Mechanical and damage mechanisms of reinforced ultra high ... · erated bridge construction (ABC) methods using prefabricated bridge elements [1]. Previous studies have shown that

Construction and Building Materials 226 (2019) 259–279

Contents lists available at ScienceDirect

Construction and Building Materials

journal homepage: www.elsevier .com/locate /conbui ldmat

Mechanical and damage mechanisms of reinforced ultra highperformance concrete under tensile loading

https://doi.org/10.1016/j.conbuildmat.2019.07.1620950-0618/� 2019 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: [email protected] (J.-Y. Wang).

Chen Bian, Jun-Yan Wang ⇑Key Laboratory of Advanced Civil Engineering Materials, Tongji University, Ministry of Education, Shanghai 201804, China

h i g h l i g h t s

� Mechanical and damage mechanisms of RUHPC depends on the tensile performance of UHPC.� Reduction of the tensile strength of UHPC in RUHPC was observed.� AE analysis method shows further insight into the tensile damage evolution of RUHPCs.� Gini index can characterize the damage distribution nonuniformity of RUHPC.

a r t i c l e i n f o

Article history:Received 26 January 2019Received in revised form 13 May 2019Accepted 17 July 2019

Keywords:Reinforced ultra high performance concreteStrain hardeningStrain softeningTensile mechanical mechanismTensile damage evolution mechanismAcoustic emission

a b s t r a c t

Understanding the tensile mechanism of reinforced ultra high performance concrete (RUHPC) is impor-tant for structural design and application of ultra high performance concrete (UHPC). In this study, thedirect tensile test accompanied with crack width detection and acoustic emission (AE) source locatingwere conducted on RUHPC specimens with the longitudinal reinforcement ratios of 0%, 2.3% and 4.6%.Two types of RUHPCs were studied: high strain hardening RUHPC (HSH-RUHPC) and strain softeningRUHPC (SS-RUHPC). Experimental results included the tensile stress (load)-strain curves, the crackwidth-strain curves and the AE source distribution maps under tensile loading. The tensile mechanismswere elaborated from two aspects. From the view of mechanical mechanism, during Stage I (the elasticstage) and Stage II (the elastic-plastic stage): (1) HSH-RUHPC had a globally uniform stress distributionwhile the steel rebar in SS-RUHPC changed from total elastic state to partial yielding and finally to partialstrain hardening; (2) the reduction of the tensile strength of UHPC was observed in RUHPC, which wasmore obvious with the higher reinforcement ratio. From the view of damage evolution mechanism basedon AE analysis method at the micro level: (1) HSH-RUHPC exhibited a homogeneous damage distributionowing to its multiple-micro-cracking mode before steel yielding; (2) SS-RUHPC showed several damageconcentrations at crack positions after UHPC softening due to its several-macro-cracking mode.Meanwhile, Gini index was proved to be an effective parameter to evaluate the distribution nonunifor-mity of the internal damages of RUHPC.

� 2019 Elsevier Ltd. All rights reserved.

1. Introduction

In consideration of the challenges of the work zone safety andenvironmental impacts, USA and China have been promoting accel-erated bridge construction (ABC) methods using prefabricatedbridge elements [1]. Previous studies have shown that the use ofprefabricated bridge elements can significantly accelerate the con-struction and rehabilitation of bridge decks, and dramatically min-imize delays and disruptions to the community [2].

Ultra high performance concrete (UHPC) is composed of com-pact cementitious matrix combined with a high amount of fibers[3,4]. Due to the high tensile strength and excellent bonding withsteel rebar, UHPC has been used in the construction of prefabri-cated double T UHPC girder. The UHPC girder can significantlyreduce the self-weight for fast installation and save the maintain-ing cost during the service life. Fig. 1 shows a case using UHPC gir-der in a bridge constructed in Shanghai, 2017. The UHPC used inthis case is a kind of high strain hardening UHPC cured under nor-mal condition provided by the authors.

The high strain hardening UHPC refers to a kind of UHPC whoseultimate tensile strain eUtu is higher than the yield strain ey of the

http://crossmark.crossref.org/dialog/?doi=10.1016/j.conbuildmat.2019.07.162&domain=pdfhttps://doi.org/10.1016/j.conbuildmat.2019.07.162mailto:[email protected]://doi.org/10.1016/j.conbuildmat.2019.07.162http://www.sciencedirect.com/science/journal/09500618http://www.elsevier.com/locate/conbuildmat

Nomenclature

fUte elastic tensile strength of UHPCeUte elastic tensile strain of UHPC corresponding to fUtefUtu ultimate tensile strength of UHPCeUtu ultimate tensile strain of UHPC corresponding to fUtufy yield strength of steel rebarey yield strain of steel rebar corresponding to fyesh strain at initial strain hardening stage of steel rebarFte tensile loading capacity of RUHPC at the elastic stageFtep tensile loading capacity of RUHPC at the elastic-plastic

stageete tensile strain of RUHPC corresponding to Fte

etep tensile strain of RUHPC corresponding to FtepFt tensile load of RUHPCFst tensile load of steel rebarFUt tensile load of UHPCI Gini indexA area between the Lorenz curve and the horizontal coor-

dinateR area between the idealized even distribution curve and

the horizontal coordinateM area between the idealized concentrated distribution

curve and the horizontal coordinate

260 C. Bian, J.-Y. Wang / Construction and Building Materials 226 (2019) 259–279

steel rebar, typically about 2000le (micro strain). Due to the highelastic modulus of steel fibers (6�7 times of that of PVA fiber) andthe tailored strong bonding between steel fiber and UHPC matrix,high strain hardening UHPC presents multiple micro-cracks (smal-ler than 0.05 mm) during the strain hardening stage [5]. The crackwidth controlling ability guarantees high strain hardening UHPC tobe a macro crack-free concrete cover for the steel rebar, which willbenefit the durability of the UHPC girder during the service life. Bycontrast, strain softening UHPC presents cracking localization dur-ing the post-peak region under tensile loading. At present, theeffect of tensile properties (strain hardening or strain softening)on the tensile mechanism of reinforced ultra high performanceconcrete (RUHPC) is still not well known.

Fig. 1. Prefabricated UHPC girder for accelerated

So far, relevant studies remain scarce on RUHPC as one typicalkind of reinforced high performance fiber reinforced cement basedcomposite (RHPFRCC). The tensile behavior of RHPFRCC has beeninvestigated by some researchers as shown in Table 1 [6–12]. Asshown in Table 1, some researches revealed that RHPFRCC per-formed the tension stiffening, some described the multiple crack-ing behaviors of RHPFRCC specimens in uniaxial tension. Othersconducted the analysis on strain profiles of steel rebar along themember length. Rare researches focused on the damage evolutionmechanism of RHPFRCC under tensile loading. Under the service-ability limit state, the UHPC would be in a plastic state while thesteel bar still in an elastic state. Damage will generate due to theinteraction between UHPC and steel rebar. The damage mechanism

bridge construction (ABC) in Shanghai, 2017.

Table 1Literature review of HPFRCC.

Details of specimen Materialtypes

Cross sectiondimension

Reinforcementratio

Contents Main conclusions Ref.

