A 12 year EDF study of concrete creep under uniaxial and biaxial loading

Cement and Concrete Research xxx (xxxx) xxx–xxx

Contents lists available at ScienceDirect

Cement and Concrete Research journal homepage: www.elsevier.com/locate/cemconres

A 12 year EDF study of concrete creep under uniaxial and biaxial loading Laurent Charpina,*, Yann Le Papeb, Éric Coustabeauc, Éric Toppanic, Grégory Heinflingf, Caroline Le Bellegof, Benoît Massond, José Montalvoc, Alexis Courtoise, Julien Sanahujaa, Nanthilde Revironc a b c d e f

EDF R & D, Les Renardières, Morêt-sur-Loing Cedex 77818, France Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, TN 37831-6148, United States DIPNN CEIDRE/TEGG, 905 av Camp de Menthe, Aix en Provence 13090, France EDF DIPNN CEIDRE/SEPTEN, Division GS - Groupe Enceintes de Confinement, 12-14 avenue Dutriévoz, Villeurbane 69628, France EDF DPIH DTG, 12 rue Saint-Sidoine, Lyon 69003, France EDF DIPDE, 140 av Viton, Marseille 13009, France

A R T I C L E I N F O

A B S T R A C T

Keywords: Concrete Creep Shrinkage Poisson's ratio Long-term

This paper presents a 12-year-long creep and shrinkage experimental campaign on cylindrical and prismatic concrete samples under uniaxial and biaxial stress, respectively. The motivation for the study is the need for predicting the delayed strains and the pre-stress loss of concrete containment buildings of nuclear power plants. Two subjects are central in this regard: the creep strain's long-term evolution and the creep Poisson's ratio. A greater understanding of these areas is necessary to ensure reliable predictions of the long-term behavior of the concrete containment buildings. Long-term basic creep appears to evolve as a logarithm function of time in the range of 3 to 10 years of testing. Similar trends are observed for drying creep, autogenous shrinkage, and drying shrinkage testing, which suggests that all delayed strains obtained using different loading and drying conditions originate from a common mechanism. The creep Poisson's ratio derived from the biaxial tests is approximately constant over time for both the basic and drying creep tests (creep strains corrected by the shrinkage strain). It is also shown that the biaxial non-drying samples undergo a significant increase in Young's modulus after 10 years.

1. Introduction Électricité de France (EDF) is a French electric utility company. Hence, it has been interested in concrete creep and shrinkage for the past 25 years due to the need to operate and extend the life span of its 58 active nuclear reactors. While concrete creep has motivated a lot of research over the past century, there is still much to learn about this physical phenomenon in order to efficiently predict the strains undergone by pre-stressed structures (mostly concrete containment buildings (CCBs) and bridges). The main objective of this article is to present a unique experimental study on the creep and shrinkage of concrete similar to that experienced by an operating nuclear power plant (NPP) in France. The tests are described and analyzed, and the results are made available to other researchers so that they can contribute their analyses or challenge numerical models against the results.

*

This article is organized as follows. First, the context of the study is presented, with a focus on the industrial need for knowledge on creep and shrinkage, as well as an overview of multiaxial concrete creep literature. Then, the testing equipment and procedures are briefly described before presenting the results of the 12-year-long study. Finally, three analyses are proposed on the evolution of the instantaneous Young's modulus and Poisson's ratio, the long-term logarithmic strains, and the viscoelastic creep Poisson's ratio. 2. Notations First the notations used throughout the paper are exposed in order to facilitate reading. Directions in space are noted i with i = h,v,w,l,r. As can be seen in Figs. 3 and 1, h,v and w refer to the horizontal, vertical and transverse directions of the 2D tests while l and r refer to the longitudinal and radial directions of the 1D tests. Strains measured in

Corresponding author. E-mail address: [email protected] (L. Charpin).

http://dx.doi.org/10.1016/j.cemconres.2017.10.009 Received 30 May 2017; Received in revised form 24 August 2017; Accepted 18 October 2017 0008-8846/ © 2017 Elsevier Ltd. All rights reserved.

Please cite this article as: Charpin, L., Cement and Concrete Research (2017), http://dx.doi.org/10.1016/j.cemconres.2017.10.009

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

Fig. 2. Left: 1D drying shrinkage test in the creep tests room at CEIDRE-TEGG. Right: zoom on the radial measurement ring for a 1D non-drying shrinkage test.

Fig. 3. Biaxial test geometry with a schematic representation of the vertical, horizontal and transverse measured strains.

Fig. 1. Uniaxial test geometry with a schematic representation of the longitudinal and radial measured strains.

In order to isolate creep effects from shrinkage effects in non-drying condition, the strain ε ndc − ε nds is used to compute:

the four kind of tests are named as following: total strain in the non-drying shrinkage test total strain in the drying shrinkage test total strain in the non-drying creep test total strain in the drying creep test Contrary to other articles in the literature, the names “dying creep” and “drying shrinkage” are used for the strains measured in the tests of the same name, and not for subtractions between the strains obtained in different tests. Also, the usual terms “basic creep” and “autogenous shrinkage” were avoided to describe the strains measured in the nondrying creep and non-drying shrinkage tests in order to remind the reader of the sealing difficulties experienced during these tests. The following quantities are also used:

J ndc νndc νndc,relax − el ν2ndc D

uniaxial compliance creep Poisson's ratio relaxation Poisson's ratio creep Poisson's ratio computed from strains excluding the elastic strain In order to isolate creep effects from shrinkage effects in drying condition, the following strain is used ε dc (t ) − ε ds (t − t0) where t0 is

εids εindc εidc

εiel md mnd m0

the loading time used. The following apparent mechanical properties are computed:

J dc νdc ν2dcD, relax ν2dcD− el

uniaxial compliance creep Poisson's ratio relaxation Poisson's ratio creep Poisson's ratio computed from strains excluding the elastic strain Finally in the context of computing instantaneous Poisson's ratios

instantaneous strain at loading mass of the drying companion sample mass of the non-drying companion sample initial mass

2

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

and Young's moduli, jumps of stresses and strains are called εi and σi. For 1D tests the following quantities are computed:

Hence, proposals were made to perform multiaxial experimental studies either by measuring the radial strain in uniaxial tests or/and by performing biaxial tests, imposing the same state of stress to the sample as that in the actual CCB. Later, Benboudjema [3] developed a new basic creep constitutive model and put even more emphasis on the need for multiaxial longterm creep data. As a result of these studies, a large experimental program was established aimed at characterizing the multiaxial creep behavior of the concrete of the CCB of Civaux 1, which was the last CCB built with an ordinary concrete mix in France. The two main objectives of the tests were:

E1D ν1D

Young's modulus Poisson's ratio For the 2D tests the sample is assumed to be transverse isotropic in the direction of the thickness of the 2D samples and the following quantities are introduced:

E2D ν2D Et νt

in-plane Young's modulus in-plane Poisson's ratio out-of-plane Young's modulus out-of-plane Poisson's ratio

• Measure the evolution of the creep Poisson's ratio (CPR) with time, • Measure the long-term asymptotic creep behavior.

3. Context of the study

3.3. Overview of the multiaxial creep testing of concrete

3.1. Safety significance of creep for nuclear power plants

While a large amount of literature on concrete creep under uniaxial loading is available, studies on concrete creep under multiaxial loading are rather limited. However, the need for a better understanding of strain in biaxially loaded structures like CCBs has motivated some studies. In this section, we summarize the experimental difficulties encountered in such studies and their main findings. The first attempt to study the multiaxial nature of concrete creep was to measure the transverse strains during a uniaxial creep experiment ([4] cited by [5]). The CPR was computed as the opposite of the ratio of lateral to axial strains. A very low CPR value of 0.05 was found. This low value was also found in Ross' work [6] but was not in agreement with other researchers' results (e.g., [7,8]), which found CPRs closer to the elastic Poisson's ratio. The main finding of these early works seemed to be that CPR values were lower in drying conditions than in sealed conditions, even though difficulties in sealing the samples had already been experienced [8]. Due to the difficulties of properly sealing samples and also properly controlling the relative humidity in test rooms, studying the dependence of the CPR on the moisture state is a difficult task. Neville et al. [5] attributes the discrepancy of the CPRs values to the different measuring techniques: the use of surface or embedded strain gauges leading to different results in drying conditions due to strain gradients in the samples. Once it was recognized that a Poisson's effect existed in the sense that transverse creep strains under axial stresses were non-zero, some researchers investigated the possible dependence of CPR on the stress state, performing creep experiments under multiaxial loading. In a very large study of creep under multiaxial stress at Oak Ridge National Laboratory (ORNL), Kennedy [9] studied multiaxial creep on cylinders under different humidity conditions [9,10]. The Poisson's effect was confirmed and was once again found more pronounced on sealed specimens. The authors did not find evidence of the time dependency of the CPR, and its value seemed lower than the elastic Poisson's ratio (PR), two assertions which are contradictory to the opinion of the present authors. The influence of the stress state on the CPR was observed, but no clear trend was found. No definite conclusion could be drawn about the long-term CPR after nearly 5.25 years of testing. Difficulties were encountered with the sealing of specimens obtained by brazing a copper sheet around the specimen directly on the loading plates and sealing the strain gauge's cable outlet holes through the loading plates with epoxy resin. Also during the 1960s, Gopalakrishnan et al. [11] performed multiaxial creep tests on concrete cubes kept close to 100% relative humidity (RH) during curing and testing [11]. Friction with the loading plates was mitigated using aluminum foils smeared with polar grease. The CPR was found to be close to the elastic PR and showed no significant variation over time. The main finding was its anisotropic nature, resulting from the stress state: larger CPR values were observed in the directions of lower compression. These gaps in understanding

EDF currently operates 58 nuclear reactors built between 1971 and 1999 in France. Nearly half of the NPP CCBs in France were designed as double containments; i.e., instead of placing a steel liner, as commonly adopted for other pressurized water reactors (PWRs) designs, a posttensioned concrete inner containment creates a barrier against potential radiological release during a hypothetical accident. Although residual air leaks are collected and dynamically filtered into the air space between the inner and outer containments, the safety of the CCB primarily depends on the integrity of the concrete, which is tested periodically during the decennial Integrated Leak Rate Tests (ILRTs) performed under internal air pressures close to 5 bars (depending on the design of the CCB). The air tightness of the post-tensioned CCB wall is largely dependent on the compression stress level induced by the pre-stressing, which decreases over the years as a result of concrete shrinkage and creep. To prevent potential corrosion-induced brittle failure of the tendons, the tendon ducts are cement-grouted, which precludes possible lift-off tests or subsequent re-tensioning procedures [1]. It is therefore very important that the compression state remains high enough so that in case of an accident, and during the ILRTs, the CCB remains in compression. In the cylindrical part of the CCB, the horizontal and vertical prestress cables impose an average state of stress of 12 MPa horizontally and 8.5 MPa vertically. Since only few cables are greased instead of cement grouted and equipped with dynamometers, the strains of the CCB are permanently monitored using embedded vibrating wire gauges. The need to predict the long-term creep deformations of the CCBs led EDF to launch a comprehensive research program on the subject since the 1990s. While some of these works study the relaxation of the steel prestressing cables, most of the work, including the present article, focuses on the delayed strains of concrete. All time-dependent phenomena that can potentially induce a decrease of the pre-stressing must be studied and quantified in order to predict the evolution of the pre-stress and, hence, the air leak rate. Creep and shrinkage are the two prominent phenomena and are also the focus of this paper. 3.2. Motivations for the experimental campaign Several research studies have been carried out at EDF over the past two decades in an attempt to answer to the industrial need for creep modeling. Granger [2] developed numerical tools for creep simulations and performed a large experimental program studying six concrete mixes similar to the concretes in CCBs of Civaux 1, Civaux 2, Chooz, Flamanville, Paluel, Penly. This work demonstrated that the multiaxial behavior of concrete required more advanced characterization and that longer tests would be preferable so as to gain knowledge on the longterm behavior of the concrete. 3

