Early age strains and self-stresses of expansive concrete members under uniaxial restraint conditions

Construction and Building Materials 131 (2017) 39–49

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Early age strains and self-stresses of expansive concrete members under uniaxial restraint conditions V. Semianiuk a,1, V. Tur b,⇑, M.F. Herrador a, M. Paredes G. a a b

Department of Construction Technology, Universidade da Coruña, Campus de Elviña, s/n, A Coruña 15172, Spain Department of Concrete Technology and Building Materials, Brest State Technical University, Moskovskaya 267, s/n, Brest 224017, Belarus

h i g h l i g h t s
Design of high expansion energy capacity concrete able to prestress structures.
Cumulative force induced by restraint influences on restrained strains progress.
Cumulative force induced by restraint is considered as an externally applied load.
Proposed modified strains development model (MSDM) allows to estimate self-stress.
Validity of the proposed MSDM is confirmed by the experimental data.

a r t i c l e

i n f o

Article history: Received 6 May 2016 Received in revised form 28 October 2016 Accepted 1 November 2016

Keywords: Expansive concrete Self-stressed member Restrained strain Self-stress Estimation model

a b s t r a c t Models for restrained strains and self-stresses estimation based on the concepts of the conservation law of chemical energy and initial strains calculation in the expansive concrete members are considered, together with their advantages and disadvantages. A modified strains development model (MSDM) is proposed, based on the initial strains calculation approach and extended by taking into account cumulative force induced by the reinforcement as an additional restraint for development of expansion strains. Validity of the proposed MSDM is confirmed by experimental results obtained from tests on uniaxially symmetrically reinforced high expansion energy capacity concrete members. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Development of concrete technologies in the last decade has opened the door to the extended use of high performance concrete (HPC). Nevertheless this concrete isn’t deprived of a number of disadvantages such as relatively low tensile strength and amplified shrinkage. Shrinkage in combination with low tensile strength, mainly in early age, leads to the risk of cracking in reinforced concrete structures, and as a result, a reduction of its durability. The use of expansive concrete is an effective way to compensate and reduce internal forces induced by shrinkage and temperature variations. There are two kinds of expansive concrete: shrinkage⇑ Corresponding author. E-mail addresses: [email protected] (V. Semianiuk), victar.tur@gmail. com (V. Tur), [email protected] (M.F. Herrador), [email protected] (M. Paredes G.). 1 Present address: Department of Concrete Technology and Building Materials, Brest State Technical University, Moskovskaya 267, s/n, Brest 224017, Belarus. http://dx.doi.org/10.1016/j.conbuildmat.2016.11.008 0950-0618/Ó 2016 Elsevier Ltd. All rights reserved.

compensating concrete (with low expansion energy capacity) and self-stressing concrete (with high expansion energy capacity). Application of self-stressing concrete not only permits to compensate shrinkage but also introduces so-called chemical prestressing of the structure. For this reason, a new wave of interest has overcome the field of the expansive concrete investigation and practical usage [1,2]. For the purpose of the self-stressed structures practical use, design models for the restrained expansion strains and self-stress values estimation are required. It should be noted that no recent codes include methods for self-stressed structure design. Only a limited number of guides, for example [3], have a chapter devoted to this concern. Even so, models for the estimation of restrained strains and self-stresses in expansive concrete at early age are intensively developed [4–8]. In general, these models are based on one of two basic concepts: conservation law of chemical energy or initial strains calculation. Moreover, a joint model based on both concepts and called CP method has been proposed [8].

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In this paper, a short review and brief analysis of the models based on these concepts is presented. Taking into account advantages and disadvantages of these models, a modified strains development model (MSDM) was formulated and verified on the experimental data from the testing on the expansion stage of uniaxially symmetrically reinforced expansive concrete members.

represents influence of the cross sectional reinforcement ratio ql and is calculated by the following formula:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1:57  ql kq ¼ 0:0057 þ ql

ð1aÞ

2. Models for analytical prediction of the restrained strains and self-stresses in expansive concrete members

ke: factor that represents influence of the reinforcement eccentricity, es (distance between centroids of the longitudinal reinforcement and concrete cross section), and is calculated by the following formula:

2.1. Models based on the conservation law of chemical energy

ke ¼ 1  c1 

One research line, developed mainly in Japan, is based on the concept of chemical energy conservation law for self-stresses prediction in expansive concrete members with different types of restraint [4,5]. This concept is based on the assumption that the work quantity U CE that expansive concrete performs against restraint per unit volume, is a constant value regardless of the degree of restraint [4] and this work quantity should be established in «reference» restraint conditions (ql = 1%, Es = 200 GPa). It is noticeable that this fundamental statement had already been formulated and described at the beginning of 1970s [9]. The semi-empirical multiplicative model based on the proposed concept for self-stresses estimation under different restraint ratios and restraint arrangements was developed and included in standards [3]. A distinctive feature of this model is the assumption of the self-stresses uniform distribution in the cross section (see Fig. 1b) of the expansive concrete member against the background of the linear strains distribution (see Fig. 1a). For a given restraint ratio and restraint arrangement in the cross section, self-stress design value, rCE , is calculated in accordance with the next equation from TCP Code [3]:

where, c1 : empirical factor that is equal to 1.26. ds : cross section effective depth. kw: factor that takes into account influence of the expansive concrete initial compressive strength at the beginning of moisture curing – f CE;k0 and is calculated by the following formula:

rCE ¼ f CE;d  ks  kq  ke  kw  k0

ð1Þ

where, f CE;d : self-stressing grade of the expansive concrete [10], and is defined as a value of the compressive stress in the prismatic specimen under uniaxial symmetrical restraint with stiffness equal to 1% (ql) of steel cross sectional reinforcement ratio (Es = 200 GPa) at the concrete expansion stabilization; ks: factor that is equal to 1.0; 1.2; 1.5 for uniaxial, biaxial and triaxial reinforcement arrangement in the concrete member respectively; kq: factor that

es ds

ð1bÞ

a

kw ¼ ð0:1  f CE;k0 Þ

ð1cÞ

where, a: empirical factor that is equal to 0.797. k0: factor that takes into account self-stressed member curing conditions on the stage of the concrete expansion and takes values from 0.18 (sealed conditions) to 1.15 (immersion in water) in accordance with TCP Code [3]. The main advantage of this type of model consists in the possibility of predicting the self-stress value assuming a certain value of the expansive concrete self-stressing grade (fCE,d). Such an approach allows to assess the value of the self-stresses without consideration of free expansion strains, Young’s modulus development and a creep function of the expansive concrete at early age. The assumption of uniform distribution of the self-stresses in the cross section of the member has got a limitation in practical use and contradicts in some cases experimental results [11], in particular, for the cases of the non-symmetrical single-layer reinforcement arrangement with a high value of eccentricity with respect to the centroid of the member cross section. For example, when all sectional reinforcement is arranged on the same depth, ds , with eccentricity, es , and ratio is equal to es =ds ¼ 0:5, it is formally necessary to accept that self-stresses are distributed uniformly in the cross section, but the value of these compressive stresses (in accordance with Eq. (1)) is 2.7 times lower than the value of the stresses in the symmetrically reinforced member (all other conditions being equal). At the same time for the case of the single-layer reinforcement

Fig. 1. Concrete strains and stresses distribution in the cross section of the self-stressed member ((a) – strains distribution in accordance with [3,4]; (b), (c) – self-stresses distribution in accordance with [3] and [4] respectively).

V. Semianiuk et al. / Construction and Building Materials 131 (2017) 39–49

arrangement it becomes impossible to estimate restrained expansion strains distribution through the cross sectional depth, even taking into account the validity of the plane cross section hypothesis on the concrete expansion stage. Based on the assumption of selfstresses uniform distribution in cross section [3], the resultant force of the cross sectional self-stresses is placed in the sectional centroid, but the misalignment of the resultant forces in concrete and reinforcement leads to the appearance of an unbalanced moment. In a general case, the value of the self-stresses should be determined from the resultant force in the reinforcing bar at the concrete expansion stabilization stage. Besides, the value of self-stresses is determined by the elastic strain produced in concrete during the expansion process. The cross sectional equilibrium conditions should be satisfied for the self-stressed member the same way they are in a traditional prestressed structure. Another estimation method [4] has been proposed based on the following hypotheses: (a) expansive strains are linearly distributed in the direction of cross sectional height (see Fig. 1a), and (b) the work quantity that expansive concrete performs against restraint per unit volume, is a constant value regardless of the degree of restraint.Equilibrium conditions for the cross section can be expressed:

8 k X > R > > r ðy ÞdA þ As;j  es;j  Es ¼ 0; > CE c c > < Ac j¼1

k > X R > > > As;j  es;j  Es  ys;j ¼ 0; > : Ac rCE ðyc Þ  yd Ac þ

ð2Þ

j¼1

or in the case of numerical integration:

8 n k X X > > > rCE;i  DAc;i þ As;j  es;j  Es ¼ 0; > > < i¼1 j¼1

n k > X X > > > rCE;i  DAc;i  yc;i þ As;j  es;j  Es  ys;j ¼ 0: > : i¼1

ð3Þ

j¼1

To find out of the solutions in the closed form, Eq. (3) should be completed with the following equations:

eCE;i ¼ eCE;b þ u  yc;i ;

rCE;i ¼

2  U CE

eCE;i

ð4Þ

:

ð5Þ

Eqs. (4) and (5) express hypotheses (a) and (b) from [4] respectively. In Eqs. (4) and (5): u: curvature on the concrete expansion stage that can be determined from the following equation:

u¼

eCE;u  eCE;b h

¼

eCE;d h

:

ð6Þ

UCE: work quantity that expansive concrete performs against standard steel restraint per unit volume [4]. Numerical studies on the self-stressed members with rectangular cross section for both cases of multiple-layer and single-layer reinforcement arrangement (with the total cross sectional reinforcement ratio maintained at the same level, ql = 1%, for all the considered cases) in accordance with the proposed estimation model [4] have been performed [12], showing that the estimation is adequate for the case of multiple-layer cross sectional reinforcement arrangement with low value of restraint eccentricity. For the opposite case (high value of the restraint eccentricity) estimation results are not accurate enough, as previously pointed out by previous studies [4]. At the same time it should be underlined that self-stresses calculation in accordance with Eq. (5) leads to the non-linearity of its distribution through the cross sectional depth (see Fig. 1c). But considering the self-stressed structure as an

41

eccentrically loaded member with compressive forces result of the restrained expansion does not lead to the above-mentioned situation. The same conclusion has been reached by other authors, but only for the case of the HSC with expansive additives as a result of its stiffer structure [6]. Internal forces redistribution on the concrete expansion stage takes place as a result of the inelastic concrete properties at early age. But the resultant force in the reinforcement is balanced only by the resultant of the concrete compressive stresses induced by its own elastic strains. Taking into account all the pointed problems in the frame of the models based on the conservation law of chemical energy [3–5], it could be appropriate to consider early age strains development models of the expanding composites in the conditions of the free expansion strains restriction. 2.2. Models based on the initial strains calculation concept and its development. Proposition of the theoretical background of the modified early age strains development model (MSDM) for concrete with high expansion energy capacity In the last years, models for the calculation of initial strains in expansive concrete based on the consideration of the free expansion (shrinkage) strains development history, together with creep and Young’s modulus development of the expansive concrete at early age, plus parameters of the restraint conditions, have been developed [6,7,13]. These models consider the expansion process on the elementary time intervals – Dti (see Fig. 2a). It is essential that the calculation procedure for restrained strains in all steps is the same as the one chosen for the first step (Dt1). In this article, the modified strains development model (MSDM) for the restrained expansion strains and self-stresses values estimation in the concrete with high expansion energy capacity under the uniaxial symmetrical finite stiffness restraint conditions is proposed. The main difference between this model and other previously developed [6,7,13] consists in taking into account in the basic equation (for the all time intervals Dti with exception of the first one) a cumulative force induced by the restraint that is considered as an external load applied to the cross section of the member (see Fig. 2b). For the proposed MSDM, the following assumptions were accepted: 1. Cross section equilibrium conditions are respected throughout the concrete expansion stage. 2. Incremental restrained expansion strain at the any i-th time interval is determined as an algebraic sum of the incremental free expansion, elastic and creep strains, plus expansive concrete additional strain produced by the cumulative force induced by the restraint at the any i-th time interval beginning. The cumulative force induced by the restraint at the end of the (i– 1)-th time interval is considered as an additional restraint for the development of free expansion strains at the i-th time interval. 3. Strain compatibility of the expansive concrete and restraint takes place when initial bond conditions is obtained, that is provided after concrete achieves initial compressive strength fcm,0(t) P 7.5 MPa as it was shown in [11]. 4. Plane cross section hypothesis is valid on the concrete expansion stage. 5. Self-stresses at the any i-th time interval should be calculated from the cumulative force induced by the restraint, in the same way it would be done for a traditional prestressed member. For the case of the uniaxial symmetrical reinforcement arrangement (see Fig. 2b, where incremental lengths which correspond to the strains Des , DeCE;f , Dec;el , Dec;pl and elastic strain from the cumulative force induced by the restraint are designated like Ds, DCE; f ,

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V. Semianiuk et al. / Construction and Building Materials 131 (2017) 39–49

Fig. 2. Scheme of incremental approach in proposed MSDM (a) and expansion development under uniaxial symmetrical finite stiffness restraint conditions (b).

