48 h, and then cooling down at the same rate until the difference between temperature of specimen surface and ambient temperature is no more than 20°C.


## 2.2.1. Raw Materials

The innovative CA-UHPC (ultrahigh-performance concrete containing coarse aggregate) which is budget saving and shrinkage inhabiting [26, 27] has been developed in this experimental program. Two kinds of clean medium coarse sands with the fineness modulus of 3.1 and 2.8 are adopted in the innovative UHPC system, which is obviously different from the UHPC material in general sense. The aggregates consisting of basalt and limestone are offered by four different domestic manufacturers, particle size of them ranges from 5 mm to 8 mm. Weight content of the main components of the innovative UHPC material is all illustrated in Figure 2, and the water-binder ratio (W/B) of the innovative CA-UHPC is 0.16.Figure 2
Weight per cubic meter of components of the innovative CA-UHPC material.High-strength straight steel fiber coated with a thin layer of copper is mixed in the matrix with the volume fraction of 2% to improve the tensile strength and ductility of UHPC matrix. Length and diameter of the steel fiber are 13 mm and 0.2 mm, respectively, and the yielding strength is 2900 MPa.


## 2.2.2. Site Casting and Curing Regime

High-quality wood formworks are adopted for the site pouring of the specimens, as shown in Figure3. Field mixing of the innovative CA-UHPC was conducted by the shaft mixer which provided 0.3 m3 concrete once, and the mixing processes are as follows. Cementitious materials and aggregates need to be dry-mixed for one minute first, and then water and additives were added to stir for four minutes. The high-strength steel fiber was put in terminally and continued stirring for three minutes. Matrix of the CA-UHPC were poured out for the forming of specimens after mixing evenly, and this operation should run parallel to the casting of samples for material properties test.Figure 3
Pouring and curing process of the innovative CA-UHPC. (a) Formwork. (b) Site casting. (c) Vibration. (d) Stream curing.
(a)
(b)
(c)
(d)Curing regime of the experiment consists of the natural curing and steam curing method. For the natural curing, test specimens need to be demolded immediately after casting for 24 h and maintained in the standard curing room at the temperature of 20 ± 2°C. The relative humidity needs to be no less than 95%, and the surface of the specimens should keep wet and not be flushed directly by water, as suggested by the Chinese code of test method for mechanical properties of ordinary concrete (GB/T 50081-2002). For the steam curing, heat maintenance starts after 24 h of casting also. Firstly, heating the curing box (Figure3) to 90°C in a rate of 10°C/h and keeping the temperature (90 ± 2°C) for 48 h, and then cooling down at the same rate until the difference between temperature of specimen surface and ambient temperature is no more than 20°C.


## 2.3. Material Properties

According to the Chinese code of reactive powder concrete (GB/T 31387-2015), all the specimens for material property experiment were tested after 28 d curing age, in which, three groups of cube specimens with dimensions of 100 mm × 100 mm × 100 mm were prepared for the compressive strength test, while six prism specimens with dimensions of 100 mm × 100 mm × 300 mm were utilized to determine the elastic modulus and Poisson ratio. The test method of bending toughness and initial cracking strength are based on the Chinese technical specification for fiber reinforced concrete structures (CECS 38-2004), and prism specimens with the size of 100 mm × 100 mm × 400 mm were utilized after maintenance for 28 d. Material properties of the innovative CA-UHPC are summarized in Table2.Table 2
Material properties of CA-UHPC.
Mix type
Curing method
Aggregate size (mm)
E
c (GPa)
ν
f
cu (MPa)
f
MOR (MPa)
f
MOR
† (MPa)
G
f (kJ·m−2)
A
Steam curing
8
50.4
0.20
165.7
13.59
19.91
24.58
B
Steam curing
5
49.5
0.20
168.5
13.92
20.16
21.52
C
Natural curing
8
49.3
0.21
146.7
12.66
17.13
24.11
E
c = elasticity modulus; ν = Poisson’s ratio; fcu = cubic compressive strength; fMOR = flexural strength at cracking state; fMOR† = flexural strength at ultimate state; Gf = fracture energy.Longitudinal and transverse reinforcement of the slab specimens consists of two types of steel bars with the diameter of 20 mm and 12 mm, while the yielding strength is 350.5 MPa and 446.6 MPa, respectively. In particular, layout of the reinforcement in slabs of Series R1.13 and Series R3.45 is reserved. It should be noted that no stirrups and bend-up bars were set in all the specimens. Material properties of reinforcement bars are presented in Table3.Table 3
Material properties of reinforcement bars in Series R3.45.
Steel type
d
s (mm)
A
s (mm2)
F
y (kN)
f
y (MPa)
F
u (kN)
f
u (MPa)
E
s (GPa)
Longitudinal reinforcement
20
314.2
110.1
350.5
183.0
582.5
200
Transverse reinforcement
12
113.1
50.5
446.6
64.1
566.3
200
Reinforcement layout of specimens in series R1.13 is contrary to that in series R3.45, which means diameter of the longitudinal reinforcement in series R1.13 is 12 mm and diameter of the transverse reinforcement is 20 mm.