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

regarding the possible dependence of the CPR on time and loading were also the starting point of research at the University of Illinois [12]. Sealing was achieved using a combination of epoxy resin and copper sealed with solder. Friction with the loading plates was limited by using teflon sheets. Again, sealing imperfections and measurement uncertainties question the quality and validity of the obtained results. While the CPR was roughly constant on both the concrete and mortar specimens, experimental uncertainties prevented definite conclusions about the CPR variations in time and depending on the stress state. In a later study conducted at ORNL in 1976, McDonalds pointed out that different definitions for deriving CPR existed [13]. He suggested to adhere to the elastic equation, like [9]. In the opinion of the authors of this paper, this approach is the most practical and reliable method, since it is perfectly consistent with the theory of viscoelasticity, as shown in [14]. In the United Kingdom, Jordaan and Illston also performed multiaxial creep experiments in the 1960s on cubic samples [15]. The samples were sealed with resin, and strain was measured using embedded strain gauges. Various states of stress were tested, and the CPR was found to be almost constant in all cases. Some studies were also performed on other types of cementitious materials. Concerning cement pastes, [16] showed that their multiaxial behavior is consistent with that of concretes and mortars. Later, [17] performed creep experiments on leached mortars and cement pastes. Their results, which were obtained using a triaxial cell, when plotted in terms of CPR, show a large increase of the CPR [18]. These authors argue that it is preferable to describe the multiaxial creep using shear and volumetric compliances, since different mechanisms are, in their opinion, related to those creep components. The authors of the present paper agree with the idea that using shear and deviatoric compliances is more convenient from many points of view and that the only advantage of the CPR appears when it is constant and allows only one creep compliance to be used to describe the isotropic delayed behavior. Recently, Hilaire [19] performed biaxial tests with a concrete very close to the one used in the present study. The strains were analyzed with digital image correlation. The obtained basic CPR decreased to zero within roughly 10 days. To conclude, those studies showed that a creep Poisson's effect exists, that the CPR does not vary much with time, and that CPR is lower when drying occurs; however, they were not conclusive about the dependence of CPR on the stress state. Most sealed tests were affected by leakage, except those that were conducted at a controlled humidity (e.g. drying tests, tests in a 100% RH environment [11], tests under water [20]).

Table 1 Concrete mix (for dry aggregates) of concrete B11 (original mix) and B11T (used in this study). The effective water-to-cement ratio, weff/c, is computed using the total water (added water + water from the superplastifier) minus the water absorbed by the aggregates, assuming that the aggregates were dried before mixing, and potentially absorb water until saturation.

0–5 mm (kg) 5–12.5 mm (kg) 12.5/25 mm (kg) Cement (kg) Total water (kg) Plastiment (kg) weff/c

B11

B11T

(original mix) 772 316 784 350 195 1.225 0.46

Le Pape [23] 772 316 786 350 215 1.225 0.49

in EDF's internal documents. Therefore, the concrete created to reproduce the B11 concrete at EDF's civil engineering lab was called B11T. The mix was not exactly the same as the original formulation, since 20 L of water had to be added to obtain the same slump as with the original mix (which was used without correcting the water content in Granger's work [2]). The mix is given in Table 1. The water absorption coefficients were measured (Table 2). These values were used to compute weff/c given in Table 1. The composition of the cement which was used is given in Table 3. Several studies in the literature also used concrete formulations close to the B11 original mix. Except for Granger [2], all were modifications of the original mix. Three Ph.D. thesis studies funded by IRSN (France) used a mix with 201 L of water [19,25,26], while other studies at GEM in Nantes (France), used a different superplastifier [27,28]. 4.2. Main results of standardized tests The main characteristics of the concrete were tested: compressive strength fc (following standards NF P 18-406 in 2002 and CE 12390-3 in 2004) and static modulus Estat, the results of which are presented in Table 4. Although the normalized tests samples were kept in a moist room before testing, the dynamic Young's modulus did not vary significantly between 85 days and almost 2 years (only 1 GPa increase). The static Young's modulus at 85 days was 35.1 GPa for the 1D campaign and 35.85 GPa for the 2D campaign, which should be the closest to the modulus at the age of loading of the creep tests, which is 90 days.

4. Overview of the materials and procedures The need for a better understanding of the influence of creep and shrinkage on the concrete of the CCBs led EDF to perform its own creep tests. It was decided to use the concrete mix of Civaux 1, which is the latest ordinary concrete CCB in France and had already been studied by Granger [2]. The tests were performed at CEIDRE-TEGG, which is an expertise center of EDF located at Aix-en-Provence, France. The 1D creep rigs kept the design of the rigs used at Laboratoire Central des Ponts et Chausséees (LCPC, now IFSTTAR), France, as used for example in Le Roy [21] or Granger [2]. An improvement is the radial measurement system as described in Boulay et al. [22]. However, there was no readily available 2D creep rigs. Therefore, a 2D creep rig was developed by EDF R & D, along with the University Paris-Est LGCU at Marne-la-Vallée and LCPC, France. The test procedure is summarized here.

4.3. Main results of post-mortem tests The properties of the concrete samples were tested after the drying, shrinkage and creep tests, in 2017. Strength, Young's modulus, porosity, permeability and water content were measured on pieces of the samples. For 1D samples cylinders of size 16 cm × 32 cm were wet-sawed. For 2D samples, cylinders of size 11 cm × 22 cm were wet-cored and wet-sawed. Strength and Young's modulus results are presented in Table 5. The comparison on these results to results in Table 4 shows that the compressive strength has decreased for drying samples while it has Table 2 Water absorption coefficients of the aggregates, measured at CEIDRE-TEGG.

4.1. Concrete mix: Civaux 1 CCB

Aggregate size

24 h absorption coefficient

The first step in the characterization of Civaux 1 concrete was to recreate the concrete as closely as possible to the original constituents used for the CCB. The recreated concrete mix was originally called B11

0–5 mm 5–12.5 mm 12.5–25 mm

2.5% 2.01% 1.19%

4

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

Table 3 Bogue composition of the cement used for this study [24]. The cement is a CEM II/AA 42,5 R CE PM CP2 from Airvault, also containing 6% of lime, 2% of collected filter dust, and an extra 3% of gypsum.

mass %

LOI

SiO2

Al2O3

Fe2O3

TiO2

MnO

CaO

MgO

SO3

K2O

Na2O

P2O5

Cl−

3.87

19.08

4.55

3.14

0.27

0.07

62.80

1.36

2.73

1.53

0.13

0.56

0.05

Table 4 Normalized tests results on the concrete used in the 1D tests started in 2002, and the 2D tests started in 2004. Age

3 d.

7 d.

14 d.

28 d.

85 d.

6 m.

1 y.

620 d.

fc1D (MPa)

30

33.6

36.1

40.0

-

46.7

46.5

-

fc2D (MPa) 1D Estat (GPa) 2D Estat (GPa)

23.7 ± 2.0

34.0 ± 2.1 (9d.)

-

46.3 ± 2.8

-

-

-

-

-

-

-

-

35.1

-

-

35.1

28.30

31.15 (9d.)

-

33.05

35.85

-

-

-

The 12 MPa stress state is imposed by a passive system using a nitrogen pressure accumulator and a flat hydraulic jack. Therefore, the pressure is not constant and decreases slightly during the test.(The order of magnitude of this decrease is 10 %, which is much larger than the 1% advised in Acker et al. [30], as shown in paragraph 5.2.) Two 1D test campaigns were undergone: the first one in 2002 referred to as the 1D-2002 campaign, and the second one in 2005 referred to as the 1D-DTG-2005 campaign. During the 1D-DTG-2005 campaign, only non-drying samples were tested.

increased for non-drying samples, and that the Young's modulus stayed stable for non-drying samples and has decreased for drying samples. These results will be further commented in Section 6. Another interesting result is that the evolution of strength and stiffness does not seem to depend on the application of a loading or not. However, the number of samples is too low to conclude on this point. 4.4. Creep test conditions Two types of creep tests were performed on cylindrical specimens and prismatic specimens, hereafter referred to as 1D tests and 2D tests, respectively.

4.4.2. Overview of the 2D test setup and instrumentation The 2D test setup was developed specifically for this study, making this test unique. There are also six tests in the 2D test program (the only change compared to the 1D tests detailed in Table 6 is the horizontal imposed stress of 8.5 MPa). The dimensions of the specimen are 30 × 30 × 15 cm but are not in compliance with the RILEM [30], which recommends that elongated specimens be used and that strain measurements only be performed in the center part. Adhering strictly to these recommendations would have led to a sample size of 100 × 100 × 15 cm, resulting in prohibitively high costs. The intent of RILEM is twofold: first, to limit the effect of friction on the loading plate in the measurement region, and, second, to provide an area inside which the strain field is invariant in the loading direction (a short drying specimen does not deform homogeneously due to larger creep and shrinkage at the drying surface). As shown in Fig. 4, in the present biaxial design, the first issue was addressed by replacing the loading plates with a comb system (a very large number of steel bars

4.4.1. Overview of the 1D test setup These tests are performed on cylindrical samples measuring 16 × 100 cm. The test protocol was largely inspired by the tests previously performed at LCPC [2,21,29] and was closely aligned to the RILEM recommendations [30]. The temperature and relative humidity of the room were controlled at T = 20 ± 1°C and h = 50 ± 5%, respectively, although it was observed that the relative humidity sporadically reached values of up to 60%, which is a deviation from the RILEM recommendations. Six different types of tests were performed, as described in Table 6. Strains were measured in the axial direction (using one LVDT sensor with a gauge length of 50 cm) and in the radial direction (using three LVDT sensors with a gauge length of 8 cm) in order to have access to multiaxial information about creep (see Figs. 1 and 2). The vertical bars are held by copper inserts, while the support ring of the radial LVDTs stands on glued supports. The theoretical uncertainty of the axial strain computed from the displacement measurement is less than 10 10− 6, while the uncertainty of the radial strain computed from the three displacement measurements is equal to 36 10− 6. These uncertainty evaluations take into account: the uncertainty of the LVDT sensor, the uncertainty due to fluctuations of the temperature of 1°C, and the uncertainty due to an error on the position of the bars or rings supporting the LVDTs. Therefore, they do not account for a larger scatter of the temperature of the room, or of the deviations of the RH in the room.

Table 6 Six tests performed in the 1D and 2D experimental campaigns. Loading is performed at 90 days. Drying starts at 24 h for shrinkage tests and at 90 days for creep tests.

