Microstructure and Relative Humidity Effects on Long-Term Indentation Creep Properties of Calcium Carbonate Cement

This paper addresses the effect of both microstructure and relative humidity on the long-term creep properties of sustainable calcium carbonate (CaCO3) cements. Those can be prepared by mixing amorphous calcium carbonate and vaterite with water. A larger starting amount of vaterite, XV, within the mixture design gives a higher elasticity and resistance to the specimens due to the larger overall bridging area within the newly formed calcite crystals. Regarding creep properties for a given relative humidity, the amplitude of creep strain decreases with XV, and makes the relation between the elastic modulus, E, and hardness, H, of the samples to be linear with the contact creep modulus, C. On the other hand, for a given composition, the amplitude of creep increases with the relative humidity, making the contact creep modulus, Ci, to rise exponentially with the elastic modulus, E, and hardness, H, of the specimens. The most probable creep mechanisms for this kind of cement seem to be a combination of microcraking in the early stages and dissolution and reprecipitation of calcite in the long-term (also known as pressure solution theory). The presence of water in pores with increasing relative humidity might enhance the local dissolution of calcite, and hence the creep amplitude.


Introduction
Due to the carbon footprint of ordinary Portland cement (OPC) there has been an increased interest in alternative hydraulic binders [1][2][3][4].Among natural cements; one of the most common is calcium carbonate (CaCO 3 ) but despite of its abundance; very few attempts have reported its usage as an artificial cementing agent for engineering purposes.Among the first ones; the method originally proposed by Cailleau [5] and later modified by Molenaar & Venmans [6] proposed the recirculation of Ca(OH) 2 solution; pumped by CO 2 ; through the sample aiming to cement.As the solution pass through the sample; CaCO 3 encounter suitable nucleating sites among the host grains and work as a bonding agent.A commercially version of this methodology was tested by Ismail et al. [7] with different soils including glass beads; calcareous sand and silica sand.However; all these approaches require soil casting under sealed conditions to flush the starting solutions; making them absolutely unpractical to apply on site in comparison with a paste option.
Alternative production paths to form calcium carbonate binders has been investigated [1;8;9].The first CaCO 3 cement pastes; with similar mouldable and malleable properties as ordinary Portland cement (OPC) pastes were synthesized by Fontaine et al. [8] and Combes et al. [9].They mixed water with two CaCO 3 solid phases: one was the highly reactive amorphous calcium carbonate; ACC; while the other was one of the metastable crystalline phases; either vaterite; V; or aragonite; Ar; which acted as a seed for their (re)crystallization into the most stable calcite polymorph during the setting reaction.
Due to environmental benefits of CaCO 3 cement; i.e. no CO 2 production; low energetic costs; etc.; in comparison with OPC; we aim at further characterizing and analysing its mechanical properties; especially the compressive strength and creep deformation; before considering a commercial upgrade.
Undoubtedly; the compressive strength is the most relevant property that engineers and architects needs to know to design and calculate structures built on this material.Combes et al. [9] reported values within [3][4][5][6][7][8][9][10][11][12][13] MPa for CaCO 3 pastes with diverse microstructures; but the effect of the mixture design on the mechanical properties still requires further understanding.
Another property that demands significant analysis before up-grading CaCO 3 cements to commercial production is its long term deformation.Since the classical experiments of Phillips [10] and Andrade [11]; considerable interest has been given to creep deformation; which stands for slow deformation of materials at constant stress conditions with respect to time.Moreover; the importance of taking creep deformation into consideration in the design of structures was recalled recently since it may cause deflection and curvature; cracking and redistribution of stresses [12;13].Creep in polycrystalline aggregates such as CaCO 3 cement usually evolves through three stages: an initial transient phase with decelerating strain rate; a second steady state creep and a final accelerating creep phase [14].Several models have been proposed to describe the behaviour for the three of them [15][16][17] although most either ignore the underlying microstructural phenomena of the creep mechanism or set aside the effect of dissolution which is usually coupled with compaction creep.Keszthelyi et al. [18]; however; presented a novel micromechanical approach to describe transient creep of rocks with fluid-filled porous by combining fracturing and pressure solution.Nevertheless; creep of cementitious materials is a complex issue and it is still difficult to predict in the long-term since it is often coupled with other phenomena such as hydration and drying; while it can be influenced by several parameters such as temperature; seasonal moisture changes; level of stress; water content and mixture design simultaneously.
Since cementitious materials are multi-scale porous materials; creep is largely influenced by the presence of water in porosity and therefore by moisture changes.Multiple studies have already pointed out the necessity of controlling the moisture equilibrium of the samples before creep evaluation.For instance; Pickett [19] found that ordinary concrete under load and being dried at same time presented a higher deformation than that of a sample under load without drying.Moreover; Tamtsia and Beaudoin [20] found that the history of drying also influence the basic creep of cement pastes.The amplitude of creep was lower for those samples which set without drying.As a consequence; radically different interpretations of experimental data; and therefore theories; have been proposed to rationalize creep of cementitious materials [21][22][23][24].Although most authors agree to point out that the origin of long-term creep in OPC lies in the amorphous calcium-silicatehydrate (C-S-H) phase [25;26]; we aim at unravelling the mechanisms for pure crystalline carbonate systems without this amorphous phase and at comparing the results with state-of-the-art creep models [18].
In the present study; free-CO 2 ; 100% pure calcium carbonate cements have been synthesized at laboratory scale following Combes method [9] as a proxy to investigate the effect of both microstructure and moisture on long-term basic creep behaviour of pure calcium carbonate materials.The effect of microstructure is studied by preparing and testing samples with varied mixture design while the effect of moisture is studied by conditioning and testing those compositions in various relative humidity (RH) conditions.Creep experiments have been carried out over hardened samples with the micro-indentation technique validated for long-term basic creep [27].

