4 Results and discussions 1 Introduction
4.4 Determination of time-zero 1 Introduction
4.4.2 Time-zero criterion i Possibilities and limitations
As has been signalized in the literature review, keeping the test object and conditions constant and, additionally to this, having thermal effects due to hydration heat excluded, the magnitude of autogenous shrinkage will vary depending on concrete age chosen as the starting point for AS data evaluation. This reference point has been commonly referred to as time-zero and it is of major importance as far as assessment of curing method efficiency is concerned. Indeed, unjustified choice of time-zero could lead to large under- or overestimation of real autogenous shrinkage while affecting interpretation of IC effect.
Despite the fact that this issue has attracted much attention including debates performed in the framework of three RILEM Technical Committees (TC-181 EAS, TC-196 ICC and TC-225 SAP) with extension to many separate, goal-oriented studies (among others [Jus 00][Med 06][Cha 07][Cus 07][Ima 07][Epp 09][Kaz 10][Dar 11][Med 11b][Yoo 13]), the choice of time-zero and its determination method is still vague. To date, the most popular procedure being in accordance with the standardized protocol [ASTM C1698-09] is evaluating autogenous shrinkage from final set in accordance with one of the specified penetration tests. When comparing it to an early publication of the method developers [Jen 95], one immediately acknowledges that the viewpoint, for reasons that can be only speculated (e.g. some experimental observations [Tia 08] and general need of limitation of deformation to the part which can actually generate tensile stresses leading to cracking), has changed; in particular, it is found that the final set replaced time of setting, which in [Jen 95] had been
used as time-zero. This alteration was likely necessary given that the latter ascription has been often interpreted as initial set/initial setting time [Igarashi and Watanabe, p.77 in RILEM pro052]. Nonetheless, because very few authors have ever attempted to justify the choice of the time-zero without depending on arbitrary chosen setting-related points only, with exceptions regarding mainly the case of studies on cement paste (e.g. [Sant et al., p. 375 in RILEM pro052][San 09]) and very rare ones on concrete (e.g. [Epp 09][Dar 11]), evaluation of autogenous shrinkage results starts with this important aspect.
Establishing a definition/criterion of time-zero is challenging especially if both phenomenological and practical aspects of the deformation are concerned at once. For instance, it is evident that autogenous shrinkage origins very early, on contact of cement with water, without [Mou 06] or with [Cha 07][Mou 06] accompanying contribution of self- desiccation. A logical step is therefore to begin with the measurements as early as possible, best directly after mixing, in order to record the entire history of early age deformation. Notably and as further showed in references [Dud 10b][Gor 11], only so important changes which start much before final set and are attributed to IC can be captured (see also discussion part in Section 4.6.3) . As will be shown in short, some criteria for finding time-zero are in fact based on this knowledge. On contrary, it is generally understood that production of effective autogenous shrinkage i.e. part of deformation which could actually lead to stresses and potentially cracking, starts much later than mixing. This could be traced back to regaining the tensile strain capacity (after the sharp drop began in the plastic state) [Med 11b] on one hand, and development of mechanical properties, especially Young’s modulus, on the other hand. Both of these events as a rule of thumb have been associated with material that has already undergone the complex fluid-solid transition and falls in the time-period when it is considered to be in the semi-solid state. This shows why starting point of autogenous shrinkage measurement and being possible from sample casting itself cannot be considered as time-zero, the initiation point of effective autogenous shrinkage.
As such, the fluid-solid transition is complex process and covers multitude of events happening about very close time vicinity, see Figure 4.38. While this notably masks the Figure 4.38: Events associated with time-zero definition and their real or likely appearance in respect to setting points.