## 2.4. Test Setup and Loading Mechanism

As shown in Figure4, static performance tests of the slabs are conducted through the four-point bending experiments. Simply supported boundary condition is applied, span of the slabs is 1300 mm, and length of the pure bending zone is 400 mm. Electrohydraulic servo actuator with the maximal measuring range of 1000 kN is chosen to apply the monotonic load, while extra force sensor is installed to ensure the accuracy of load data. Three groups of LVDT are set on midspan and bearings to monitor the displacement of specimens during each load stage, and strain gauges are arranged at the middle of the bottom of longitudinal reinforcements uniformly.Figure 4
Loading mechanical scheme.In order to inspect the loading system and eliminate inelastic deformation, all the slabs were loaded and unloaded repeatedly according to 40% of the predicted cracking load before officially loading. Preloading will not stop until deformation and strain are kept stable approximately, and the specific test processes are as follows. Firstly, loading to 80% of the predicted cracking load in the speed of 10∼20 kN per step and recording the deflection and strain. Then, reducing the load step to find out the actual cracking load of the specimen cautiously; displacement control is recommended once visible cracks are found. Finally, unloading the actuator slowly when the ultimate load is reached, and the cracks are too large for the sake of safety.


## 3. Experimental Results and Discussions

### 3.1. Failure Mode and Crack Distribution

All the eighteen CA-UHPC slabs were tested to failure. For the reinforced specimens in Series R1.13 and Series R3.45, bending cracks first appeared at the bottom near the midspan where the largest tensile force has been withstood. Because of the absence of shear reinforcement and relatively high longitudinal reinforcement ratio, width of diagonal cracks was even slightly larger than that of bending cracks in the early loading process. With the increment of applied load, flexural cracks developed rapidly at decreasing of the fiber bridging effect with intensive sizzle sound especially when approaching the ultimate bearing capacity (nearly 200 kN for Series R1.13 and 500 kN for Series R3.45); the yielding of longitudinal reinforcement and the large expansion of flexural cracks led to the final failure. In general, ductile flexural failure occurred in all the reinforced CA-UHPC slabs, and typical failure mode and crack distribution of the specimens with high reinforcement ratio at failure are shown in Figure5. Different from conventional RC structures, it was interesting to find that extensively concrete crushing was not observed even when exceeding the ultimate compressive strain of UHPC. Delamination failure appeared in compression zone of the CA-UHPC slabs owing to the fibers bridging effect. As steel fibers bridging the adjacent concrete layers and keeping connected, the surface layer of the CA-UHPC specimens warped instead of crushing, which presented the multilayer bridged by interlaminar fibers failure mode that the steel fiber remained even though the concrete layer was separated.Figure 5
(a) Typical failure mode and (b) typical crack distribution of the slabs in Series R3.45.
(a)
(b)For the plain CA-UHPC slabs in Series R0, flexural cracks appeared first in the pure bending area closed to the midspan. As the applied load increased, the cracks developed rapidly and associated with the sound of fibers pulling out, and some main flexural cracks formed quickly due to the decreasing of fiber bridging effect and directly caused the final failure when approaching to ultimate bearing capacity (nearly 100 kN). Therefore, sufficient longitudinal reinforcement should be embedded to prevent the brittle failure and disastrous damage that is unexpected.Table4 summarizes important characteristic information of all the specimens. As initial cracking strength is primarily dominated by the tensile strength of UHPC matrix, nominal stress at initial cracking in different series is basically consistent. This characteristic also indicated that CA-UHPC could still ensure excellent and stable material properties even cast in place and is suitable for large-scale construction on-site. Applied load corresponding to different crack widths increases significantly with the increment of the reinforcement ratio, while the same trend appears on the deflection which reflects the enhancement of ductility.Table 4
Summary of experimental data.
Specimen ID
First cracking
Crack width of 0.05 mm
Crack width of 0.10 mm
Crack width of 0.15 mm
Reinforcement yielding state
Peak load
Ultimate load
Failure mode
P
cr (kN)
Δcr (mm)
σ
cr (MPa)
P
0.05 (kN)
Δ0.05 (mm)
P
0.10 (kN)
Δ0.10 (mm)
P
0.15 (kN)
Δ0.15 (mm)
P
y (kN)
Δy (mm)
P
max (kN)
Δmax (mm)
P
u (kN)
Δu (mm)
R0-S-8
94.66
1.63
14.3
98.83
1.78
100.22
2.02
105.1
2.74
Unreinforced
105.1
2.735
84.22
4.62
Flexural‡
R0-S-5
96.05
1.5
14.5
100.92
1.75
107.53
2.07
110.66
2.20
Unreinforced
115.88
2.82
92.57
4.51
Flexural‡
R0-N-8
79.34
1.69
12.0
81.08
1.71
100.2
2.94
105.1
3.8
Unreinforced
107.53
4.56
86.3
6.02
Flexural‡
R1.13-S-8
76.91
2.17
11.6
83.87
2.61
100.57
3.56
123.19
4.81
176.44
9.35
200.1
20.2
160.08
48.42
Flexural†‡
R1.13-S-5
75.86
1.88
11.4
80.39
2.13
110.32
2.73
151.03
4.62
169.13
5.49
214.72
17.75
178.87
46.85
Flexural†‡
R1.13-N-8
77.26
1.64
11.6
80.04
1.72
104.4
2.68
150.34
4.86
176.09
6.69
194.53
16.38
155.56
41.03
Flexural†‡
R3.45-S-8
82.48
1.43
12.4
88.39
1.49
199.75
3.31
258.56
4.28
455.53
8.96
486.5
15.66
389.2
107.2
Flexural†‡
R3.45-S-5
80.39
1.71
12.1
83.52
1.73
171.22
3.45
273.88
5.45
459.01
12.88
464.58
16.56
371.66
99.91
Flexural†‡
R3.45-N-8
82.13
1.05
12.4
84.91
1.11
175.04
2.69
325.38
5.4
430.82
9.09
479.2
17.83
383.36
84.5
Flexural†‡
P
cr = flexural cracking load; Δcr = flexural cracking deflection; σcr = nominal stress at initial cracking; Py = longitudinal reinforcement yielding load; Δy = longitudinal reinforcement yielding deflection; Pmax = peak load; Δmax = peak load deflection; Pu = ultimate load; Δu = ultimate load deflection; †yielding of longitudinal reinforcement; ‡large expansion of flexural crack.


