Restrained Shrinkage Mechanism of Ultra High Performance ... · 2) There were no cracks of UHPC...

KSCE Journal of Civil Engineering (0000) 00(0):1-12

Copyright ⓒ2019 Korean Society of Civil Engineers

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pISSN 1226-7988, eISSN 1976-3808

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Structural Engineering

Restrained Shrinkage Mechanism of Ultra High Performance Concrete

Jun-Yan Wang*, Chen Bian**, Ru-Cheng Xiao***, and Biao Ma****

Received March 6, 2019/Accepted August 1, 2019/Published Online

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Abstract

The understanding and controlling of the restrained shrinkage is critical for the application of ultra high performance concrete(UHPC). This study made an analysis of restrained shrinkage mechanism of four kinds of UHPCs based on the direct tensile testaccompanied with acoustic emission (AE) source location, free shrinkage test and restrained shrinkage test (ASTM C1581-04 (2004)ring test). The effects of UHPC tensile properties (strain softening or strain hardening) and high performance calcium sulphoaluminate(HCSA, a new kind of expansion agent) dosages (0%, 3% and 6% by mass of total binder) were investigated. The restrained shrinkagecracking mechanism of strain hardening UHPC and strain softening UHPC was analyzed based on AE analysis method under directtensile loading. The results indicates that strain hardening UHPC shows multiple micro-defects to relax the restrained tensile stressmarginally while strain softening UHPC shows several hairline cracks to relax the restrained tensile stress evidently. In ASTM C1581-04(2004) ring test, the restrained shrinkage of strain hardening UHPC with HCSA dosage of 0%, 3% and 6% at 80d is 141 με, 96 με and 16με, respectively. The HCSA expansion agent can effectively reduce the restrained shrinkage of UHPC and the influence on the structure.

Keywords: UHPC, restrained shrinkage mechanism, expansive agent, ASTM C1581-04 (2004) ring test, AE analysis method

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1. Introduction

Ultra high performance concrete (UHPC) is composed of

compact cementitious matrix combined with a high amount of

fibers (Murali et al., 2018; Yoo et al., 2017; Yoo et al., 2016),

which exhibits high strength and excellent resistance against

aggressive environments (Charron et al., 2007; Denarié et al.,

2011). The distinguishing characteristics of UHPC make it an

attractive option for some civil engineering construction and

repair application (Ren et al., 2019; Yoo et al., 2016). For

example, steel-UHPC composite deck system as shown in Fig. 1

(a) can increase the stiffness and reduce the self-weight of the

structure compared with the traditional steel-concrete composite

deck system (Wang et al., 2016), the existing structure strengthened

with UHPC as shown in Fig. 1(b) can overcome the drawbacks

in the existing structure strengthened with fiber polymer such as

delamination and brittle failure retrofitting (Prem et al., 2018). In

above structures, UHPC is restrained by the steel slab with the

stud shear connector or the existing structure.

Given the very low water-to-binder ratio (w/b), UHPC can

exhibit high degree of self-desiccation that can cause significant

autogenous shrinkage (Xie et al., 2018; Valipour et al., 2018;

Yoo et al., 2019). It may lead to the generation of the high tensile

stress of UHPC in restrained condition, making UHPC vulnerable

to cracking. This can limit some of the potential applications of

UHPC where shrinkage plays a major role such as long-span

bridges, thin pavement overlays. The control of shrinkage

characteristics of such applications is critical for the service life

of structures. One kind of effective methods to control the

shrinkage of UHPC is the incorporation of expansive agent (EA)

(Corinaldesi et al., 2015).

At present, the relevant researches on the restrained shrinkage

of UHPC seem obviously insufficient. There are no standard test

methods to assess the restrained shrinkage behavior of UHPC.

Different methods were used to simulate the restrained condition

of UHPC, such as axially or linearly restrained condition (Yoo et

al., 2015), plate/slab-shaped geometry (Yoo et al., 2014) or

restrained circular ring (Park et al., 2014; Yoo et al., 2013; Wang,

2012). These studies are summarized in Table 1.

It can be seen from Table 1 that the benefit of admixture on the

shrinkage compensation of UHPC was mainly about a synergistic

effect in the combined use of shrinkage reducing agent (SRA)

and EA. The effectiveness of EA on reducing the shrinkage of

UHPC was confirmed. However, EA used in these studies

mainly aimed at applying in the normal concrete, which was

unstable in long term used in UHPC. It is necessary to invent a

suitable kind of EA for UHPC with a low w/b. Shunzeng Zhao et

al. (2009) has invented a new kind of EA, namely high performance

TECHNICAL NOTE

*Professor, Key Laboratory of Advanced Civil Engineering Materials, Tongji University, Shanghai 201804, China (Corresponding Author, E-mail:

[email protected])

**Ph.D. Student, Key Laboratory of Advanced Civil Engineering Materials, Tongji University, Shanghai 201804, China (E-mail: [email protected])

***Professor, College of Civil Engineering, Tongji Univ., Shanghai 200092, China (E-mail: [email protected])

****Professorate Senior Engineer, Shanghai Municipal Engineering Design Institute (Group) Co., Ltd., Shanghai 200092, China (E-mail: [email protected])

Jun-Yan Wang, Chen Bian, Ru-Cheng Xiao, and Biao Ma

− 2 − KSCE Journal of Civil Engineering

calcium sulphoaluminate (HCSA) which is especially suitable

for high performance concrete that has a low w/b. HCSA has

numerous advantages such as the high expansion energy, the rapid

expansion rate and the significant expansion in humidity insulation.

