Creep Mechanisms of Calcium–Silicate–Hydrate: An Overview of Recent Advances and Challenges

Creep is a material property commonly defined as a time-dependent deformation under sustaining loads. Creep is essentially important to cementitious materials since excess deformation can negatively impact the long-term serviceability and sustainability of concrete structures (Neville 1981; Bažant 2001; Mindess et al. 2003; Singh et al. 2013; Li 2012; Ye et al. 2015). The creep behavior of cementitious materials was reported to be internally associated with the viscous nature of its main hydration product, i.e. calcium–silicate–hydrate (C–S–H), proportion of other secondary hydrated phases (e.g. portlandite), as well as externally affected by atmospheric conditions, e.g. relative humidity (RH) and temperature (Neville 1981; Bažant 2001; Powers 1968; Wittmann 2008; Alizadeh et al. 2010; Bu et al. 2015; Nguyen et al. 2013). The so-called basic creep and drying creep in cementitious materials are termed as the additional acquired deformation under constant water content (i.e. no moisture exchange with ambient and specimens, but not necessarily in saturated state) and decreasing water content (i.e. drying condition), respectively (Wittmann and Roelfstra 1980). Regardless of what type of creep, its behavior is drastically related to the interior water status in pore structure, which is further influenced by ambient RH (Ali and Kesler 1964; Bažant et al. 1997). For instance, cementitious material can reduce up to 80 % deformation after a sever drying pre-treatment (e.g. heating to 105 °C) (Mindess et al. 2003; Glucklich and Ishai 1962), whilst its deformation can be more than three times higher when it is exposed to a simultaneous loading and drying conditions (Mindess et al. 2003; Pickett 1942). Nevertheless, different experimental observations lead researchers to propose different creep mechanisms to explain their data. Therefore, no one creep mechanism has been universally accepted despite the extensive investigation was conducted over decades.

One of the major debates among various theories (will be elaborated in Sect. 2) lies on the role of water involving in creep, as some researchers argued that water is inessential to creep (Feldman 1972) while others believed that water is important (Powers 1968; Alizadeh et al. 2010). Additionally, for the creep mechanisms that are relevant to water, discrepancy also exists regarding the function of water at various scales in C–S–H (Powers 1968; Alizadeh et al. 2010; Glucklich and Ishai 1962; Ruetz 1968). Roughly, water in C–S–H is classified into three types: capillary water, adsorbed water and interlayer water (Powers and Brownyard 1946). However, the classification of water at various dimensions also varies slight among different nanostructures of C–S–H (Powers and Brownyard 1946; Aligizaki 2006). In addition, the role of water is reported to be different for different mechanisms, and even same type of water is reported to have different functions in different mechanisms. The first subject of this paper is to review the role of water proposed in various modern creep theories and potentially provide some insights on further research.

On the other hand, it is essentially necessary to introduce shrinkage since creep (especially drying creep) and shrinkage has some sorts of intimate relation (Wittmann 2008; Wittmann and Roelfstra 1980). Drying shrinkage is defined as the deformation of a specimen during drying without external loading. Both creep and shrinkage are believed to be affected by the water content in material interior, as well as external conditions. However, the mechanism between these two may not be exactly identical. It is difficult or even impossible to distinguish drying shrinkage and creep components when a material is under a circumstance of simultaneous loading and decreasing RH (i.e. drying creep) (Bažant et al. 1997). First of all, drying shrinkage (especially for irreversible component) also exhibits a time-dependent characteristic, which is intrinsically correlated to reorganization of C–S–H induced by internally drying-induced stress (e.g. capillary stress, desorption-induced solid surface tension increase, and disjoining pressure) rather than externally-applied stress (Jennings 2000; Ye et al. 2014). All of these stresses may be considerably different in their locations and magnitudes. For instance, capillary pressure exerts stress on solid skeleton by putting adjacent particle closer, external load exerts stress on the bulk materials, while desorption-induced stress exerts primarily on the solid surface (Kovler and Zhutovsky 2006; Beltzung and Wittmann 2005). The second part of this paper is to understand how the drying and thermal condition can potentially influence the creep performance.