No loading 12 MPa No loading

Non-drying

Drying

Non-drying shrinkage Non-drying creep Non-drying mass loss

Drying shrinkage Drying creep Drying mass loss

Table 5 Compressive strength and Young's modulus measurements performed in 2017 on the samples used for the creep and shrinkage test campaign. DS=drying shrinkage, NDS=non-drying shrinkage, DC=drying creep, NDC=non-drying creep, ND=non-drying (used for a mass-loss sample and averages of all non-drying samples) D=drying (used for averaging of all drying samples). 1D

fc (MPa) Estat (GPa)

DS 42.9 30.6

2D NDC 54.2 36.4

NDS 52.9 36.6

NDC 53.1 38.3

DC 42.9 33.9

DS 36.5 33

5

Averages NDC 50 35.3

NDS 49.8 35

ND 55.6 39.1

ND 52.6 36.8

D 40.8 32.5

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

perpendicular to the sample surface, which can slightly bend during loading, thus avoiding lateral restraint), as already described for other presses in [31,32]. Regarding the second issue, the main response was that the vertical and horizontal strains are only measured in the center region of the specimen, with a 20 cm gauge length while the sample is 30 cm wide as shown in Fig. 3. To avoid a similar loss of sealing observed in the 1D tests, the sealing of the 2D test specimens was doubled using four layers of adhesive aluminum foils. For the 2D test drying samples, the adhesive aluminum foils were placed on the 15 cm wide faces in contact with the steel comb to create uniaxial drying conditions. A sealed 2D specimen is shown in Fig. 5. The strain measurement system is presented in Figs. 4 and 5. The horizontal and vertical strains are measured by averaging the results of four LVDT sensors (two on each face) with a gauge length of 20 cm. The low-friction spherical magnets at each end of the sensors are connected to a stainless steel plate held by stainless stell inserts in the concrete. The strain measurement in the unloaded transverse direction is also obtained by using four LVDT sensors, with each pair connected to parallel invar bars. These bars are screwed on ring supports glued to the surface of concrete, realizing a 15 cm gauge length (see Fig. 5). The strain measurement theoretical uncertainties are 15 10− 6 in the vertical and horizontal directions (computed from the averaging of four displacement measurements) and 27 10− 6 in the transverse direction, respectively. The mechanical loading is imposed by controlled low-flow rate hydraulic jacks, which guarantee a high stability of the applied stress on the specimen over time, as recommended in Acker et al. [30]. Few occurrences of unloading were observed over 10 years of operation, which were mainly caused by sporadic circuit shutdowns.

Fig. 5. 2D drying creep test in the creep tests room at CEIDRE-TEGG.

and creep are highly dependent on the internal humidity of concrete. Usually, two main hydric boundary conditions are experimentally achievable: the sealed condition, aimed at representing the state of the concrete bulk in massive structures, and the drying condition, which is closer to the state of the surface of actual structures. However, both conditions are difficult to achieve in practice, as mentioned in subsection 3.3. Sealing is difficult to maintain over very long periods because few materials are easy to place on the sample, impervious, and inert when exposed to the interstitial solution of concrete all at the same time. Also, the inserts supporting the instrumentation, and, in some cases, additional embedded sensors (not described in this article) requiring the penetration of cable create vulnerable leaking points. A complete list of these defaults is the following: degradation of the aluminum foil (in the 1D tests with 2 layers mostly), penetrations due to a temperature sensor glued on the samples and LVDT sensors supports (for creep and shrinkage tests), joint between the bare face of the sample and the loading plate (in 1D creep tests only), additional penetrations due to embedded vibrating wire sensors (only in the 1D-DTG-2005 tests), degradation of the aluminum foil due to the force application by the comb system (only in the 2D creep tests). Maintaining steady drying conditions is also difficult because it requires low-variation controlled humidity in the room and because long-term carbonation can affect the moisture transfer properties at the concrete surface. While controlling the humidity of the air can be

4.5. Summary of the tests dealt with in this paper Before presenting the results, all creep and shrinkage tests mentioned in this paper are summarized in Table 7. 5. Results The main results of the creep tests are presented in this section. 5.1. Laboratory environmental conditions and drying-induced loss of mass of concrete This section has two objectives: (1) to present the loss of mass data measured on the drying and non-drying control samples and (2) to discuss the quality of sealing for non-drying specimens, since shrinkage

Table 7 Summary of the creep and shrinkage 1D and 2D tests on B11T concrete.

Fig. 4. 2D drying creep test in the creep tests room at CEIDRE-TEGG.

6

Campaign

Test name

Number

1D-2002 1D-2002 1D-2002 1D-2002 1D-DTG-2005 1D-DTG-2005 2D 2D 2D 2D

Non-drying shrinkage Non-drying creep Drying shrinkage Drying creep Non-drying shrinkage Non-drying creep Non-drying shrinkage Non-drying creep Drying shrinkage Drying creep

of samples 3 3 3 3 3 3 1 1 1 1

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

“oscillations” (see for example Fig. 18). After 2000 days of testing, an upgrade of the air drying system mitigated that seasonal effect to some extent. The same type of monitoring data is also available for the 1D-tests started in 2002. Moreover, each sample was equipped with a thermocouple for measuring the surface temperature. The corresponding temperature measurements were consistent with the room temperature data and hence are not reproduced here.

Table 8 Average and standard deviation of the ambient air temperature and relative humidities (two measurements for each) during the 2D creep tests within the testing facility between 2004 and 2014.

Average Std. dev.

T3 (°C)

H3 (%)

T4 (°C)

H4 (%)

19.8 0.7

57.9 6.1

21.1 0.8

54.9 6.3

5.1.2. Mass loss 5.1.2.1. Drying samples. Drying was measured from the time of exposure to the room atmosphere right after demoulding at 24 h. The mass loss of the 1D drying samples called B11_1D D reached 3% after 2.5 years of drying (Fig. 8). Interestingly, between 2.5 years and the end of the test, the mass increased slightly. This behavior is currently attributed to carbonation (the depth of carbonation has been measured to be around 2 cm after 10 years of drying and around 3 cm in 2017 after 15 years), but further investigation is needed to confirm this assumption. The mass loss of the 2D drying samples is much slower than that of the 1D samples (see Fig. 8). Even after 10 years, drying does not seem to be fully stabilized; the mass loss rate appears to be nearly linear between 4 years and 10 years of testing. Three assumptions can be proposed. First, despite close characteristic lengths, i.e., 16 cm diameter for the cylinder specimens and 15 cm thickness for the prisms, the drying rate of cylinder specimens is higher than uniaxial drying (cylindrical vs. cartesian diffusion equations). Second, the 1D test and 2D test specimens are made from different concrete batches cast at 2 year intervals. Finally, the 1D test and 2D test samples were stored at different locations in the facility. The relatively large dimensions of the testing room may result in possible variation in drying conditions. It is currently thought that neither the first nor the second explanation can account for such differences in drying speeds. The first option is discussed in subsection 8.2.2 where it is shown that the shape effect alone is not sufficient to account for such a difference. The second option seems unlikely since the tests performed on the various batches show no significant difference of the behavior of the obtained concrete. More tests are currently undergone on the samples to verify that the porosity and the gas permeability of the 1D and 2D mass loss samples are identical. The third option is supported by the fact that a slight breeze exists in the room depending on the location. Moreover, for some prismatic samples belonging to tests campaigns not described in this paper, drying creep has been found to be different on the two faces of the same sample when only one of the faces was exposed to that breeze.

achieved to a certain extent, the CO2 content in the room is not controlled. 5.1.1. Humidity and temperature Table 8 summarizes the room ambient conditions between 2004 and 2014. While the temperature was well controlled, the relative humidity varied much more than expected. As can be seen in Figs. 6 and 7, the recorded temperatures showed very limited variation over a decade, except for two spikes of short duration around 24–25 °C. Conversely, the relative humidity exhibited large seasonal variations, causing drying strain deformation as

Fig. 6. Ambient temperature in the creep testing room from 2004 to 2014.

5.1.2.2. Non-drying samples. The initial technological solution proposed in 2002 for the sealing of the 1D test specimens was to use two layers of adhesive aluminum foils (from the SCAPA company). It was quickly observed that this method was ineffective after a few months. See curve B11_1D ND, Fig. 9. When the 2D non-drying shrinkage test was started at 24 h, only two layers of aluminum were used. After 11 days of tests, leaking became too critical an issue, so the sample was uninstrumented, and two additional layers were put in place. Later on, four layers were systematically used for sealed tests of the 2D campaign and for a second 1D test campaign started in 2005 (called 1D-DTG throughout this document). A comparison of 1D weight loss on sealed samples from 2002 and 2005 is shown in Fig. 9. Using four layers instead of two proved to be more efficient. Using this improved method, the tightness of samples without instrumentation was considered very good (see Fig. 9), since the samples with four layers showed almost no mass loss for 2 years and subsequently the mass loss was limited to 0.15% of the total mass of the sample. Because of this change in the procedure, the leak tightness of

Fig. 7. Ambient relative humidity in the creep testing room from 2004 to 2014.

7

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

Fig. 10. Longitudinal strain in 1D tests. Contraction strains are shown positive.

Fig. 8. Relative mass loss for drying 1D and 2D samples. Squares: drying 1D sample, triangles: drying 2D sample, green circles: drying 1D DTG sample.

delayed strains differed by a factor of 2 between two of the sample. The sealed shrinkage was also quite different from one sample to another in the 1D-DTG-2005 campaign. One can wonder why these differences were much less extensive in the original 1D-2002 campaign; however, there were two differences between the 2002 and 2005 campaigns: the number of aluminum layers and the presence of vibrating wire strain gauges inside the samples of the 1D-DTG-2005 campaign, and as a consequence more wires going through the aluminum. In the 1D-2002 campaign, chemical degradation of the aluminum due to interaction with the pore solution caused massive leaks, which occurred in a similar manner among the samples. Conversely, in the 1D-DTG-2005 campaign, drying occurred through the wire holes in the aluminum, probably of a lesser extent, causing more variability among the samples. 5.1.2.4. Weighed non-drying shrinkage test. In 2014, at the end of the 1D test campaign of 2002, a weighed non-drying shrinkage test was performed in order to measure the mass loss that could occur on a sealed and instrumented sample. A reserve sample from the 1D-DTG2005 campaign was used. The sample was instrumented, and both mass loss and shrinkage were monitored over 2 years (the test is still ongoing). During this period, the mass loss and shrinkage evolved roughly linearly with time. The speed of mass loss was 0.11 %/year, while the speed of shrinkage was 58 μm/m/year. As a comparison, the non-drying shrinkage of 1D-DTG-2005 samples during the same period of time had an average speed (three samples) of 21 μm/m/year, which shows that installing the instrumentation to the reserve sample led to a loss of mass as well as almost tripling the shrinkage speed.