As a result, it is supposed to be a proper method to add HCSA into

UHPC to reduce the shrinkage of UHPC, which needs to be verified

by an experimental study. Among various experimental methods,

the ring test is the most appropriate for evaluating the effectiveness

of EA due to its high cracking sensitivity. In addition, the ring test is

economical and convenient to conduct. Therefore, ASTM C1581-

04 (2004) ring test has been chosen to study the restrained shrinkage

behavior of UHPC and the effect of HCSA on the shrinkage

compensation of UHPC in this paper.

The tensile properties of UHPC under direct tensile loading is the

foundation to evaluate the restrained shrinkage cracking behavior of

UHPC. In some previous studies, restrained shrinkage behavior of

UHPC has been studied through the combination of direct tensile

test, free shrinkage test and restrained shrinkage test as summarized

in Table 1. However, these researches mainly focused on the

quantitative calculation of restrained tensile stress, tensile strength

and restraint degree of UHPC, hardly involving the analysis of

restrained shrinkage mechanism based on direct tensile test. It is

supposed that different tensile behaviors of UHPCs lead to different

restrained shrinkage mechanisms and there is a dearth of information

on the restrained shrinkage mechanisms.

Based on the tensile properties, UHPC is divided into three

types in 2016 MCS-EPFL recommendation (M.C.S.-E.P.F.L,

2016): UO (strain softening), UA (ultimate tensile strain is

higher than 1,500 με) and UB (ultimate tensile strain is higher

than 2,000 με). Namely there are two kinds of UHPCs: strain

softening UHPC and strain hardening UHPC. The shrinkage

cracking risk of UHPC in restrained condition basically depends

on the crack width controlling ability of UHPC under direct

tensile loading. The popular method to judge the crack width

controlling ability of UHPC is using the crack width measurement

instrument which is at the macro level and not accurate. Acoustic

emission (AE) technique has been proved to be an effective

method at the micro level to illustrate the relationship between

the crack width controlling ability and the different tensile

Fig. 1. UHPC used in Civil Engineering Construction and Repair

Application: (a) Steel-UHPC Composite Deck System in

Shanghai, 2019, (b) Normal Concrete beam Strengthened

with UHPC in Shanghai, 2017

Table 1. Literature Review of Restrain Shrinkage of UHPC & UHPFRC

Details of specimen Contents Main conclusions Ref.

Effect of shrinkage-reducing admix-ture (SRA) on the free and restrainedautogenous shrinkage of UHPFRCwith three SRA ratios of 0%, 1%and 2% and three reinforcementratios of 1.3%, 2.9% and 8.0%

1) 28d tensile strength of UHPFRC slightlyincreased with an increase in the SRA contentup to 2%;2) Tensile strengths were higher than the autoge-nous shrinkage stresses. Autogenous shrinkagestress decreased at lower reinforcement ratiosand higher SRA contents;3) A higher degree of restraint was obtainedwith a higher reinforcement ratio, but it wasmarginally influenced by the SRA content.

Yoo et al., 2015

Combined effect of SRA and expan-sive admixture (EA) on the shrink-age and cracking behaviors ofrestrained UHPFRC slabs with threedifferent thicknesses (40, 60, and80 mm)

1) Combined use of SRA and EA has a benefi-cial effect on increasing strength, free shrink-age and reducing shrinkage crack width ofUHPC;2) Higher UHPC thickness improves the shrink-age cracking resistance;

Yoo et al., 2014


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behaviors of UHPCs (Wang et al., 2018). Thus, the direct tensile

test accompanied with AE technique can be used to well explain

the shrinkage cracking mechanism of UHPC in restrained

condition at the micro level.

In this study, the direct tensile test accompanied with AE source

location, free shrinkage test and restrained shrinkage test (ASTM

C1581-04 (2004) ring test) were conducted to further understand the

restrained shrinkage mechanism of UHPC. Four kinds of UHPCs

were used, namely three kinds of strain hardening UHPCs with

different HCSA dosages (0%, 3% and 6% by mass of total binder)

and one kind of strain softening UHPC. Based on the tensile

behavior accompanied with AE analysis method, the restrained

shrinkage mechanism of UHPC was elaborated from three aspects

of the restrained stress, relaxation degree and strain transfer

modelling.

