MODELLING COMPRESSIVE BEHAVIOUR OF CEMENT PASTE …

MODELLING COMPRESSIVE BEHAVIOUR OF CEMENT PASTE WITH SUPERABSORBENT POLYMER

Shengying Zhao (1), Xinchun Guan (1) and Guofu Qiao (1)

(1) School of Civil Engineering, Harbin Institute of Technology, China

Abstract Superabsorbent polymer (SAP) can modify the microstructure and influence the

mechanical properties of cement paste in at least two ways: while cavities left by SAP increase the total porosity, water released by SAP affects the hydration degree of the surrounding paste. As a starting point for investigation into the overall effect, this study presents a numerical model comprised of spherical voids, affected zones, and the unaffected matrix. In comparison, a binary model consisting only of the voids and the unaffected matrix is built up. Compressive loads are applied to both paste models. The results show that in either model a considerable negative normal stress (compressive) is typical in the middle part of SAP pore walls. The void-surrounding area subject to positive normal stress seems to be larger in the SAP-containing paste than in the other one. Nevertheless, there is a 10% reduction in maximum principal stress caused by the tougher affected zone. Keywords: cement paste; superabsorbent polymers; numerical modelling; mechanical behaviour 1. INTRODUCTION

The principle of water entrainment by superabsorbent polymers (SAP) was elucidated onthe basis of Power’s model [1]. Since then, knowledge of how SAP influences mechanical properties of properties has become critical for the design of SAP-containing cement mortar and concrete. For example, one of the goals of incorporating SAP into concrete is to enhance its frost scaling resistance by means of the air void system. This goal is less likely to achieve if the mature concrete before being subjected to freezing-thawing cycles has too low a strength [2]. Intensive research has thus been revolving around whether SAP compromises the mechanical property of concrete [3–6].

The mechanical property of concrete can be affected by the addition of SAP in at least two ways. On the one hand, SAP particles shrink when releasing water as the hydration of cement goes on. The space once taken by swollen SAP particles partially or fully becomes air voids [7]. As a rule of thumb, every percent of air in concrete reduces the compressive strength by approximately 5% relative to air-free concrete [8]. As there have been numerous comparative studies on the mechanical behaviour of air-free concrete and concrete where air is entrained

4th International RILEM conference on Microstructure Related Durability of Cementitious Composites (Microdurability2020)

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by traditional air-entraining agent, the influence of air voids on the mechanical behaviour of concrete is without the scope of the present paper.

On the other hand, the cement paste becomes internally cured by the released water [9]. In a w/c = 0.3 hardened cement paste, the porosity of an internal curing zone (i.e. cement paste within the travel distance of the released water, as distinguished by red dye) is reported to be 55% lower than that of an unaffected zone, and the degree of hydration of an internal curing zone is comparable to that of a w/c = 0.34 paste without SAP [10].

It therefore seems that difference in mechanical behaviour of a SAP-containing cement paste and an air-entrained cement paste lies in the internal curing zone. The aim of this paper is to investigate by numerical approach how this mechanically strengthened zone can make a difference on the mechanical property of an air-entrained cement paste. The mechanical responses under compressive loads are to be observed by comparing two models under numerical compressive load, one with a strengthened zone between the air void and the cement matrix while the other one without.

2. MODELLING APPROACH

2.1 Consideration over material property Cement paste with SAP comprises three parts: air voids left by SAP, internal curing zone,

and matrix unaffected by internal curing. These phases are distinguished by various elastic modulus in this study. By indentation, Wang et al. determined found that the microhardness of the SAP void wall is 1.4 times that of the unaffected matrix [10]. The data regarding the elastic moduli of different phases is not reported, though. However, in non-metallic materials, a large fraction of the indentation deformation is elastic, so microhardness and elastic modulus are not totally independent. A case in point is the almost linear correlation found by Velez et al. between hardness and elastic moduli of pure constituents of Portland cement clinker [11], see Fig. 1. On this basis it is assumed that the elastic modulus, just as microhardness, decreases as the distance from the SAP void increases.