UHPC 160 mm � 160 mm 1%, 2.5%, 4.1% An experimental study ontensile behavior ofreinforced UHPC

(1) The strength of RUHPC iscomposed of the steelstrength and a contributionof UHPC;(2) The tension stiffening isvery high due to the veryhigh bond and tensilestrength of UHPC

[6]

UHPC 40 mm � 110 mm 3.4% An experimental study ontensile behavior ofreinforced UHPC

The tensile behavior ofreinforced UHPC may bedescribed by the linearsuperposition of the tensilebehavior of UHPC and steelrebars

[7]

ECC 90 mm � 90 mm120 mm � 120 mm150 mm � 150 mm

0.59%, 0.89%,0.92%, 1.4%,1.64%

An experimental study onthe tension stiffeningbehavior of reinforced ECC

(1) Reinforced ECC developedmore significant tensionstiffening than reinforced NC;(2) Deformation capacities ofreinforced ECC memberswere greatly reducedcompared to reinforced NC;(3) The required minimumreinforcement ratio todevelop full ductility ofreinforced ECC wasdetermined

[8]

HPFRCCs:(1) FRC(2) SCFRC(3) ECC

127 mm � 127 mm 1.2% An experimental study onthe elastic and plasticresponse of three kinds ofmild steel reinforcedHPFRCCs in uniaxialtension

(1) All reinforced specimenstested here exhibitedmultiple cracking in uniaxialtension;(2) The embedded steel inHPFRCCs exhibited earlystrain hardening and fracturerelative to traditionalconcrete;(3) A modified approachbased on planar analysis toestimate flexural strength ofreinforced HPFRCCcomponents using tension-stiffening data is proposed

[9]

ECC 100 mm � 100 mm 1.14% An experimental study ofreinforced ECC on itstension stiffening processusing an image-baseddeformation measurementand analysis system

(1) ECC was shown toincrease the stiffness of thecomposite and maintainlinear stiffness throughouttesting;(2) The cracking process ofreinforced ECC consistentlyshowed multiple crackingwith considerably smallercrack widths than those inreinforced NC;(3) The tensile strainbehavior of ductile ECC andlow E-modulus GFRP bar areshown to be compatibleresulting in a good compositeinteraction

[10]

HPFRCCs:(1) FRC(2) ECC

N.A. N.A. An experimental study onunderstanding theinteraction between thereinforcement and theHPFRCCs

(1) Multiple cracking wasobserved in all reinforcedHPFRCC dogbones testedhere;(2) The multiple crackingobserved in all specimens ishypothesized to have led toboth distributed yielding andhardening in thereinforcement

[11]

(continued on next page)

C. Bian, J.-Y. Wang / Construction and Building Materials 226 (2019) 259–279 261

Table 1 (continued)

Details of specimen Materialtypes

Cross sectiondimension

Reinforcementratio

Contents Main conclusions Ref.

SCFRC 112 mm � 112 mm 1.6% An experimental study oncrack initiation andpropagation of reinforcedSCFRC elements in tension

(1) Reinforced SCFRCspecimens exhibited anoticeably higher tensionstiffening than the specimenswithout fibres;(2) The presence of fibreenhances tension stiffening,resulting in a stiffer memberresponse with more cracksbut less deformation

[12]

Note: ECC is Engineered Cementitious Composite; HPFRCC is High Performance Fiber Reinforced Cement based Composite; HFRC is Fiber Reinforced Concrete; SCFRC is Self-Consolidating Fiber Reinforced Concrete; NC is Normal Concrete.


of UHPC has significant effect on the crack width controlling abil-ity, permeability and stiffness degradation of RUHPC structure.

Acoustic emission (AE) technique provides a possible avenue todetect internal damages of concrete from the microcosmic point ofview effectively [13–18]. AE source locating is a method to obtainAE source distribution in three-dimensional space. Specific detailsof the AE analysis method can be found in the Ref. [5]. To quanti-tatively describe the distribution nonuniformity of AE sources,proper statistical tools can be applied such as Lorenz curve [19]and Gini index [20]. Both have been widely applied in economics,ecology and medicine but is absent in civil engineering [21]. Thusin this paper, Lorenz curve and Gini index are used in the damagenonuniformity index calculation of RUHPC specimens under ten-sile loading.

As a result, the objective of this study is to analyze the tensilemechanism of RUHPC. To achieve this objective, the direct tensiletest accompanied with crack width detection and AE source locat-ing were conducted on RUHPC specimens in the work herein. Theeffects of UHPC types (high strain hardening UHPC, strain softeningUHPC) and longitudinal reinforcement ratios (0%, 2.3% and 4.6%) ontensile properties of RUHPC were investigated. The tensilemechanical mechanism of RUHPC was analyzed based on the ten-sile load-strain curve, while the tensile damage evolution mecha-

Table 2Specimen details.

Materials Specimen name Specimen

High strain hardening UHPC HSH-UHPC 3Strain softening UHPC SS-UHPCHigh strain hardening UHPC HSH-RUHPC-I

HSH-RUHPC-IIStrain softening UHPC SS-RUHPC-I

SS-RUHPC-II

Table 3Mix proportions of UHPC matrix.

Cement Silica fume Ground filler

1 0.3 0.3

Table 4Properties of steel fibers.

Fiber types Tensile strength/MPa Elastic modulus/GPa Len

Steel fiber 2500 200 16

nism of RUHPC was studied by AE analysis method at the microlevel.

2. Experimental program

Direct tensile test accompanied with crack width detection and AE source locat-ing was conducted to study the tensile mechanism of RUHPC. There are six kinds ofspecimens, whose details and naming convention are shown in Table 2.

2.1. UHPC materials

The performance of UHPC matrix and steel fiber both can influence the tensilebehavior of UHPC, namely strain hardening or strain softening behavior. In thispaper, HSH-UHPC and SS-UHPC were made by changing the volume fraction of steelfiber based on the same UHPC matrix.

In this paper, UHPC materials used here consist of three components: water,UHPC premixed powder and steel fibers. Table 3 provides the mix proportion ofUHPC matrix. A type of straight steel fiber with brass coating was used, whose prop-erties are given in Table 4. The volume fraction of steel fibers used in HSH-UHPCand SS-UHPC was 2.0% and 1.0%, respectively.

A laboratory mixer with sixty-liter capacity was used to prepare the UHPC mix-ture. UHPC premixed powder was first dry-mixed for about 1 min. Water was thenadded gradually and mixed for another 3 min. When the mixture showed the suit-able workability, steel fibers were dispersed into the mixture and mixed for another3 min. A flow chart of material preparation is shown in Fig. 2. Finally, the UHPC mix-ture was placed in the molds without vibration due to its self-compacting property.Since the casting method has effect on the mechanical properties of UHPC [22–24],

number Reinforcement ratio/% Steel rebar

0 N.A.

2.3 One HRB400 rebar4.6 Two HRB400 rebars2.3 One HRB400 rebar4.6 Two HRB400 rebars

Quartz sand Water Superplasticizer

1.34 0.2 0.013

gth/mm Diameter/lm Aspect ratio Density/(kg�m�3)200 80 7850

Fig. 2. A flow chart of material preparation.

(a) Stress-strain curves of three HRB 400 deformed steel rebars


the same casting method was used for all the specimens in this paper. UHPC mix-ture was placed from one corner of the mold to another for 3�5 times to fill themold. Casting photos of dog-bone specimens are shown in Fig. 3.

Compressive strength (100 mm cubic specimen) of UHPC was obtained accord-ing to Chinese standard GB/T 31387-2015 [25] using a universal testing machine(UTM) with a maximum load capacity of 3000kN. The 28d average compressivestrength (three specimens) of HSH-UHPC and SS-UHPC were 138.7 MPa and129.4 MPa, respectively.

(b) Average stress-strain curve of the HRB 400 deformed steel rebar

Fig. 4. Tensile stress-strain relationship of HRB 400 deformed steel rebar.

2.2. Steel rebar

For RUHPC specimens, HRB400 deformed steel rebar with diameter of 12 mmand length of 500 mmwas used for the longitudinal reinforcement. Three bare steelrebars were tested to obtain their tensile stress-strain characteristics. They weretested in a universal testing machine, and a 50 mm extensometer was used to mea-sure the tensile strain. Finally, the tensile stress-strain relationship of steel rebarwas obtained as shown in Fig. 4. As shown in Fig. 4, the steel rebar used has theyield strength of around 490 MPa and the yield strain of around 2500le.

Fig. 3. Casting photos of

2.3. Test methods

The test is made up of three parts which proceed simultaneously: (1) direct ten-sile test, (2) crack width detection and (3) AE source locating. Tensile stress (load)-

dog-bone specimens.


strain curve was attained by direct tensile test, the crack width-tensile strain curvewas acquired by crack width detection and AE source distribution map wasobtained by AE source locating.