2. Experimental Program

2.1 UHPC Materials

In this study, two volume fractions of steel fiber (1%, 2%) and

three dosages of HCSA by mass of total binder (0%, 3% and

6%) were used to make four kinds of UHPCs, namely SSU-0,

SHU-0, SHU-3 and SHU-6, whose mix proportions are listed in

Table 2. The physical properties of the used steel fibers are

summarized in Table 3. HCSA as a kind of EA was added to

UHPC matrix to reduce the shrinkage of UHPC. Its chemical

composition is shown in Table 4.

A laboratory mixer with sixty-liter capacity was used to

Table 1. (continued)

Details of specimen Contents Main conclusions Ref.

Effects of EA and SRA on themechanical and shrinkage prop-erties of UHPC

1) The free shrinkage strain was obviouslyreduced by including SRA and EA;2) The inner steel strain was also decreased byincorporating SRA and EA.

Park et al., 2014

Influence of ring size on therestrained shrinkage behavior ofUHPFRC

1) UHPFRC ring specimen with a thinner steelring had a higher strain level than that of athicker steel ring;2) The stress relaxation of UHPFRC were sel-dom affected by the diameter of the steel ringand the ring specimen with a thicker steel ringpresented a higher maximum stress relaxation;3) A higher degree of restraint was obtainedwith a thicker steel ring than that with a thin-ner steel ring.

Yoo et al., 2013

Influence of super absorbent poly-mer (SAP) on the restrained shrink-age behavior of UHPC

1) SAP could improve the restrained shrinkagebehavior of UHPC;2) There were no cracks of UHPC with steelfibers in ring test.

Wang, 2012

Note: UHPFRC is Ultra High Performance Fiber Reinforced Concrete

Table 2. Mix Proportions of Four Kinds of UHPCs/(kg/m3)

No. Cement Silica fume Filler Silica sand Water Superplasticizer Steel fiber HCSA

SHU-0 745.0 223.5 223.5 998.3 179.0 13.1 157.0 0

SHU-3 722.7 216.8 216.8 998.3 179.0 13.1 157.0 35.8

SHU-6 700.3 210.1 210.1 998.3 179.0 13.1 157.0 67.2

SSU-0 745.0 223.5 223.5 998.3 179.0 13.1 78.5 0

Table 3. Properties of Steel Fiber

Tensile strength /MPa Elastic modulus /GPa Length/mm Diameter /µm Aspect ratio Density/(kg/m3)

2,500 200 16 200 80 7850



prepare the UHPC mixture. UHPC premixed powder was firstly

dry-mixed for about 1 minute. Water was then added gradually

and mixed for another 3 minutes. When the mixture showed the

suitable workability, steel fibers were dispersed into the mixture

and mixed for another 3 minutes. Finally, the UHPC mixture was

poured into the molds without vibration due to its self-compacting

property. The used UHPCs are shown in Fig. 2.

The 28d average elastic modulus (three 100 mm × 100 mm ×

300 mm prisms) and 28d average compressive strength (three

100 mm cubic specimens) of SHU-0, SHU-3 SHU-6 and SSU-0

were tested according to Chinese standard GB/T31387-2015

(2015). The results are shown in Table 5.

2.2 Action Mechanism of HCSA

The main hydration equations of HCSA are Eqs. (1) and (2).

There are two expansive sources in HCSA. CaO is the main

expansive origin whereas anhydrite (CaSO4) and C4A3S are the

secondary expansive origin. The main hydration products of HCSA

are Ca(OH)2 and ettringite (AFt), motivating the expansion of

UHPC. Because CaO was hydrated preferentially to C4A3 , the

early expansion energy is provided mainly by Ca(OH)2. However,

AFt is relatively slow to generate and fill the pores and defects

gradually to make the matrix compact and dense (Zhao et al., 2012).

(1)

(2)

2.3 Test Methods

2.3.1 Direct Tensile Test Accompanied with AE Source

Location

Direct tensile test was conducted through a universal testing

machine (WDW-300 servo-controlled testing system) running in

S

( )22

OHCaOHCaO →+

6CaO C4A3S 8CaSO4 96H2O 3 C3A 3CaSO4 32H2O⋅ ⋅( )→+ + +

Table 4. Chemical Composition of HCSA/%

Loss SiO2 Al2O3 Fe2O3 CaO MgO SO3 Total

1.19 1.50 10.61 1.37 65.60 2.08 17.50 99.85

Fig. 2. Used UHPC in This Paper

Table 5. Basic Mechanical Properties of Four Kinds of UHPCs

No.Average Elastic modulus/GPa 28d average compressive

strength/MPa2d 7d 28d

SHU-0 41.2 44.6 47.4 138.7

SHU-3 42.1 44.7 47.4 138.1

SHU-6 41.9 45.0 47.7 136.0

SSU-0 41.0 42.3 47.0 117.8

Fig. 3. Direct Tensile Test System for UHPC: (a) Specimen Dimensions, (b) AE Transducers Layout, (c) Direct Tensile Test Setup

jyguo

高亮


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the displacement control manner of 0.3 mm/min. The direct

tensile test system is given in Fig. 3: 1) Dog-bone shaped

specimen was fabricated according to the dimension as shown in

Fig. 3(a). The width (50 mm) of the specimens is longer than

three times of the length of the fibers (16 mm), which reduces the

influence of the fiber orientation distribution; 2) A set of

customize fixture was used to avoid secondary flexural stress

and to ensure a centric-loading condition as shown in Fig. 3(c);