Finally, this paper briefly discusses how the chemical composition, pore solution, and atomic ordering (presence of defects) of C–S–H can affect creep. In addition, the potential application of generalized creep equation on C–S–H research is also discussed.

The nanostructure of C–S–H, which is believed to be strongly related to its creep performance, is still mysterious and controversial. Therefore, this paper briefly reviews some popular models for nanostructure of C–S–H before going deep to its creep mechanism (in Sect. 3). A more comprehensive review on nanostructure of C–S–H can be found in the literature (Papatzani et al. 2015).

2.1 Powers and Brownyard Model (First Colloidal Model) (Powers and Brownyard 1946)

The first nanostructure model (denoted as P–B model) that published by Powers and Brownyard, basically announces that C–S–H is a colloidal material with more or less crystalline phases. In P–B model, water is classified into three types: capillary water, physically adsorbed water (gel water) and interlayer water. As illustrated in Fig. 1a, capillary water refers to the water that is unreacted by cement hydration, primary remaining in the space between partial-/fully- hydrated particles; gel water refers to the physically adsorbed evaporable water in gel pores of C–S–H; interlayer water refers to the chemically bonded non-evaporable water incorporated in the solids of C–S–H (loss of interlayer water causes dehydration of C–S–H) (Mindess et al. 2003; Powers 1958). It should be noted that the above classification is somewhat arbitrary since differentiating capillary water and gel water is not easy in realistic circumstance. As further noted by Powers, the C–S–H consists mostly of fibrous particles with straight edges, where bundles of such fibers seem to form a cross-linked network, containing some more or less amorphous interstitial material (Powers 1958).

Drying creep (also known as Pickett effect) (Wittmann and Roelfstra (1980); Pickett (1942)) is the excess of creep at drying over the sum of shrinkage and basic creep. It indicates that there is a strong correlation between creep and shrinkage, and no-linear relation between deformation and loading for drying creep. However, the exact mechanism of Pickett effect is still mysterious although several dubious hypotheses were proposed. For example, Ali and Kesler (1964) suggested drying creep is a stress-modified shrinkage, while Ruetz (1968) suggested that shearing action takes place under loading, accelerated by a concurrent moisture movement.

Secondly, the RH controls the diffusion rate of interior moisture moving to the exposed boundary. For instance, at high RH, the gradient of chemical potential of vapor is less and diffusion occurs slowly. Under that circumstance, the slow water movement may contribute to the long-term rearrangement of C–S–H nanoparticles or sheets. As evidenced by a recently study (Vlahinić et al. 2012), transient creep occur as the RH changes, mainly originating from the water movement due to the triggered chemical potential gradient. However, as mentioned before that capillary pressure decreases as RH increases, therefore there may exist a trade-off for the influence of RH on the creep behaviors. In addition, RH affects the viscoelastic behavior of the C–S–H due to the modification of its bulk properties (Maruyama et al. 2014).

Additionally, the initial formed gel-like colloid particle in pore solution are held by a equilibrium of various forcers, like crystal-forming tendency, surface tension, solid to liquid attraction and electrical attraction and repulse. The drying of C–S–H destroys the initial quasi-balance forces in wet condition, and promotes the semi-amorphous phases to re-crystallize. Admittedly, crystallization result in a volumetric reduction as the structure becomes more stable and periodic.

Another important aspect is that the stress distribution of C–S–H under simultaneous external loads and drying is extremely complicated, and has not been addressed yet. It may help to understand the creep mechanism during drying if one could unveil the constitutive relation of C–S–H in nano-scale.

The creep performance of cementitious material is also dependent on the ambient temperature and thermal history (Bažant 1983). It was reported that short-term creep increases approximately linearly with temperature up to 80 °C, where it is about three times value at ambient temperature (Mindess et al. 2003). Regardless of the creep mechanisms involved, temperature can alter several factors those are important to creep rate. First, temperature affects the rates of dissolution, diffusion, and reaction process during any chemical action in C–S–H structural reorganization. Furthermore, temperature can slightly alter the physical properties of pore solution (e.g. viscosity) and statured vapor pressure, both of which influence the water status in concrete (Chaube et al. 1993). Another important aspect is that creep is an activation energy-associated process, which is considerably controlled by temperature as well (Green 1998). However, a pre-heating treatment can reduce the long-term creep deformation for C–S–H (Mindess et al. 2003), which may be attributed to a modification in the pore structure, (packing) density, and crystallinity of C–S–H (Thomas and Jennings 2006).