### 3.2. Structural Behavior

#### 3.2.1. Load versus Midspan Deflection

Figure6 presents the relationship between load and midspan deflection of all the specimens. A similar pattern is reflected that the load-deflection curves and displays linear relationship before bending cracks occur and almost keep linear after flexural cracking with a slightly decline in stiffness, but the stiffness of specimens drops when the longitudinal reinforcement yields. As shown in the deflection curve, ductility of specimens increases with the increment of the reinforcement ratio obviously. It should be noted that a long ductile plateau stage is detected for specimens with high reinforcement ratio (Series R3.45).Figure 6
Load versus midspan deflection.
(a)
(b)
(c)


#### 3.2.2. Load versus Longitudinal Reinforcement Strain

Strain gauges evenly arranged at the midspan section of the longitudinal reinforcement are adopted to monitor the change of steel strain, and relationship curves of load versus longitudinal reinforcement strain of all the specimens are shown in Figure7. Stresses in the tension side of longitudinal reinforcement stay at low level before cracking, and the curves are approximately kept linear; growth rate of the steel stress accelerates dramatically after flexural cracking until yielding strength. After entering the yielding state, strains of the longitudinal reinforcement continue to rise quickly for the increment of deflection until failure. As ductile failure still occurs on the innovative CA-UHPC slabs with high reinforcement ratio, steel bars with high strength and ductility would be recommended for the CA-UHPC structures.Figure 7
Load versus longitudinal reinforcement strain.
(a)
(b)


#### 3.2.3. Load versus Top and Bottom Concrete Surface Strain of Midspan Section

Figure8 depicts relationship between the concrete strain of midspan section and the applied load of the test CA-UHPC slabs, in which positive value represents the tensile strain while negative value represents the compressive strain. As seen in these figures, compressive strain of concrete increases slowly before cracking and acts as linear behavior and the rapid growth of the concrete compressive strains begins to appear right after cracking and keep expanding until failure. The concrete strain of tension and compression side of the slabs nearly maintains symmetry before flexural cracks occur. For the plain CA-UHPC slabs in Series 0, it should be noted that the cracking tensile strain is larger than 200 μ which reflects excellent material properties. While for the reinforced CA-UHPC slabs, extensively concrete crush is not observed even when ultimate compressive strain of UHPC (≈3,500 μ) is exceeded, which is quite different from the failure mode of normal strength concrete.Figure 8
Load versus top and bottom concrete surface strains of midspan section.
(a)
(b)
(c)


### 3.3. Effects of Curing Method and Aggregate Size

Thermal treatments of traditional UHPC are mainly preferred in order to reduce curing time and increase mechanical strengths [28–30], and it does not usually contain coarse aggregates larger than 6-7 mm in size [21]. It is difficult to meet the curing condition during large-scale on-site construction. However, the addition of coarse aggregate can save budget and broaden the application field of UHPC by reducing the amount of glue material and decreasing hydration temperature rise. Therefore, effects of the curing method and maximum aggregate size are studied in this paper also. As shown in Figure 9, results indicate that flexural strength increases approximately linearly with the increment of longitudinal reinforcement ratio, while maximum aggregate size and curing method have no significant influences on structural behavior of the innovative CA-UHPC slabs.Figure 9
Effects of curing method and aggregate size on flexural capacity.
(a)
(b)