3) A test frame was amounted to the specimen to measure the

tensile elongation by using two linear variable differential

transformers (LVDTs), whose gauge length was 150 mm. During

the direct tensile test, the crack width measuring instrument with

0.01 mm resolution was used to detect the maximum crack

width.

AE source location to characterize the damage evolution

process of UHPC was carried out in parallel with the direct

tensile test as shown in Fig. 3(c). Eight AE transducers were

placed in a rectangular array just above the surface of double

sides of the tensile specimens as shown in Fig. 3(b), aiming at

picking up AE signals caused by the damage of specimens. More

details about AE analysis method can be found in reference

(Wang et al., 2018).

Direct tensile tests accompanied with AE source locations for

SHU-0, SSU-0 at 2d, 7d, 28d and 80d were done to investigate

their tensile strength development and damage revolution

process. Besides, direct tensile tests for SHU-3 and SHU-6 at

28d were also carried out. Each test has three specimens. UHPC

specimens were cured in a room at the temperature of 20 ± 2oC

and 50% humidity.

2.3.2 Free Shrinkage Test

Three prismatic specimens with dimensions of 100 mm × 100

mm × 515 mm were prepared for SHU-0, SHU-3 SHU-6 and

SSU-0, respectively. The fresh UHPC mixture was casted into

the mold and the free shrinkage was measured over a period of

28d. Free shrinkage of UHPC was determined at 20 ± 2oC and

50% humidity. The setup is shown in Fig. 4. The free shrinkage

strain of UHPC was measured with non-contact method at 0-2d

whereas the free shrinkage strain of UHPC was measured with

contact method at 3d − 28d.

2.3.3 Restrained Shrinkage Test (ACTM C1581 ring test)

Restrained shrinkage test of SHU-0, SHU-3 SHU-6 and SSU-

0 was carried out according to ASTM C1581-04 (2004) in a

controlled environmental chamber at 20 ± 2oC and 50%

humidity. Details of the mold and specimen are shown in Fig. 5.

Four strain gauges were attached at quarter points (one per

quadrant) on the inner steel ring midway up the height using a

data logger system whose frequency was set as 5Hz. After

casting UHPC, the initial strain value of inner steel ring was set

to be zero and began to monitor the strain value until 80d. One

day after casting UHPC, the outer ring mold of the specimen was

removed. Meanwhile, the crack width measuring instrument

with 0.01 mm resolution was used to detect the crack width once

a day.

3. Test Results and Discussion

3.1 Tensile Performance of Strain Hardening UHPC and

Strain Softening UHPC at Different Ages

3.1.1 Tensile Stress-strain Curves

Average tensile stress-strain curves of SHU-0 (strain hardening

UHPC) and SSU-0 (strain softening UHPC) at different ages

(2d, 7d, 28d and 80d) are shown in Fig. 6. As shown in Fig. 6(a),

the tensile stress-strain curves of SHU-0 (at 2d, 7d, 28d and 80d)

consist of elastic stage, strain hardening stage and strain softeningFig. 4. Test Setup to Measure the Free Shrinkage of UHPC with

Non-contact Method

Fig. 5. ASTM C1581 Ring Test: (a) ASTM C1581 Ring Test, (b)

UHPC Ring Test Specimen



stage. The maximum crack width of SHU-0 at different ages at a

tensile strain of 1,000 με is about 0.02 mm which is invisible to

naked eyes. It is well known that strain hardening UHPC

exhibits high ductility by forming multiple micro-cracks in the

strain hardening stage (Makita et al., 2014). By contrast, the

tensile stress-strain curves of SSU-0 (2d, 7d, 28d and 80d) as

shown in Fig. 6(b) consist of elastic stage and strain softening

stage. The maximum crack width of SSU-0 at different ages is

about 0.12 mm at a tensile strain of 1,000 με.

The tensile properties of SHU-0 and SSU-0 are illustrated in

Table 6. It can be observed that the elastic tensile strength of

SHU-0 and SSU-0 increase significantly with the increase of

age. At the age of 28d, the elastic limit tensile strength of SHU-0

is 9.2 MPa and its ultimate tensile strength is 11.4 MPa, and the

elastic limit tensile strength of SSU-0 is about 9.7 MPa.

However, the age has negligible effect on the elastic limit tensile

strain of SHU-0 and SSU-0, which is about 100 με − 200 με. At

different ages (2d, 7d, 28d and 80d), the ultimate tensile strain of

SHU-0 is about 4,000 με − 5,000 με and the residual tensile

strength of SSU-0 at a tensile strain of 2,000 με is about 80% of

its elastic limit tensile strength.