2.3.1. Test method for direct tensile testDirect tensile test was carried out through a universal testing machine (WDW-

300 servo-controlled testing system) running in displacement control manner. Thedirect tensile test system is given in Fig. 5 where: (1) a dog-bone shaped specimenas shown in Fig. 5(a) was fabricated according to the dimension as shown in Fig. 5(b); (2) a set of customize fixture was used to avoid secondary flexural stress and toensure a centric-loading condition as shown in Fig. 5(c); (3) a test frame wasamounted to the specimen to measure the tensile elongation by using two linearvariable differential transformers (LVDTs), whose gauge length was 150 mm.

2.3.2. Test method for crack width detectionDuring the direct tensile test, two methods were combined to detect the crack

opening as shown in Fig. 6: (1) the crack width was measured directly by the crackwidth measuring instrument with 0.01 mm resolution; (2) at the same time, the

(a) Specimen (b) Dimensions and reinforc

Fig. 5. Direct tensile tes

(a) Crack detection with the width measuring instrument

Fig. 6. Crack measu

crack image was taken by a Canon camera with a micro photo lens (MP-E65mmf/2.8 1-5x). Aiming at taking the crack image more clearly, the loading rate of thedirect tensile test was set as 0.1 mm/min.

2.3.3. Test method for AE source locatingAE source locating was carried out in parallel with the direct tensile test as

shown in Fig. 5(c). Eight AE transducers were placed in a rectangular array justabove the surface of double sides of the tensile specimens to pick up AE signals orig-inating from specimens. In this study, pencil lead test and AE source locating wereconducted.

Pencil lead test was firstly done according to the ASTM E976-99 standard [26].Its purpose was to determine the AE wave propagation velocity through the speci-men and the noise level of the test environment. After it, the threshold of the AEsystem was selected as 35 dB, the preamplifier gain was set as 40 dB and the sam-pling frequency was set as 3 MHz.

AE source locating aimed at characterizing the damage evolution process ofspecimens, whose analysis system is shown in Fig. 7. The transmitted waves causedby internal damages of specimens were detected by eight AE transducers on the

ement ratios (c) Test setup

t system for UHPC.

(b) Crack image taken by a Canon camera

ring methods.

Fig. 7. AE analysis system.


surface of specimens. AE source locating can be determined by time differencesamong the recorded signals from these eight AE transducers. Through the AEpreamplifier and the trigger signal identifier, all waveforms were recorded andstored by a windows-based AE data operation program to extract the AE parametersfor analysis. Finally, the coordinates and origin time of AE sources were monitoredby this system to plot the AE source distribution maps at different tensile strains.The detection range of AE sources in AE source distribution map is50 mm � 100 mm � 500 mm.

(a) Three specimens of HSH-UHPC

3. Tensile mechanical mechanism of RUHPCs

3.1. Tensile stress-strain curves of HSH-UHPC and SS-UHPC

Tensile stress-strain curves of UHPCs are presented in Fig. 8. Asshown in Fig. 8(a), the elastic tensile strength fUte of HSH-UHPCranges from 9.3 MPa to 10.3 MPa and the corresponding strain eUteis about 200le. The ultimate tensile strength fUtu ranges from11.2 MPa to 12.0 MPa, and the corresponding strain eUtu reachesabout 4000 le–5000 le. As shown in Fig. 8(b), the elastic tensilestrength fUte of SS-UHPC ranges from 10.1 MPa to 10.6 MPa andthe corresponding strain eUte is around 200le. Both fUte and eUteof SS-UHPC are close to those of HSH-UHPC because the sameUHPC matrix is present. The residual tensile strength of SS-UHPCis 70%–86% of its elastic tensile strength fUte at a correspondingstrain of 2000 le.

(b) Three specimens of SS-UHPC

Fig. 8. Tensile stress-strain curves of UHPCs.

3.2. Tensile performance of HSH-RUHPCs

The tensile load-strain curves of HSH-RUHPCs are presented inFig. 9. A typical specimen of HSH-RUHPC was taken for example asshown in Fig. 9(c)-(d). The tensile load-strain curves of HSH-RUHPCs could be divided into stage I (the elastic stage), stage II(the elastic-plastic stage) and stage III (the plastic stage). The firsttwo stages showed a smooth transition. The curve slope at stage IIwas almost the same as that of bare steel rebar. Furthermore, thestrain at the beginning of stage III was almost the same as the yieldstrain ey of HRB400 steel rebar (around 2500le). It was supposedthat there was hardly slip generated between HSH-UHPC and steelrebar before the yielding of steel rebar. For HSH-RUHPC-I and HSH-RUHPC-II, the total tensile loading capacity at the end of stage Iwas 30kN, 35kN, respectively while that at the end of stage IIwas 110kN, 170kN, respectively.

The schematic illustration of tensile load-strain curve of HSH-RUHPC is shown in Fig. 10. Point A refers to the end of the StageI, where UHPC is supposed to reach the elastic limit. Fte and ete

(a) Three specimens of HSH-RUHPC-I

(b) Three specimens of HSH-RUHPC-II

(c) Comparison of steel rebar and HSH-RUHPC-I

(d) Comparison of steel rebar and HSH-RUHPC-II

Fig. 9. Tensile load-strain curves of HSH-RUHPCs.

Fig. 10. Schematic illustration of tensile load-strain curve of HSH-RUHPC.


are defined as the tensile loading capacity and the correspondingstrain of RUHPC at Point A, respectively. Point B refers to the endof the Stage II, where steel rebar begins to yield. Ftep and etep are

defined as the tensile loading capacity and the correspondingstrain of RUHPC at Point B, respectively.

The mechanical analytical model of different stages of HSH-RUHPC is shown in Fig. 11. At Stage I such as Point A in Fig. 11(a), HSH-UHPC and steel rebar were both in the elastic stages,where HSH-UHPC was the main contributor to the total loadingcapacity. At Stage II such as Point B in Fig. 11(b), HSH-UHPC wasin the strain hardening stage while the steel rebar was still in theelastic stage. During this stage, the loading capacity provided byHSH-UHPC was almost stable, the contribution of steel rebar tothe total loading capacity increased with the increase of the tensilestrain and finally became the main contributor to the total loadingcapacity at point B. At Stage III, HSH-UHPC and steel rebar wereboth in the plastic stages, where the total loading capacity keptconstant at the beginning and decreased later due to the strainsoftening of HSH-UHPC.

During Stage I and Stage II, the tensile deformation of HSH-UHPC was consistent with that of steel rebar and the strain hard-ening behavior of HSH-UHPC ensured a globally uniform stress dis-tribution of HSH-RUHPC.

3.3. Tensile performance of SS-RUHPCs

The tensile load-strain curves of SS-RUHPCs are given in Fig. 12.A typical specimen of SS-RUHPC was taken for example as shownin Fig. 12(c)-(d). Similar to HSH-RUHPCs, the tensile load-straincurves of SS-RUHPCs can also be divided into stage I, stage II andstage III. The first two stages showed a horizontal transition asmarked in Fig. 12(c)-(d), which may be related to the strain soften-ing behavior of SS-UHPC. The corresponding strain at the end ofstage II was higher than the yield strain ey of HRB400 steel rebar(around 2500le) and the difference between these two strainswas about 1000le for SS-RUHPC-I and 260le for SS-RUHPC-II. Itwas supposed that there was slip generated between SS-UHPCand steel rebar before the yielding of steel rebar. For HSH-RUHPC-I and HSH-RUHPC-II, the total tensile loading capacity atthe end of stage I was 30 kN, 35 kN, respectively while that atthe end of stage II was 110 kN, 166 kN, respectively.