### 3.4. Effects of Reinforcement Ratio on Deflection Ductility

The ductility index is always utilized to characterize the ductility of reinforced concrete specimens, and the deflection ductility index is always adopted for the simplicity of its expressions. These expressions [31] are usually used as ductility index:(1)μp=ΔpΔy,μu=ΔuΔy,where Δp is the midspan deflection at peak load, Δy is the midspan deflection at the longitudinal reinforcement yielding, and Δu is the midspan deflection at ultimate load which is geometrically determined by the point corresponding to 80% of the maximum load [32]. Qi et al. [33] put forward a new ductility index, which is expressed in the form of dividing ultimate deflection by flexural cracking deflection to characterize the postcracking ductility capacity:(2)μcr=ΔuΔcr.The ductility indices of the UHPC slabs are summarized in Table5. It can be seen from the results that longitudinal reinforcement shows significant influences on the postcracking capacity. Postcracking ductility of the innovative CA-UHPC slabs increases as the reinforcement ratio increases obviously and gradually decreased with the expansion of cracks, while the ductility index μp decreases as the reinforcement ratio increases which in accordance with the researches of Yoo and Yoon [34]. The proposed new ductility index excellently reflects the effects of reinforcement ratio on deflection ductility, and μcr of specimens with the reinforcement ratios of 0%, 1.13%, and 3.45% was 2.83, 22.31, and 74.97, respectively. The ultimate ratio of deflection to span increases from 1/281 to 1/12 when the longitudinal reinforcement ratio of the innovative CA-UHPC slabs ranges from 0% to 3.45%.Table 5
Postcracking capacity and deformability analysis.
Specimen ID
Postcracking capacity
Deflection ductility
P
u/Pcr
P
u/P0.05
P
u/P0.10
P
u/P0.15
Δ0.05/Δcr
Δ0.10/Δcr
Δ0.15/Δcr
Δp/Δy
Δu/Δy
Δu/Δcr
R0-S-8
0.89
0.85
0.84
0.80
1.09
1.24
1.68
/
/
2.83
R0-S-5
0.96
0.92
0.86
0.84
1.17
1.38
1.47
/
/
3.01
R0-N-8
1.09
1.06
0.86
0.82
1.01
1.74
2.25
/
/
3.56
R1.13-S-8
2.08
1.91
1.59
1.30
1.20
1.64
2.22
2.16
5.18
22.31
R1.13-S-5
2.36
2.23
1.62
1.18
1.13
1.45
2.46
3.23
8.53
24.92
R1.13-N-8
2.01
1.94
1.49
1.03
1.05
1.63
2.96
2.45
6.13
25.02
R3.45-S-8
4.72
4.40
1.95
1.51
1.04
2.31
2.99
1.75
11.96
74.97
R3.45-S-5
4.62
4.45
2.17
1.36
1.01
2.02
3.19
1.29
7.76
58.43
R3.45-N-8
4.67
4.51
2.19
1.18
1.06
2.56
5.14
1.96
9.30
80.48


### 3.5. Effects of Reinforcement Ratio on Specimen Stiffness

In order to clarify the law of stiffness degradation of the CA-UHPC specimens, the relationship between the specimen stiffness and the ratio of the midspan deflectionΔ at any time divided by the midspan deflection Δcr corresponding to flexural cracking load is presented in Figure 10; the secant stiffness is adopted here. As can be seen in the figure, the longitudinal reinforcement ratio presents great influences on stiffness of the specimens. Stiffness of the plain slabs (Series R0) descends rapidly and continuously until failure due to the absence of longitudinal reinforcement. However, the rate of stiffness degradation of the reinforced slabs (Series R1.13 and R3.45) apparently slows down after the longitudinal reinforcement yielding, although the trend of the curve is the same.Figure 10
Stiffness degradation analysis.
(a)
(b)
(c)Structural performances of the innovative CA-UHPC slabs evaluated by the stiffness degradation in different states are summarized in Table6. The parameters k0,kcr,ky, and ku represent the stiffness at initial state, flexural cracking state, steel bar yielding state, and ultimate state, respectively. There is no significant decline on the stiffness at initial cracking except for specimen R0-S-8 (71%) and specimen R1.13-S-8 (72%); nearly half the initial stiffness still remains when the longitudinal reinforcement is yielding. Therefore, reinforcement with high strength and long yield platform would be appropriate choice for the CA-UHPC structures. At the ultimate state, only approximately 6% of the initial beam stiffness remained.Table 6
Relative stiffness degradation.
Specimen ID
Flexural cracking
Yielding state
Ultimate state
Δcr/Δu
k
cr/k0
Δy/Δu
k
y/k0
Δu/Δu
k
u/k0
R0-S-8
0.44
0.71
/
/
1.00
0.26
R0-S-5
0.33
0.91
/
/
1.00
0.32
R0-N-8
0.28
0.79
/
/
1.00
0.24
R1.13-S-8
0.04
0.72
0.19
0.37
1.00
0.07
R1.13-S-5
0.03
0.80
0.12
0.51
1.00
0.06
R1.13-N-8
0.03
0.93
0.16
0.49
1.00
0.07
R3.45-S-8
0.02
0.90
0.08
0.73
1.00
0.05
R3.45-S-5
0.02
0.97
0.13
0.50
1.00
0.05
R3.45-N-8
0.01
0.98
0.11
0.59
1.00
0.06