3.1.2 AE Source Distribution Maps

AE source location can effectively detect the internal damage

of UHPC under direct tensile loading to further analyze its crack

width controlling ability at the micro level. AE source distribution

maps of SHU-0 and SSU-0 at different ages (2d, 7d, 28d and

80d) before the tensile strain of 1,000 με are shown in Fig. 7. The

values in brackets in Fig. 7 are the total numbers of AE sources

that can be registered in the range of 50 mm × 100 mm × 500

mm of specimens.

For strain hardening UHPC, SHU-0 is taken for an example to

illustrate the damage evolution owing to the similar tensile

stress-strain responses of SHU-0, SHU-3 and SHU-6. It can be

seen from Fig. 7(a) that there are hardly AE sources during

elastic stage (0 − 200 με). However, AE sources are homogeneously

distributed during 200 με − 1,000 με, which means that the

Fig. 6. Tensile Stress-strain Curves of SHU-0 and SSU-0 at Differ-

ent Ages: (a) Tensile Stress-strain Curve of SHU-0, (b)

Tensile Stress-strain Curve of SSU-0

Fig. 7. AE Source Distribution Maps of SHU-0 and SSU-0 at Dif-

ferent Ages: (a) AE Source Distribution Map of SHU-0, (b)

AE Source Distribution Map of SSU-0


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internal damages caused by multiple micro-cracks (below 0.02

mm) are distributed over the specimen, indicating a uniform

stress state (Li et al., 2000). The AE sources might be motivated

by UHPC matrix cracking and fiber-matrix debonding. AE analysis

method provides strong evidence to the multiple micro-cracking

mode of strain hardening UHPC during its strain hardening

stage.

For strain softening UHPC (SSU-0) shown in Fig. 7(b), some

AE sources are accumulated at the elastic limit strains (159 με at

2d, 131 με at 7d, 191 με at 28d and 201 με at 80d) and these AE

sources are mainly distributed at the single plane corresponding

to the localized crack. With the increase of tensile strain, the

number of AE sources increase significantly. The AE sources

might be motivated by UHPC matrix cracking and fiber pull-out

action. AE analysis method makes a clear explanation to the

single macro-cracking mode of strain softening UHPC.

3.2 Effect of HCSA Dosage on the Tensile Stress-strain

Curve Of Strain Hardening UHPC at the Age of 28d

Tensile stress-strain curves of SHU-0, SHU-3 and SHU-6 at

28d are shown in Fig. 8. All the specimens exhibit the strain

hardening behavior and the ultimate tensile strength is about 11 −

12 MPa and the ultimate tensile strain is about 4,000 με− 5,000 με,

meaning that these three kinds of UHPCs all belong to strain

hardening UHPC and HCSA has no influence on the strain

hardening characteristics. Specific values are summarized in

Table 6. As shown in Table 6, the addition of HCSA may slightly

increase both of the elastic tensile strength and ultimate tensile

strength of strain hardening UHPC. The maximum crack width

of SHU-0, SHU-3 and SHU-6 at a strain of 1,000 με is below

0.02 mm which is invisible to naked eyes.

3.3 Free Shrinkage of Four Kinds of UHPCs

Free shrinkage strain-age curves of SHU-0, SHU-3, SHU-6

and SSU-0 are shown in Fig. 9. The shrinkage values are plotted

as negative while the expansion values are shown as positive.

For four kinds of UHPCs, the free shrinkage strain εsh shows a

very steep increase at the early age. After certain points (about

1d), slight expansion is observed. Then with the increase of age,

the free shrinkage εsh increases slowly. At 28d, the free shrinkage

strain εsh of SHU-0, SHU-3 SHU-6 and SSU-0 are 1,006 με, 600

με, 462 με and 1197 με, respectively. The free shrinkage of SHU-

0 is smaller than that of SSU-0 due to the higher ratio of steel

fibers of SHU-0, showing that steel fibers can contribute to the

reduction of the free shrinkage of UHPC. Besides, the free

shrinkage of strain hardening UHPC decreases accordingly with

the increase of HCSA dosages from 0% to 6%. It indicates that

HCSA has a positive effect on decreasing the free shrinkage of

UHPC.

3.4 Restrained Shrinkage of Four Kinds of UHPCs

Average compressive strain of inner steel ring-age curves of

SHU-0, SHU-3 SHU-6 and SSU-0 are plotted in Fig. 10. The

compressive strain of inner steel ring is approximately equal to

the restrained shrinkage strain εst of UHPC due to the low ratio of

thickness and radius.

It is supposed that the value of strain gauge should increase

smoothly and continuously with the increase of age if UHPC

doesn’t crack in ASTM C1581-04 (2004) ring test. Therefore, a

rapid and instantaneous fluctuation of the value of strain gauge

indicates cracking of UHPC according to ASTM C1581-04

(2004).