Fig. 9. Relative mass loss for sealed 1D and 2D samples. Black line: two-layer-sealed 1D samples, red line: four-layer-sealed 2D samples, green line: four-layer-sealed 1D samples.

samples without instrumentation was considered good in both the 1DDTG-2005 campaign and the 2D campaign. Unfortunately, the samples with instrumentation were not weighed. Therefore, direct information on the true mass loss of the samples on which creep and shrinkage were measured lacks. Indeed, an additional mass loss is suspected to have occurred due to the electric wire holes made in the aluminum and to the inserts, which also go through the aluminum. Indeed, these holes in the aluminum were covered with mastic, but this likely was not enough to prevent leakage. The best indicators of this potential additional mass loss are the variability of the 1D creep and shrinkage test results and a weighed non-drying shrinkage test that was performed in 2014–2015.

5.1.2.5. Conclusion on the sealing of the samples. All sealed specimens exhibit drying to some extent. As shown by the 1D-DTG-2005 tests, this mass loss can induce significantly different strain results. The problem is that the exact amount of drying is not known, because the samples for which strains were measured were not weighed. Therefore, it is possible that the 2D tests also face this difficulty. To gain a better understanding of this phenomenon, EDF is now starting shrinkage tests with simultaneous and continuous weighing, which will give information on the amount of water lost for future test campaigns (including the VeRCoRs creep test campaign [33]).

5.1.2.3. Variability of the 1D DTG non-drying tests. During the 1D test campaigns that started in 2002 and 2005, three specimens were tested for each test condition in order to assess the reproducibility of the tests. As can be seen in Fig. 10, the sealed creep measured in the 1D-DTG2005 campaign is very different from one sample to another (εlndc ). While the instantaneous strains at loading were almost the same, the

5.2. Measured forces and strains in the 1D creep tests The monitored loads and deformations of the 1D creep test are presented throughout this section. 8

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

Fig. 11. Longitudinal force in 1D drying creep (DC) and non-drying (NDC) tests from both 1D test campaigns on B11T concrete. Time zero corresponds to the loading of the samples, which is 90 days after casting.

Fig. 13. Longitudinal strains of 1D shrinkage tests. The displayed strains are as measured, without any subtractions made between different tests. Time zero corresponds to the beginning of strain measurements for each test (24 h for shrinkage tests, 90 d for creep tests).

The load is applied quasi-instantaneously in 2 s by releasing a nitrogen accumulator. Although not completely instantaneous, such a loading rate is about 10 to 30 times higher than that prescribed for the instantaneous Young's modulus standard test (ISO 1920-10:2010). The load cells are periodically monitored. Fig. 11 shows the force evolutions for the six rigs of the 1D-2002 tests (labeled B11) and the three rigs of the 1D-2005 tests (labeled DTG). The scatter is due to imprecisions of the force measurement method. The loss of applied force was maintained under 10% during the 10 years of testing. It should be noted that RILEM [30] recommends a loss of < 1%, although such stability is difficult to achieve in practice over long periods. All analyses performed in this article assume that the force in 1D tests is constant and equal to 240 kN. The longitudinal strains are obtained by dividing the displacement given by the LVDT sensor by the gauge length (50 cm) and are plotted in Figs. 12 and 13. Contraction strains are represented as positive.

Data were recorded using three different acquisition times: 0.1 s during loading, and then hourly and daily (in different text files) for the rest of the test. Using these collection times results in an enormous amount of data being generated over the full length of the tests. The data presented here mainly comes from the one-per-day acquisition enriched with fast sampling data during loading and unloading. The definition of loading age, tl, for the creep test is somewhat ambiguous from a theoretical perspective since the loading is not exactly applied instantaneously. Two methods were attempted: 1. The displacements were plotted in semilog plot as a function of t − tl for different times tl close to the end of loading, and tl was chosen as the shortest time such that the displacements were linear with respect to log(t − tl). 2. As advised by Hubler et al. [34], the data at very short intervals was plotted against (t − tl)0.1, and tl was chosen as the shortest time yielding a linear plot. These methods gave identical results and helped identify the exact time of end of loading that we call tl and take as time zero for the semilog strain plots. For shrinkage tests, points taken during fast sampling were also added at the beginning of the test. In order to keep the figures readable, only one point per month is plotted after one month of testing. The measured longitudinal creep strains for all 1D tests are presented in Fig. 12, while the longitudinal shrinkage strains are presented in Fig. 13. All notations are explained in Section 2: ndc, dc, nds, and ds stand for non-drying creep, drying creep, non-drying shrinkage, and drying shrinkage respectively. Both creep and shrinkage strains are more important in drying than non-drying conditions. However, the difference decreases with time, which can partly be explained by the fact that even non-drying tests have lost water as attested by the weighing of the control samples in the case of the first campaign (labeled B11) and is suspected due to the variability of the results in the second campaign (labeled DTG) and the weighed shrinkage test performed in 2014–2015. Drying shrinkage tests start after unmolding the specimens at 24 h. For drying creep tests, specimens are wrapped in aluminum foils after unmolding. At 90 days, the sealing is removed prior to creep loading. The non-concomitance of

Fig. 12. Longitudinal strains of 1D creep tests. The displayed strains are as measured, without any subtractions made between different tests. Time zero corresponds to the beginning of strain measurements for each test (24 h for shrinkage tests, 90 d for creep tests).

9

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

Fig. 16. Vertical and horizontal forces in the drying and non-drying creep tests.

Fig. 14. Radial strains in 1D creep tests. The displayed strains are as measured, without any subtractions made between different tests. Time zero corresponds to the beginning of strain measurements for each test (24 h for shrinkage tests, 90 d for creep tests).

gauge length, i.e., 8 cm, and (3) leaks that might have occurred through the sealing of non-drying tests at the exact location where a small glass square is glued on the sample to provide a flat surface to the radial LVDTs. Only, the third assumption can explain the higher variability observed on non-drying radial strains compared to the drying radial strains.

the drying ages for the shrinkage and the creep tests is problematic for results analysis. Improvements are ongoing but are not discussed in this article. Strain measurements start at 24 h for shrinkage tests and at 90 days for creep tests. As seen in Fig. 12 or 13, on drying results, seasonal oscillations can be observed related to changes in the relative humidity in the testing room, affecting the moisture exchange with the concrete and all dryinginduced mechanisms. The variations in temperature appear to have a limited impact on the measured strains (longitudinal strains in nondrying tests are not affected by seasonal oscillations). The radial strains are obtained by averaging the measurements of the three radial LVDT sensors and are plotted in Fig. 14 for creep and Fig. 15 for shrinkage. The radial measurements show higher “oscillating” variations caused by (1) the smaller amplitude of the deformations, (2) the small

5.3. Measured forces and strains in the 2D creep tests The 2D-test results are now presented, starting with the measured forces in Fig. 16 using a similar time sampling method as that for the 1D-test. The force is very stable in time. Minor loss of hydraulic-controlled pressure resulted in sporadic unloadings that never exceeded more than a few hours or days. After reloading, very good continuity of the strains measurement was observed, showing that no damage had occurred and that creep recovery was not significant during such short unloadings. Interestingly, these unplanned unloadings and reloadings were taken advantage of in order to estimate the evolution of the Young's modulus and Poisson's ratio over time (Section 6). Let us first present the vertical strains (the vertical load is 12 MPa), which are computed by averaging the measurements of four LVDT sensors and dividing by the 20 cm gauge length. The four test results are represented in Fig. 17. The drying creep strain is quite large, reaching 0.25 % after 2 years. The drying creep and shrinkage strains develop much faster than the non-drying ones but are almost (although not completely) stabilized after 2 years of testing, while the non-drying ones still increase after 10 years of testing. However, it is unclear whether that behavior is the result of leakage through the sealant or from the intrinsic behavior of concrete in sealed conditions. In order to show the strain recovery which was measured for almost a year after unloading, the vertical strain is also plotted against time (linear scale) in Fig. 18. While the recovery strains are stabilized after a few months, the creep strains appear to be largely irrecoverable, i.e., permanent. The increase in the Young's modulus is also visible, particularly on the nondrying creep curve. The strains in the horizontal direction are given in Fig. 19. In this direction, the stress is only 8.5 MPa, so the magnitude of the creep strains is lower than in the vertical direction. The magnitude of the drying shrinkage is the same as that of the non-drying creep after 3 years of testing, but the non-drying creep continues to increase while the drying shrinkage flattens. Finally, the transverse strains are plotted in Fig. 20. The Poisson's

Fig. 15. Radial strains in 1D shrinkage tests. The displayed strains are as measured, without any subtractions made between different tests. Time zero corresponds to the beginning of strain measurements for each test (24 h for shrinkage tests, 90 d for creep tests). For one of the B11_1D tests, the recording of the radial displacements failed shorly after the start of the test until the 5th day, which explains the straight red line.

10

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

Fig. 17. Vertical strains for the four 2D tests. The displayed strains are as measured, without any subtractions between different tests. Time zero corresponds to the beginning of drying for shrinkage tests, and the loading time for creep tests.

Fig. 19. Horizontal strains for the four 2D tests. The displayed strains are as measured, without any subtractions made between different tests. Time zero is the beginning of drying for shrinkage tests and the loading time for creep tests.

Fig. 18. Vertical strains for the four 2D tests in linear time scale. The displayed strains are as measured, without any subtractions made between different tests. Time zero is the beginning of drying for shrinkage tests and the loading time for creep tests.

Fig. 20. Transverse strains for the four 2D tests. The displayed strains are as measured, without any subtractions made between different tests. Time zero is the beginning of drying for shrinkage tests and the loading time for creep tests.

corresponds to the thickness of the sample, while in the other two directions, it is only 20 cm compared to the height and width of the sample which is 30 cm, excluding the edge of the sample from the measurement zone. Second, the precision of the thickness measurement is less (the uncertainty on the strain is 27 10− 6 compared to 15 10− 6 in other directions), but the differences observed on the non-drying shrinkage are two to three times greater than those theoretical uncertainties. One can also see that the difference between vertical and horizontal strains is larger than the measurement uncertainty, possibly resulting from the influence of the vertical casting direction. Finally, it is remarkable that the non-drying shrinkage strains in the 2D test are still not stable after 10 years of testing. This result contradicts many results published in the literature showing the plateauing of autogenous shrinkage strains [2], but is consistent with results by Persson [35]. According to Hubler et al. [34], very long-term autogenous shrinkage data is lacking to assess that autogenous shrinkage

effect creates large transverse expansions which compensate for shrinkage both in the drying and non-drying creep tests. Comparing Fig. 17 to Figs. 12 and 13 provides another interesting result. We see that the difference between drying and non-drying creep is larger in 2D than in 1D, which can be attributed to the larger leaks that occurred in both 1D-2002 and 1D-DTG-2005 test campaigns. The magnitude of the non-drying shrinkage in the three directions is shown in Fig. 21. The transverse strain is approximately 15 % larger than the strains in the other two directions. There are two possible explanations for this. First, how representative the sample is may be limited in the transverse direction, given that the larger aggregates in the studied concrete are 2.5 cm large while the sample thickness is 15 cm. A wall effect on the arrangement of the aggregates can induce locally a higher volume fraction of cement paste near the surface of the sample. The relative thickness of such a layer has a greater effect in the transverse direction, which is the smallest dimension of the sample. In addition, in the transverse direction, the gauge length (15 cm) 11

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al. t εw ⎧ ν = − ⎪ Et σh + σv ⎪ σ ε − σv εh ν 2D = h v σv ε v − σh εh ⎨ ⎪ σv2 − σh2 2 D ⎪E = σv ε v − σh εh ⎩