Dc; el, Dc; pl and DF respectively), basic equation for the calculation of the incremental restrained expansion strain ðDes Þi at the any i-th time interval with regard to restraint reaction can be presented as following algebraic sum:

Pi1 ðDes Þi ¼ ðDeCE;f Þi þ ðDec;el Þi þ ðDec;pl Þi þ

j¼1 ðD

rc Þ j

Ec ðt ði1Þþ1=2 Þ

ð7Þ

where, ðDeCE;f Þi : incremental free expansion strain at the i-th time interval; (Dec,el)i: incremental concrete elastic strain at the i-th time interval; (Dec,pl)i: incremental concrete creep strain at the i-th time interval under the constant incremental self-stresses induced on P the previous time intervals; i1 ðDrc Þj : resultant stress in concrete P j¼1  i1 from the cumulative force j¼1 ðDF s Þj induced by the restraint at the end of previous (i–1)-th time interval of concrete expansion, determined as a sum of incremental self-stresses; Ec(t(i1)+1/2): Young’s modulus of expansive concrete at the end of previous (i– 1)-th time interval. The sum of expansive concrete elastic and creep incremental strains at the any i-th time interval can be expressed by the following equation:  i1  X D/ðt i ; tj Þ ð8Þ ðDec;el Þi þ ðDec;pl Þi ¼ ðDrc Þi  Jðt iþ1=2 ; ti Þ þ ðDrc Þj  Ecm;28 j¼1

with:

D/ðti ; t j Þ ¼ /ðt iþ1=2 ; t j Þ  /ðtði1Þþ1=2 ; t j Þ

ð9Þ

where, ðDrc Þi : incremental self-stress at the considered i-th time interval; J(ti+1/2; ti): creep compliance function, representing the total stress dependent strain per unit stress; (Drc)j: incremental self-stress at the j-th time interval; Ecm,28: Young’s modulus of expansive concrete at 28 days; /(ti+1/2; tj): creep coefficient at tiþ1=2 under constant incremental self-stress applied at t j ; / (t(i1)+1/2; tj): creep coefficient at tði1Þþ1=2 under constant incremental self-stress applied at t j . Substituting Eq. (8) into Eq. (7), incremental restrained expansion strain ðDes Þi at the any i-th time interval can be expressed by the following equation:

ðDes Þi ¼ ðDeCE;f Þi  ðDrc Þi  Jðtiþ1=2 ; t i Þ Xi1  i1  ðDrc Þj X D/ðti ; t j Þ j¼1  ðDrc Þj   E E ðt Þ cm;28 c ði1Þþ1=2 j¼1

ð10Þ

For the case of the uniaxial symmetrical cross sectional reinforcement arrangement, incremental self-stress ðDrc Þi at the any i-th time interval can be expressed:

V. Semianiuk et al. / Construction and Building Materials 131 (2017) 39–49

ðDrc Þi ¼ ðDes Þi  Es  ql

ð11Þ

where, Es : Young’s modulus of restraint; ql: cross sectional reinforcement ratio. Generally, term of the Es  ql represents restraint axial stiffness. Substituting Eq. (11) into Eq. (10), the following equation is obtained:

ðDes Þi ¼ ðDeCE;f Þi  ðDes Þi  Es  ql  Jðt iþ1=2 ; ti Þ  Pi1 i1  X D/ðt i ; tj Þ j¼1 ðDrc Þj  ðDrc Þj   E E ðt cm;28 c ði1Þþ1=2 Þ j¼1

Incremental restrained expansion strain ðDes Þi at the i-th time interval is determined by solving Eq. (12) and then in accordance with Eq. (11) incremental self-stress ðDrc Þi at the considered i-th time interval is calculated. Finally, self-stress of the concrete ðrc Þi at the end of the i-th time interval is calculated as a sum of the incremental selfstresses at the time intervals j 2 ½1; i:

ðrc Þi ¼

i X ðDrc Þj

ð13Þ

j¼1

In the considered model creep compliance function, Jðt iþ1=2 ; t j Þ, is accepted in the traditional form in accordance with fib Model Code [14]:

Jðtiþ1=2 ; t j Þ ¼

/ðt iþ1=2 ; t j Þ 1 þ Ecm;28 Ec ðtj Þ

ð14Þ

where, Ec ðtj Þ: Young’s modulus of expansive concrete at t j in temperature adjusted concrete age. Young’s modulus of expansive concrete at early age, Ec ðtÞ, can be obtained from the relation based on the Eurocode 2 model [15]:

 0:5 !# t m;28  a Ec ðtÞ ¼ Ecm;28  exp s 1  ti  a

"

ð15Þ

where, s: empirical factor that takes into account cement type; taken as s = 0.11 in the present study; a: empirical factor that takes into account initial setting time effect; taken as a = 0.2 in the present study; tm,28: temperature adjusted concrete age at 28 days; ti: temperature adjusted concrete age at t days.Temperature adjusted concrete age at t days is established with regard to changes in temperature conditions at the concrete hardening and expansion stages at early age. It is determined in accordance with the Eurocode 2 model [15]. The creep coefficient /ðt; t0 Þ for expansive concrete at early ages was evaluated based on the modified fib Model Code proposal [14]:

/ðt; t0 Þ ¼ /0  bc ðt; t 0 Þ

where, /0 : the notional creep coefficient that in the present study was estimated with regard to relative Young’s modulus Ec ðt 0 Þ=Ecm;28 (i.e., the ratio of Young’s modulus of expansive concrete at t 0 to that of expansive concrete at 28 days in temperature adjusted concrete age) by the expression suggested in [6] on the basis of the implemented concrete creep tests:

/0 ¼ 5:31  ðEc ðt 0 Þ=Ecm;28  1:0Þ2 þ 1:11 ð12Þ

ð16Þ

43

ð16aÞ

bc(t, t0): the coefficient to describe the development of creep with time after loading and it is determined in accordance with fib Model Code [14] by the equation:

bc ðt; t 0 Þ ¼

ðt  t 0 Þ bH þ ðt  t 0 Þ

ð16bÞ

where, t: temperature adjusted concrete age; t0: temperature adjusted concrete age of loading age; bH: coefficient representing the effect of loading age on rate of creep development and it is determined with regard to relative Young’s modulus Ec ðtÞ=Ecm;28 (i.e., the ratio of Young’s modulus of expansive concrete at t to that of expansive concrete at 28 days in temperature adjusted concrete age) by the expression suggested in [6]:

8 0 6 Ec ðtÞ=Ecm;28 < 0:346 > > > > > > < bH ¼ 0:000001 > > 0:346 6 Ec ðtÞ=Ecm;28 < 1 > > > > : bH ¼ 40:5  ðEc ðtÞ=Ecm;28  0:346Þ þ 0:485

ð16cÞ

3. Experiments For the verification of the proposed modified strains development model (MSDM) for uniaxial symmetrical finite stiffness restraint conditions, specific experimental studies were performed. 3.1. Experimental specimens Experimental studies were carried out on three series of expansive concrete prismatic specimens with the cross sectional dimensions 100  100 mm and 400 mm length. Each separate series consisted of free prismatic specimens (without reinforcement) and prismatic specimens reinforced with single steel bars of different diameters, symmetrically placed at the center of the cross section (see Fig. 3). In the performed experimental studies, variations of the following parameters were considered: – Cross sectional reinforcement ratio ql, modeled by the influence of the longitudinal uniaxial restraint stiffness.

1 – expansive concrete; 2 – uniaxially symmetrically arranged single steel bar; 3 – flexible plastic tube; 4 – steel end plate; 5 – nut. Fig. 3. Construction and geometry of the experimental specimens.

44

V. Semianiuk et al. / Construction and Building Materials 131 (2017) 39–49

General view of the molds with reinforcing element before casting is presented on Fig. 4. Demolding of the specimens was carried out 7–9 h after casting. At that time, expansive concretes of the series I, II and III achieved compressive strengths of 9.0 MPa, 8.8 MPa and 8.0 MPa respectively. Immediately after demolding, specimens were immersed in water and cured there until stabilization of concrete expansion was reached.

– Self-stressing grade of the concrete established in the standard restraint conditions in accordance with STB 2101 [10] (see Table 1). Construction and geometry of the experimental specimens are presented on Fig. 3. Geometry and reinforcement of the experimental specimens are listed in Table 1.

Table 1 Geometry and reinforcement of the experimental specimens. Series

I-III

Specimen marking

Geometry, mm

x-PEC-0 (1, 2, 3) x-PEC-8 (4, 5) x-PEC-12 (6) x-PEC-18 (7, 8)

Reinforcement

Curing conditions

ql, %

bh

l

As, mm2

100  100

400

Reinforcement without 37.0 0.37 82.0 0.82 179.0 1.79

Water curing

Notes: 1. In the table the following marking of specimens was accepted: x – number of the series (I, II and III); the last sign – nominal diameter (in mm) of the reinforcing steel bar; sign in the brackets – number of specimens in the series. 2. Expansive concrete with self-stressing grades in accordance with STB 2101 [10] f CE;d ¼ 1:6 MPa was used for series I and f CE;d ¼ 2:0 MPa for series II and III.

Fig. 4. General view of the molds with reinforcing element before casting.

Table 2 Chemical composition of the expansive cement and its components. Component

Chemical composition, %

Portland cement CEMI-42,5R Gypsum (CaSO42H2O) High-alumina cement (HAC) Expansive cement

LOI

SiO2

Fe2O3

Al2O3

CaO

MgO

SO3

4.17 21.89 0.59 2.60

16.80 1.63 3.80 14.10

3.80 0.17 17.07 4.83

3.70 0.76 37.20 6.53

66.73 34.03 38.27 60.87

0.80 1.77 0.34 0.83

3.90 38.90 0.09 7.0

Table 3 Expansion and strength characteristics of the expansive cement. Expansive cement grade

Expansion

CE-6

Strength

Free expansion strain ef, %

Self-stressing grade fCE,d, MPa

Flexural fflex, MPa

Compressive fcm, MPa

2.63

7.94

3.71

30.0

Notes: 1. Free expansion strain and strength characteristics were established at the 28 days age of the mortar bars hardened in the unrestrained conditions.