## 3.1. Failure Mode and Crack Distribution

All the eighteen CA-UHPC slabs were tested to failure. For the reinforced specimens in Series R1.13 and Series R3.45, bending cracks first appeared at the bottom near the midspan where the largest tensile force has been withstood. Because of the absence of shear reinforcement and relatively high longitudinal reinforcement ratio, width of diagonal cracks was even slightly larger than that of bending cracks in the early loading process. With the increment of applied load, flexural cracks developed rapidly at decreasing of the fiber bridging effect with intensive sizzle sound especially when approaching the ultimate bearing capacity (nearly 200 kN for Series R1.13 and 500 kN for Series R3.45); the yielding of longitudinal reinforcement and the large expansion of flexural cracks led to the final failure. In general, ductile flexural failure occurred in all the reinforced CA-UHPC slabs, and typical failure mode and crack distribution of the specimens with high reinforcement ratio at failure are shown in Figure5. Different from conventional RC structures, it was interesting to find that extensively concrete crushing was not observed even when exceeding the ultimate compressive strain of UHPC. Delamination failure appeared in compression zone of the CA-UHPC slabs owing to the fibers bridging effect. As steel fibers bridging the adjacent concrete layers and keeping connected, the surface layer of the CA-UHPC specimens warped instead of crushing, which presented the multilayer bridged by interlaminar fibers failure mode that the steel fiber remained even though the concrete layer was separated.Figure 5
(a) Typical failure mode and (b) typical crack distribution of the slabs in Series R3.45.
(a)
(b)For the plain CA-UHPC slabs in Series R0, flexural cracks appeared first in the pure bending area closed to the midspan. As the applied load increased, the cracks developed rapidly and associated with the sound of fibers pulling out, and some main flexural cracks formed quickly due to the decreasing of fiber bridging effect and directly caused the final failure when approaching to ultimate bearing capacity (nearly 100 kN). Therefore, sufficient longitudinal reinforcement should be embedded to prevent the brittle failure and disastrous damage that is unexpected.Table4 summarizes important characteristic information of all the specimens. As initial cracking strength is primarily dominated by the tensile strength of UHPC matrix, nominal stress at initial cracking in different series is basically consistent. This characteristic also indicated that CA-UHPC could still ensure excellent and stable material properties even cast in place and is suitable for large-scale construction on-site. Applied load corresponding to different crack widths increases significantly with the increment of the reinforcement ratio, while the same trend appears on the deflection which reflects the enhancement of ductility.Table 4
Summary of experimental data.
Specimen ID
First cracking
Crack width of 0.05 mm
Crack width of 0.10 mm
Crack width of 0.15 mm
Reinforcement yielding state
Peak load
Ultimate load
Failure mode
P
cr (kN)
Δcr (mm)
σ
cr (MPa)
P
0.05 (kN)
Δ0.05 (mm)
P
0.10 (kN)
Δ0.10 (mm)
P
0.15 (kN)
Δ0.15 (mm)
P
y (kN)
Δy (mm)
P
max (kN)
Δmax (mm)
P
u (kN)
Δu (mm)
R0-S-8
94.66
1.63
14.3
98.83
1.78
100.22
2.02
105.1
2.74
Unreinforced
105.1
2.735
84.22
4.62
Flexural‡
R0-S-5
96.05
1.5
14.5
100.92
1.75
107.53
2.07
110.66
2.20
Unreinforced
115.88
2.82
92.57
4.51
Flexural‡
R0-N-8
79.34
1.69
12.0
81.08
1.71
100.2
2.94
105.1
3.8
Unreinforced
107.53
4.56
86.3
6.02
Flexural‡
R1.13-S-8
76.91
2.17
11.6
83.87
2.61
100.57
3.56
123.19
4.81
176.44
9.35
200.1
20.2
160.08
48.42
Flexural†‡
R1.13-S-5
75.86
1.88
11.4
80.39
2.13
110.32
2.73
151.03
4.62
169.13
5.49
214.72
17.75
178.87
46.85
Flexural†‡
R1.13-N-8
77.26
1.64
11.6
80.04
1.72
104.4
2.68
150.34
4.86
176.09
6.69
194.53
16.38
155.56
41.03
Flexural†‡
R3.45-S-8
82.48
1.43
12.4
88.39
1.49
199.75
3.31
258.56
4.28
455.53
8.96
486.5
15.66
389.2
107.2
Flexural†‡
R3.45-S-5
80.39
1.71
12.1
83.52
1.73
171.22
3.45
273.88
5.45
459.01
12.88
464.58
16.56
371.66
99.91
Flexural†‡
R3.45-N-8
82.13
1.05
12.4
84.91
1.11
175.04
2.69
325.38
5.4
430.82
9.09
479.2
17.83
383.36
84.5
Flexural†‡
P
cr = flexural cracking load; Δcr = flexural cracking deflection; σcr = nominal stress at initial cracking; Py = longitudinal reinforcement yielding load; Δy = longitudinal reinforcement yielding deflection; Pmax = peak load; Δmax = peak load deflection; Pu = ultimate load; Δu = ultimate load deflection; †yielding of longitudinal reinforcement; ‡large expansion of flexural crack.


## 3.2. Structural Behavior

### 3.2.1. Load versus Midspan Deflection

Figure6 presents the relationship between load and midspan deflection of all the specimens. A similar pattern is reflected that the load-deflection curves and displays linear relationship before bending cracks occur and almost keep linear after flexural cracking with a slightly decline in stiffness, but the stiffness of specimens drops when the longitudinal reinforcement yields. As shown in the deflection curve, ductility of specimens increases with the increment of the reinforcement ratio obviously. It should be noted that a long ductile plateau stage is detected for specimens with high reinforcement ratio (Series R3.45).Figure 6
Load versus midspan deflection.
(a)
(b)
(c)


