CAPILLARY PRESSURE AND CRACKING IN EARLY AGE CONCRETE

Transcription

1 CAPILLARY PRESSURE AND CRACKING IN EARLY AGE CONCRETE Volker Slowik (1), Tobias Hübner (1), Beate Villmann (1) and Markus Schmidt (1) (1) Leipzig University of Applied Sciences, Germany Abstract Shrinkage and cracking of concrete in the early age, i.e. within the first few hours after casting, is mainly caused by the capillary pressure build-up in the two-phase system consisting of solid particles and water. Due to evaporation at the concrete surface, the water content in the system decreases and, eventually, the solid particles can not be covered by a continuous and plane water film anymore. As the curvature of the water surface between the superficial particles increases, a negative capillary pressure is built up in the liquid phase resulting in shrinkage. The presented 2D model allows to simulate the described physical process and to investigate influences of the material composition on the capillary pressure and on the early age cracking risk. Circular rigid particles are uniformly distributed in a liquid phase and the water front between the particles is calculated by assuming constant surface curvature. Evaporation leads to an increase of this curvature and simultaneously to an increase of the capillary pressure. Particle mobility is controlled by interparticular forces. It is demonstrated that under increasing capillary pressure air penetrates locally into the system. This may lead to discontinuities in the displacement field and to the formation of cracks. 1. INTRODUCTION The presented work is aimed to the modelling and simulation of concrete cracking in the early age, i.e. within the first about four hours after casting. In this early age, physical phenomena rather than chemical reactions are the predominant reason for volume changes and cracks. The beginning hardening process has not yet led to a significant tensile strength of the material. Similar phenomena as those investigated here may be observed in drying suspensions with inert solid particles. In fact, for studying shrinkage and cracking in early age concrete, inert suspensions consisting of fly ash and water may serve as model materials due to the spherical particle shape and due to the cement-like particle size distribution. If the surface of a suspension is subjected to evaporation, capillary forces result in a negative pressure in the liquid phase of the material. Accordingly, the resulting contraction of 673

2 the material is referred to as capillary shrinkage. In the case of cementitious materials, the term plastic shrinkage is also used since the volume change takes place when the material is still in its plastic stage. Plastic shrinkage may lead to cracks, see Fig. 1, especially in concrete floors or slabs where the upper surface is subjected to high water evaporation rates. The cracks shown in Fig. 1 developed in a 25 cm thick concrete slab on grade within the first four hours after casting. They have a typical net-like pattern with a spacing of about 1 m and a maximum crack width of more than 1 mm. Figure 1: Early age shrinkage cracks in a concrete slab on grade Early age cracks are a severe problem in concrete technology since they may degrade the durability of the structures. Even if they are not visible or if they have been temporarily closed during surface finishing, they do have an influence on damage processes taking place during the service life of the structure. In many cases, undesigned and avoidable crack patterns in concrete structures may only be explained by considering the early age material behaviour. The problem of early age cracking becomes even more important for high-performance concrete compositions characterized by small particle sizes, high binder content and low water-cement ratio. These characteristics may lead to a more intense self-desiccation, to comparably high values of capillary pressure and shrinkage strain and, consequently, to an increased early age cracking risk. 2. CAPILLARY PRESSURE BUILD-UP IN DRYING SUSPENSIONS Fig. 2 explains the physical process leading to the capillary pressure build-up in a drying suspension consisting of solid particles, cementitious or inert, surrounded by a liquid. The upper surface is subjected to evaporation. After casting, a settlement of the solid particles may take place due to downward gravitational forces. On the top face of the sample, the liquid 674

3 forms a film with plane surface (Fig. 2, A). In concrete technology, this effect is called bleeding. All solid particles are completely covered by the water and the latter forms a system of hydraulically interconnected pores. Experiments performed by the authors have shown that at this stage and up to a depth of at least 10 cm the hydraulic pressure is nearly independent on the location. Figure 2: Water front in a drying suspension Due to evaporation or in certain materials also due to self-desiccation, the total water volume reduces and the water film on the upper face is getting thinner. At some point, the superficial particles can not be completely covered by the water anymore (Fig. 2, B). Due to adhesive forces and surface tension, water menisci are formed between the solid particles and a negative pressure is built up in the liquid phase. According to the Gauss-Laplace equation, eq. 1, the pressure value p depends on the surface tension of the liquid and on the main radii R of its curvilinear surface. p = γ R1 R (1) 2 At the superficial particles, the negative pressure results in inward forces leading to a compaction or vertical shrinkage displacement and, if not hindered, also to a horizontal shrinkage strain (Fig. 2, C). Consequently, the interconnected pores are getting smaller. However, this compaction is not sufficient for completely relieving the pressure since repellent interparticular forces counteract the pore size reduction. If a certain pressure is reached, the largest pores between the superficial particles can not be bridged by menisci anymore and air penetrates into the pore system (Fig. 2, D). Due to the irregularity of the solid particle arrangement, the air entry does not occur simultaneously in all pores. In the following, the pressure value at the first event of air entry into the pore system is referred to as air entry point. This term is also used in soil mechanics describing a similar phenomenon. Although the described physical process is well known in the concrete research community and has been investigated experimentally [1] [2] [3] [4], its practical consequences are frequently disregarded in concrete technology leading to severe structural faults. It is assumed that the risk of cracking is especially high at the air entry point because the air filled pores are weak points in the microstructure [5]. This assumption could be confirmed by electron microscopic observations [4]. In suspensions consisting of fly ash and water it was observed that shortly after the local air entry cracks were formed along a line connecting the weak points originating from air entry. Knowing the air entry point for a certain material, it might be possible to define a capillary threshold pressure which should not be exceeded during concrete processing in order to minimize the risk of early age cracking. As a practical consequence, a method of controlled concrete curing was proposed [4] which allows to significantly reduce the early age cracking 675