Fig. 8. Tensile Stress-strain Curves of SHU-0, SHU-3 and SHU-6

at 28d

Table 6. Tensile Properties of Four Kinds of UHPCs

No. Age/dElastic

limit tensile strength/MPa

Elastic limit tensile

strain/με

Ultimate tensile

strength/MPa

Ultimate tensile

strain/με

SHU-0

2 3.3 160.5 4.3 1,998.6

7 5.8 162.7 9.5 4,397.0

28 9.2 220.3 11.4 4,561.4

80 11.5 206.7 14.1 4,743.3

SHU-3 28 10.7 224.5 12.0 4,000.0

SHU-6 28 11.3 200.2 12.8 4,271.3

SSU-0

2 4.2 199.7 N.A N.A

7 6.1 200 N.A N.A

28 9.7 191.5 N.A N.A

80 11.3 215.5 N.A N.A

Fig. 9. Free Shrinkage Strain-age Curve of SHU-0, SHU-3, SHU-

6 and SSU-0



The restrained shrinkage strain εst of SHU-0 and SSU-0

develop greatly and smoothly during the early age of 14d and

their values are similar which are about 100 με. After that, the

curves of SHU-0 still vary continuously and no crack can be

detected by the crack width measuring instrument with 0.01 mm

resolution, and the restrained shrinkage strain εst of SHU-0 is

about 141 με at 80d. By contrast, there are several evident

instantaneous fluctuations of the strain gauge value of SSU-0

and four hairline cracks (0.035 mm, 0.05 mm, 0.04 mm and 0.02

mm) are checked as shown in Fig. 11. The restrained shrinkage

strain εst of SSU-0 is about 99 με at 80d. It shows that the

restrained shrinkage strain εst of SHU-0 increases continuously in

the crack-free state while the restrained shrinkage strain εst of

SSU-0 decreases due to cracking. As a result, SHU-0 has a better

crack width controlling ability than SSU-0, considering the effect

of the restrained shrinkage on cracking of UHPC.

On the other hand, the restrained shrinkage strain εst of SHU-

3, SHU-6 are about 96 με and 16 με, respectively at 80d, lower

than that of SHU-0. Thus, HCSA can mitigate the restrained

shrinkage of strain hardening UHPC effectively. It is supposed

that HCSA can reduce the restrained tensile stress of strain

hardening UHPC. Besides, no crack can be detected in SHU-3,

SHU-6 by the crack width measuring instrument with 0.01 mm

resolution.

4. Restrained Shrinkage Mechanism of UHPC inASTM C1581-04 (2004) Ring Test

4.1 Restrained Shrinkage Cracking Mechanism of Strain

Hardening UHPC and Strain Softening UHPC based

on Their Direct Tensile Properties

4.1.1 Restrained Tensile Stress Analysis

In this paper, the maximum tensile criterion (Hossain et al.,

2004; Moon et al., 2006) was chosen to analyze the failure

mechanism of UHPC in ASTM C1581-04 (2004) ring test. The

maximum tensile criterion is to analyze the relationship between

the “load response” (restrained tensile stress) of UHPC and its

“tensile resistance” (uniaxial tensile strength).

The “load response” of UHPC induced by its own shrinkage in

ASTM C1581-04 (2004) ring can be calculated directly with the

monitored strain of the inner steel ring, because the stress of

UHPC is presumed to be approximately uniform (See et al.,

2003). The stress calculation of UHPC ring and inner steel ring

can be simplified as the plane stress model shown as Fig. 12.

There exists fictitious interface pressure Pres at the interface

Fig. 10. Compressive Strain of Inner Ring-age Curve of SHU-0,

SHU-3, SHU-6 and SSU-0

Fig. 11. Cracking Diagram of SSU-0

Fig. 12. Idealization of Restrained Ring Specimen (Yoo et al., 2013)


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between the inner steel ring and the UHPC ring. ric and ris refer to

the inner radius of UHPC ring and inner steel ring, respectively,

roc and ros refer to the outer radius of UHPC ring and inner steel

ring, respectively.

The fictitious interface pressure Pres (Yoo et al., 2013) can be

computed as the pressure which generates a strain that is

equivalent to the monitored steel strain of the inner ring using

Eq. (3):

(3)

Where Es is the elastic modulus of the inner ring (210 GPa)

and εst is the monitored steel strain of the inner steel ring. The

restrained tensile stress of UHPC refers to the circumferential

normal stress. The maximum restrained tensile stress σres-max is

calculated with Eq. (4) (Yoo et al., 2013):

(4)

The “tensile resistance” of UHPC at different ages (2d, 7d, 28d

and 80d) by the direct tensile test is used to plot the tensile

strength-age curve. The maximum restrained tensile stress-age

curve and the tensile strength-age curve of strain hardening

UHPC (SHU-0) and strain softening UHPC (SSU-0) are plotted

in Fig. 13.