IS FS
PSS
Early concrete age
SO L ID , M A X d σt /d t CONTACT TO WATER SUSPENSION (plastic and workable mix) SEMI- SOLID (stiff and un- workable mix) RIGID SOLID GAINING STRENGTH M IN ER A L , E- PR O PER T IES SK EL ET O N , ST R ESS, M A X d ε/ d t Events = DENSIFYING/REDUCING POROSITY
Without identified occurrence in respect to setting points:
P point – percolation point [Fey 01]; occurs when shrinkage is impaired by agglomeration of the sample as whole
I point – ‘isostatic’ point; related to locking of solid skeleton and end of global freedom to largest particles of the medium (small interstitial particles however still remain mechanically uncoupled inside the frame) [Fey 01]; giving rise to rapid evolution of Young’s modulus and bulk modulus (at this stage: bulk modulus > Young’s modulus) as well as decrease of Poisson’s ratio [Fey 01]
H point – hyperstatic (mechanical) point; takes place when all particles of the material are linked together ([Fey 01] to the main framework) = material is totally connected [Mor 02] and no degree of freedom remains for any particle [Mor 01]; Young’s modulus becomes higher than the bulk one [Fey 01][Mor 02] and degree of hydration is approx. 3 %.
Where:
IS, FS – initial set, final set, respectively PSS – point of self-support [Ham 06b]
MINERAL – mineral percolation threshold [Bar 01]
E-PROPERTIES – development of elastic properties (low w/c paste) [San 09]
SKELETON – formation/development of load-resisting skeleton in case of pastes [San 09]; event sometimes shifted to later ages after setting, e.g. [Zhu 08]
STRESS – onset of tensile stress generation under external restraint in some UHPC [Epp 09]; takes place earlier for other UHPC [Epp 09] and later for pastes [San 09]
MAX dε/dt – max deformation rate change (maximum velocity) in some UHPC [Epp 09] and paste without additives [Ass 13]; taking place later in some UHPC [Epp 09], other concretes [Med 11b], and paste/mortar with mineral additions [Pir 06]
SOLID – threshold of solidification and vicinity of maximum thermal flux (= max rate of temperature change) [Med 06][Med 11b]
borderline between plastic shrinkage and effective autogenous shrinkage, more criteria for finding time-zero have been proposed (based on physical and chemical aspects of autogenous deformation development) which are necessarily to be taken into account.
The criteria can be arbitrary divided into two main groups including priority criteria and secondary criteria, see Table 4.6. Priority criteria/defintions (PC) are defined hereafter as ones according to which development of effective autogenous shrinkage is accompanied by the onset of stress build-up or events at the origin of (micro)cracking. Secondary criteria (SC) represent the rest of the proposals, majority of which are based on the belief that distinct changes in variables (or their derivatives) can be indicating formation of load-bearing structure or otherwise the unverified expert knowledge. The criteria which cannot be applied due to technological limitations or originated from outdated standards for AS measurement are not considered in the discussion.
Table 4.6: Review of criteria proposed for time-zero determination, in general order of increasing concrete age.