The schematic illustration of tensile load-strain curve SS-RUHPCis shown in Fig. 13. Point A refers to the end of the Stage I, whereUHPC is supposed to reach the elastic limit. Fte and ete are definedas the tensile loading capacity and the corresponding strain of


RUHPC at Point A, respectively. Point B refers to the end of the hor-izontal transition at the initial stage of Stage II. Point C refers to thepoint corresponding to the yield strain ey of steel rebar at Stage II.Point D refers to the end of the Stage II, Ftep and etep are defined asthe tensile loading capacity and the corresponding strain of RUHPCat Point D, respectively.

(a) Stage I (the elastic sta

(b) Stage II (the elastic-pl

Fig. 11. Mechanical analytica

The mechanical analytical model of different stages is shown inFig. 14. At Stage I such as Point A in Fig. 14(a), SS-UHPC and steelrebar were both in the elastic stage, during which SS-UHPC wasthe main contributor to the total loading capacity.

From Point A to Point B of Stage II as shown in Fig. 14(a)and (b), SS-UHPC suffered from strain softening and the first

ge) at point A in Fig.10

astic stage) at point B in Fig.10

l model of HSH-RUHPC.


macro-crack opening gradually and its loading capacity reducedaccordingly. While at the same time, the contribution providedby steel rebar at crack position kept increasing due to its elastic

(a) Three specimens of SS-RUHPC-I

(b) Three specimens of SS-RUHPC-II

(c) Comparison of steel rebar and SS-RUHPC-I

(d) Comparison of steel rebar and SS-RUHPC-II

Fig. 12. Tensile load-strain curves of SS-RUHPCs.

behavior. Therefore, the total loading capacity remainedconstant.

From Point B to Point C as shown in Fig. 14(b) and (c), thestrain softening effect of SS-UHPC reduced and the loading capac-ity of SS-UHPC decreased slowly, while the loading capacity ofsteel rebar was increasing linearly. Therefore, other macro-cracks generated and the steel rebar gradually became the maincontributor to the total loading capacity. Finally several macro-cracks were formed at Point C corresponding to the stress concen-tration points in Fig. 14(c), where the steel rebar at crack posi-tions yielded and the steel rebar at uncracking regions was stillin the elastic stage. Hence, the total loading capacity of SS-RUHPC was able to increase until Point D in Fig. 14(d), wheresome parts of the steel rebar at cracking positions entered thestrain hardening stage. In the entire process, the steel rebar chan-ged from total elastic state to partial yielding and finally to partialstrain hardening.

3.4. Analysis of tension stiffening effect of RUHPCs

The total tensile loading capacity of RUHPC is made up of steelrebar and UHPC [27]. By deducting the bare steel rebar responsefrom the tensile load-strain curve, the contributions of UHPC inthe RUHPCs, often called the tension stiffening effect [8,9], areobtained and compared with UHPC in the direct tensile test asshown in Fig. 15.

As shown in Fig. 15(a), the elastic tensile strength fUte of HSH-UHPC in HSH-RUHPC-I and HSH-RUHPC-II were about 5 MPa,4.3 MPa, respectively, which were 69.4%, 59.7% of that in the directtensile test of HSH-UHPC, while the ultimate tensile strength ofHSH-UHPC in HSH-RUHPC-I and HSH-RUHPC-II were about7.8 MPa, 5.5 MPa, respectively, which were 68.4%, 48.2% of thatin direct tensile test. As shown in Fig. 15(b), the elastic tensilestrength fUte of SS-UHPC in SS-RUHPC-I and SS-RUHPC-II wereabout 6.5 MPa, 4.5 MPa, respectively, which were 61.9%, 42.9% ofthat in direct tensile test, while the residual tensile strength ofSS-UHPC in SS-RUHPC-I and SS-RUHPC-II at a corresponding strainof 2000le were about 4.5 MPa, 3.7 MPa, respectively, which was56.2%, 46.3% of that in direct tensile test.

It can be found that the tensile strength of UHPC in RUHPCs waslower than that in the direct tensile test as shown in Fig. 15.Besides, the higher the steel ratio is, the more significant the reduc-tion of the tensile strength of UHPC is. The localized stress concen-tration of UHPC around the ribs and the reduction of the tensilestrength of UHPC in RUHPCs were most likely due to the interac-

Fig. 13. Schematic illustration of tensile load-strain curve of SS-RUHPC.


tion between UHPC and the ribs of steel rebar as shown in Fig. 16.The evidence may be provided by the comparison of AE source dis-tribution maps of HSH-UHPC in Fig. 19 and HSH-RUHPCs in Fig. 20

(a) Stage I (the elastic stag

(b) Stage II (the elastic-plastic

Fig. 14. Mechanical analytic

provided in the next section. A more spread-out distribution of AEsources was observed throughout the HSH-RUHPCs compared withHSH-UHPC.

e) at point A in Fig.13

stage) at point B in Fig.13

al model of SS-RUHPC.

(c) Stage II (the elastic-plastic stage) at point C in Fig.13

(d) Stage II (the elastic-plastic stage) at point D in Fig.13

Fig. 14 (continued)


(a) HSH-RUHPC

(b) SS-RUHPC

Fig. 15. Tension stiffening effect of RUHPCs.

Fig. 16. Interaction between UHPC and steel rebar.

Fig. 17. Maximum crack width-tensile strain curves of HSH-UHPC and HSH-RUHPCs.


4. Tensile damage evolution mechanism of RUHPCs based on AEanalysis method

4.1. Tensile damage evolution of HSH-RUHPCs

4.1.1. Crack width-tensile strain curves of HSH-RUHPCsThe 0.05 mm crack width is usually critical for concrete perme-

ability. In this paper, a micro-crack is defined as a crack invisible tothe naked eyes (less than 0.05 mm), while a macro-crack is definedas a crack visible to the naked eyes (more than 0.05 mm) [28].

Crack width-tensile strain curves of HSH-UHPC and HSH-RUHPCs are shown in Fig. 17. As shown in Fig. 17, for HSH-UHPCand HSH-RUHPCs, their micro-crack widths at the yield strain eyof steel rebar (around 2500le) were all below 0.03 mm. This phe-nomenon suggested that HSH-UHPC and HSH-RUHPCs bothdemonstrated a good crack width controlling ability due to themultiple micro-cracks opening.

To present the crack opening process during the strain harden-ing stage, photos of a HSH-RUHPC-II specimen as an example weretaken at different tensile strains and given in Fig. 18. As shown inFig. 18, the first detectable crack (bigger than 0.01 mm) generatedat the strain of 667le, which was much higher than the elastic ten-sile strain eUte of HSH-UHPC (around 200le). It is supposed thatnon-detectable micro defects (or cracks) smaller than 0.01 mmgenerated between 200le and 667le. When the tensile strainincreased to 3000le, the width of detectable crack slightlyincreased to 0.03 mm and the number of the detectable crackswas only four. Therefore, more non-detectable micro defects werepresumed to continuously generate to balance the total corre-sponding tensile deformation (0.45 mm) of the HSH-RUHPC-IIspecimen at the strain of 3000le, given a gauge length of150 mm. This phenomenon can be well explained by AE analysismethod in the following section.

4.1.2. Damage evolution process of HSH-RUHPCs using AE analysismethod

AE analysis method can effectively detect the internal damagesof UHPC under direct loading from the microcosmic point of view.AE source distribution maps of a typical specimen of HSH-UHPCand HSH-RUHPCs are shown in Fig. 19 and Fig. 20, respectively.The values in brackets are the accumulated numbers of AE sourcesthat can be registered by AE analysis system.

The damage evolution mechanism of HSH-UHPC and HSH-RUHPCs is similar as shown in Figs. 19 and 20. It can be seen thatthere were few AE sources generated during the elastic stage ofHSH-UHPC and the stage I of HSH-RUHPCs. When the tensile strainreached 1000le, the accumulated numbers of AE sources were 47,152 and 132 in HSH-UHPC, HSH-RUHPC-I and HSH-RUHPC-II,respectively. These AE sources were distributed homogeneously,reflecting that multiple micro-cracks (or defects) were distributedall over the specimen, which indicated a globally uniform stressstate [29]. AE analysis method provides strong evidence to thenon-detectable defects (lower than 0.01 mm) and makes a clearexplanation to the damage evolution process of the HSH-UHPCand HSH-RUHPCs at the micro level.