Considering the rearrangement of nanostructure under external or internal stress, the dislocation site (i.e. defects) in C–S–H is likely to be a major factor. Generally, a crystalline phase is more resistant to plastic deformation than its glassy state with a similar chemical composition due to the extensive presence of defects (Green 1998). A molecular dynamic simulation of crystalline and glassy C–S–H under shear stress indicates that glassy C–S–H has a lower shear strength and larger irreversible deformation (Manzano et al. 2013). This would be a reason why the creep of semi-amorphous C–S–H prepared by synthesis is higher than that of tobermorite minerals as experimentally measured (Nguyen et al. 2014). However, it is still unknown how to accurately access the atomic ordering in C–S–H due to its small dimensions, although some advanced nanoscale characterization techniques have shed some lights on it (Nonat 2004; Lothenbach and Nonat 2015; Chae et al. 2013). In addition, the chemical composition and pore solution species are both likely to affect the structure of C–S–H (Lothenbach and Nonat 2015). Therefore, it is not surprising that the Ca/Si ratio of C–S–H, additive of admixtures (e.g. slag, silica fume, colloid silica) can affect the creep performance (Alizadeh et al. 2010; Li and Yao 2001; Singh et al. 2015), probably due to a modification in the degrees of micro-defects and polymerization (Nguyen et al. 2013). On the other hands, a large incorporation of alumina and alkalis into C–S–H has shown to drastically change its structure and behaviors (Lodeiro et al. 2010). This becomes increasingly crucial to innovative alternative binders like alkali-activated slag, which has shown larger creep deformation than ordinary Portland cement (Ye et al. 2014; Häkkinen 1986).

It is still unknown whether there is more than one mechanism for creep, or whether the creep mechanism varies depending on the experienced stress levels and ambient conditions (e.g. RH and temperature). Nevertheless, the primary issue regarding the creep mechanism is the criteria to differentiate various mechanisms at least qualitatively.

Upon application on C–S–H, the primary challenge is how to change the grain size of C–S–H nanoparticles, since varying the stress level is much easier. However, the determination of the particle size of C–S–H and how the interlayer structure incorporated into the colloid structure needs to be pre-understood. According to the CM-II model, the interlayer is perfectly incorporated and stacked together to form a grain called globules, while in Feldman and Sereda model, the separation between particle boundary and interlayer is not clear. By admitting the CM-II model, another important aspect before applying the generalized creep equation is how to vary the particle size experimentally. Physically, the application of stress and high temperature evaluation could possibly reduce the grain size for some materials, like metals (Green 1998). However, CM-II model emphasizes that both of them basically increase the packing density of grains rather than reduce the size. Nevertheless, it is still mysterious whether the grain boundary involved in creep behavior is identical to that described by CM-II.

Creep of cementitious materials is a complicated phenomenon, which is influenced by the loading magnitude/history, temperature, relative humidity, thermal and drying histories, as well as chemical composition and structure of C–S–H itself. These mechanical- thermal- physical- chemical interactions are simultaneously presented and non-linearly coupled. Understanding the creep mechanism requires a proper pre-examination of the nanostructure of C–S–H. The exact creep mechanism should be reflected by a concurrent evolution of nanostructure, chemical composition of hydrated phases, and pore solution composition during creep. Although a combination of various advanced technique for nanostructure characterization may shed some lights on the creep mechanism, there still exist several disagreements among the results obtained by different techniques. As elaborated in the text, two fundamental questions regarding creep are still unclarified yet. One is ‘where does the creep take place’, and another is ‘how does creep occur’. Answering these questions will provide the theoretical backgrounds on how to mitigate creep, quantitatively predict creep deformation, and enhance the volumetric stability of cementitious materials.