(1)

For the 1D tests, the expressions are simpler and can be written assuming the isotropy of the specimens:

ε ⎧ ν1D = − r ⎪ εl ⎨ E1D = σl ⎪ εl ⎩

(2)

6.2. Results As pointed out by Neville et al. [5], there is no clear difference between the instantaneous strain and the creep strain, which starts during the loading. Therefore, the determination of instantaneous moduli yields results that must be viewed with caution. First, the evolution of the instantaneous Young's modulus in all tests (for stress variations higher than 10.5 MPa vertically and 7 MPa horizontally) is shown in Fig. 22. Let us recall that the Young's modulus measured at 85 days on concrete samples kept in the moist room was 35.85 GPa for the 2D tests and slightly less for the 1D tests (see subsection 4.2). The Young's modulus at initial loading is larger in the 1D test (25 to 32 GPa) than in the 2D tests (25 GPa). Then the Young's modulus of the 2D non-drying ,l test (E2ndc D , Fig. 22), the one which was best prevented from drying (subsection 5.1.2), increases over time to reach 34 to 39 GPa, both at loading and unloading, while the modulus of the 2D drying sample remains stable at around 22 to 25 GPa. In 2017 a post-mortem experimental campaign on the samples used for 1D and 2D creep and shrinkage tests was undergone. It included compressive strength and Young's modulus measurements on these samples, as shown in Section 4.3. These measurements showed that samples kept in drying condition have a compressive strength and a Young's modulus which is lower than the samples kept in (even imperfect) sealed conditions. On average, this difference amounts to 12 MPa for strength and 4 GPa for Young's modulus (5 drying samples and 3 sealed samples have been

Fig. 21. Non-drying shrinkage in 2D tests in the three directions.

reaches a finite value at some point. In these authors' opinion, even the autogenous shrinkage should do so because of the finite amount of reactants in the concrete. However in the opinion of the present authors, the viscoelastic nature of shrinkage can explain the prolonged strain rate at fixed RH due to delayed strains under capillary tensions (or other efforts imposed by the fluid phase) which is the basis of the model proposed in Aili et al. [36]. However, in our tests, the suspected leaking of the samples makes it difficult to come to a conclusion on the long-term evolution of the non-drying strains, as will be shown in Section 7, which addresses the long-term behavior. 6. Instantaneous Young's modulus and Poisson's ratio The force and strain measurements have been used during loading and unloading phases to estimate the apparent Young's modulus and Poisson's ratio. It must be noted that a larger set of monitoring data is available during the initial loading (more frequent sampling) than during the unexpected unloadings (one acquisition per hour). In an effort to make a valid comparison with the loading rates recommended for standard testing of the Young's modulus of concrete, the values of the strains used in the present analysis correspond to the available measurements in the hour after loading or unloading instead of the strain measurements immediately following the beginning of the loading/unloading. Note that the Young's modulus in the standard tests is determined during the third loading, which can also be a source of difference between the moduli computed from the creep tests. 6.1. Computation of the elastic properties A summary of the expressions used to compute the elastic characteristics is now given. First, for the 2D tests, if we assume that a step application of force occurs at time t, we can define the average stress and strain jumps σ and ε . Their proportionality is described by the stiffness tensor ℂ(t), which is dependent on the rate of loading or unloading, a dependence that is neglected due to the intermediate rates of loading used here. If the material is assumed transverse isotropic in the transverse direction, i.e., in the direction of moisture transfer gradient, relations between the stress and strain steps and the in-plane Young's modulus E2D(t), the inplane Poisson's ratio ν2D(t), and the out-of-plane ratio νt(t)/Et(t) can be written:

Fig. 22. Young's moduli in 1D (markers) and 2D (markers + lines) drying and nondrying tests. Exponent l (respectively u) refers to a loading (respectively unloading) of the sample.

12

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

7. Long-term logarithmic strains

tested). Therefore, both the interpretation of the instantaneous strains measured in the creep tests and the standards tests results show that the storage condition (drying or sealed) influences the magnitude of Young's modulus after more than 10 years. However, while creep tests seem to show that the Young's modulus of sealed samples has increased, the standard tests show that the Young's modulus of drying samples has decreased. Therefore, it seems that these observations are the result of combined factors:

The literature on basic creep seems to indicate that long-term basic creep is not asymptotic but rather evolves as a logarithm with time [20,34,40-44]. The independent assessment of this result on structural concrete representative of an operating NPP CCB is one of the motivations of the experimental campaign described in this article. Hence, shrinkage and creep curves are plotted as a function of the logarithm of time. Time is counted from the beginning of the strain measurements, i.e., at t0 = 24 h for shrinkage tests and tl = 90 d for creep tests. The measurement data presented in the previous section are interpolated on a logarithmic time vector in three parts: 50 log-spaced points between t0 and tl, 50 log-spaced points between tl and the unloading time tu, and finally five log-spaced points between tu and the end of the tests tf. In this article, only the strains that are measured directly are called by a specific notation. These strains are non-drying (or sealed) shrinkage, drying shrinkage, non-drying creep and drying creep, measured in the tests of the same name. We will also present differences between these strains, but we will not give them a specific name, in order to avoid possible confusion. All notations are explained in Section 2. Contraction strains are represented as positive. In this section, strains are displayed and analyzed. Only one 1D test is used, which is the number 2 specimen of the 1D-2002 campaign. As shown in Fig. 24, all long-term drying shrinkage strains exhibit a linear trend in a logarithmic timescale. The radial and transverse strains are larger since they correspond to the direction of drying for both geometries. Longitudinal strains are slightly larger than vertical and horizontal ones since drying rate for cylindrical geometries is higher. Linear fitting was performed for the biaxial tests (between 1000 days and the end of the loading phase). The coefficients are given in Table 9 at the end of the section. The non-drying shrinkage strains are shown in Fig. 25. All curves have a similar logarithmic trend between 1000 days and the end of the tests. However, as mentioned earlier, it is difficult to differentiate the intrinsic non-drying shrinkage to that produced by unwanted leaks during the tests. Drying creep strains are plotted in Fig. 26. A clear logarithmic behavior is observed at the end of the test for both 1D and 2D tests. Finally, non-drying creep strains are plotted in Fig. 27. A logarithmic evolution was fitted on all strain curves between 1000 days and the end of the loading phase. The coefficients of the equation x1 log(t − ti) + x2 have been optimized and gathered in Table 9. Time ti is t0 for shrinkage tests, and tl is for creep tests.

• Hydration-induced

•

hardening continued developing in the nondrying samples, leading to a continuous increase of the Young's modulus. The high water-to-cement ratio of the concrete used in this study is greater than the lower limit of 0.418 proposed by Powers and Brownyard [37] to ensure that the cement can be fully hydrated. Underestimation of the Young's modulus at first loading in the creep test (compared to the third loading used in standardized tests and unloadings or loadings after a long time under load for the creep tests).

Let us draw a parallel with Brooks' data [20]. The Young's moduli were determined at loading and unloading of 15 or 30 years of tests on a wide variety of concretes with different water-to-cement ratios and made of different kinds of aggregates. The loading was performed at 15 days, which is much less time than the 90 days of the present test campaign. The non-drying samples were kept underwater instead of being sealed, as in the present study. It was found out that the Young's moduli of samples underwater increased by a factor of 1.7 compared to the 15 day Young's modulus, while in the drying condition, the increase was only of a factor of 1.36. In our study, the modulus in non-drying condition increases by a factor of 1.3 to 1.4, while the drying Young's modulus remains stable, which is close to Brooks' conclusions (the difference can probably be explained by the difference of age of loading). Decrease of Young's modulus with drying was also observed in other experimental campaigns such as [38,39]. The Poisson's ratios have also been calculated and are shown in Fig. 23. High initial values of the PRs are observed, as well as a decrease over time. There is also an important difference between the 1D and 2D apparent PRs in the drying tests, which could perhaps be explained by different crack patterns due to drying shrinkage.

Fig. 23. Poisson's ratios in 1D (markers) and 2D (markers + lines) drying and non-drying tests. Exponent l (respectively u) refers to a loading (respectively unloading) of the sample.

Fig. 24. Drying shrinkage strains.

13

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

Table 9 Coefficients of the logarithmic law identified for each strain evolution between 1000 days and the end of the loading phase. Time is in days, and strain is dimensionless.

εhndc − εhnds ε vndc − ε vnds εwndc − εwnds εhdc − εhds ε vdc − ε vds εwdc − εwds εhnds ε vnds εwnds εhds ε vds εwds

x1 [1/log(d)]

x2 [-]

5.08 10− 4

− 1.02 10− 3

8.48 10− 4

− 1.56 10− 3

−9.89 10

−4

− 2.31 10− 3

−4

2.13 10

2.51 10− 4

4.65 10− 4

6.08 10− 4

−6.22 10− 4

3.63 10− 4

−4

3.20 10

−7.80 10− 4

3.56 10− 4

−8.76 10− 4

4.09 10− 4

−1.00 10− 3

−4

3.21 10− 4

−4

1.16 10

2.49 10− 4

1.88 10− 4

2.39 10− 5

1.10 10

Fig. 27. Non-drying creep strains.

None of the evolution is stabilized, and the fit obtained with the logarithmic law is very good. Since a logarithmic behavior is only obtained after roughly 3 years, the present tests confirm that short tests which are usually performed (< 1 year) are too short to characterize long-term creep. Following Torrenti and Le Roy [41], we will apply logarithmic fits on the computed uniaxial compliance in the next section. We have shown that in all the tests performed, the very long-term strains are proportional to the logarithm of time since demoulding. It is also the case if the time since casting or since loading is used for creep tests. This fact can be explained by a number of reasons, which are probably true simultaneously:

• The shrinkage and creep-delayed strain are manifestations of the

Fig. 25. Non-drying shrinkage strains.

• •

same physical mechanisms under different loadings (interstitial water depression or external loading). Therefore, their long-term behavior is the same once those loadings are stabilized (at the end of drying for the capillary depression, all the time for the external loading). The carbonation shrinkage [45], which probably evolves as the square root of time since carbonation is far from being completer in the samples in 10 years of test, is of low amplitude compared to drying shrinkage. The long-term drying occurring in sealed specimen due to leaking also induces logarithmic long-term strains (see Fig. 30, where the mass-loss measured on 2D drying and sealed samples are approximately logarithmic after 1000 days even if there is no fundamental reason explaining this).

In order to understand which of these phenomena are predominant, experimental programs on smaller samples (made for example with cement paste) are needed and will be performed at EDF R & D. On small samples, it becomes possible to control the RH and also the CO2 content in the air surrounding the sample and, hence, gather more information about the coupling of these phenomena. Let us emphasize that we do not consider the fact that long-term strains seem logarithmic to be an explanation for the physical mechanisms involved. Much more research is needed to explain why these strains seem logarithmic, as in this study, or more generally why the strain rate seems to evolve as negative powers of the time, more or less close to one. On that topic, it has already been possible to use a micromechanical model for basic creep to show that the logarithmic behavior can emerge through upscaling from a local viscoelastic behavior

Fig. 26. Drying creep strains.