Nb. Cate- gory
Proposed definition/implication of time-zero
Potential event accompanied or argumentation for usage
Refe- rence(s)
1 SC/PC
Before initial set [Aït 99b] e.g. moment at which penetration
equals 1.5 MPa and UPV is 621 m/s [Yoo 13][Yoo 14] or at the
solid phase percolation (percolation threshold) [Pic 07]1
Self-desiccation likely starting before setting [Mou 06] therefore immediate character of autogenous shrinkage development and need of
curing before initial set [Aït 99b]; at this time restrained shrinkage stress development begins while AS captured by embedded strain gauge of nearly zero stiffness is buiding-up [Yoo 13][Yoo
14]; very early age (2h) cracking in the ITZ of mortar found in simulations [Sch 07b]
[Aït 99b] [Yoo 13] [Pic 07]
2 SC/PC Initial set
Beginning of strength gain around this time- point or after [Min 81] while material considered
as a porous elastic solid with non-zero bulk and shear moduli and with water in pores [Pop 94]; initiation of shrinkage as measured by embedded
strain gauges [Kad 02]; temperature onset and very close vicinity of final set [Sch 02]
In JCI defintion of AS; used e.g. by [JCI 99] [Kad 02] 3 PC
End of swelling [Hab 06a]/ Maximum swelling [Gra 04] (if occurred and if, acc. to [Med 06][Kam 08] due to causes other
than hydration heat); otherwise final set [Dar 11]
End of dormant period [Gra 04][Med 11b]; initial set [Hab 06a] (apparent stiffness > 1 GPa
[Hab 06b]); the temperature rapidly increases [Kam 08] while the stresses under restraint begin
to be produced [Hab 06a][Kam 08]
[Gra 04] [Hab 06a]
[Dar 11]
4 PC Onset [Sch 02] or rapid rise [Zha 03] in temperature of concrete
Initiation of shrinkage as measured by embedded strain gauges [Zha 03]; generation of tensile
stresses begins [Ima 07]; shrinkage rate increases for the second time, this taking place in close time vicinity of initial and final set [Sch
02]
[Sch 02] [Zha 03]
5 PC Rate of temperature starts to increase sharply End of dormant period/initial setting; axial force is developed in restrained specimen [Cus 07]
Table 4.6: Review of criteria proposed for time-zero determination, in general order of increasing concrete age (continued). Nb. Cate- gory Proposed definition/implication of time-zero
Potential event accompanied or argumentation for usage
Refe- rence(s)
6 SC
Maximum rate of temperature change (threshold of
solidification)
Plastic shrinkage stops and thermal expansion begins; solid structure counteracting
deformations is formed
[Med 06]
7 PC
(Second) Maximum rate of deformation (maximum velocity of deformation = inflection point of
deformation curve)
Close vicinity of or, more likely after final set [Pir 06][Med 11b]; microcracking occurs shortly after this time-zero [Pir 06][San 09]
[Pir 06] [Med
11b] 8 SC Rates of deformation (vertical and
horizontal) become equal
Deformation becomes isotropic since dead
weight no longer contributes to volume change [Bel 02]
9 SC
Maximum temperature (second temperature peak) [Ma 03][Ma 04]
unless no swelling [Gra 04] and measurement cannot be performed
in isothermal conditions (otherwise initial set [Ma 04])
Similarly to final set criterion, CTE is assumed constant [Ma 03]; approximity of final set [Cus
07]
[Ma 03] [Gra 04]
10 SC/PC Final set
Physical manifestation of complete solidification of plastic cement paste [Cha 07]; coefficient of
thermal expansion is stabilized and remains constant (in subsequent period Kad 02]); corresponds to UPV of about 1165 m/s [Yoo 13]; corresponds to hydration heat-related onset
of temperature rise and initiation of dynamic elastic modulus development [Kaz 10]
[ASTM C1698- 09] [Kaz 10] [Dar 11] 11 PC
Abrupt change of capillary pressure (in the so-called transition
zone [Cha 07])
or pure onset of pressure build-up
Physical significance of time-zero (formation of the solid structure [Cha 07]); possesses no strict ascription to setting process (from comparison of
studies [Hol 01][Cha 07][Zhu 08])
[Cha 07] [Zhu 08]
12 PC
Onset of restrained shrinkage strain (stress) given no separation
of AS from thermal effects [Ima 07]
or the shift from compressive stresses towards tensile stresses
Former corresponds to start of heat evolution [Min 81][Ima 07] (deviation point [Yoo 13]) and, if swelling occurs, initial set [Hab 06a], but
it is always subjective empirical judgement according to [Ima 07]
[Ima 07] [Yoo 13]
13 SC Some hours after final set Pure result of self-desiccation in subsequent period [Zhu 08] [Hol 01]
1 It should be understood that setting of cement paste results from percolation of the particles. Consequently,
event called (mineral/solid) percolation threshold, i.e. when first solid path is formed within material [Bar 01], should generally occur earlier than first of important setting points measured by destructive methods and referred to as initial set [Mou 06]. This is different especially when the w/c is low, for which percolation threshold is expected to situate in very close vicinity of initial set, e.g. [Zha 12b]. As such, percolation threshold therefore delivers a rigorous theoretical definition of the set point of cement paste.