### 3.2.2. Load versus Longitudinal Reinforcement Strain

Strain gauges evenly arranged at the midspan section of the longitudinal reinforcement are adopted to monitor the change of steel strain, and relationship curves of load versus longitudinal reinforcement strain of all the specimens are shown in Figure7. Stresses in the tension side of longitudinal reinforcement stay at low level before cracking, and the curves are approximately kept linear; growth rate of the steel stress accelerates dramatically after flexural cracking until yielding strength. After entering the yielding state, strains of the longitudinal reinforcement continue to rise quickly for the increment of deflection until failure. As ductile failure still occurs on the innovative CA-UHPC slabs with high reinforcement ratio, steel bars with high strength and ductility would be recommended for the CA-UHPC structures.Figure 7
Load versus longitudinal reinforcement strain.
(a)
(b)


### 3.2.3. Load versus Top and Bottom Concrete Surface Strain of Midspan Section

Figure8 depicts relationship between the concrete strain of midspan section and the applied load of the test CA-UHPC slabs, in which positive value represents the tensile strain while negative value represents the compressive strain. As seen in these figures, compressive strain of concrete increases slowly before cracking and acts as linear behavior and the rapid growth of the concrete compressive strains begins to appear right after cracking and keep expanding until failure. The concrete strain of tension and compression side of the slabs nearly maintains symmetry before flexural cracks occur. For the plain CA-UHPC slabs in Series 0, it should be noted that the cracking tensile strain is larger than 200 μ which reflects excellent material properties. While for the reinforced CA-UHPC slabs, extensively concrete crush is not observed even when ultimate compressive strain of UHPC (≈3,500 μ) is exceeded, which is quite different from the failure mode of normal strength concrete.Figure 8
Load versus top and bottom concrete surface strains of midspan section.
(a)
(b)
(c)


## 3.2.1. Load versus Midspan Deflection

Figure6 presents the relationship between load and midspan deflection of all the specimens. A similar pattern is reflected that the load-deflection curves and displays linear relationship before bending cracks occur and almost keep linear after flexural cracking with a slightly decline in stiffness, but the stiffness of specimens drops when the longitudinal reinforcement yields. As shown in the deflection curve, ductility of specimens increases with the increment of the reinforcement ratio obviously. It should be noted that a long ductile plateau stage is detected for specimens with high reinforcement ratio (Series R3.45).Figure 6
Load versus midspan deflection.
(a)
(b)
(c)


## 3.2.2. Load versus Longitudinal Reinforcement Strain

Strain gauges evenly arranged at the midspan section of the longitudinal reinforcement are adopted to monitor the change of steel strain, and relationship curves of load versus longitudinal reinforcement strain of all the specimens are shown in Figure7. Stresses in the tension side of longitudinal reinforcement stay at low level before cracking, and the curves are approximately kept linear; growth rate of the steel stress accelerates dramatically after flexural cracking until yielding strength. After entering the yielding state, strains of the longitudinal reinforcement continue to rise quickly for the increment of deflection until failure. As ductile failure still occurs on the innovative CA-UHPC slabs with high reinforcement ratio, steel bars with high strength and ductility would be recommended for the CA-UHPC structures.Figure 7
Load versus longitudinal reinforcement strain.
(a)
(b)


## 3.2.3. Load versus Top and Bottom Concrete Surface Strain of Midspan Section

Figure8 depicts relationship between the concrete strain of midspan section and the applied load of the test CA-UHPC slabs, in which positive value represents the tensile strain while negative value represents the compressive strain. As seen in these figures, compressive strain of concrete increases slowly before cracking and acts as linear behavior and the rapid growth of the concrete compressive strains begins to appear right after cracking and keep expanding until failure. The concrete strain of tension and compression side of the slabs nearly maintains symmetry before flexural cracks occur. For the plain CA-UHPC slabs in Series 0, it should be noted that the cracking tensile strain is larger than 200 μ which reflects excellent material properties. While for the reinforced CA-UHPC slabs, extensively concrete crush is not observed even when ultimate compressive strain of UHPC (≈3,500 μ) is exceeded, which is quite different from the failure mode of normal strength concrete.Figure 8
Load versus top and bottom concrete surface strains of midspan section.
(a)
(b)
(c)


## 3.3. Effects of Curing Method and Aggregate Size

Thermal treatments of traditional UHPC are mainly preferred in order to reduce curing time and increase mechanical strengths [28–30], and it does not usually contain coarse aggregates larger than 6-7 mm in size [21]. It is difficult to meet the curing condition during large-scale on-site construction. However, the addition of coarse aggregate can save budget and broaden the application field of UHPC by reducing the amount of glue material and decreasing hydration temperature rise. Therefore, effects of the curing method and maximum aggregate size are studied in this paper also. As shown in Figure 9, results indicate that flexural strength increases approximately linearly with the increment of longitudinal reinforcement ratio, while maximum aggregate size and curing method have no significant influences on structural behavior of the innovative CA-UHPC slabs.Figure 9
Effects of curing method and aggregate size on flexural capacity.
(a)
(b)