14

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

occurs. However, if isotropy was not assumed, it would not be possible to determine all viscoelastic functions. Under these assumptions, the uniaxial compliance and the creep Poisson's ratio in the 1D tests write:

described by a simple Maxwell rheological scheme [46]. 8. Creep Poisson's ratio and uniaxial compliance

J1D (t 0, t ) =

Several articles in the literature on concrete creep discuss the evolution of the creep Poisson's ratio (CPR) [8-12,14-16,18,47-50], as explained in subsection 3.3. Some authors argue that the CPR for basic creep is constant [2,15,48]. There is no fundamental reason why it should be constant since many materials exist for which the deviatoric and volumetric delayed strains evolve with different characteristic times. However, if it is shown experimentally that its variations are small, it is of important practical use to the modeling of basic creep and also for the experimental data needed to identify the parameters of the model. In this section we detail the approach used in this paper to compute the CPR and show the results obtained. The classical theory of viscoelasticity is used in this paper. It yields appropriate expressions of the CPR for both 1D and 2D creep tests, assuming that the material behaves as an isotropic linear viscoelastic solid. The theoretical equations are not detailed here, but the reader can refer to the article Charpin and Sanahuja [14] where the isotropic linear viscoelastic constitutive law is developed in detail.

εl (t ) ε (t ) , ν1D (t 0, t ) = − r . σl εl (t )

(3)

8.1.3. Expressions for 2D tests Concerning the 2D tests, the force was maintained constant by pressure regulation. Therefore, we only assume that stress is homogeneous in the sample and that the material remains isotropic to perform our macroscopic analysis and compute apparent creep compliances. The uniaxial compliance and the CPR in 2D can be computed using:

⎧ J (t ) = σv ε v (t ) − σh εh (t ) 2D ⎪ σv2 − σh2 ⎨ σh ε v (t ) − σv εh (t ) ⎪ ν2D (t ) = σ ε (t ) − σ ε (t ) v v h h ⎩

(4)

One can also use

J2D (t ) ν2D (t ) = −

8.1. Theoretical expressions for compliances and Poisson's ratios The method used here to define and compute the Poisson's ratios is based on the theory of linear viscoelasticity [14,51-54]. This framework allows rigorously defining relaxation and creep Poisson's ratio. Unfortunately, the expressions used in the literature vary, which sometimes makes comparisons difficult.

εw (t ) . σv + σh

(5)

8.1.4. Computation of the relaxation Poisson's ratio The literature on viscoelasticity emphasizes that the CPR and the relaxation Poisson's ratio are different if they are not constant [14,18,50,55,56]. While the computation of the CPR from strain measurements is straightforward for a creep test, the computation of the relaxation PR requires a numerical inversion of the relation between the relaxation and the creep Poisson's ratio (see [14]). Assuming that concrete is non-aging, this inversion is performed by discretization of the integral and inversion of the obtained matrix following Sorvari and Malinen [57] or Bažant [58]. This is why the relaxation Poisson's ratio is rarely computed when dealing with creep tests, and since relaxation tests on concrete are scarce, it is rarely computed at all, except by some authors who avoid the use of the CPR in order to be able to use the correspondence principle [47,59].

8.1.1. Definitions The CPR, here called νc(t0,t), is called creep Poisson's ratio because in the case of a uniaxial imposed stress, it is equal to the opposite of the ratio of transverse to axial strains, which coincides with the definition of the Poisson's ratio in elasticity but is specific to the fact that a constant stress was used. This coefficient is defined in the time domain and is related to the volumetric and deviatoric compliances by the same relationships as if the behavior was elastic (see [14]). This coefficient has been used by many authors in the past, such as [9,10,12]. The relaxation Poisson's ratio can be defined in the time domain, or, in the specific case of non-aging viscoelasticity, in the Laplace-Carson domain. Here we will define it in the time domain. Of course, both definitions are consistent. The relaxation Poisson's ratio is here called νr(t0,t) and is equal to the opposite of the ratio of the lateral strains to axial strains during a uniaxial experiment where a step of strain is imposed. The relaxation Poisson's ratio has the convenient property that in the case of non-aging linear isotropic viscoelasticity, the relationships between its Laplace-Carson transform and those of the relaxation functions are identical to relationships between the Poisson's ratio and stiffnesses in elasticity. Hence, the correspondence principle can be used, when the material is non-aging, with the relaxation Poisson's ratio but not with the CPR (see [14]).

8.2. Experimental uniaxial compliance and creep Poisson's ratio The CPR and uniaxial compliance are plotted using expressions from subsection 8.1. 8.2.1. Non-drying tests Uniaxial compliances J ndc are computed based on the difference between the creep strains and shrinkage strains, i.e., εndc − εnds (see Section 2), and are plotted in Fig. 28. Three test campaigns appear in Fig. 28: the 2D test, the 1D-2002 tests (labeled B11_1D), and the 1D-DTG-2005 test campaign (labeled DTG). These three campaigns yield close but different results. As discussed at subsection 5.1.2, the DTG results vary widely from one sample to another, which is believed to result from the different leaking rates of each sample caused by additional instrumentation that was not present in B11_1D tests, including additional wires passing through the sealing (made of four layers of adhesive aluminum). On the contrary, the leaking of B11_1D tests was mainly due to decomposition of the aluminum itself. A question that cannot be answered based solely on the available data is whether the B11_2D tests leaked in the same manner as the DTG tests. Yet unpublished numerical studies seem to show that significant mass loss occurred in the 2D sealed tests as well. The variations in the CPR, and also the relaxation PR, are plotted in Fig. 29. The CPR are quite different from one test to another (and to a greater extent than the creep compliances shown in Fig. 28). The initial

8.1.2. Expressions for 1D tests The analysis of the tests presented here is based on some assumptions. First, the slight evolution of the applied force (which is on the order of 10%) is neglected. It could be taken into account, assuming non-aging of the material, but this work has not been performed. Second, it is assumed that the state of stress is homogeneous in the sample (which is incorrect, especially for drying tests, but is useful for macroscopic analysis of the tests performed in this article). Some yet unpublished analyses of these tests through finite-element modeling have been performed and show that given the size of our samples, cracking in drying tests only affects the strain measurements during the first year of drying. Finally, the material is assumed isotropic, which is locally false, especially in the case of drying tests where cracking 15

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

Fig. 28. Uniaxial non-drying creep compliance (non-drying shrinkage has been subtracted).

Fig. 30. Average mass loss on 2D non-drying mass control samples.

decreases to 0.27 during the next 8 years of the test. During the last 8 years, this occurs simultaneously with the slight loss of mass observed on the mass loss control specimen, but it is hard to know if there is a causal link between the two. The 1D CPR goes down to zero, which means there is no more radial creep strain under longitudinal imposed stress. This is rather surprising. In the authors' opinion, the radial measurement in non-drying tests cannot be trusted because the tests were affected by local drying and, hence, shrinkage, which is unknown since it is different from the macroscopic shrinkage of the sample. Along with the measured CPR, Fig. 29 shows relaxation PR of the 2D , relax test ν2ndc , computed using the inversion method found in [57], D which only requires two assumptions: shrinkage must be subtracted so that only the creep strain is used and the material must be assumed nonaging. As pointed out by Aili et al. [50] for other tests, these two quantities remain close to each other, even if they are theoretically different [55,56]. The CPR determined from the creep strain, not in− el cluding the elastic strain (ν2ndc ), is also shown in Fig. 29. Its initial D value is higher than the one including the elastic strain and equal to that computed by Torrenti et al. [49]. In this article, the authors present a comparison of the CPR computed with their method from the present tests to other results from the literature [9,11,15,60]. The results computed from the present tests are clearly different from the other tests, since the computed CPRs in Torrenti et al. [49] range from 0.45 to 0.35, whereas all other CPRs are close to 0.2. However, this is partly due to a shift in the results related to the fact that the elastic strain was not taken into account. The results computed in this article are still higher than the other results. The present results also differ from the results of [19], where the basic CPR quickly decreases to zero, even if the concrete used is very close. However, the experimental setups are vastly different, as well as the sealing method.

Fig. 29. Creep Poisson's ratios, relaxation Poisson's ratio, and CPR computed from the creep strain diminished of both shrinkage and elastic strain.

values are equal, by definition, to the instantaneous Poisson's ratio and are very high, since in the 2D tests, the CPR is 0.31, while in the 1D tests, it is between 0.2 and 0.23 for the original 1D-2002 campaign, and between 0.23 and 0.28 for the 1D-DTG-2005 campaign. The DTG results are the most variable ones, while the B11_1D CPR drop down to zero after 2 years. It seems that the more the sample dries, the more the CPR drops (observation made in many previous studies of CPR [5]). However, we cannot verify this assumption due to the lack of mass loss measurements on the exact same samples as those on which strain was measured. Moreover, we must be very cautious with the 1D results since leaks affect the radial measurements. Hence, we consider the most meaningful result to be the 2D result. This sample lost some water due to leaks, as attested by the control sample after 2 years (Fig. 30), but the measurement system was less sensitive to leaks since it was fixed to the sample with rather deep (2 cm) inserts, which seem to make local drying shrinkage due to leaks less influent on the strain measurement. The decrease of the CPR in the 2D test is limited. It changes from 0.31 to 0.35 in a few days, then it is stable for 2 years, and slowly

8.2.2. Drying tests The drying tests are analyzed in this section. Since the state of stress in these tests is very heterogeneous due to drying, the computed viscoelastic properties are only apparent properties, not material properties. A model for drying, shrinkage, and creep is needed to identify the material properties on such tests. This work is also performed at EDF R & D but will not be presented in this article. The assumption of isotropy is still used, even though the material becomes anisotropic due to local cracking related to drying shrinkage, and the samples are also anisotropic due to the fact that drying occurs only in the radial direction for 1D tests and in the thickness direction for 2D tests. 16

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

Fig. 31. Apparent uniaxial drying creep compliances (drying shrinkage is subtracted).

Fig. 32. Apparent drying creep Poisson's ratios (drying shrinkage has been subtracted).

The strain tensor which is used to compute the apparent uniaxial compliances and apparent CPR is ε dc (t ) − ε ds (t − t0) (see notations,

important seasonal oscillations due to issues associated with humidity regulation in the room, which are not corrected by the subtraction of the shrinkage due to the 90 days shift of the drying shrinkage curve, to account for the different start dates of drying. These observations seem to show that drying does not necessarily lead to a decrease in the CPR. Coming back to the non-drying tests, which showed significant decrease in CPR in 1D while just a slight decrease in CPR in 2D, it is now possible to say that this effect was not solely due to the global drying of the sample because of leaks. Instead, it might be due to local drying close to the radial measurement point, which is a weak point in the sealing. This underlines once again that the radial results in the non-drying 1D tests cannot be used. Due to these measurement difficulties, the non-drying CPR in 2D is the only reliable estimate. Therefore, it is not possible to determine if the type of loading can cause changes in the CPR, as proposed by Neville et al. [5] and Gopalakrishnan et al. [11]. The radial measurement in drying tests can be trusted, but it is only an apparent property, which depends on the sample geometry and makes the comparison between 1D and 2D results less useful. Finally, a question remains unanswered: what is the reason for the high values of Poisson's ratios (elastic and creep PRs) computed for the 2D tests?