For strain hardening UHPC as shown in Fig. 13(a), the elastic

limit tensile strength and the ultimate tensile strength are

considered as two thresholds to judge the stress state of SHU-0.

Once the maximum restrained tensile stress σres-max of SHU-0

exceeded its elastic limit tensile strength, multiple invisible

micro-defects whose existence was verified in section 3.1.2 were

generated in UHPC matrix. The steel fibers acted as stitches and

managed to control the propagation of these multiple invisible

micro-defects (Yousefieh et al., 2017; Brandt et al., 2008). Thus,

the maximum restrained tensile stress σres-max was kept below the

ultimate tensile strength by many times of marginal instantaneous

stress relaxation, which was in accordance with the measurement

result of no detected cracks (below 0.01 mm) in the ASTM

C1581-04 (2004) ring test before 80d. Finally, the maximum

restrained tensile stress σres-max of SHU-0 was kept at about 8.7

MPa at 80d.

For strain softening UHPC as shown in Fig. 13(b), once the

maximum restrained tensile stress σres-max of SSU-0 exceeded its

elastic limit tensile strength, the matrix cracked, the steel fibers

debonded and were pulled out between two cracked sections,

then the crack localized, which was verified in section 3.1.2, to

relax the tensile stress instantaneously. The relaxed tensile stress

was smaller than that of the normal concrete due to the high

residual tensile strength of SSU-0. The maximum restrained

tensile stress σres-max of SSU-0 was reduced to below its elastic

limit tensile strength by four times of evident instantaneous

stress relaxation, which was in accordance with the measurement

result of four hairline cracks (0.035 mm, 0.05 mm, 0.04 mm and

0.02 mm) at the surface of SSU-0. Finally, the maximum restrained

tensile stress σres-max of SSU-0 was decreased to 8.1 MPa at 80d.

4.1.2 Strain Transfer Modelling

A strain transfer modelling of UHPC based on the shrinkage

behavior is proposed and shown in Fig. 14. When UHPC is

under the restrained condition, the difference between free

shrinkage strain εsh and restrained shrinkage strain εst transforms

into tensile strain caused by restrained tensile stress of UHPC,

which is made up of two parts: elastic tensile strain εet (recoverable

tensile deformation) and plastic tensile strain εpt (irrecoverable

tensile deformation). Namely, the strain exists in the form of εsh

in the free condition, while the strain exists in the form of εst, εet

and εpt in the restrained condition. The elastic tensile strain εet is

the ratio of the tensile stress of UHPC to its elastic modulus.

The underlying mechanism of plastic tensile strain εpt for strain

hardening UHPC is different from that for strain softening

UHPC. Based on the direct tensile properties accompanied with

AE analysis method of SHU-0 and SSU-0, the plastic tensile

strain εpt of SHU-0 is the irrecoverable deformation mainly

caused by multiple invisible micro-defects which are related to

its multiple micro-cracking mode under direct tensile loading.

Pres

ros

2

ris

2

–( )

2ros

2--------------------Esεst=

( )( )

( ) ( )( )

2 2 2 2 2 2

22 2 2 22

os oc os is os oc

res max res s st

osoc os oc os

r r r r r r

P Err r r r

σ ε−

+ − +

= =

− −

Fig. 13. Restrained Tensile Stress Analysis of SHU-0 and SSU-0:

(a) Restrained Tensile Stress Analysis of SHU-0, (b)

Restrained Tensile Stress Analysis of SSU-0



By contrast, the plastic tensile strain εpt of SSU-0 is the irrecoverable

deformation mainly caused by several hairline cracks which are

related to its single macro-cracking mode under direct tensile

loading. The details of this point are illustrated by the AE sources

distribution given in Fig. 14, where the uniform distribution of

AE sources are caused by the multiple micro-defects generated

in strain hardening UHPC and the localized distribution of AE

sources are caused by the several hairline cracks in strain

softening UHPC.

4.2 Calculation of Relaxation Degree of Four Kinds of

UHPCs

To exclude the effect of the expansion by hydration heat during

the early age (about 1d), the analysis of relaxation degree caused

by UHPC shrinkage in ASTM C1581-04 (2004) ring test was

conducted from the time of 2d.

The restrained tensile stress and the theoretical elastic tensile

stress can be used together to describe the effect of stress

relaxation of UHPC in the restrained condition. The maximum

restrained tensile stress σres-max of UHPC can be calculated by Eq.

(4). The maximum theoretical elastic tensile stress σela-max can be

calculated by Eq. (5) (Yoo et al., 2013). The effect of stress

relaxation is represented by the relaxation degree λ, which is

defined as the amount of relaxed stress σrel of UHPC relative to

the maximum theoretical elastic tensile stress σela-max as Eq. (6)

(Altoubat et al., 2017).

(5)

(6)

Where νs and νc are the Poisson’s ratios for steel (0.3) and

UHPC (0.2), respectively. Ec is the elastic modulus of UHPC

which is taken from Table 5. The larger the relaxation degree λ is,

the weaker the interaction between UHPC and steel ring is.