4.2. Tensile damage evolution of SS-RUHPCs

4.2.1. Crack width-tensile strain curves of SS-RUHPCsCrack width-tensile strain curves of SS-UHPC and SS-RUHPCs

are illustrated in Fig. 21. As shown in Fig. 21, steel rebar improvedthe crack width controlling ability of SS-UHPC significantly. Thecrack width of SS-UHPC at a strain of 2500le was 0.36 mm, whilethe crack width of SS-RUHPC-I and SS-RUHPC-II at a strain of

Fig. 18. Crack photos of HSH-RUHPC-II at different strains.

Fig. 19. AE source distribution maps of HSH-UHPC.


2500le was about 0.1 mm, which was almost 3–4 times of that ofHSH-RUHPCs.

Photos of a SS-RUHPC-II specimen as an example were taken atdifferent tensile strains and given in Fig. 22. As shown in Fig. 22,the SS-RUHPC-II specimen has maximum crack width of 0.02 mm

at a tensile strain of 300le and has maximum crack width of0.06 mm at a tensile strain of 2000le. By contrast, the HSH-RUHPC-II specimen can withstand a tensile strain up to 2000leto control the maximum crack width lower than 0.02 mm, whichmeans a much better crack width controlling ability.

(a) HSH-RUHPC-I

(b) HSH-RUHPC-II

Fig. 20. AE source distribution maps of HSH-RUHPCs.

Fig. 21. Maximum crack width-tensile strain curves of SS-UHPC and SS-RUHPCs.


4.2.2. Damage evolution process of SS-RUHPCs using AE analysismethod

AE source distribution maps of a typical specimen of SS-UHPCand SS-RUHPCs are shown in Fig. 23 and Fig. 24, respectively. ForSS-UHPC and SS-RUHPCs, there were few AE sources during theelastic stage of SS-UHPC and the stage I of SS-RUHPCs. At the endof elastic stage for SS-UHPC and HSH-UHPC, as shown in Figs. 23and 19, the accumulated numbers of AE sources were 64 and 0,respectively. At the end of stage I for SS-RUHPC-I, SS-RUHPC-II,HSH-RUHPC-I and HSH-RUHPC-II, as shown in Fig. 24(a), (b), (a)and (b), the accumulated numbers of AE sources were 34, 33, 3and 3, respectively. It shows that when the UHPC matrix cracked,HSH-UHPC and HSH-RUHPCs hardly had AE sources while SS-

UHPC and SS-RUHPCs showed a remarkable number of AE sources.These AE sources in SS-UHPC were supposed to generate by thedebonding of the fiber and UHPC matrix. Therefore, the steel fibersbridging the micro-cracks in HSH-UHPC may still have well bond-ing with UHPCmatrix and contribute to the increasing tensile load-ing capacity at the strain hardening stage, given an elongation ofthe steel fibers. By contrast, the steel fibers bridging the cracks inSS-UHPC may suffer from slippage and pull-out from the UHPCmatrix and result in a decrease in tensile loading capacity at thestrain softening stage.

With the tensile strain increasing, most AE sources in SS-UHPCand SS-RUHPCs were regularly distributed on the same plane sub-sequently. The location of these concentrated AE sources basicallyconcurred with the actual location of macro-cracks. Most AEsources of SS-UHPC specimen were regularly distributed on onesingle plane while those of SS-RUHPC specimens were finally dis-tributed on three planes, which meant the generation of threemacro-cracks.

It could be found that the damage was more concentrated in SS-UHPC and SS-RUHPC, and more evenly distributed in HSH-UHPCand HSH-RUHPC before 4000le. The reason was that SS-UHPCand SS-RUHPC immediately showed crack localization after elasticstage, while HSH-UHPC and HSH-RUHPC showed multiple micro-cracks with width less than 0.05 mm before 4000le.

4.3. Damage distribution regularity analysis of RUHPCs using AEanalysis method

4.3.1. Analysis of AE sources distribution of RUHPCsTo deeply understand the distribution of AE sources along the

height of RUHPC specimens, ten equal ranges were divided along

Fig. 22. Crack photos of SS-RUHPC-II at different strains.

Fig. 23. AE source distribution maps of SS-UHPC.


the height of 500 mm to count the number of AE sources at differ-ent tensile strains (1000le, 2000le, 2500le and 4000le, respec-tively). The results are shown in Tables 5–8 according to Figs. 20and 24. Point C, point D, point E and point F are in accordance withthose in Figs. 20 and 24. For each point of these four points, themaximum number of AE sources and its corresponding maximumratio of ten equal ranges are in bold font as shown in Tables 5–8.

As shown in Tables 5 and 6, the maximum ratio of total AEsources for each range along specimen height at different strains

(Point C, point D, point E and point F) was 20.39% for HSH-RUHPC-I and 20.45% for HSH-RUHPC-II, respectively. It’s interest-ing to find that the range with maximum number of AE sourceswas changing, such as Range 3 at point C, Range 7 at point D andRange 8 at point F for HSH-RUHPC-II.

Tables 7 and 8 shows that the maximum ratio of total AEsources for each range along specimen height at different strains(Point C, point D, point E and point F) was 58.25% for SS-RUHPC-Iand 45.12% for SS-RUHPC-II, respectively. Particularly, the range

(a) SS-RUHPC-I

(b) SS-RUHPC-II

Fig. 24. AE source distribution maps of SS-RUHPCs.

Table 5Number of AE sources for HSH-RUHPC-I.

RangeCode

Range alongspecimen height/mm

Point C(1000le) Point D(2000le) Point E(2500le) Point F(4000le)

Number ofAE sources

Ratio of totalAE sources/%

Number ofAE sources


Number ofAE sources


Number ofAE sources


1 [0,50] 8 5.26 10 3.85 11 3.78 17 4.502 [50,100] 7 4.61 15 5.77 18 6.19 35 9.263 [100,150] 31 20.39 41 15.77 42 14.43 49 12.964 [150,200] 18 11.84 28 10.77 33 11.34 38 10.055 [200,250] 9 5.92 21 8.08 24 8.25 31 8.206 [250,300] 19 12.50 36 13.85 43 14.78 50 13.237 [300,350] 31 20.39 45 17.31 45 15.46 71 18.788 [350,400] 18 11.84 47 18.08 50 17.18 54 14.299 [400,450] 6 3.95 12 4.62 17 5.84 21 5.5610 [450,500] 5 3.40 5 1.92 8 2.75 12 3.17Total [0,500] 152 100 260 100 291 100 378 100

Table 6Number of AE sources for HSH-RUHPC-II.

RangeCode



Number ofAE sources


Number ofAE sources


Number ofAE sources


Number ofAE sources


1 [0,50] 5 3.79 7 3.27 10 3.92 12 3.392 [50,100] 7 5.30 19 8.88 21 8.24 32 9.043 [100,150] 27 20.45 34 15.89 34 13.3 43 12.154 [150,200] 9 6.82 12 5.61 12 4.71 17 4.805 [200,250] 14 10.61 16 7.48 16 6.27 24 6.786 [250,300] 17 12.88 32 14.95 34 13.33 41 11.587 [300,350] 23 17.42 42 19.63 48 18.82 65 18.368 [350,400] 15 11.36 33 15.42 46 18.04 66 18.649 [400,450] 7 5.30 9 4.21 17 6.67 36 10.1710 [450,500] 8 6.06 10 4.67 17 6.67 18 5.08Total [0,500] 132 100 214 100 255 100 354 100


Table 7Number of AE sources for SS-RUHPC-I.