Materials and methods
CaCO 3 cement samples with diverse mixture design (varied ACC:V wt.% ratio) have been prepared and conditioned at different relative humidities (RH).After setting; a first set of samples have been used to evaluate their compressive strength using uniaxial compressive strength tests; while a second set have been used to assess their long-term creep deformation properties via micro-indentation (μ-indentation) tests.

Preparation of CaCO 3 reagent powders and cement samples
The preparation of CaCO 3 cements requires the synthesis of different calcium carbonate polymorphs in order to design the initial cement mixture [9].Accordingly; both ACC and vaterite phases were prepared as described in [28].Briefly; they were precipitated by double decomposition between calcium chloride (CaCl 2 •6H 2 O; Sigma Aldrich) and sodium carbonate (Na 2 CO 3 ; Sigma Aldrich) equimolar (0.5 M) solutions at room temperature using a magnetic stirrer set at 400 rpm.The reaction time was just 10 sec for ACC and 30 min for vaterite taking as a reference Ogino et al. studies [29].To wash off any dissolved sodium chloride (NaCl); the CaCO 3 precipitates were rinsed under vacuum with deionized water and ethanol; using a filtering kit and 0.5 µm pore-size filter papers (Millipore; USA).Subsequently; the CaCO 3 precipitates were flushed with liquid N 2 to block any evolution of these metastable phases.The frozen precipitates were lyophilized (Alpha 1-4 LD plus; Martin Christ; Germany) for 48 h at 0.05 mbars and -50 °C and stored in a freezer (-22˚C) with additional silica powder bags prior to cement manufacturing.The precipitates were scanned by X-ray diffraction (XRD) (Bruker D8 Discover X-ray diffractometer) to identify the crystalline phases present using Cu Kα radiation (30 mA and 40 kV) and recording 2θ angles from 20 to 50° at a 0.04 s -1 sweep rate.Additionally; they were imaged with scanning electron microscopy (SEM) (Hitachi SU5000 Field-Emission; 1kV acceleration voltage and 3.0 mm working distance).CaCO 3 cements with different microstructures were synthesized by mixing ACC and vaterite powders in different weight ratios (wt.%): 1:1; 1:2 and 1:3; respectively; with distilled water keeping a water-to-powder ratio; w/p; of 0.5.Just after mixing the powders with the liquid phase; the resulting pastes were viscous and easily mouldable for several minutes and they were placed in specially designed oedometric presses (Figure 1) in between two porous; plastic-made; auxiliary discs.The inner walls of the presses were coated with Teflon ®.A steel spring loaded the assembly uniaxially.Using the spring constant of the spring and the surface of the auxiliary discs it was estimated that the sample was under a stress value of approximately 0.15 MPa.The specimens were unmolded after 24 h and left under atmospheric conditions for final drying (21 °C; ~55% RH).This process was followed by means of their weight evolution using digital scales (Sartorious Lab Instruments; Germany; accuracy = 0.1 mg).After 28 days of drying; a first set of samples were cut into smaller cylinders using a metallic saw and polishing paper (silicon carbide P80D) brought to 1.00±0.02cm in height and 0.50±0.02cm in diameter to perform compressive strength tests; while a second set were brought to 1.00±0.02cm in height and 2.00±0.02cm in diameter to carry out μ-indentation tests.
The final dimensions of the specimens were measured using a calliper and used to determine their apparent density; ρ a .To ensure reproducibility; sufficient cement quantities were made to perform all analyses on the same sample batch.(12.0 cm in height and 2.0 cm inner diameter) coated with Teflon ® spray.The cement paste is compacted in between two porous plastic discs and the assembly is loaded by a steel spring with the aid of two plastic stoppers at the edges.