Table 4 Expansion and mechanical characteristics of the expansive concrete. Series

I II III

Expansion characteristics at the concrete expansion stabilization

Mechanical characteristics

Free expansion strain eCE,f, %

Self-stressing grade fCE,d, MPa

Compressive strength fcm,28, MPa

Young’s modulus Ecm,28, MPa

0.166 0.233 0.226

1.6 2.0 2.0

64.5 64.5 65.9

33,203 31,076 32,235

Notes: 1. Free expansion strain, eCE,f, was established on the unrestrained specimens. 2. Self-stressing grade, fCE,d, was established in standard restraint conditions: ql = 1% and Es = 200 GPa. 3. Expansive concrete compressive strength was established in accordance with EN 12390-3 [19]. 4. Young’s modulus of expansive concrete was established on the cylindrical samples (Ø = 150 mm, h = 300 mm).

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V. Semianiuk et al. / Construction and Building Materials 131 (2017) 39–49

35

70

30

60 1

Young's modulus Ecm, GPa

Compressive strength fcm, MPa

3

1

3 2

50 40 1-series I 2-series II 3-series III

30 20

2 25 20 15

1-series I 2-series II 3-series III

10 5

10

0

0 0

4

8 12 16 20 24 Expansive concrete age, days

0

28

4

8 12 16 20 24 Expansive concrete age, days

(a)

28

(b)

Fig. 5. Development of mechanical characteristics of expansive concrete ((a) – compressive strength; (b) – Young’s modulus).

180 1234-

Expansion strain

CE·10

5

150 120

l =0%;

1

l =0,37%; l =0,82%; l =1,79%.

2

3

90 60

4

30 0 0

3

6

9

12 15 18 21 Expansive concrete age, days

24

27

30

(a)

Expansion strain

CE·10

5

250 1234-

200

l =0%;

l =0,37%;

1

l =1,79%.

2

l =0,82%;

150 3 100 4

50 0 0

3

6

9

12 15 18 21 Expansive concrete age, days

24

27

30

27

30

(b) 250 1234-

Expansion strain

5 CE·10

200 150

1

l =0%;

l =0,37%; l =0,82%; l =1,79%.

2 3

100 4

50 0 0

3

6

9

12 15 18 21 Expansive concrete age, days

24

(c) Fig. 6. Development of expansion strains under different restraint conditions ((a) – series I; (b) – series II; (c) – series III).

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V. Semianiuk et al. / Construction and Building Materials 131 (2017) 39–49

3.2. Expansive cement Expansive cement composition consisted of 3 components in the following proportions (by weight): Portland cement (CEMI42,5R) – 80%; high-alumina cement (HAC) – 10%; gypsum (CaSO42H2O) – 10%. Chemical composition of the expansive cement and its components is listed in Table 2. The main physical-mechanical characteristics of the expansive cement established in accordance with STB 1335 [16] and EN 196-1 [17] are listed in Table 3. 3.3. Expansive concrete Expansive concrete mix composition per 1 m3 was as follows: expansive cement CE-6 – 600 kg; fine aggregate (dmax = 8 mm) – 600 kg; coarse aggregate (Dmax = 16 mm) – 960 kg; water – 240 kg (w/c = 0.4). Concrete consistency was reached by polycarboxilic hyperplasticizer with the consumption by cement weight 0.65% for series I and 0.55% for series II and III. The consistency class of expansive concrete mix corresponded to S4 and was established in accordance with EN 206 [18]. Expansion and mechanical characteristics of the expansive concrete are listed in Table 4. Development of compressive strength and Young’s modulus of the expansive concrete at early age in the water curing conditions is shown in Fig. 5. Development of expansion strains under different restraint conditions (ql from 0 to 1.79%) of the water cured expansive concrete prismatic specimens is shown in Fig. 6. Final experimental values of the expansion strains and self-stresses under different restraint conditions at the concrete expansion stabilization are listed in Table 5. 3.4. Discussion Restrained expansion strains under different restraint conditions obtained in the experimental campaign were compared to those calculated in accordance with the proposed MSDM and the