RangeCode



Number ofAE sources


Number ofAE sources


Number ofAE sources


Number ofAE sources


1 [0,50] 2 1.94 11 5.58 11 4.30 11 3.772 [50,100] 2 1.94 7 3.55 7 2.73 7 2.403 [100,150] 6 5.83 13 6.60 19 7.42 19 6.514 [150,200] 4 3.88 36 18.27 41 16.02 41 14.045 [200,250] 4 3.88 4 2.03 4 1.56 4 1. 376 [250,300] 13 12.62 13 6.60 13 5.08 13 4.457 [300,350] 67 58.25 75 38.07 115 44.92 151 51.718 [350,400] 7 6.80 25 12.69 33 12.89 33 11.309 [400,450] 2 1.94 10 5.08 10 3.91 10 3.4210 [450,500] 3 2.91 3 1.52 3 1.17 3 1.03Total [0,500] 103 100 197 100 256 100 292 100

Table 8Number of AE sources for SS-RUHPC-II.

RangeCode



Number ofAE sources


Number ofAE sources


Number ofAE sources


Number ofAE sources


1 [0,50] 4 4.88 4 2.61 4 1.96 4 1.572 [50,100] 3 3.66 3 1.96 3 1.47 3 1.183 [100,150] 37 45.12 58 37.91 91 44.61 100 39.224 [150,200] 0 0 0 0 0 0 7 2.755 [200,250] 4 4.88 4 2.61 4 1.96 4 1. 576 [250,300] 2 2.44 44 28.76 50 24.51 50 19.617 [300,350] 0 0 7 4.58 9 4.41 9 3.538 [350,400] 31 37.80 32 20.92 40 19.61 75 29.419 [400,450] 1 1.22 1 0.65 3 1.47 3 1.1810 [450,500] 0 0 0 0 0 0 0 0Total [0,500] 82 100 153 100 204 100 255 100


with maximum number of AE sources was constant, that is, Range7 for SS-RUHPC-I and Range 3 for SS-RUHPC-II, corresponding tothe localized crack.

AE source number distribution is plotted in Fig. 25 to furtheranalyze the distribution regularity of AE sources. It shows thatfor HSH-RUHPCs, the difference of AE source number at each rangewas small and the number of AE sources at each range before4000lewas basically below 60. It reflects that the internal damagewas relatively uniform along the specimen height before 4000ledue to collaborative working between steel rebar and HSH-UHPC.

However, in terms of SS-RUHPCs, the fluctuation of AE sourcenumber was significant and the maximum number of AE sourcesof each range after 2000le was more than 60. Both SS-RUHPC-Iand SS-RUHPC-II had several peaks of AE source number, for exam-ple, Range 3, Range 6 and Range 8 for SS-RUHPC-II which were cor-responded to three macro-cracks. The number of AE sources at theconcentrated ranges was several times of that between adjacentranges, which represented the damage concentration. The reasonof damage concentration was stress redistribution between theSS-UHPC matrix and steel rebar, leading to a sudden increase ofthe steel rebar strain and the crack width at the crack positions.

4.3.2. AE sources distribution nonuniformity based on Lorenz curveand Gini index

To better evaluate the distribution nonuniformity of AE sourcesalong the height of RUHPC specimens, Lorenz curve and Gini indexwere selected [19,20]. The proposed Lorenz curve of AE sources is adynamic mirror of the nonuniform distribution along specimenheight. The data samples were chosen from Tables 5–8, includingrange code and ratio of total AE sources.

The data samples were sorted in descending order according toratio of total AE sources. Thus the Lorenz curves of four kinds ofRUHPCs are drawn in Fig. 26, where the vertical coordinate is theaccumulated percentage of AE sources and the horizontal coordi-nate is the accumulated range number. More detailed informationabout drawing Lorenz curve can be found in the reference [30]. Thediagonal line means idealized even distribution while the level linemeans idealized concentrated distribution. The more convex thecurve is, the more nonuniform the distribution is. It’s obvious thatthe Lorenz curve of HSH-RUHPCs was less convex than that of SS-RUHPCs, indicating that the distribution of the AE sources in HSH-RUHPCs was more uniform than that of SS-RUHPCs.

In order to give an overall evaluation of such distributionnonuniform, the Gini index I is defined in Eq. (1) as a quantitativemetric between 0 and 1. The more convex curve leads to the largerGini index I, implying the more nonuniform distribution.

I ¼ A� RM � R ð1Þ

Parameter A is the area between the Lorenz curve and the hor-izontal coordinate, parameter R is the area between the idealizedeven distribution curve and the horizontal coordinate, parameterM is the area between the idealized concentrated distributioncurve and the horizontal coordinate. Parameter A can be integratedby Matlab software.

Gini index I at different strains was calculated according to theLorenz curve and the results are listed in Fig. 27. It shows that theGini index I of HSH-RUHPC was lower than 0.33 and Gini index I ofSS-RUHPC was higher than 0.49, respectively, showing that the AEsource distribution along specimen height for SS-RUHPC was moreconcentrated. With the increase of the tensile strain during 1000-

Fig. 25. AE source number distribution of RUHPCs.


4000le, Gini index I of HSH-RUHPC was almost stable due to therandom and even distribution of multiple-micro-cracks, while Giniindex I of SS-RUHPC decreased firstly due to the development ofseveral-macro-cracks and then increased slightly due to theappearance of the localization of the main crack.

The difference in Lorenz curve and Gini index I between HSH-RUHPCs and SS-RUHPCs was remarkable. As a result, Lorenz curveand Gini index I is an effective and visual method to characterizethe nonuniformity distribution of the internal damages of RUHPCsusing AE analysis method.

5. Conclusions

In this paper, the direct tensile test accompanied with crackwidth detection and AE source locating was conducted to investi-gate the tensile mechanical mechanism as well as the tensile dam-age evolution mechanism of RUHPC. Main conclusions are given asfollows.

(1) HSH-UHPC used herein had the elastic tensile strength rang-ing from 9.3 MPa to 10.3 MPa at a corresponding strain ofabout 200le, and ultimate tensile strength ranging from

11.2 MPa to 12 MPa at ultimate strain of about 4000–5000le. SS-UHPC used herein had elastic tensile strengthranging from 10.1 MPa to 10.6 MPa at a corresponding strainof about 200le, and the residual tensile strength rangingfrom 7.1 MPa to 9.1 MPa at a corresponding strain of2000le.

(2) During Stage I (the elastic stage) and Stage II (the elastic-plastic stage), HSH-RUHPC had a globally uniform stresscontribution due to the compatible deformation betweenHSH-UHPC and steel rebar while the steel rebar in SS-RUHPC changed from total elastic state to partial yieldingand finally to partial strain hardening.

(3) The interaction between the UHPC and the ribs of steel barmay cause the localized stress concentration of UHPCaround the ribs, resulting in the reduction of the tensilestrength of UHPC in RUHPC. Besides, the higher the steelratio is, the more significant the reduction in the tensilestrength of UHPC is.

(4) HSH-RUHPC showed a multiple-micro-cracking mode andits crack width was about 0.03 mm at the tensile strain of2500le. SS-RUHPC displayed a several-macro-crackingmode and its crack width was around 0.1 mm at the tensile

Fig. 26. AE source distribution of RUHPCs.

Fig. 27. Gini index I of AE source distribution for RUHPCs.


strain of 2500le. The effect of increasing reinforcement ratioon the improvement of crack width controlling ability for SS-RUHPC was more significant than that of HSH-RUHPC.

(5) Based on AE analysis method, HSH-RUHPC exhibited ahomogeneous damage distribution before steel yieldingdue to its multiple-micro-cracking mode while SS-RUHPCshowed the damage concentration at the crack positiondue to the stress redistribution caused by the strain soften-ing of SS-UHPC. AE analysis method provides strong evi-dence to the non-detectable defects (lower than 0.01 mm)and makes a clear explanation to the damage evolution pro-cess of RUHPCs at the micro level.