Uniaxial compressive strength tests
To evaluate the elastic modulus; E; and the uniaxial compressive strength; Y; of hardened CaCO 3 cement compositions prepared as described on the previous section (cylinders with 1.00±0.02cm in height and 0.50±0.02cm in diameter); uniaxial compression tests were carried out using a DEBEN CT5000 (UK) tensile/compression stage (5000 N load cell; 0.01 N resolution); at a crosshead speed of 0.2 mm/min; corresponding to strain rates of 10 -3 s -1 .Three samples of each composition were tested to ensure repeatability.

Data analysis
From the recorded data (applied force and elongation); a stress-strain curve was constructed for each test.Figure 2 shows an example stress-strain curve constructed for one of the indentations performed at 54% RH to an specimen with an starting composition ACC:V 1:3 wt.%.As shown; the initial relationship between the stress and the strain follows a curved trend which can be explained as a geometrical re-adjustment between the sample and the machine's jaws typically due to a lack of parallelism within the sample's top and bottom surfaces.Eventually; the relationship become linear being the elastic modulus; E; the proportional factor between the two parameters:  =  • .Consequently; the elastic modulus; E; can be calculated from the slope of this linear region.More specifically; it has been calculated using the "straight line fitting -least squares" method described in [30].
With increasing stress; the sample begins to deform plastically and the curve deviates from linearity.This point is known as the yield point and represents the compressive strength; Y; of the specimen.The dashed arrow on Figure 2 indicates the stress hold by the sample by the end of the elastic regime.Both the elastic modulus; E; and compressive strength; Y; were extracted from the curves using an in-house developed script in Matlab®.

Micro-indentation creep experiments 2.3.1. Sample conditioning
Prior to μ-indentation tests; one specimen of each composition was moved into a desiccator with a controlled relative humidity (RH) for conditioning.The RH conditions were created by filling the desiccators with saturated aqueous salt solutions sufficient time in advance to equilibrate the desiccator atmosphere before moving the samples in.More specifically; the chemicals MgCl 2 ; Mg(NO 3 ) 2 and KNO 3 were used to create RH of 33%; 54% and 93%; respectively; at the temperature of 23 °C [31].
In order to determine the duration of conditioning necessary for the samples to achieve moisture equilibrium with conditioning environment; the mass evolution of the three different samples being conditioned at 33% RH were measured in parallel with sample conditioning.
The measurements showed very similar drying kinetics for the three compositions; which required 3 days to achieve moisture equilibrium with conditioning environment.Consequently; all samples were let for 5 days inside the desiccators to ensure total moisture equilibrium at each RH prior to microindentation creep experiments.Under these conditions; autogenous shrinkage during creep tests is avoided and hence the contact creep compliance; L(t); only characterizes basic creep; i.e.; the deformation of the samples is exclusively due to the application of an external mechanical load.

Measurement protocol
Microindentation creep experiments were carried out using the indentation apparatus in Lafarge Research Center (France) [32].It is equipped with a motor controller; a monitoring system; an indentation platform and a removable chamber for relative humidity control during indentation.The indentation platform consists of a sample-mounting board; a force sensor and a displacement sensor.Prior to the experiments; the microindenter was calibrated according to the ASTM standard E 2546-07 [33] and its compliance was determined according to Kalidindi et al. [34].
After sample conditioning; microindentation creep experiments were carried out in relative-humiditycontrolled environment by circulating air with controlled RH inside the indentation chamber.The air was obtained by pumping dry CO 2 -free air into saturated salts solutions [32].
On each sample; 10 microindentation tests were performed on a different location with a Vickers indenter probe; applying a maximal force of 1 N. Based on previous studies [35][36][37]; this value is low enough to ensure proportionality between creep strain and applied stress.For each indent; the load was increased linearly over time at a rate equal to 10 N/min; kept constant during the holding phase; and decreased linearly over time back to zero at the same rate as the loading one.Out of the 10 indents performed on each sample; 5 were with a relatively short 20-sec-long holding phase; while 5 were performed with a relatively long 180sec-long holding phase.