125

130

135

140

145

150

6 7 8 9 10 11 12

H(G

Pa)

E (GPa)

C2S

C3S

C3A

Figure 1: Correlation between hardness H and elastic modulus E of C3S, C2S and C3A, plotted after data in [11]


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2.2 Model set-up Two cement models are built in commercial software Abaqus. Model 1 is a simulation of

cement paste with traditional air-entraining agent. It is built by removing 27 spheres from a 1 mm3 cube. All the air voids have a diameter of 150 μm and they altogether account for 4.8% of the cube volume.

Model 2 simulates a SAP-containing hardened cement paste. It includes both the air voids and the internal curing zones. A gradient of elastic modulus is generated in the following way. First, 27 spheres each with a diameter of 270 μm are removed from a 1 mm3 cube, leaving 27 voids. Inside each void, a hollow sphere with outer diameter (D) 270 μm and inner diameter (d) 210 μm is inserted to mimic the outer part of the internal curing zone. Likewise, anotherhollow sphere (D=210 μm, d=150 μm) is inserted to mimic the inner part of the internalcuring zone. This means that the internal curing zone is 60 μm in thickness, which is a typicalvalue, as found by Mönnig [12].

In each model, Possion’s ratio is assumed to be 0.25 for each solid phase. The dimension and elastic modulus of each phase are shown in Fig. 2.

150150

E0=25 GPa

E1=28 GPa

E2=32 GPa

(a) (b)

Figure 2: Dimension of SAP voids, dimension of the internal curing zones (in μm) and assigned elastic moduli to solid phases in (a) Model 1 and (b) Model 2

For each model, uniaxial compressive test is performed by applying an evenly distributed load (50 N/mm2) at one side and fixing the deformation of the opposite side. Fig. 3 shows the boundary condition, loading and meshing of Model 2.

Figure 3: The meshed Model 2, where the surfaces of spheres (D=270 μm) denote the largest distance water released by SAP can travel


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3. RESULTS AND DISCUSSION

3.1 Maximum principal stress The maximum principal stress S is often used as a measure to evaluate the failure strength

of brittle materials under one-dimensional compression. The largest S in Model 1 is found to be 44.3 MPa, whereas this value for Model 2 is 40.2 MPa, approximately 10% lower than that in Model 1. Fig. 4 plots the maximum principal stress distribution in Model 2. Both models display a similar pattern of distribution of maximum principal stress. This means that under uniaxial compressive load the crack propagation is alike for air-entrained cement paste and SAP-containing cement paste with the exactly same location, size and number of air voids, and that the SAP-containing model is likely to withstand a larger evenly distributed load due to the strengthened zone between the air voids and the cement matrix.

Figure 4: Distribution of maximum principal stress in Model 2 (in MPa). The section in display is parallel to the loading direction.

It should be mentioned the load bearing capacity improvement may vary greatly according to a number of factors. For example, we positioned the SAP voids in such a way that the affected zones of two SAP particles don’t overlap. However, when the spacing of air voids is smaller, it is of course possible that a point in the cement matrix is internally cured by water released from more than one SAP particle, and that the elasticity of such a point is even higher than E2. More cases are to be studied to attain a comprehensive knowledge of how maximum principal stress is affected by air void content, thickness of affected zone, etc.

3.2 Normal stress in the loading direction Both models are sectioned parallel to the loading direction, and the distribution of the

normal stress within the sections in the loading direction Syy is plotted in Fig. 5. In each model, there is a blue band going across the middle of each air void perpendicular to the loading direction, which denotes a compressive stress (Syy<0). However, Syy at the top and bottom of each void in each model is above zero, meaning a tensile stress which decreases with the increased y distance from the air void.

Comparing Fig. 5 (a) and (b), it seems that the Syy>0 region (in red and yellow) in the vicinity of air voids is larger in volume in Model 2 than in Model 1. Accordingly, the strengthened internal curing zone might increase the volume of region subjected to tensile stress.