(6) Gini index Iwas proved to be an effective parameter to char-acterize the nonuniformity distribution of the internal dam-ages of RUHPCs using AE analysis method. Gini index ofHSH-RUHPC was lower than 0.33 and that of SS-RUHPCwas higher than 0.49.

Declaration of Competing Interest

We declare that we have no financial and personal relationshipswith other people or organizations that can inappropriately


influence our work, there is no professional or other personal inter-est of any nature or kind in any product, service and/or companythat could be construed as influencing the position presented in,or the review of, the manuscript entitled, ‘‘Mechanical and damagemechanisms of reinforced ultra high performance concrete undertensile loading”.

Acknowledgments

This work was supported by the Science and TechnologyDepartment of Zhejiang Province [grant number 2019-GXKY-01],the National Nature Science Foundation of China [grant number51609172] and the Shanghai Municipal Science and TechnologyProject [grant number 17DZ1204200]. The financial supports aregreatly appreciated.

References

[1] M.A. Khan, Accelerated bridge construction: best practices and techniques,2015.

[2] S. Aaleti, B. Petersen, S. Sritharan, Design Guide for Precast UHPC Waffle DeckPanel System, including Connections, Technical report, Federal HighwayAdministration, 2013.

[3] D.Y. Yoo, N. Banthia, Mechanical and structural behaviors of ultra-high-performance fiber-reinforced concrete subjected to impact and blast, Constr.Build. Mater. 149 (2017) 416–431.

[4] D.Y. Yoo, N. Banthia, Mechanical properties of ultra-high-performance fiber-reinforced concrete: a review, Cem. Concr. Compos. 73 (2016) 267–280.

[5] J.Y. Wang, J.Y. Guo, Damage investigation of ultra high performance concreteunder direct tensile test using acoustic emission techniques, Cem. Concr.Compos. 88 (2018) 17–28.

[6] J. Jungwirth, A. Muttoni, Structural behavior of tension members in UHPC, in:M. Schmidt, E. Fehling, C. Geisenhanslüke (Eds.), Proceedings of theInternational Symposium on Ultra High Performance Concrete. Kassel,Germany, 2004, pp. 533–544.

[7] T. Makita, E. Brühwiler, Tensile fatigue behaviour of ultra-high performancefibre reinforced concrete combined with steel rebars (R-UHPFRC), Int. J.Fatigue. 59 (2014) 145–152.

[8] S.B. Kang, K.H. Tan, X.H. Zhou, Bo Yang, Influence of reinforcement ratio ontension stiffening of reinforced engineered cementitious composites, Eng.Struct. 141 (2017) 251–262.

[9] D.M. Moreno, W. Trono, G. Jen, S.L. Billington, Tension stiffening in reinforcedhigh performance fiber reinforced cement-based composites, Cem. Concr.Compos. 50 (2014) 36–46.

[10] L. Lárusson, G. Fischer, J. Jönsson, Mechanical interaction between concreteand structural reinforcement in the tension stiffening process, in: G.J. Parra-Montesinos, H.W. Reinhardt, A.E. Naaman (Eds.), Proceedings of the SixthInternational RILEM Conference on High Performance Fiber Reinforced CementComposites (HPFRCC6), Netherlands, 2012, pp. 247–254.

[11] D.M. Moreno, W. Trono, G. Jen, C. Ostertag, S.L. Billington, Tension-stiffening inreinforced high performance fiber-reinforced cement-based composites under

direct tension, in: G.J. Parra-Montesinos, H.W. Reinhardt, A.E. Naaman (Eds.),Proceedings of the Sixth International RILEM Conference on High PerformanceFiber Reinforced Cement Composites (HPFRCC6), Netherlands, 2012, pp. 263–270.

[12] A. Jansson, M. Flansbjer, I. Löfgren, K. Lundgren, K. Gylltoft, Experimentalinvestigation of surface crack initiation, propagation and tension stiffening inself-compacting steel–fibre-reinforced concrete, Mater. Struct. 45 (2012)1127–1143.

[13] S. Huguet, N. Godin, R. Gaertner, L. Salmon, D. Villard, Use of acoustic emissionto identify damage modes in glass fibre reinforced polyester, Compos. Sci.Technol. 62 (2002) 1433–1444.

[14] Q.L. Dai, K. Ng, J. Zhou, E.L. Kreiger, T.M. Ahlborn, Damage investigation ofsingle-edge notched beam tests with normal strength concrete and ultra highperformance concrete specimens using acoustic emission techniques,Construct. Build. Mater. 31 (6) (2012) 231–242.

[15] A. Carpinteri, J. Xu, G. Lacidogna, A. Manuello, Reliable onset timedetermination and source location of acoustic emissions in concretestructures, Cem. Concr. Compos. 4 (34) (2012) 529–537.

[16] Q.H. Han, J. Xu, A. Carpinteri, G. Lacidogna, Localization of acoustic emissionsources in structural health monitoring of masonry bridge, Struct. Control.Health. Monit. 22 (2015) 314–329.

[17] J. Xu, Z.W. Fu, Q.H. Han, G. Lacidogna, A. Carpinteri, Micro-cracking monitoringand fracture evaluation for crumb rubber concrete based on acoustic emissiontechniques, Struct. Control. Health. Monit. 17 (2017) 946–958.

[18] J. Xu, S.R. Shu, Q.H. Han, C. Liu, Experimental research on bond behavior ofreinforced recycled aggregate concrete based on the acoustic emissiontechnique, Construct. Build. Mater. 191 (2018) 1230–1241.

[19] M.O. Lorenz, Methods of measuring the concentration of wealth, Publ. Am.Stat. Assoc. 70 (9) (1905) 209–219.

[20] C. Gini, Measurement of inequality and income, Econom. J. 31 (1921) 124–126.[21] A. Radice, Use of the Lorenz Curve to quantify statistical nonuniformity of

sediment transport rate, J. Hydraul. Eng. 4 (135) (2009) 320–326.[22] D.Y. Yoo, S.T. Kang, Y.S. Yoon, Effect of fiber length and placement method on

flexural behavior, tension-softening curve, and fiber distributioncharacteristics of UHPFRC, Constr. Build. Mater. (64) (2014) 67–81.

[23] S.J. Barnett, J.F. Lataste, T. Parry, S.G. Millard, M.N. Soutsos, Assessment of fibreorientation in ultra high performance fibre reinforced concrete and its effecton flexural strength, Mater. Struct. 7 (43) (2010) 1009–1023.

[24] D.Y. Yoo, N. Banthia, S.T. Kang, Y.S. Yoon, Effect of fiber orientation on the rate-dependent flexural behavior of ultra-high-performance fiber-reinforcedconcrete, Compos. Struct. (157) (2016) 62–70.

[25] Standardization Administration of the People’s Republic of China (SAC), GB/T31387-2015 Reactive power concrete, Standards Press of China, Beijing, 2015.

[26] ASTM International, ASTM E976-99 Standard Guide for Determining theReproducibility of Acoustic Emission Sensor Response, West Conshohocken,PA, 2000.

[27] C. Oesterlee, Structural response of reinforced UHPFRC and RC compositemembers, Doctoral thesis No. 4848, Ecole Polytechnique Fédérale de Lausanne(EPFL), 2010, http://infoscience.epfl.ch/record/150553.

[28] T. Makita, E. Brühwiler, Tensile fatigue behaviour of ultra-high performancefibre reinforced concrete (UHPFRC), Mater. Struct. 47 (2014) 475–491.

[29] F. Li, Z. Li, Acoustic emission monitoring of fracture of fiber-reinforcedconcrete in tension, ACI Mater. J. 97 (6) (2000) 629–636.