Data analysis
Figure 3 shows the evolution of the indentation depth; h; with the applied load; P; recorded from a microindentation test performed on a sample with an starting composition ACC:V 1:1 wt.%; conditioned and tested at 54% RH.In this figure; h = 0 stands for the onset of contact between the indentation probe and the sample.Moreover; the three phases of the test -loading; holding and unloading -are represented with different colours to facilitate their identification.

Assessment of time-independent properties
The mechanical problem involved in indentation testing is a typical problem of contact mechanics: the indentation probe penetrates into a flat surface of a material of interest and then is withdrawn from the surface.Galin et al. [38] presented; for the first time; a solution for the indentation of an elastic half-space by a rigid axisymmetric indentation probe.If the latter is characterized by z=g 0 •r g with r being the radius; g 0 and g being geometry coefficients; the following equation links the indentation load; P; to indentation depth; h; via the effective modulus; E eff ; and parameters depending on the geometry of the indenter: where  represents a constant parameter which includes the Euler Gamma function.A differentiation of the equation above with respect to the indentation depth; h; gives [39]: where S is the contact stiffness defined by S = dP/dh; and A c is the projected contact area (or briefly; contact area) between the indentation probe and the indented surface.Moreover; the effective modulus; E eff; can be linked to the Elastic modulus; E; by the following equation: where υ in and υ are the Poisson's ratio of the indentation probe and that of the tested material; respectively; E in and E are the Elastic modulus of the indentation probe and that of the tested material; respectively.For a rigid indentation probe; Eq. 3 can be simplified as the following; in which M is termed as the indentation modulus: Another time-independent property which can be assessed is the indentation hardness; H.It is defined as the average pressure below the indenter and can be calculated with the following equation: Consequently; the short (20-sec-long) holding phase tests enabled us to determine the Elastic modulus; E; with Eq. 2 and Eq. 4 and the hardness; H; with Eq. 5; of the different cement compositions assuming a Poisson's ratio υ = 0.20 for all of them.

Determination of the projected contact area; A c : the Oliver and Phaar method
To determine the Elastic modulus; E; and the hardness; H; we need to find out the projected contact area; A c .
In the present study the method introduced by Oliver and Pharr [40] has been used.As presented on Figure 4; in this method the indentation depth; h; can be decomposed into two parts: a depth h C over which the indentation probe is in contact with the indented surface and a depth h S over which the probe is not in contact with the indented surface: Applying the solution of Sneddon [41] for a conical indentation probe; the depth h S over which the probe is not in contact with the indented surface can be linked to the residual depth h f of the indent after withdrawing the indentation probe (See Figure 3): Deriving from Sneddon's load-displacement relation expressed in Eq. 1 and applying it for a conical indentation probe yields: where  = is the maximum contact stiffness at the maximum load and the parameter ε depends on the geometry of the indentation probe; being equal to 0.72 for a conical indentation probe.Thus; Eq. 8 offers a method to estimate the contact depth between indenter and indented surface and it can be used to determine the projected contact area; A c .The relationship between h C and A c is known as the shape area function; A c (h C ); and it has different values depending on the geometry of the indenter.For the Vickers indentation probe used here; its value is the following:

Assessment of time-dependent properties
Indentation tests can also be used to measure the creep properties of materials.By introducing a fictitious indentation test with an instantaneous loading phase; an instantaneous unloading phase and an instantaneousreloading-and holding phase; Vandamme et al. [42] derived a method to back-calculate creep properties from an indentation in which time-independent plasticity occurs.
The main assumption in their derivation is that time independent plasticity occurs only during the loading phase but not during the holding nor unloading phases.Their demonstration starts by writing; in the case of elastic indentation; the contact radius; a c ; as a function of indentation depth:  = (ℎ).
The analytical expression of the function f is generally unknown; but it is not necessary in the derivation.
Integrating Eq. 2 with respect to indentation depth; h; yields: P = 2 M F(h); where F(h) is the primitive function of f(h) for which F(0)=0.Rewriting the yield expression in the time domain for a linear viscoelastic material by applying the correspondence principle; one obtains: Performing Laplace transform to Eq. 10; one obtains: In the case of a step load; one can link the contact creep compliance; L(t); to indentation data in Laplace domain.By performing inverse Laplace transform; one obtains the time-dependent contact creep compliance in the time domain as a function of indentation depth during the holding phase: After differentiating the previous equation with respect to time; one obtains the relation of interest which links the derivative of the contact creep compliance to the rate of penetration of the indentation probe during the holding phase [42]: where a c is the radius the projected contact area; A c .Excluding a flat punch; a c (t) evolves with h c ; but assuming that it does not change too much during the holding phase is realistic.Then; the contact radius during holding can therefore be estimated by the contact radius at the start of unloading and can be estimated by the Oliver and Pharr's method [40].Integrating Eq. 13 with respect to time from the beginning of holding phase yields: where Δh(t) is the change of indentation depth during the holding phase.The difference L(t) -L(0) between the contact creep compliance L(t) and the reciprocal of indentation modulus L(0) = 1/M 0 at the moment of loading is termed the contact creep function.The use of Eq. 14 to back-calculate creep properties enables to obtain a contact compliance which is a material property.
Thus; 180-sec-long holding phase indents were used in the present study to measure the change of indentation depth; Δh(t); during the holding phase and to subsequently calculate the contact creep function;