## 3.4. Effects of Reinforcement Ratio on Deflection Ductility

The ductility index is always utilized to characterize the ductility of reinforced concrete specimens, and the deflection ductility index is always adopted for the simplicity of its expressions. These expressions [31] are usually used as ductility index:(1)μp=ΔpΔy,μu=ΔuΔy,where Δp is the midspan deflection at peak load, Δy is the midspan deflection at the longitudinal reinforcement yielding, and Δu is the midspan deflection at ultimate load which is geometrically determined by the point corresponding to 80% of the maximum load [32]. Qi et al. [33] put forward a new ductility index, which is expressed in the form of dividing ultimate deflection by flexural cracking deflection to characterize the postcracking ductility capacity:(2)μcr=ΔuΔcr.The ductility indices of the UHPC slabs are summarized in Table5. It can be seen from the results that longitudinal reinforcement shows significant influences on the postcracking capacity. Postcracking ductility of the innovative CA-UHPC slabs increases as the reinforcement ratio increases obviously and gradually decreased with the expansion of cracks, while the ductility index μp decreases as the reinforcement ratio increases which in accordance with the researches of Yoo and Yoon [34]. The proposed new ductility index excellently reflects the effects of reinforcement ratio on deflection ductility, and μcr of specimens with the reinforcement ratios of 0%, 1.13%, and 3.45% was 2.83, 22.31, and 74.97, respectively. The ultimate ratio of deflection to span increases from 1/281 to 1/12 when the longitudinal reinforcement ratio of the innovative CA-UHPC slabs ranges from 0% to 3.45%.Table 5
Postcracking capacity and deformability analysis.
Specimen ID
Postcracking capacity
Deflection ductility
P
u/Pcr
P
u/P0.05
P
u/P0.10
P
u/P0.15
Δ0.05/Δcr
Δ0.10/Δcr
Δ0.15/Δcr
Δp/Δy
Δu/Δy
Δu/Δcr
R0-S-8
0.89
0.85
0.84
0.80
1.09
1.24
1.68
/
/
2.83
R0-S-5
0.96
0.92
0.86
0.84
1.17
1.38
1.47
/
/
3.01
R0-N-8
1.09
1.06
0.86
0.82
1.01
1.74
2.25
/
/
3.56
R1.13-S-8
2.08
1.91
1.59
1.30
1.20
1.64
2.22
2.16
5.18
22.31
R1.13-S-5
2.36
2.23
1.62
1.18
1.13
1.45
2.46
3.23
8.53
24.92
R1.13-N-8
2.01
1.94
1.49
1.03
1.05
1.63
2.96
2.45
6.13
25.02
R3.45-S-8
4.72
4.40
1.95
1.51
1.04
2.31
2.99
1.75
11.96
74.97
R3.45-S-5
4.62
4.45
2.17
1.36
1.01
2.02
3.19
1.29
7.76
58.43
R3.45-N-8
4.67
4.51
2.19
1.18
1.06
2.56
5.14
1.96
9.30
80.48


## 3.5. Effects of Reinforcement Ratio on Specimen Stiffness

In order to clarify the law of stiffness degradation of the CA-UHPC specimens, the relationship between the specimen stiffness and the ratio of the midspan deflectionΔ at any time divided by the midspan deflection Δcr corresponding to flexural cracking load is presented in Figure 10; the secant stiffness is adopted here. As can be seen in the figure, the longitudinal reinforcement ratio presents great influences on stiffness of the specimens. Stiffness of the plain slabs (Series R0) descends rapidly and continuously until failure due to the absence of longitudinal reinforcement. However, the rate of stiffness degradation of the reinforced slabs (Series R1.13 and R3.45) apparently slows down after the longitudinal reinforcement yielding, although the trend of the curve is the same.Figure 10
Stiffness degradation analysis.
(a)
(b)
(c)Structural performances of the innovative CA-UHPC slabs evaluated by the stiffness degradation in different states are summarized in Table6. The parameters k0,kcr,ky, and ku represent the stiffness at initial state, flexural cracking state, steel bar yielding state, and ultimate state, respectively. There is no significant decline on the stiffness at initial cracking except for specimen R0-S-8 (71%) and specimen R1.13-S-8 (72%); nearly half the initial stiffness still remains when the longitudinal reinforcement is yielding. Therefore, reinforcement with high strength and long yield platform would be appropriate choice for the CA-UHPC structures. At the ultimate state, only approximately 6% of the initial beam stiffness remained.Table 6
Relative stiffness degradation.
Specimen ID
Flexural cracking
Yielding state
Ultimate state
Δcr/Δu
k
cr/k0
Δy/Δu
k
y/k0
Δu/Δu
k
u/k0
R0-S-8
0.44
0.71
/
/
1.00
0.26
R0-S-5
0.33
0.91
/
/
1.00
0.32
R0-N-8
0.28
0.79
/
/
1.00
0.24
R1.13-S-8
0.04
0.72
0.19
0.37
1.00
0.07
R1.13-S-5
0.03
0.80
0.12
0.51
1.00
0.06
R1.13-N-8
0.03
0.93
0.16
0.49
1.00
0.07
R3.45-S-8
0.02
0.90
0.08
0.73
1.00
0.05
R3.45-S-5
0.02
0.97
0.13
0.50
1.00
0.05
R3.45-N-8
0.01
0.98
0.11
0.59
1.00
0.06