Relaxation degree-age curves of SHU-0, SHU-3, SHU-6 and

SSU-0 are shown in Fig. 15. As shown in Fig. 15, for SHU-0 and

SSU-0 without HCSA, the relaxation degree decreased within

the range of 2-6 days and finally became stable at 28d. SHU-0

showed a lower relaxation degree λ of 0.78 than SSU-0 of 0.81 at

28d, which meant that the interaction between SHU-0 and steel

ring was stronger than that of SSU-0, namely SHU-0 accumulated

more restrained tensile stress than SSU-0. It will become a

negative factor when SHU-0 is applied in the steel-UHPC composite

deck system as shown in Fig. 1(a). From the comparison of

SHU-0, SHU-3 and SHU-6, it can be observed that SHU-3 and

SHU-6 reached the stable state at around 3 days, which was

earlier than SHU-0. It was possibly due to the addition of HCSA.

At the latter age (7d − 28d), the relaxation degree of SHU-0

decreased smoothly, while that of SHU-3 and SHU-6 was almost

stable with the slight fluctuations. It may be related to the effect

of HCSA expansion agent. HCSA expansion agent can be

( )( ) ( ) ( ) ( )

2 2

2 2 2 21 1 1 1

c s os oc sh

ela max

c s is s os s c os c oc

E E r r

E ν r ν r E ν r ν r

ε

σ−

+=

⎡ ⎤ ⎡ ⎤+ + − + − + +⎣ ⎦ ⎣ ⎦

maxela

maxres1λ

−

−

−=

σ

σ

Fig. 14. Strain Transfer Modelling of UHPC: (a) Strain Hardening UHPC, (b) Strain Softening UHPC

Fig. 15. Relaxation Degree-age Curves of SHU-0, SHU-3, SHU-6

and SSU-0


Vol. 00, No. 0 / 000 0000 − 11 −

affected by the air moisture, which leads to the fluctuations. The

relaxation degree λ of SHU-3, SHU-6 at 28d was 0.8, 0.88,

respectively. It can be found that the relaxation degree λ of strain

hardening UHPC increased with the increase of HCSA dosage

from 0% to 6%, which meant that HCSA can be used to reduce

the interaction between strain hardening UHPC and steel ring

caused by the restrained shrinkage and reserve more tensile

capacity for strain hardening UHPC in the service condition.

HCSA will benefit the application of strain hardening UHPC in

the steel-UHPC composite deck system.

5. Conclusions

In this study, the restrained shrinkage mechanism of UHPC

was analyzed based on its tensile properties accompanied with

AE analysis method, free shrinkage behavior and restrained

shrinkage performance. The effects of UHPC tensile properties

(strain softening or strain hardening) and HCSA dosages (0%,

3% and 6% by mass of total binder) were investigated. The

restrained shrinkage cracking mechanism of strain hardening

UHPC and strain softening UHPC was analyzed, and the effect

of HCSA dosages on the restrained shrinkage and relaxation

degree of strain hardening UHPC was studied. Based on the

experimental results, the following conclusions can be drawn:

1. Strain hardening UHPC has a better crack width controlling

ability than strain softening UHPC, considering the effect of

the restrained shrinkage on cracking of UHPC. The crack

width of strain hardening UHPC is lower than 0.01 mm

while there are four hairline cracks (0.035 mm, 0.05 mm,

0.04 mm and 0.02 mm) generated in strain softening UHPC

in ACTM C1581 ring test.

2. In the restrained condition, the restrained stress of strain

hardening UHPC is released by the generation of many mar-

ginal instantaneous stress relaxations, while the restrained

stress strain softening UHPC is released by the generation of

several evident instantaneous stress relaxations.

3. In the restrained condition, free shrinkage strain transforms into

restrained shrinkage strain, elastic tensile strain and plastic ten-

sile strain for UHPC. The plastic tensile strain is the irrecover-

able deformation mainly caused by multiple invisible micro-

defects for strain hardening UHPC and mainly caused by sev-

eral hairline cracks for strain softening UHPC.

4. In ASTM C1581-04 (2004) ring test, the restrained shrink-

age of strain hardening UHPC with HCSA dosage of 0%,

3% and 6% at 80d is 141 με, 96 με and 16 με, respectively.

The relaxation degree of strain hardening UHPC with

HCSA dosage of 0%, 3% and 6% at 28d is 0.78, 0.8 and

0.88, respectively. The HCSA expansion agent can effec-

tively reduce the restrained shrinkage of UHPC and the

influence on the structure.

Acknowledgements

This work was supported by the Science and Technology

Department of Zhejiang Province (grant number 2019-GXKY-

01), the National Nature Science Foundation of China (grant

number 51609172) and the Shanghai Municipal Science and

Technology Project [grant number 17DZ1204200]. The financial

supports are greatly appreciated.

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