analytical model described in [6]. Results are shown in Fig. 7. Incremental restrained expansion strains were calculated using 1-day time steps. Comparison of the experimental and predicted self-stress values under different restraint conditions to the concrete expansion stabilization calculated in accordance with proposed MSDM and prescribed models [3,4,6] with experimental data is presented on Fig. 8. As follows from the comparison results (see Figs. 7 and 8a), the proposed MSDM is more accurate than previous models when predicting self-stress values. Calculation results in accordance with model proposed in [6] (see Figs. 7 and 8d) have demonstrated the most noticeable differences with experimental data. But it should be noticed that restrained expansion strains values calculated in accordance with model proposed in [6] show a good agreement with experimental data regardless of restraint conditions during the first 3 days of expansion. It can be explained by the fact that on the early stage of the expansion, the cumulative force induced by the restraint has a relatively low value, on account of the low stiffness and high susceptibility to creep of early age concrete; for that reason, it does not have an important influence on the reduction of incremental restrained expansion strains. However, by taking into account the cumulative value of the force induced by the restraint (considered, in the proposed MSDM, as an additional restraint at the i-th time interval), the difference in incremental restrained expansion strains between experimental values and those calculated according to [6] becomes more considerable. Nevertheless, the analytical model proposed in [6] can be applicable for the restrained expansion strains estimation for the case of the members made of expansive concrete with a low self-stressing grade, such as the ones used for shrinkage compensation only. Estimation methods based on the conservation law of chemical energy [3–5] are useful to obtain acceptable self-stress values up to concrete expansion stabilization for the case of the uniaxial symmetrical restraint arrangement in the cross section (see Fig. 8b and c). But by the application of the estimation models

Table 5 Final experimental values of the expansion strains and self-stresses under different restraint conditions at the concrete expansion stabilization. Series

Specimen designation

eCE, %

eCE,m, %

rCE, MPa

rCE,m, MPa

I

I-PEC-0 (1) I-PEC-0 (2) I-PEC-0 (3) I-PEC-8 (4) I-PEC-8 (5) I-PEC-12 (6) I-PEC-18 (7) I-PEC-18 (8) II-PEC-0 (1) II-PEC-0 (2) II-PEC-0 (3) II-PEC-8 (4) II-PEC-8 (5) II-PEC-12 (6) II-PEC-18 (7) II-PEC-18 (8) III-PEC-0 (1) III-PEC-0 (2) III-PEC-0 (3) III-PEC-8 (4) III-PEC-8 (5) III-PEC-12 (6) III-PEC-18 (7) III-PEC-18 (8)

0.168 0.162 0.168 0.112 0.113 0.089 0.061 0.062 0.238 0.227 0.233 0.157 0.156 0.113 0.075 0.075 0.231 0.219 0.229 0.155 0.148 0.112 0.076 0.076

0.166

– – – 0.83 0.84 1.46 2.18 2.22 – – – 1.16 1.15 1.85 2.69 2.69 – – – 1.15 1.10 1.84 2.72 2.72

–

II

III

0.113 0.089 0.062 0.233

0.157 0.113 0.075 0.226

0.152 0.112 0.076

0.84 1.46 2.20 –

1.16 1.85 2.69 –

1.13 1.84 2.72

Notes: In the table the next signs were accepted: eCE – expansion strain; eCE,m – average expansion strain; rCE –self-stress of the expansive concrete; rCE,m – average self-stress of the expansive concrete.

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V. Semianiuk et al. / Construction and Building Materials 131 (2017) 39–49

Series I 160

120 5

4

4

80

140

2

Restrained expansion strain

100

5 3

60 6 40 l

0,37% 0,82% 1,79%

20

5

CE·10

5 CE·10

Restrained expansion strain

1

Experiment Estimation 1 4 2 5 3 6

6

120 1

100 80

2 3

60 40

l

0,37% 0,82% 1,79%

20

0

Experiment Estimation 1 4 2 5 3 6

0 0

5 10 15 20 25 Expansive concrete age, days

30

0

5 10 15 20 25 Expansive concrete ade, days

(a)

30

(b)

5

1

140

210

5

120 2

100

3

80

6

60 40

Experiment Estimation 1 4 2 5 3 6

l

0,37% 0,82% 1,79%

20 0 0

240

CE·10

4

Restrained expansion strain

Restrained expansion strain

CE·10

5

Series II 160

5 10 15 20 25 Expansive concrete age, days

5

4

180

6

150

1

120 2

90 60

0

30

Experiment Estimation 1 4 2 5 3 6

l

0,37% 0,82% 1,79%

30 0

3

5 10 15 20 25 Expansive concrete age, days

(c)

30

(d)

5

5

120

4

2

100

6

80

3

60 40

l

0,37% 0,82% 1,79%

20

Experiment Estimation 1 4 2 5 3 6

0 0

250

CE·10

1

140

Restrained expansion strain

Restrained expansion strain

CE·10

5

Series III 160

5 10 15 20 25 Expansive concrete age, days

30

(e)

4

200

5 6

150 1 100

2 3

l

50

0,37% 0,82% 1,79%

Experiment Estimation 1 4 2 5 3 6

0 0

5

10 15 20 25 Expansive concrete age, days

30

(f)

Fig. 7. Restrained expansion strains development under different restraint conditions (experimental versus calculated values in accordance with proposed MSDM: (a), (c), (e) and in accordance with analytical model [6]: (b), (d), (f)).