## 4. Comparison between Current Flexural Provisions

According to the experimental data, three current concrete codes, including Chinese Code (CECS 38-2004), American Code (ACI 544.4R) and British Standard (BS EN 1992), are selected to predict the flexural bearing capacity of test specimens. In the CECS 38-2004 model, the equivalent stress blocks for the compressive and tensile regions of the concrete are used to calculate the beam moment capacities, and maximum strain value in the outermost compression fiber of concrete is basically assumed as 0.003, as shown in Figure11. Bending capacity of normal section of rectangular section flexural members can be calculated by the following equations:(3)Mfu=ffcbxh0−x2+fy′As′h0−as′−fftubxtxt2−a,ffcbx=fyAs−fy′As′+fftubxt,fftu=ftβtuλf,where ffc denotes the design value of axial compressive strength of UHPC, while fftu is the tensile strength of equivalent rectangular stress of the UHPC in tension zone, λf is the characteristic value of steel fiber content, and βtu is fiber tensile influence coefficient, they can be calculated by the CECS Code. Additionally, h0 is the effective depth, b is cross-sectional width, x and xt are depth of equivalent compressive and tensile stress block, respectively.Figure 11
Stress-strain distribution for reinforced UHPC beams in CECS 38-2004.
(a)
(b)
(c)Relative error of the prediction value calculated by different codes is summarized in Table7, and the results indicate that the Chinese Code presents the minimum prediction error. Prediction accuracy of the ACI 544.4R for specimens in Series R1.13 is better than that of Series R3.45, which illustrates that it may not suitable for the flexural calculation of CA-UHPC specimens with high reinforcement ratio. British Standard may be the worst calculation method for the innovative CA-UHPC slabs, and the average error even reaches nearly 60%. As the innovative CA-UHPC has excellent material properties, contribution of the concrete tensile strength should be considered when carrying out the prediction of bending capacity. If combined with the calculation method of concrete tensile zone proposed by CECS 38-2004, the average relative error of Britain Standard will drop to 0.19. In general, evaluation of all the three existing codes on flexural capacity of the innovative CA-UHPC slabs are conservative, and the prediction of the Chinese CECS 38-2004 code has relatively the best accuracy with a relative error of 0.16.Table 7
Calculation result comparison of different codes.
Specimen ID
EV
CECS 38-2004
ACI 544.4R
BS EN 1992
BS EN 1992∗
CV
RE
CV
RE
CV
RE
CV
RE
Series R1.13
R1.13-S-8
200.1
172.57
0.14
245.29
0.23
64.96
0.68
268.22
0.34
R1.13-S-5
214.72
173.45
0.19
247.99
0.15
64.97
0.70
270.24
0.26
R1.13-N-8
194.53
166.43
0.14
226.97
0.17
64.92
0.67
254.01
0.31
Series R3.45
R3.45-S-8
486.5
399.53
0.18
309.15
0.36
237.35
0.51
439
0.10
R3.45-S-5
464.58
400.8
0.14
309.97
0.33
237.44
0.49
441.26
0.05
R3.45-N-8
479.2
390.59
0.18
303.6
0.37
236.68
0.51
423.03
0.12
Average value
/
/
0.16
/
0.27
/
0.59
/
0.19
Standard deviation
/
/
0.02
/
0.09
/
0.09
/
0.11
EV = experimental value; CV = calculated value; RE = relative error.∗Based on consideration of the tensile strength of UHPC.


## 5. Conclusions

Eighteen innovative CA-UHPC specimens with high and low reinforcement ratios were tested to failure, and the effects of the longitudinal reinforcement ratio, curing method, and aggregate size on the flexural behavior of the innovative CA-UHPC slabs were investigated. The deflection ductility, flexural stiffness degradation, and postcracking behaviors of the test specimens were discussed. In addition, three different current calculation specifications for bending resistance were compared to evaluate the flexural capacity of the innovative CA-UHPC slabs. Based on the experimental observations and results, the following conclusions can be drawn:(1)
Sufficient longitudinal reinforcement should be provided in the innovative CA-UHPC slabs, and ductile failure occurred even with high reinforcement ratio. Instead of extensively crushing in normal concrete, multilayer bridged by interlaminar fibers failure mode appeared in compression zone of the CA-UPHC slabs due to the fibers bridging effect.(2)
Postcracking ductility of the CA-UHPC slabs increases with the increment of reinforcement ratio obviously and gradually decreases with the expansion of cracks. The proposed new ductility indexμcr increases from 2.83 to 74.97 when the reinforcement ratio rises from 0% to 3.45%, which excellently reflects the effects of reinforcement ratio on deflection ductility. In addition, a long ductile plateau stage in load-deflection curve is detected for specimens with high reinforcement ratio.(3)
Longitudinal reinforcement ratio presents greatly influences on stiffness of the specimens, which effectively delays the stiffness degradation of the specimens. For the reinforced slabs, nearly 50% of the initial stiffness remains when the longitudinal reinforcements yield. Thus, reinforcement with high strength and long yield platform will be an appropriate choice for the CA-UHPC structures.(4)
Flexural strength increases approximately linearly with the increment of longitudinal reinforcement ratio, while maximum aggregate size and curing method have no significant influence on structural behavior of the innovative CA-UHPC slabs, which greatly saves the budget and broadens the application field of CA-UHPC.(5)
The Chinese Code (CECS 38-2004), American Code (ACI 544.4R), British Standard (BS EN 1992) and modified British Standard (considering concrete tensile) are generally conservative in predicting the flexural capacity of the reinforced CA-UHPC slabs, with an average relative error of 0.16, 0.27, 0.59, and 0.19 relatively.



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*Source: 6027341-2019-04-08.xml*