L(t)− L(0)
. Moreover; since this function is logarithmic with respect to time; it could be fitted to the following equation; which allowed a quantitative comparison of the characteristic parameters of each sample: where C i represents the contact creep modulus and τ i is the characteristic creep time.The former provides an idea about the amplitude of the creep function; so that low creep rates are represented by large creep modulus values; while the latter represent the length of the transient period required to reach the logarithmic kinetics of creep.It is worth mentioning that the characteristic creep time; τ; is not a universal parameter but depends on the applied stress.Since we have applied the same stress to all compositions; their characteristic creep time; τ; values are still comparable.

Results
The synthesized amorphous calcium carbonate; ACC; and vaterite; V; polymorphs; necessary to manufacture CaCO 3 cements are introduced.Afterwards; the compressive strength and the elasticity of the set cement samples are presented.Finally; the elastic and creep strain results obtained from microindentation tests are shown as function of the sample microstructure and moisture equilibrium with relative humidity.

Characterization of CaCO 3 precipitates
As shown in [28]; ACC precipitates (Figure 5A) consist of equidimensional spherical nanoparticles (<50 nm in diameter) accompanied by rhombohedral crystals of about 50-100 nm.These are interpreted to be calcite and confirmed by XRD analysis (Figure 5C).Vaterite precipitates (Figure 5B) consist of spherical grains of 4-5 µm in diameter also accompanied by rhombohedral grains (4-5 µm); which are calcite according to the XRD scans (Figure 5C).Therefore; both ACC and vaterite precipitates are about 90% pure (from XRD analysis) with only minor amounts of calcite.

Uniaxial compressive strength tests on CaCO 3 cement
The compressive strength; Y; and the elastic modulus; E; of three CaCO 3 cement compositions have been calculated from uniaxial compressive tests.Figure 6 shows the elastic modulus; E; and compressive strength; Y; values obtained following the previous methodology for the different cement compositions tested in the present study as function of their initial vaterite weight fraction; X V .Moreover; Table 1 includes a summary of the results to facilitate their comparison with the elastic parameters obtained from microindentation experiments.

Figure 6. Elastic modulus; E; and compressive strength; Y; extracted from uniaxial compression tests for three CaCO 3 cements conditioned at 54 % RH; as function of their initial vaterite content; X V .
The results show a clear trend: a larger starting amount of vaterite; X V ; causes more elastic and resistant specimens.Indeed; the results show that the elastic modulus; E; and the compressive strength; Y; follow a linear relationship with this variable.The elastic modulus yields the relation E i = 0.029 • X V -0.560 GPa (R 2 = 0.96); while the compressive strength Y i = 0.091 • X V -1.462 MPa (R 2 = 0.99).