Section 2). This formula is used to take into account the fact that drying was started after 1 day for the drying shrinkage test but after 90 days (i.e., at loading) for the drying creep test. Therefore, to remove the shrinkage component from the creep test, a shift of the shrinkage results is performed, assuming that the drying and shrinkage behaviors of the material are non-aging (which is probably abusive when dealing with times as different as 24 h and 90 days). Clearly the fact that the drying did not start at the same age for creep and shrinkage tests is a major drawback of this experimental campaign. However, no simple method can take this into account, since involved modeling of the ageing affecting drying as well as shrinkage would be required. Another difficulty is the fact that cracking in the drying shrinkage test is different from cracking in the creep test due to the fact that the loading prevents cracking perpendicular to the load. To account for such complex phenomena, numerical models including the simulation of creep and cracking are needed [61–63]. Such work is currently being conducted at EDF R & D. 1D and 2D apparent uniaxial drying creep compliances are very different, as for the non-drying case (Fig. 31). The 1D tests are very close to each other. In 1D, drying is faster than in 2D, due to the sample geometry. In Granger's work [2], a shape factor of 4/9 was proposed to scale radial drying of a cylinder with uniaxial drying of a prism (if the diameter of the cylinder is equal to the thickness of the prism). However, the shape factor in this study seems much higher (drying of the cylinder is faster than that of the prisms by a factor much higher than 9/4). Despite the fact that drying is faster in 1D, the drying creep is much higher in the 2D tests. This is surprising since usually the dominant effect is the Pickett effect, that is the acceleration of creep by drying. However, we must recall that the quantities plotted here are only apparent properties, and also that since the sample are of different geometries, the cracking due to drying might differ vastly, resulting in different cracking patterns for 1D and 2D tests [61,62], a phenomenon which needs to be studied through finiteelement modeling of these experiments including creep, shrinkage, and cracking. The apparent drying CPRs also differ but are almost constant after significant changes occur within the first 100 days, as shown in Fig. 32. These CPRs are closer in 1D and 2D than for the non-drying case. The shrinkage was deduced, which leads to predicting almost constant CPR (around 0.40 for the 2D and around 0.33 for 1D), except for

8.2.3. Influence of the CPR on 2D non-drying creep The CPR and uniaxial compliance identified on the non-drying 2D creep tests is now used in order to assess the effect of variations in the CPR on biaxial results, i.e., on the strains in the concrete containment building which is subjected to the same state of stress. To do so, we use the uniaxial compliance combined with different assumptions for the CPR:

• The CPR identified on the 2D tests ν , CPR equal to the initial (elastic value) of the measured • A constant CPR ν (t ) , • A constant CPR equal to the final of the measured CPR ν (t ), • A constant CPR equal to zero, and • A constant CPR equal to 0.5. ndc 2D

ndc 2D

l

ndc 2D

∞

Using the combination of the uniaxial compliance to these CPRs, the vertical and horizontal strains are computed for each assumption. The response in the horizontal direction (Fig. 33) is much more affected by changes in the CPR than in the horizontal direction because the horizontal stress is only 8.5 MPa, whereas the vertical stress is 12 MPa. 17

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

Fig. 33. Horizontal strain computed from the uniaxial compliance identified on the 2D non-drying creep test and various assumptions for the CPR.

Fig. 34. Logarithmic fit of the uniaxial compliances in drying and non-drying tests following [41].

The measured horizontal strains lie between the strains computed with the assumption of a constant CPR equal to the initial and final values. This confirms that it is a good modeling strategy to consider that the basic creep Poisson's ratio is constant and equal to the elastic one (which is done in many models [64–67]) The strains obtained assuming a zero or 0.5 CPR differ vastly from the measured ones, and the magnitude of this difference gives an idea of the effect of an error on the CPR. The final strains for these two extreme and unrealistic cases differ by a factor of 3.

Table 10 Coefficients identified for the logarithmic fit of the compliances function proposed in [41].

1 1 t − tl ⎞ + log10 ⎛1 + . E C τ (tl ) ⎠ ⎝ ⎜

E (GPa)

C (GPa)

τ(tl) (d)

Non-drying Non-drying (1000 d) Drying test

23.0 24.5 24.5

25.1 45.2 12.6

16.6 2.15 4.43

classical cylindrical tests and original biaxial tests were conducted using sealed and drying conditions. The aim was to characterize the multiaxial nature of basic and drying creep and of endogenous and drying shrinkage. The two main goals of the experimental campaign were achieved. It was confirmed that the long-term evolution of basic creep follows a logarithmic trend and that all strain components follow this same trend between the third year and the end of the tests. This strongly supports the idea that all delayed strains find their origin in the same physical phenomena at the lowest scales. It was also shown that the creep Poisson's ratios, both in basic and drying conditions, remain roughly constant during the 10- to 12-year-long tests that were performed, supporting the assumption used in many numerical computations of concrete creep that the CPR is constant. The basic CPR roughly evolved from 0.32 to 0.27, while the drying apparent CPR remained between 0.3 and 0.35. However, it was not understood why such high Poisson's ratios (both elastic and delayed) were found in this study, while in the literature most Poisson's ratios lie between 0.2 and 0.25. Interestingly, the Young's modulus of the sealed biaxial samples increased by roughly 30% during the 10 year test. The results are now being used at EDF R & D and in partner labs to challenge the phenomenological creep models. The availability of a true multiaxial information makes the biaxial tests much more discriminating regarding the multiaxial nature of the models than the usual uniaxial tests. The authors believe that if the radial strain measurement in the 1D tests was more reliable, the 1D tests could serve the same role. Unfortunately this was not the case mostly due to sealing issues. The experimental knowledge gained from this campaign is now being used to improve procedures of subsequent campaigns. The main point is that mass needs to be measured on the actual samples that undergo creep and shrinkage either continuously, if possible, or at least by measuring the difference between the beginning and the end of the

8.2.4. Logarithmic fits to the uniaxial compliances Let us now briefly come back to the topic of the logarithmic longterm creep, with an analysis of the uniaxial creep compliance. While for structural modeling purposes some authors propose that the characteristic time to reach a logarithmic behavior is related to the strain of concrete at loading [64,65], we propose here to use a simpler approach in order to perform logarithmic fits of our curves. Based on works of [68] cited by [5] but also [42,69,70], Torrenti proposed to use the same logarithmic function to fit creep curves [41]. The proposed expression is

J (t ) =

Test

⎟

(6)

This function has three parameters, but Torrenti showed that only τ(tl) depends on the age of the sample at loading. Here, only one age at loading is available. We have identified the three parameters for the drying and non-drying compliances. The fits are shown in Fig. 34. The coefficients identified are shown in Table 10. While the fit is very good for the 2D drying test on the full period, it is not accurate for the 2D non-drying test. It seems that starting from 1000 days, the strains accelerate in a way which is incompatible with the proposed logarithmic function (Eq. (6)). The fit in the non-drying case was attempted on the first 1000 days of the test and is much more accurate. This might be due to an increase in leaks starting at 1000 days, as can be seen on companion samples (Fig. 30). 9. Conclusion The objective of this experimental campaign was to gain knowledge about the creep and shrinkage of concrete, which cause pre-stress losses in the CCBs and, hence, influence their leak tightness. The tests were performed using a concrete similar to that of Civaux 1, France. Both 18

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

[22] C. Boulay, F. Le Maou, J.-L. Clément, Some solutions to experimental problems, in: F-J. Ulm, Z.P. Bazant, F.H. Wittmann (Eds.), Concreep 6, Creep, Shrinkage and Durability Mechanics of Concrete and other Quasi-Brittle Materials, 2001. [23] Y. Le Pape, H-T25-03-020-A - comparaison des caractéristiques mécaniques et physiques du béton réalisé dans le cadre des essais de déformations différées TEGG avec des données relatives à la formulation B11 de Civaux, Technical report, EDF R & D, 2003. [24] C. Foussat, EFTCE / 02-132-A - Essai de caractérisation du ciment Airvault utilisé pour l’étude PPRD MVGC FLUAGE DES BETONS, Technical report, EDF CEIDRE TEGG/CEMETE, 2002. [25] N. Reviron, Etude du fluage des bétons en traction. Application aux enceintes de confinement des centrales nucléaires à eau sous pression, École normale supérieure de Cachan-ENS Cachan, 2009 (PhD thesis). [26] M. Briffaut, Etude de la fissuration au jeune âge des structures massives en béton: influence de la vitesse de refroidissement, des reprises de bétonnage et des armatures, École normale supérieure de Cachan-ENS Cachan, 2010 (PhD thesis). [27] M. Omar, Déformations différées du béton: étude expérimentale et modélisation numérique de l’interaction fluage-endommagement, Nantes, 2004 (PhD thesis). [28] J. Saliba, Apport de l’émission acoustique dans la compréhension et la modélisation du couplage fluage-endommagement du béton, Ecole Centrale de Nantes, 2012 (PhD thesis). [29] F.-J. Ulm, F. Le Maou, C. Boulay, Creep and shrinkage coupling: new review of some evidence, Rev. Fr. Génie Civ. 3 (3–4) (1999) 21–37. [30] A. Acker, Z.P. Bažant, J.C. Chern, C. Huet, F.H. Wittmann, RILEM TC 107-CSP recommendation. Measurement of time-dependent strains of concrete, Mater. Struct. 31 (1998) 507–512. [31] J.-M. Torrenti, B. Djebri, A. Bascoul, J.-L. Granju, Comparative study of two biaxial presses for concrete, Mater. Struct. 24 (1) (1991) 52–60. [32] J.G.M. Van Mier, Strain-softening of concrete under multiaxial loading conditions, Technische Hogeschool Eindhoven, 1984. [33] B. Masson, E. Galenne, E. Oukhemanou, C. Aubry, G. Laou-Sio-Hoi, Vercors: a 1/3 scaled mockup and an ambitious research program to better understand the different mechanisms of leakage and aging, Proc. Fontevraud 8: Conference on Contribution of Materials Investigations and Operating Experience to LWRs' Safety, Performance and Reliability, 2014. [34] M.H. Hubler, R. Wendner, Z.P. Bažant, Comprehensive database for concrete creep and shrinkage: analysis and recommendations for testing and recording, ACI (2014). [35] B. Persson, Eight-year exploration of shrinkage in high-performance concrete, Cem. Concr. Res. 32 (8) (2002) 1229–1237. [36] A. Aili, M. Vandamme, J.-M. Torrenti, B. Masson, On a poromechanical approach to long-term autogenous shrinkage, Poromechanics VI, 2017, pp. 961–966. [37] T.C. Powers, T.L. Brownyard, Studies of the physical properties of hardened Portland cement paste, ACI Journal Proceedings, vol. 43, ACI, 1946. [38] N. Burlion, F. Bourgeois, J.-F. Shao, Effects of desiccation on mechanical behaviour of concrete, Cem. Concr. Compos. 27 (3) (2005) 367–379. [39] H. Kallel, H. Carré, C. La Borderie, B. Masson, N.C. Tran, Effect of temperature and moisture on the instantaneous behaviour of concrete, Cem. Concr. Compos. 80 (2017) 326–332. [40] G.E. Troxell, J.M. Raphael, R.E. Davis, Long-time creep and shrinkage tests of plain and reinforced concrete, ASTM Proceedings, vol. 58, 1958, pp. 1–20. [41] J.-M. Torrenti, R. Le Roy, Analysis and modelling of basic creep, CONCREEP 10, Vienna, Austria, 2015, pp. 1400–1409. [42] M. Vandamme, F.-J. Ulm, Nanoindentation investigation of creep properties of calcium silicate hydrates, Cem. Concr. Res. 52 (2013) 38–52. [43] R. Le Roy, F. Le Maou, J.-M. Torrenti, Long term basic creep behavior of high performance concrete: data and modelling, Mater. Struct. 50 (1) (2017) 85. [44] J.-M. Torrenti, R. Le Roy, Analysis of some basic creep tests on concrete and their implications for modeling, Struct. Concr. (2017). [45] Y.F. Houst, Carbonation shrinkage of hydrated cement paste, Proc. 4th CANMET/ ACI International Conference on Durability of Concrete, CANMET, Ottawa, Canada, 1997, pp. 481–491 number LTP-CONF-1997-005. [46] L. Charpin, J. Sanahuja, N.C. Tran, L. Petit, O. Bremond, J. Montalvo, J. Azenha, J. Granja, Multiscale modeling of hydration, elasticity and creep of VeRCoRs concrete. Focus on creep characteristic times. Proceedings of TINCE 2016, Paris, France, 2016. [47] Z.C. Grasley, D.A. Lange, The viscoelastic response of cement paste to three-dimensional loading, Mech. Time-Depend. Mater. 11 (1) (2007) 27–46. [48] I.J. Jordaan, Analysis of creep in concrete structures under general states of stress, Seminar on Concrete Structures Subjected to Triaxial Stresses, Bergamo, Italy, 1974, pp. 111–118. [49] J.-M. Torrenti, F. Benboudjema, F. Barré, E. Gallitre, On the very long term delayed behaviour of concrete, Proc. Int. Conf. Ageing Mater. Struct. (2014). [50] A. Aili, M. Vandamme, J.-M. Torrenti, B. Masson, Theoretical and practical differences between creep and relaxation Poisson's ratios in linear viscoelasticity, Mech. Time-Depend. Mater. 19 (4) (2015) 537–555. [51] J. Salençon, Viscoélasticité, Presses de l’Ecole Nationale des Ponts et Chaussées, 1983. [52] R. Christensen, Theory of Viscoelasticity: An Introduction, Elsevier, 2012. [53] J. Mandel, Mécanique des milieux continus, Gauthier-Villars, Paris, 1966. [54] C. Truesdell, W. Noll, The Non-linear Field Theories of Mechanics, Springer, 2004. [55] H. Hilton, The elusive and fickle viscoelastic Poisson's ratio and its relation to the elastic-viscoelastic correspondence principle, J. Mech. Mater. Struct. 4 (7) (2009) 1341–1364. [56] R.S. Lakes, A. Wineman, On Poisson's ratio in linearly viscoelastic solids, J. Elast. 85 (1) (2006) 45–63.