[3–5] it is impossible to obtain solutions for the following boundary conditions: (a) in the case of the absolute stiffness restraint (restrained expansion strain es ¼ 0) and (b) for the case of free expansion (restrained expansion strain es ¼ eCE;f ).

The MSDM hereby proposed, based on the initial strains calculation approaches [6,7,13], is universal and allows to obtain adequate solutions for any boundary conditions and for finite stiffness restraints with any cross sectional arrangement.

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V. Semianiuk et al. / Construction and Building Materials 131 (2017) 39–49

3

3 series I series II series III

2

series I series II series III

2.5 σCE,exp, MPa

σCE,exp, MPa

2.5

1.5 1 0.5

2 1.5 1 0.5

0

0 0

0.5

1 1.5 2 σCE,calc, MPa

2.5

3

0

0.5

1 1.5 2 σCE,calc, MPa

(a)

3

6

7

(b) 7

3

5 σCE,exp, MPa

2

series I series II series III

6

series I series II series III

2.5 σCE,exp, MPa

2.5

1.5 1

4 3 2

0.5

1 0

0 0

0.5

1 1.5 2 σCE,calc, MPa

2.5

3

0

1

2

3 4 5 σCE,calc, MPa

(c)

(d)

Fig. 8. Comparison of the experimental and predicted self-stress values under different restraint conditions to the concrete expansion stabilization calculated in accordance with models: (a) – proposed MSDM; (b) – [3]; (c) – [4]; (d) – [6].

4. Conclusions

Acknowledgements

1. Models used for estimation of the self-stress values in expansive concrete members can be divided into two main groups: (a) models based on the conservation law of chemical energy [3–5] and (b) models based on initial strains calculation approach [6,7,13]. The first group is characterized by their simplicity, using a limited amount of input data (mainly selfstressing grade in standard conditions), but have at the same time a limited range of application. Models in the second group are universal but more complicated in practical uses since they require additional data, namely concrete early age free expansion strains and Young’s modulus development as well as a proper creep function. 2. A modified strain development model (MSDM) is proposed. In contrast to basic model [6], the proposed model is extended by accounting for the cumulative force induced by the reinforcement, considered as an additional restraint for the development of incremental expansion strains. 3. To verify the proposed MSDM, experiments with uniaxially symmetrically reinforced specimens made with high expansion energy capacity concrete were performed. The values predicted by the proposed MSDM and the obtained experimental data have demonstrated a good agreement that confirms the validity of the former. 4. The proposed MSDM can be easily extended to nonsymmetrical reinforcement arrangement as well as any boundary conditions.

This paper is a part of work in the frame of the TEMPUS grant supported by Erasmus Mundus Programme of the European Union. The authors are grateful to the research team ‘‘Construction Group” of the University of A Coruña (Spain) for the assigned financial support for the experimental studies. Also, the authors would like to express sincere gratitude to the student researchers of the Construction Laboratory of the Centre for Technological Innovations in Construction and Civil Engineering (CITEEC) of the University of A Coruña for the assistance in the experimental campaign. This work and its results are integrated among those developed in project ‘‘Efecto tamaño en la resistencia a cortante de elementos de hormigon: estudio experimental, validación de modelo teórico y extensión a elementos con refuerzo exterior (HORVITAL-SP4)”, code BIA2015-64672-C4-2-R, funded by the ‘‘Programa Estatal de I+D+i Orientada a los Retos de la Sociedad”, Ministerio de Economía y Competitividad, Spain.

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[11] V. Tur, Experimental-theoretical Basics of the Structures Prestressing by Expansive Concrete Utilizing, Brest Sate Technical University, Brest, 1998 (in Russian). [12] V. Tur, V. Semianiuk, Models for restrained strains and self-stressing stresses in the members made of expansive concrete calculation, Vestnik BrGTU 1 (97) (2016) 53–69. [13] X. Lei, H. Chengkui, L. Yi, Expansive performance of self-stressing and selfcompacting concrete confined with steel tube, J. Wuhan Univ. Technol. (2007) 341–345. [14] fib Model Code 2010, Vol. 1, Federal Institute of Technology Lausanne – EPFL, Lausanne, March 2010. [15] CEN, TC250, EN 1992-1 Eurocode 2: Design of concrete structures - Part 1–1: General rules and rules for buildings, 2004. doi: 978 0 580 73752 7. [16] STB 1335-2002, Expansive cement: technical specifications, 2003 (in Russian). [17] European Committee for Standardization, EN 196-1, Methods of testing cement - Part 1: Determination of strength, 2005. [18] European Committee for Standardization, EN 206, Concrete: specification, performance, production and conformity, 2014. [19] European Committee for Standardization, EN 12390-3, Testing hardened concrete - Part 3: compressive strength of test specimens, 2009.