While making decision about time-zero, applicability of old criteria was proved so as to exclude necessity for a new criterion definition. To date, ignoring this step has in fact led and is still leading to new proposals, without final agreement on one time-zero criterion useful for cement-based materials. Numerous criteria collected in Table 4.6 should be also noted to be regarding materials with low w/c but typically less advanced in terms of composition than UHPC, with few exceptions [Sch 02][Ma 03][Ma 04][Hab 06a][Kam 08][Yoo 13]. Combined
with imprecise sound of some of criteria offered, especially ones referring to temperature increase and current practical needs (such as reading time-zero directly from deformation curve), this urge becomes apparent.
ii. Solution and establishments
The main demand considered in search for time-zero was finding evaluation point of the part of deformation which could be responsible for generation of stresses under restraint. Simultaneously, it was set to be easily identifiable using pure free deformation curve for all UHPC mix combinations, or otherwise the underlying causes hindering this aim were meant to be recognized. Eventually, some phenomenological issues were taken into account too when making final choice about this time-point.
In-depth analysis of all collected data has been performed. It was concluded that time-zero related in best manner with one of the local extrema in the deformation curve as measured using corrugated tube protocol. The corresponding graphical solution of this issue is demonstrated in Figure 4.39. In the graph, for finding the point of interest, deformation curve as plotted in time was first fit to the best curve with help of FindGraph software [UNIPHIZ] and rationals type of function42. Subsequently, the first and second derivatives already in their best, smoothed appearance were derived using derivative calculator [MATHPORTAL]. Finally, the inflection point of deformation curve that matches new time-zero was found either from the former by evaluating the local maximum (assumption: deformation is presented in negative values) or directly using the second derivative of deformation (intersection point with X-axis).
42 With free version of the software, the model based on rationals function had to be used instead of applying the
more commonly preferred multi-logistic or more-parameter exponential models, e.g. based on Boltzmann equation. Whereas the rival solutions generally present the more appropriate scientific approach (better description of quantities that grow exponentially), own solution allowed to determine points of interest and was as reliable as guaranteed very high precision of fit with R² > 0.999 for the polynomial degree of fitting of minimum 8. Another advantage was also that it could be used for more purposes, e.g. when fitting other complicated curves meanwhile always ensured possibility of in-depth inspection of the curve.
-2000 -1500 -1000 -500 0 500 0 4 8 12 16 20 24 Time t [h] S tr a in ε [ µ m /m ] -160 -120 -80 -40 0 40 d ε o r d 2 ε [µ m /( m h ) o r µ m /( m h ²) ]
ε-t fit test start line time-zero line
max dε/dt line dε-t d2ε-t
It was noticed that the new time-zero was best defined as the first minimum absolute value of the strain rate or, in other words, the last extremum before the attaining maximum (negative) strain rate. Starting from this point the rate of deformation started to increase rapidly, in some hours achieving the maximum of deformation velocity. Its manifestation confirmed possibility of finding time-zero directly from deformation-versus-time curves as suggested by Bentz et al. [Ben 01c] and therefore remarkably facilitated evaluation of results.
Whether the selected time-point had any relation to setting as being the case of ‘abrupt change in slope in deformation-versus-time’ [Ben 01c], this will be discussed in the following Section 4.4.3. However, what is more remarkable is the number of other events having start or otherwise important stage found as coinciding with time-zero. These events or coincidences could be treated as arguments for particular time-zero selection and can be summarized along with a single counter-argument as follows:
- argument 1
In Figure 4.40, a representative picture of evolution of deformation rate is compared with that of temperature and the latter’s change in time.