test. Second, the tremendous effect of humidity has led EDF to start an experimental program of RH profile measurements in cylindrical samples similar to the uniaxial creep samples. These results will help in understanding the behavior of the concrete used to build the VeRCoRs mock-up and will be made available to the community through benchmarks [33]. Acknowledgments This article aims to publish the main conclusions of a long test campaign that involved many researchers and workers from different teams at EDF and other organizations. The main contributors and their affiliation at the time of their contribution are recalled here. The original idea of the campaign came from G. Heinfling (EDF R & D) and E. Toppani (EDF CEIDRE-TEGG), and the funding came from EDF SEPTEN. The design of the 1D rigs came from LCPC (with the help of F. Le Maou), and that of the 2D rigs involved researchers from the LGCU at Marne-la-Vallée (F. Meftah, A. Sellier). The tests were then started at CEIDRE-TEGG by E. Coustabeau and E. Toppani and were followed at EDF R & D by Y. Le Pape. After Y. Le Pape joined ORNL, the tests were followed by a working group composed of B. Masson (EDF Septen), A. Courtois (EDF DTG), C. Le Bellego, N. Reviron and J. Montalvo (CEIDRE-TEGG), J. Sanahuja, and L. Charpin (EDF R & D). Finally, the analysis was performed by L. Charpin, and this article was written by L. Charpin and Y. Le Pape. The authors wish to thank all the contributors to this study. References [1] NEA, NEA/CSNI/R(2015)5 - Bonded or Unbonded Technologies for Nuclear Reactor Prestressed Concrete Containments, Technical report, 2017. [2] L. Granger, Comportement différé du béton dans les enceintes de centrales nucléaires : analyse et modélisation (PhD thesis), Laboratoire Central des Ponts et Chaussées, France, 1995. [3] F. Benboudjema, Modélisation des déformations différées du béton sous sollicitations biaxiales. Application aux enceintes de confinement de bâtiments réacteurs des centrales nucléaires, Université de Marne la Vallée, 2002 (PhD thesis). [4] W.H. Glanville, Studies in reinforced concrete - III: the creep or flow of concrete under load, Building Research technical paper No. 12, 1930. [5] A.M. Neville, W.H. Dilger, J.J. Brooks, Creep of Plain and Structural Concrete, Construction Press, 1983. [6] A.D. Ross, Experiments on the creep of concrete under two-dimensional stressing, Mag. Concr. Res. 6 (16) (1954) 3–10. [7] D.J. Hannant, Strain behaviour of concrete up to 95 C under compressive stresses, Proc. Conference on Prestressed Concrete Pressure Vessels Group C, Institution of Civil Engineers, London, 1967, pp. 57–71. [8] H.G. Meyer, On the influence of water content and of drying conditions on lateral creep of plain concrete, Matér. Constr. 2 (2) (1969) 125–131. [9] T.W. Kennedy, Evaluation and summary of a study of the long-term multiaxial creep behavior of concrete, Technical report, Oak Ridge National Lab., Tenn.(USA), 1975. [10] G.P. York, T.W. Kennedy, E.S. Perry, Experimental Investigation of Creep in Concrete Subjected to Multiaxial Compressive Stresses and Elevated Temperatures, Department of Civil Engineering, University of Texas at Austin, 1970. [11] K.S. Gopalakrishnan, A.M. Neville, A. Ghali, Creep Poisson's ratio of concrete under multiaxial compression, ACI Journal Proceedings, vol. 66, ACI, 1969. [12] C.E. Kesler, Creep behavior of Portland cement, mortar, and concrete under biaxial stress, Technical report, Illinois Univ., Urbana (USA), 1977. [13] J.E. McDonald, Creep of concrete under various temperature, moisture, and loading conditions, ACI Spec. Publ. 55 (1978). [14] L. Charpin, J. Sanahuja, Creep and relaxation Poisson's ratio: back to the foundations of linear viscoelasticity. Application to concrete, Int. J. Solids Struct. 110 (2017) 2–14. [15] I.J. Jordaan, J.M. Illston, The creep of sealed concrete under multiaxial compressive stresses, Mag. Concr. Res. 21 (69) (1969) 195–204. [16] L.J. Parrott, Lateral strains in hardened cement paste under short-and long-term loading, Mag. Concr. Res. 26 (89) (1974) 198–202. [17] O. Bernard, F.-J. Ulm, J.T. Germaine, Volume and deviator creep of calciumleached cement-based materials, Cem. Concr. Res. 33 (8) (2003) 1127–1136. [18] A. Aili, M. Vandamme, J.-M. Torrenti, B. Masson, Difference between creep and relaxation Poisson's ratios: theoretical and practical significance for concrete creep testing, CONCREEP 10, 2015, pp. 1219–1225. [19] A. Hilaire, Etude des déformations différées des bétons en compression et en traction, du jeune âge au long terme : application aux enceintes de confinement, (2014). [20] J.J. Brooks, 30-year creep and shrinkage of concrete, Mag. Concr. Res. 57 (11) (2005) 545–556. [21] R. Le Roy, Déformations instantanées et différées des bétons à hautes performances, École Nationale des Ponts et Chaussées, 1995 (PhD thesis).

19

Cement and Concrete Research xxx (xxxx) xxx–xxx

L. Charpin et al.

sustainable Concrete Structures, Aix, 2012. [65] A. Sellier, S. Multon, L. Buffo-Lacarrière, T. Vidal, X. Bourbon, G. Camps, Concrete creep modelling for structural applications: non-linearity, multi-axiality, hydration, temperature and drying effects, Cem. Concr. Res. 79 (2016) 301–315. [66] L. Charpin, T.O. Sow, X. D'Estève de Pradel, F. Hamon, J.-P. Mathieu, Numerical simulation of 12 years long biaxial creep tests: efficiency of assuming a constant Poisson's ratio, Poromechanics VI, 2017, http://dx.doi.org/10.1061/ 9780784480779.124. [67] Z.P. Bažant, A.B. Hauggaard, S. Baweja, F.-J. Ulm, Microprestress-solidification theory for concrete creep. I: aging and drying effects, J. Eng. Mech. 123 (11) (1997) 1188–1194. [68] US Bureau of Reclamation, Creep of concrete under high intensity loading, Concrete laboratory report No. C-820, 1956. [69] P. Acker, F.-J. Ulm, Creep and shrinkage of concrete: physical origins and practical measurements, Nucl. Eng. Des. 203 (2) (2001) 143–158. [70] Model Code, International Federation for Structural Concrete (fib), Federal Institute of Technology Lausanne-EPFL, Section Génie Civil, Switzerland, 2010 978–3.

[57] J. Sorvari, M. Malinen, On the direct estimation of creep and relaxation functions, Mech. Time-Depend. Mater. 1385-2000, 11 (2) (2007) 143–157. [58] Z.P. Bažant, Numerical determination of long-range stress history from strain history in concrete, Mater. Struct. 5 (27) (1972) 135–141. [59] X. Li, Z.C. Grasley, J.W. Bullard, E.J. Garboczi, Computing the time evolution of the apparent viscoelastic/viscoplastic Poisson's ratio of hydrating cement paste, Cem. Concr. Compos. 56 (2015) 121–133. [60] J. Bergues, P. Habib, Fluage triaxial des bétons. la déformation et la rupture des solides soumis à sollicitations pluriaxiales, Colloque international de la RILEM, 1972. [61] Z.P. Bažant, Y. Xi, Drying creep of concrete: constitutive model and new experiments separating its mechanisms, Mater. Struct. 27 (1) (1994) 3–14. [62] F. Benboudjema, F. Meftah, J.-M. Torrenti, Interaction between drying, shrinkage, creep and cracking phenomena in concrete, Eng. Struct. 27 (2) (2005) 239–250. [63] C. de Sa, F. Benboudjema, M. Thiery, J. Sicard, Analysis of microcracking induced by differential drying shrinkage, Cem. Concr. Compos. 30 (10) (2008) 947–956. [64] A. Sellier, L. Buffo-Lacarrière, S. Multon, T. Vidal, X. Bourbon, Nonlinear basic creep and drying creep modelling, Conference Numerical Modeling Strategies for

20