Microindentation experiments on CaCO 3 cement.
Figure 7 shows the evolution of the indentation depth; Δh; with time; t; during the holding phase of indentation experiments performed on CaCO 3 cement samples with dissimilar starting compositions but all conditioned and tested at 54 % RH.In this figure; t = 0 s stands for the onset of the holding phase and the corresponding indentation depth; h; is normalized to 0 mm.for the contact creep modulus; C. It is worth mentioning that the elastic modulus values; E; are in good agreement with those calculated from uniaxial compression tests; being the two-tailed P value between them of 0.6469; which by conventional criteria is considered to be not statistically significant (See Table 1).
Regarding microindentation results; both the elastic modulus; E; and hardness; H; raise with the initial vaterite weight ratio.Nonetheless; the rise of the elastic modulus; E; is not as remarkable as that for the  Since all tested samples were prepared with the same water-to-powder ratio (w/p = 0.5) and were conditioned for the same duration prior to the experiments; a similar moisture equilibrium; and therefore influence on creep strain; can be assumed for all of them.Moreover; cementitious materials are porous materials and their mechanical properties depend on this parameter.As recalled on the previous section; all CaCO 3 cements develop a similar porosity under the maturation conditions here used so an analogous influence of this variable on creep deformation can also be assumed for all of them.Therefore; the differences among their creep functions must be due to their particular microstructure (composition and volume fraction of each phase) and the joint's strength among the CaCO 3 grains after the setting reaction.
An analogous dependence was found by Zhang [32]: diverse elastic modulus; E; hardness; H; and contact creep modulus; Ci; values were reported for tricalcium silicate (C 3 S) and dicalcium silicate (C 2 S) pastes with the same porosity; remarking the importance of the solid phases; their volumetric distribution and the joints strength in controlling the final mechanical properties.
A multitude of creep theories have been proposed in the last century including; for example; the mechanical deformation theory; plastic theory; viscous and visco-elastic theory; solid solution theory; seepage theory; micro-cracking theory and long-term aging theory among many others [21][22][23][24].However; none of them can explain all experimental observations and possible creep mechanisms.Since CaCO 3 cements lack the amorphous C-S-H phase; the most probable creep mechanisms; according to the American Concrete Institute Committee [49]; can be a combination of microcraking in the early stages and dissolution and precipitation of calcite when is it under pressure in the long-term.
Under microindentation tests; a small region of the sample is subjected to large compressive stresses.The origin of the non-logarithmic part of the creep functions might be ascribed to cracking or microcracking of CaCO 3 grain joints since many cementitious materials and rocks are known to be quasi brittle [37;50;51].
Thus; this mechanism is naturally affected by the amount and strength of grain joints.Similar time dependence for the growth of microcraks was reported by Bazant and co-workers for concrete samples [52].
Moreover; frictional grain boundary sliding may also occur if the frictional force between calcite grains is overcome; causing them to slide past each other [53].However; this mechanism is more likely to occur at low effective stresses.
In the long-term; probably the best candidate to explain the creep of CaCO 3 cements is the so-called theory of dissolution; transport and precipitation under pressure (or pressure solution theory); which is considered to be the most important one to explain the time dependent deformation of rocks [54][55][56].The theory stands that the macroscopic creep is a result of the geometry change of the solid matrix (e.g.crystals) at microscopic scale.This change is driven at the microscale by chemical potential differences between the stressed and unstressed part of the solid and is governed by a mass transfer that occurs in three steps: i) dissolution of solid under pressure; ii) diffusion of dissolved mass through the interface of crystals or their aggregates [57] in a very thin liquid film [58]; and finally iii) precipitation at less stressed sites.
In this line; creep of CaCO 3 cements can be due to the local dissolution of calcite crystals when they are stressed.Croize et al. [59] claimed that the deformation of calcite monocrystals occurs either by dissolution and diffusion along the contact calcite/indenter interface; i.e.; pressure solution; or by a combination of pressure solution and subcritical crack growth from the contact area toward less stressed parts of the crystal.
It should be noted that calcite is a brittle mineral and the formation of microcracks on its surface under the indenter seems plausible.The authors also claimed that the occurrence of one or the other mechanism is not ruled by the applied stress but most likely by the presence or not of a flaw within the crystal.Thus; how the overall bridging area within a calcite crystal network regulate or influence the creep rate of CaCO 3 cements might be rationalized in the following way: a lower bridging area favours local stress concentration and thus the sample can exhibit more creep.Dissolved CaCO 3 grains can be transported and precipitated elsewhere.As commented previously; the porosity of all CaCO 3 cements compositions here tested is very similar (ϕ = 39%).When a porous material dries; the larger pores desaturates firstly followed by the smallest ones.
Indeed; the largest pore entry radius; r pe ; i.e.; the largest pore which remains saturated for a porous material in moisture equilibrium with a given relative humidity; can be calculated by applying the Kelvin-Laplace law for drying with the following equation [62]: where γ gl is the air-water interface energy; T is the temperature; R is the ideal gas constant; θ is the wetting angle; V m;H2O is the molar volume of water and RH is the relative humidity at a given temperature.At a temperature T = 295 K; with γ gl = 73 mJ/m 2 ; θ = 0; R = 8.31 J/(mol•K) and V m;H2O = 18 cm 3 /mol; the relation between the relative humidity within the sample and the largest pore entry radius is presented in Figure 13.As can be observed; the lower the relative humidity is; the smaller this radius is.