-140 -120 -100 -80 -60 -40 -20 0 20 40 0 4 8 12 16 20 24 Time [h] S tr a in r a te d ε [µ m /( m h )] -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 T e m p e ra tu re r a te o r it s c h a n g e i n ti m e d T o r d 2 T [ °C /h o r °C /h ²]
dε-t time-zero line max dT/dt line max dε/dt line dT-t d2T-t
It could be observed that time-zero chosen corresponded to end of period between start of ‘wet mixing’ and moment when temperature did not increase any more. In other words, starting from particular time-point rather pronounced gain in hydration heat took place. In this way, time-zero validates the chemical nature of autogenous shrinkage. Meanwhile, the criterion received more precise sound when compared to some temperature-based definitions of time-zero reported previously in Table 4.6.
An important comment to be made regards the fact that part of hydration heat was clearly used to heat up the sample over the ambient temperature, thus providing more favourable conditions for hydration. In theory, this could result in shifting of the time-zero towards other concrete age and certain effect on magnitude of autogenous shrinkage, e.g. [Zha 03][Tia 08][Med 11b]. However, since the geometry of the element measured, particularly the cross- section of the tube, was small, the extra heat produced in the small sample dissipated easily and fast, owing to which increase of sample temperature remained negligible. This implies that autogenous shrinkage overtook the thermal expansion/swelling quite rapidly, leading to negative strain development. Due to this or another reason, both time-zero defined and maximum deformation rate were obtained before the temperature reached its maximum rate. Figure 4.40: Time evolution of rate of free deformation and corresponding sample temperature in the first and second derivative.
Although not demonstrated here, the observation held true in case of bigger tubes as well, that if used in measurement yielded closely settled extrema of deformation and maximum temperature rate compared to ones determined from small tubes. That is to say, it seemed that from the two, age associated with time-zero and autogenous shrinkage magnitude developed after time-zero, only the latter required certain correction on the scale of investigation performed. As in interest of finding effectiveness of IC the temperature aspect was avoided by using always the same sample size while small tubes could be used for finding temperature effect-free AS, further in-depth investigation of the aspect has been abandoned.
- argument 2
Looking back at Table 4.6, no additional evidence is required to show that new evaluation point better applies as time-zero than maximum deformation rate. Indeed, since microcracking has been reported to start around the latter [Pir 06], the former event seemed to provide an appropriate basis for deriving the time-zero at the first glance. From this perspective, the new definition of time-zero could be better representing the moment the structure is resistant enough to carry the force causing the cracking. Reference to some earlier time-points than the maximum rate of deformation should not be excluded also in opinion of Meddah and Tagnit- Hamou [Med 11b], who although widespread maximum deformation rate criterion as well as delivered theoretical background standing behind this choice, but did not support it with other than free shrinkage and temperature measurements.
- argument 3
Other tests comprehensively confirmed particular engineering significance of the new time- zero. This is demonstrated in Figure 4.41, where the time-point determined is compared with start of stresses build-up in both types of rings i.e. ones subjected to temperature effect and ones where increase in temperature due to hydration heat was as negligible as in small tubes43.
43 Under restraint of uniform shrinkage, example of which autogenous shrinkage is, wall thickness of the steel as
well as concrete ring become parameters decisive for level of stresses generated, relaxed and, holding true only for former, measured, e.g. [Hos 06]. In comparison, no impact of the onset time of stress generation is typically recorded on changing walls thickness of steel ring at a constant thickness of the concrete ring; meanwhile, change of diameter of the steel ring is showed to be of secondary importance, see [Yoo 14]. This implies that effect of changing the set-up on time-zero could only be attributed to change of concrete wall thickness and height, leading to main underlying consequence of different time-zero situation, i.e. increase of concrete temperature due to non-dissipated heat of hydration. It will provide better conditions for hydration, thus faster development of Young’s modulus and autogenous shrinkage, with expansion being hindered by stiff sand aggregates.
With regards to former case, it could be followed that new time-zero either very well matches initiation of restrained shrinkage stress development or, as alternatively considered, is in good agreement with change