4 risk. It is based on the in situ measurement of capillary pressure in early age concrete. If the latter reaches a previously defined threshold value, which should be lower than the air entry point, the concrete surface is rewetted. Experience has shown, that a short rewetting period of a few seconds is sufficient [4]. The capillary pressure decreases temporarily due to the water supply, but it is not completely relieved. For this reason, the rewetting does not create a continuous water film on the concrete surface which might degrade the near-surface material properties due to an increased water-cement ratio. The determination of the air entry point as a critical capillary pressure value for a specific material composition is subject of the ongoing research. It depends on the particle size distribution, on the water-solid ratio, on the air content as well as on the mobility of the solid particles in the liquid phase. The model presented here allows to simulate capillary pressure build-up and air entry in drying suspensions as well as the subsequent cracking. Its application is aimed to a better understanding of the early age concrete behaviour and, prospectively, to an estimation of the early age cracking risk by computational means. 3. MODELLING AND SIMULATION Suspensions consisting of inert or cementitious solid particles and a liquid phase are modelled in 2D by assuming a two-phase system with circular rigid inclusions uniformly distributed in a matrix, see Fig. 3. For generating these models, a stochastic-heuristic algorithm is used which was originally developed for mesolevel models of concrete with ellipsoidal aggregate particles [6]. It allows to obtain models with realistic particle contents and distributions. Particle positions, and in the case of ellipsoids also their orientations, are randomly chosen. If a particle overlaps previously locates ones, several attempts of translational or rotational movements are undertaken for finding a possible position. This strategy allows significantly shorter computing times and higher particle volume contents than purely stochastic algorithms. Figure 3: Interparticular forces between solid particles and resulting forces from capillary pressure The interaction between the solid particles is described by interparticular forces, but only the interactions between neighbouring particles are considered, see Fig. 3. This simplification 676

5 is justified by the comparably strong decrease of the interparticular forces with increasing particle distance. As external loads, gravitational forces as well as the forces resulting from the negative capillary pressure in the liquid phase, see Fig. 3, are taken into account. The interparticular forces include electrostatic forces, van-der-waals forces and Born repulsion in the near field. They depend on particle distance and radii as well as on the physical and chemical properties of the solid and liquid phase. According to the generally accepted DLVO-Theory, named after Derjaguin, Landau, Verwey and Overbeck, the different types of physical interaction are superimposed giving a resulting interparticular force, see Fig. 4, which is dependent on the particle distance. Figure 4: Superposition of interparticular forces The van-der-waals force describes the interaction between electrically neutral particles and is calculated here by using a simplified approach according to eq. 2 where r are the particle radii, a the particle distance and A H the Hamaker constant. The latter is a property of the solid phase and, according to Flatt [7] [8], for cementitious materials nearly linearly dependent on the solid density. The simplified calculation according to eq. 2 is justified since cementitious suspensions are characterized by high ion concentrations and small particle distances [7] [8]. F vdw R AH with R 2 12 a 2 r r r + r 1 2 = (2) For determining the electrostatic force, eq. 3 is used which was also proposed by Flatt [9]. This force describes the repulsion of the ion clouds which are surrounding particles in aqueous solutions. In eq. 3, 0 is the vacuum permittivity, r the relative permittivity, the