Figure 13. Largest radius r pe of pores remaining saturated at various relative humidity.
By applying Eq. 16 for the RH values here studied; the radius of the largest pores remaining saturated under each situation; r pe ; can be estimated.Values of ~ 1 nm; ~ 2 nm and ~ 10 nm are obtained for 33%; 54% and 93% RH; respectively.Thus; from this analysis it seems that water in pores with an entry radius smaller than those values -at each specific condition -is linked to the long-term basic creep properties of CaCO 3 cements.In addition; a contribution from the water activity by itself cannot be discarded for this kind of material.The presence of more intergranular water might enhance the local dissolution of calcite and thus increase the amplitude of creep strains; in agreement with the pressure solution theory introduced on the previous section.Moreover; other mechanisms may be activated by the presence of fluids within the calcite network as the aforementioned frictional grain boundary sliding mechanism.Under this scenario; calcite dissolution can remove asperities and will reduce the friction between grains; making the creep amplitude to rise.
While the contact creep modulus; Ci; of gypsum plaster; calcium carbonate cements and calcium hydroxide compacts increases by a factor of 100; 50 and 12 respectively; from water-saturated condition (~95%) to medium relative humidity (~50%); this increment is only by factor 2 for C 3 S and C-S-H compacts.
Therefore; the creep properties of CaCO 3 cements; in line with other crystalline binders; appear to be more sensitive to the relative humidity than other materials which contain amorphous phases like C-S-H.

Conclusions
In this paper; we have studied the compressive strength; the elasticity and the long-term creep properties of calcium carbonate cements with diverse microstructures; conditioned at several relative humidity.The results show that a larger starting amount of vaterite; X V ; within the mixture design derives on more elastic and resistant specimens due to the larger overall bridging area within the newly formed calcite crystals.
The micro-indentation results show that creep is logarithmic with respect to time; and hence the contact creep modulus; Ci; and the characteristic creep time; τ; could be extracted from each test.For a given relative humidity; the amplitude of creep strain decreases with increasing initial amount of vaterite; making the contact creep modulus; Ci; to rise on a linear manner with the elastic modulus; E; and hardness; H; of the specimens.The differences among their properties must be due to their particular microstructure and the joint's strength among the CaCO 3 grains after the setting reaction.Moreover; the most probable creep mechanisms seem to be a combination of microcraking in the early stages and dissolution and reprecipitation of calcite in the long-term (also known as pressure solution theory).
On the other hand; for a given composition; the amplitude of creep grows with the increase of relative humidity; inducing the contact creep modulus; Ci; the elastic modulus; E; and hardness; H; of the samples to decrease.The presence of water in pores with an entry radius smaller than 1nm; 2nm or 10nm under 33%; 54% and 93% RH conditions respectively; may enhance the local dissolution of calcite and explain the raise of the creep amplitude.This hypothesis is also in agreement with the pressure solution theory and support the fact that crystalline binders; such as our calcium carbonate cements; are more sensitive to the relative humidity than others which contain amorphous phases like C-S-H.Furthermore; the results suggest that the mechanical properties of calcium carbonate cements are enforced when reducing the fraction of ACC in the mixture design.However; their mechanical properties become more sensitive to relative humidity; especially creep.These results are in accordance with the findings for C-S-H (amorphous) and gypsum (crystalline).

Figure 1 .
Figure 1.Schematic drawing of the oedometric press designed to cast CaCO 3 cements.The main body is a metallic hollow cylinder (12.0 cm in height and 2.0 cm inner diameter) coated with Teflon ® spray.The cement paste is compacted in between two porous plastic discs and the assembly is loaded by a steel spring with the aid of two plastic stoppers at the edges.

Figure 2 .
Figure 2. Stress-strain; -ε; curve constructed from the applied force and elongation recorded during uniaxial compressive test of a CaCO 3 cement sample with a starting composition ACC:V 1:3; conditioned and tested at 54% RH.The red solid line represents the best fit performed to determine the elastic modulus; E; of the sample while the dashed arrow indicates its compressive strength; Y.

Figure 3 .
Figure 3. Indentation load; P; as function of indentation depth; h; recorded during a microindentation experiment over a CaCO 3 sample with an starting composition ACC:V 1:1 wt.% previously conditioned at 54% RH.The quantities shown are: the peak indentation load; P max ; the indenter maximum displacement at peak load; h max ; the final depth of the contact impression after unloading; h f ; and the unloading stiffness of the sample; S.