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(a) (b)

Figure 5: Distribution of Syy in (a) Model 1 and (b) Model 2

3.3 Comments The gradient in normal stress sustained by cement paste around an air void is quite

pronounced in both models, as shown in Fig. 5. However, there is not much difference in maximum principal stress at an affected zone and at its neighbouring unaffected zone. This implies that results from this study are still not sufficient to determine the fracture behaviour of the internal curing zone or to evaluate the load bearing capacity. Moreover, the maximum-principal-stress criterion postulates that the growth of the crack will occur in a direction perpendicular to the maximum principal stress [13]. As a continuous criterion, it fails to register the discreteness of the numerical modelling of the crack-extension procedure. As such, more detailed investigation concerning how cracks propagate is in need for a better understanding the mechanical behaviour of cement paste with SAP by means of e.g. the lattice fracture model [14–16].

4. CONCLUSIONSTwo numerical models are built for FEM analysis done by Abaqus. One simulates air-

entrained cement paste, while the other simulates SAP-containing cement paste. Both models have a porosity of 4.7% and the same loci for the air voids. The only difference between the two models is that in the second one the air voids are encapsulated by two layers of strengthened internal curing zones with elastic modulus higher than the cement matrix. This paper does not conclude if SAP has a positive effect on overall mechanical property of cement paste, but some findings from computational uniaxial loading might be useful: The maximum principal stress distribution pattern in the air-entrained cement paste is

similar to that in the cement paste with SAP. In the present paper, the largest value of maximum principal stress is reduced by 10% in

by the increased elastic modulus of the internal curing zone. The reduction is subject to e.g. thickness of affected zone.

Strengthening the mechanical property of the cement paste near the air voids can increase the volume of zones subject to tensile normal stress along the loading direction.


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It is of further interest to investigate how the mechanical behaviour changes according to air void parameters. Fracture analysis under stepwise loading might be promising towards a better understanding of the deterioration process of cement-based materials with SAP.

ACKNOWLEDGEMENTS This study is funded by National Key Research and Development Program of China (Grant

No. 2018YFC0705404) and National Natural Science Foundation of China (Grant No. 51778189).

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[7] Justs, J., Wyrzykowski, M., Bajare, D. and Lura, P., 2015. Internal curing by superabsorbentpolymers in ultra-high performance concrete. Cement and Concrete Research, 76, pp.82-90.

[8] S. Popovics. Strength and related properties of concrete – a quantitative approach. John Wiley& Sons Inc. (1998)

[9] Hasholt, M.T., Jespersen, M.H.S., Jensen, O.M., 2010. Mechanical properties of concrete withSAP. Part I: Development of compressive strength. In: International RILEM conference on useof superabsorbent polymers and other new additives in concrete. RILEM publications.

[10] Wang, F., Yang, J., Hu, S., Li, X. and Cheng, H., 2016. Influence of superabsorbent polymerson the surrounding cement paste. Cement and Concrete Research, 81, pp.112-121.

[11] Velez, K., Maximilien, S., Damidot, D., Fantozzi, G. and Sorrentino, F., 2001. Determinationby nanoindentation of elastic modulus and hardness of pure constituents of Portland cementclinker. Cement and Concrete Research, 31(4), pp.555-561.

[12] S. Mönnig, Superabsorbing additions in concrete: applications, modeling and comparison ofdifferent internal water sources, PhD Thesis, University of Stuttgart, Stuttgart, 2009.

[13] Aliabadi, M.H., Boundary element methods in linear elastic fracture mechanics.Comprehensive Structural Integrity, Volume 3, 2003, Pages 89-125

[14] Schlangen, E. and Van Mier, J., 1992. Experimental and numerical analysis ofmicromechanisms of fracture of cement-based composites. Cement and concrete composites,14(2), pp.105-118.


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[16] Zhang, H., Gan, Y., Xu, Y., Zhang, S., Schlangen, E. and Šavija, B., 2019. Experimentallyinformed fracture modelling of interfacial transition zone at micro-scale. Cement and ConcreteComposites, 104, p.103383.


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MODELLING COMPRESSIVE BEHAVIOUR OF CEMENT PASTE …