6 zeta-potential, k B the Boltzmann constant, T the absolute temperature, e the elementary charge, z + the valence and n + b the concentration of an equivalent symmetric electrolyte. F el a δ 2 1 e ε 0 ε r k B T = 2 π ε 0 ε r ζ R with δ = (3) a b δ e z n δ e The Born repulsion becomes significant as an additional interparticular force in the case of very small particle distances. It is caused by the interaction of the adjacent electron clouds. Although approaches for the quantitative determination of this force are available, in the model presented here the description of short-distance particle interaction mainly depends on requirements given by the numerical solution method. This is not expected to significantly affect the final results since the calculated particle distances are normally larger than the one at which Born repulsion becomes decisive. During the iterative solution, however, very short particle distances as well as overlapping might occur. In the model, a continuous and comparably steep increase of interparticular forces with decreasing distance is assumed. It qualitatively resembles Born repulsion. Fig. 5 shows the 2D numerical simulation of a drying process. The capillary pressure in the liquid phase is incrementally increased. For a constant surface curvature corresponding to the given pressure, the course of the water front is calculated. Taking into account the forces resulting from the capillary pressure, the gravitational forces as well as the interparticular forces equilibrium iterations are performed seeking the minimum of potential energy. In each of the iterations, a new water front needs to be determined. When previously set convergence criteria are met, the next capillary pressure increment is applied. The maximum pressure is reached when no water front connecting the side faces of the mould can be found anymore. The first line in Fig. 5 corresponds to zero pressure. All particles (dark circles) are located below the surface of the water (gray). When water is evaporating, menisci are formed between the superficial particles and the capillary pressure in the water-filled pore system increases. The pressure results in downward forces on the superficial particles leading to a settlement of the material. It may be seen that the air entry into the solid-fluid-system does not occur equally. A local gap is formed and widened by the increasing capillary pressure. Eventually, the attracting interparticular forces between the opposite sides of the gap have reached a negligible value and a crack has developed. When evaluating the simulation results, this phenomenon of strain localization and separation is regarded as cracking. Results of the simulations include crack patterns, deformations, as well as values of the capillary pressure and of the evaporated water volume. It was found that despite the 2D simplification, numerically determined capillary pressure values are in good agreement with experimental results. For this reason, conclusions concerning a critical threshold value of the capillary pressure may be drawn. As far as the evaporated water volume is concerned, the simulation results differ from the experimental findings. This may be attributed to the 2D simplification and also to the very small specimen height in the simulations. In parametric studies, several influences on capillary pressure and early age cracking were investigated. It could be demonstrated that shrinkage and cracking risk are significantly reduced if all particle sizes are increased by a constant factor. The comparably high selfweight of the enlarged particles results in a more stable structure and limits particle mobility. Furthermore, the increase of the capillary pressure versus water loss is less steep. 678

7 p = 0 kpa p = 16 kpa p = 24 kpa p = 32 kpa p = 48 kpa p = 56 kpa p = 64 kpa p = 72 kpa p = 80 kpa p max = 88 kpa Figure 5: Simulation of the capillary pressure build-up in a drying suspension (capillary pressure p increasing from the top down, particle sizes ranging from 4 µm to 32 µm) 679

8 If the portion of fine particles is increased or if the smallest particle size is decreased, the slope of the pressure versus water loss curve becomes steeper because of the smaller spaces between the superficial particles. It was also found that the material appears to be more vulnerable to cracking in this case. Because of their comparably small self-weight, the fine particles are more mobile than larger ones. This allows a stronger strain localization which may eventually lead to cracks. The equilibrium particle distance, see Fig. 4, does also have an effect on the cracking behaviour. It depends on the properties of the solid and liquid phase and affects the cracking risk in two different ways. On one hand, particle mobility will increase with this distance and, on the other hand, the pressure increase will be less steep. Simulation results have shown that with increasing equilibrium particle distance the material tends to form a more pronounced crack pattern. 4. CONCLUDING REMARK In principle, the proposed model allows to simulate the capillary pressure build-up as well as shrinkage and cracking of drying suspensions. So far, only the behaviour of suspensions with inert solid particles has been investigated. It is planned, however, to take into account the hardening induced evolution of particle sizes as well as of physical and chemical properties of the solid and liquid phase. The properties of the liquid are influenced by plasticisers and other admixtures. Their effect on early age cracking might also be investigated. ACKNOWLEDGEMENT The financial support of the research by the German Federal Ministry of Education and Research is gratefully acknowledged. REFERENCES [1] Wittmann, F.H., 'Zur Ursache der so genannten Schrumpfrisse', Zement und Beton 85/86 (1975) [2] Wittmann, F.H., 'On the Action of Capillary Pressure in Fresh Concrete', Cement and Concrete Research 6 (1976) [3] Radocea, R.A., 'Study on the Mechanism of Plastic Shrinkage of Cement-Based Materials', PhD thesis, (Chalmers University of Technology, Göteborg, 1991). [4] Schmidt, D., Slowik, V., Schmidt, M., Fritzsch, R., 'Auf Kapillardruckmessung basierende Nachbehandlung von Betonflächen im plastischen Materialzustand' ('Early age concrete curing based on capillary pressure measurement'), Beton- und Stahlbetonbau 102 (11) (2007) [5] Hammer, T.A., 'The Use of Pore Water Pressure to follow the Evolution from Fresh to Hardened Concrete', in 'Advances in Concrete through Science and Engineering', Proceedings of the 2nd International Symposium, Quebec City, Canada, September, [6] Leite, J.P.B., Slowik, V., Apel, J., 'Computational model of mesoscopic structure of concrete for simulation of fracture processes', Computers and Structures 85 (17-18) (2007) [7] Flatt R.J., 'Interparticle forces and superplasticisers in cement suspensions', PhD thesis, No. 2040, Swiss Federal Institute of Technology (Zurich, 1999). [8] Flatt R.J., 'Dispersion forces in cement suspensions', Cement and Concrete Research 34 (2004) [9] Flatt R.J., 'Towards a prediction of superplasticized concrete rheology', Materials and Structures 37 (2004)