Figure 4 .
Figure 4. Schematic representation of a section through an indentation showing various parameters used in Oliver and Pharr method; schematic adapted from [40].

Figure 5 .
Figure 5. SEM micrographs of synthesized calcium carbonate powders in the form of (a) ACC phase and (b) Vaterite phase.(c) XRD patterns of (a) and (b) powders.

Figure 7 .
Figure 7. Indentation depth; Δh; as function of time during the holding phase of microindentation tests performed on CaCO 3 cement samples with diverse starting composition (1:1; 1:2 and 1:3 wt% ACC:V) all conditioned at 54% RH.As observed; the indentation depth reached during the holding phase decreases for samples with a larger staring amount of vaterite; X V ; within the cement mixture design.These results; indeed; follow the same trend reported for the elastic modulus; E; and compressive strength; Y. From these data; the contact creep functions; L(t) − 1/M 0 ; yielded by the three different CaCO 3 cement samples were determined using Eq.14 and plotted in Figure8.The results show that for a given relative humidity; the amplitude of creep decreases with the initial amount of vaterite within the cement mixture design.Moreover; the contact creep functions; L(t) − 1/M 0 ; determined for every composition and environmental condition tested were fitted into equation 15 (yellow dashed lines) to get the correspondent contact creep modulus; C i ; and the characteristic creep time; τ i .

Figure 8 .
Figure 8. Contact creep functions L(t)-1/M 0 of CaCO 3 cement samples with diverse starting composition (1:1; 1:2 and 1:3 wt% ACC:V) conditioned and tested at 54% RH; obtained by microindentation tests.For each sample; out of the 5 experiments performed; only the median curve is displayed.The dashed lines represent the best fits to Eq. 15.
contact creep modulus; Ci.A comparative study of those two moduli yields a linear relationship; as shown on Figure 10.All data points nicely align around the following equation: Ei = 0.618• Ci + 0.180 GPa with R 2 = 0.999.Moreover; the evolution of the hardness; H; in comparison with the contact creep modulus; Ci; seems also to follow a linear relationship; Hi = 0.0046• Ci + 0.0012 GPa; although the coefficient of determination is slightly lower (R 2 = 0.90).Thus; both the elastic modulus; E; and the hardness; H; follow a linear relationship with the contact creep modulus; Ci.These relationships differ from the ones observed for C-S-H phases obtained by nanoindentation tests in Portland cements.Vandamme and Ulm [48] also found a linear relationship between the contact creep modulus; Ci; and indentation hardness; H; but a power law relation between the contact creep modulus; Ci; and elastic modulus; E. This fact highlights the diverse behaviour of the amorphous Portland phase and the crystalline CaCO 3 cements against creep deformation.

Figure 10 .
Figure 10.Contact creep modulus; Ci; versus elastic modulus; E; and hardness; H; for CaCO 3 cements with diverse ACC:V initial mixtures and in moisture equilibrium with 54% RH.

Figure 11 .
Figure 11.Young's modulus; E; Contact creep modulus; C; Indentation hardness; H; and Characteristic creep time; τ; calculated from microindentation tests performed on 28-day-old ACC:V 1:3 CaCO 3 cement specimens as function of the conditioning and testing relative humidity (RH).The elastic modulus; E; and hardness; H; calculated -as detailed in Section 2.3.3 -; from the short-holdingphase μ-indentation tests (assuming a Poisson's ratio υ =0.20) are also included on Figure 11 as function of the relative humidity.As can be observed; both parameters decrease with the RH but not as dramatically as

Table 1
includes a summary of all results obtained from both uniaxial compression tests (elastic modulus; E; and uniaxial compressive strength; Y) and microindentation tests (contact creep modulus; C i ; characteristic creep time; τ i ; elastic modulus; E; and hardness; H) as function of the relative humidity and CaCO 3 initial mixture design (ACC:V wt.%).

Table 1 .
Elastic modulus; E; and compressive strength; Y; of CaCO 3 cement samples obtained from uniaxial compressive strength tests at 54 % RH.Contact creep modulus; C i ; characteristic creep time; τ; elastic modulus; E; and hardness; H; of CaCO 3 cement samples conditioned and tested at 33%; 54% and 93% RH; obtained from microindentation tests.*Reference microindentation results from a Portland cement sample with the same water to powder ratio as CaCO 3 cements are also included [27].