[30] Y.B. Chen, H.W. Tan, B. Umberto, A data-driven approach for building energybenchmarking using the Lorenz curve, Energ. Build. 169 (2018) 319–331.

http://refhub.elsevier.com/S0950-0618(19)31835-5/h0015http://refhub.elsevier.com/S0950-0618(19)31835-5/h0015http://refhub.elsevier.com/S0950-0618(19)31835-5/h0015http://refhub.elsevier.com/S0950-0618(19)31835-5/h0020http://refhub.elsevier.com/S0950-0618(19)31835-5/h0020http://refhub.elsevier.com/S0950-0618(19)31835-5/h0025http://refhub.elsevier.com/S0950-0618(19)31835-5/h0025http://refhub.elsevier.com/S0950-0618(19)31835-5/h0025http://refhub.elsevier.com/S0950-0618(19)31835-5/h0030http://refhub.elsevier.com/S0950-0618(19)31835-5/h0030http://refhub.elsevier.com/S0950-0618(19)31835-5/h0030http://refhub.elsevier.com/S0950-0618(19)31835-5/h0030http://refhub.elsevier.com/S0950-0618(19)31835-5/h0030http://refhub.elsevier.com/S0950-0618(19)31835-5/h0030http://refhub.elsevier.com/S0950-0618(19)31835-5/h0030http://refhub.elsevier.com/S0950-0618(19)31835-5/h0035http://refhub.elsevier.com/S0950-0618(19)31835-5/h0035http://refhub.elsevier.com/S0950-0618(19)31835-5/h0035http://refhub.elsevier.com/S0950-0618(19)31835-5/h0040http://refhub.elsevier.com/S0950-0618(19)31835-5/h0040http://refhub.elsevier.com/S0950-0618(19)31835-5/h0040http://refhub.elsevier.com/S0950-0618(19)31835-5/h0045http://refhub.elsevier.com/S0950-0618(19)31835-5/h0045http://refhub.elsevier.com/S0950-0618(19)31835-5/h0045http://refhub.elsevier.com/S0950-0618(19)31835-5/h0050http://refhub.elsevier.com/S0950-0618(19)31835-5/h0050http://refhub.elsevier.com/S0950-0618(19)31835-5/h0050http://refhub.elsevier.com/S0950-0618(19)31835-5/h0050http://refhub.elsevier.com/S0950-0618(19)31835-5/h0050http://refhub.elsevier.com/S0950-0618(19)31835-5/h0050http://refhub.elsevier.com/S0950-0618(19)31835-5/h0050http://refhub.elsevier.com/S0950-0618(19)31835-5/h0050http://refhub.elsevier.com/S0950-0618(19)31835-5/h0050http://refhub.elsevier.com/S0950-0618(19)31835-5/h0055http://refhub.elsevier.com/S0950-0618(19)31835-5/h0055http://refhub.elsevier.com/S0950-0618(19)31835-5/h0055http://refhub.elsevier.com/S0950-0618(19)31835-5/h0055http://refhub.elsevier.com/S0950-0618(19)31835-5/h0055http://refhub.elsevier.com/S0950-0618(19)31835-5/h0055http://refhub.elsevier.com/S0950-0618(19)31835-5/h0055http://refhub.elsevier.com/S0950-0618(19)31835-5/h0055http://refhub.elsevier.com/S0950-0618(19)31835-5/h0055http://refhub.elsevier.com/S0950-0618(19)31835-5/h0055http://refhub.elsevier.com/S0950-0618(19)31835-5/h0060http://refhub.elsevier.com/S0950-0618(19)31835-5/h0060http://refhub.elsevier.com/S0950-0618(19)31835-5/h0060http://refhub.elsevier.com/S0950-0618(19)31835-5/h0060http://refhub.elsevier.com/S0950-0618(19)31835-5/h0065http://refhub.elsevier.com/S0950-0618(19)31835-5/h0065http://refhub.elsevier.com/S0950-0618(19)31835-5/h0065http://refhub.elsevier.com/S0950-0618(19)31835-5/h0070http://refhub.elsevier.com/S0950-0618(19)31835-5/h0070http://refhub.elsevier.com/S0950-0618(19)31835-5/h0070http://refhub.elsevier.com/S0950-0618(19)31835-5/h0070http://refhub.elsevier.com/S0950-0618(19)31835-5/h0075http://refhub.elsevier.com/S0950-0618(19)31835-5/h0075http://refhub.elsevier.com/S0950-0618(19)31835-5/h0075http://refhub.elsevier.com/S0950-0618(19)31835-5/h0080http://refhub.elsevier.com/S0950-0618(19)31835-5/h0080http://refhub.elsevier.com/S0950-0618(19)31835-5/h0080http://refhub.elsevier.com/S0950-0618(19)31835-5/h0085http://refhub.elsevier.com/S0950-0618(19)31835-5/h0085http://refhub.elsevier.com/S0950-0618(19)31835-5/h0085http://refhub.elsevier.com/S0950-0618(19)31835-5/h0090http://refhub.elsevier.com/S0950-0618(19)31835-5/h0090http://refhub.elsevier.com/S0950-0618(19)31835-5/h0090http://refhub.elsevier.com/S0950-0618(19)31835-5/h0095http://refhub.elsevier.com/S0950-0618(19)31835-5/h0095http://refhub.elsevier.com/S0950-0618(19)31835-5/h0100http://refhub.elsevier.com/S0950-0618(19)31835-5/h0105http://refhub.elsevier.com/S0950-0618(19)31835-5/h0105http://refhub.elsevier.com/S0950-0618(19)31835-5/h0110http://refhub.elsevier.com/S0950-0618(19)31835-5/h0110http://refhub.elsevier.com/S0950-0618(19)31835-5/h0110http://refhub.elsevier.com/S0950-0618(19)31835-5/h0115http://refhub.elsevier.com/S0950-0618(19)31835-5/h0115http://refhub.elsevier.com/S0950-0618(19)31835-5/h0115http://refhub.elsevier.com/S0950-0618(19)31835-5/h0120http://refhub.elsevier.com/S0950-0618(19)31835-5/h0120http://refhub.elsevier.com/S0950-0618(19)31835-5/h0120http://infoscience.epfl.ch/record/150553http://refhub.elsevier.com/S0950-0618(19)31835-5/h0140http://refhub.elsevier.com/S0950-0618(19)31835-5/h0140http://refhub.elsevier.com/S0950-0618(19)31835-5/h0145http://refhub.elsevier.com/S0950-0618(19)31835-5/h0145http://refhub.elsevier.com/S0950-0618(19)31835-5/h0150http://refhub.elsevier.com/S0950-0618(19)31835-5/h0150

Mechanical and damage mechanisms of reinforced ultra high performance concrete under tensile loading1 Introduction2 Experimental program2.1 UHPC materials2.2 Steel rebar2.3 Test methods2.3.1 Test method for direct tensile test2.3.2 Test method for crack width detection2.3.3 Test method for AE source locating

3 Tensile mechanical mechanism of RUHPCs3.1 Tensile stress-strain curves of HSH-UHPC and SS-UHPC3.2 Tensile performance of HSH-RUHPCs3.3 Tensile performance of SS-RUHPCs3.4 Analysis of tension stiffening effect of RUHPCs

4 Tensile damage evolution mechanism of RUHPCs based on AE analysis method4.1 Tensile damage evolution of HSH-RUHPCs4.1.1 Crack width-tensile strain curves of HSH-RUHPCs4.1.2 Damage evolution process of HSH-RUHPCs using AE analysis method

4.2 Tensile damage evolution of SS-RUHPCs4.2.1 Crack width-tensile strain curves of SS-RUHPCs4.2.2 Damage evolution process of SS-RUHPCs using AE analysis method

4.3 Damage distribution regularity analysis of RUHPCs using AE analysis method4.3.1 Analysis of AE sources distribution of RUHPCs4.3.2 AE sources distribution nonuniformity based on Lorenz curve and Gini index

5 ConclusionsDeclaration of Competing InterestAcknowledgmentsReferences

Documents

Mechanical and damage mechanisms of reinforced ultra high ... · erated bridge construction (ABC) methods using prefabricated bridge elements [1]. Previous studies have shown that