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COMPUTA TIONAL MA TF RIALS SCIE/Vrp
MODELING POSSIBILITIES OF CONCRETE STRUCTURE
FOR DURABILITY PURPOSES
P. Stroeven', H . He", L . B . N . L e ' and K . L i ' ( ' D e l f t , the Netherlands, ^ B e i j i n g , China)
I n t r o d u c t i o n
Most common approach to porosimetry in concrete technology is by M I P , although loiown to yield pore size distribution data significantly smaller than obtained by quantitative image analysis Also direct investigations o f transport-based durability issues are in vogue; however they are generally laborious and time consuming. Therefore, computer simulation is getting more popular It is economic and has the potentials o f providing reliable information when a proper simulation system IS employed. Unfortunately, random sequential addition (RSA) systems are quite popular in concrete technology despite not dispersing the particles realistically on the different levels o f t h e microstructure. Porosity is somewhat structure-sensitive however pore size distribution is highly sensitive to particle dispersion characteristics. Hence, discrete element modelling ( D E M ) should be selected f o r this purpose. We have been developing during the past 1 ~ 2 decades a dynamic D E M system for particle packing, w i t h the acronym H A D E S . It can simulate packing o f non-spherical particles by impulse-based algoriüims. For that purpose, the particles are surrounded by a thin guard zone tliat upon interference w i t h such a neigh-bouring zone activates the relevant elements o f t h e tessellated surface [1]. Repulsive forces develop as a result. Otlier forces can be introduced as well so that -as a sole example- coagulation or particle clustering can be simulated. Crushed rock and nuvial aggregates o f various compositions have been properly simulated into the dense random packing state. Also, cement particles o f octaliedron shape (Fig. 1 - right) w i t h similar surface to volume ratio as experimentally found [2] have been compacted and shown to yield visually analogous section patterns as found by X-ray micro-tomography [ 3 ] .
0 5000 10000 15000 20000 25000 Volume (fim^)
FigJ (lefi) Compmersimulalion of 1000 cement panicles in the 10-50 f,m size range and experi mental regression resuhs [2] and (right) visualized structitre of grains compacted by HADES [1].
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„ e t r y on micro-level
cally the starting situation f o r simulation o f hardened pastes. A new extended I P K M based'hydration system has been developed [4] and applied for this purpose.^ It is based on Portland cement (PC) compounds and the silica i n a pozzolanic blend like rice husk porosi'
This is
vector-the f°''';"',"-'°of course "vector-the'virtuafhydration process can be stopped any time for a study o f pore ' i t on With the predecessor o f H A D E S , SPACE, this has been performed for spherical ir vas'demon-strated that the depercolation process was pooriy represented by RSA and by ^Trandom digital model-ing system at N I S T [3]. A l l three methods, however, roughly detected the
^ ^ " ^ f rrer?ffw\™'™full hydration, or an intermediate state, the problem arises o f delineating the L o r k system This can be performed by so called serial sectioning and 3D reconstruction Ï T t i ^ i s a laborious approach, developed for the RSA system H Y M 0 S T R U C 3 D . Moreover Ye's method o f determining the pore size distribution by f i l l i n g up the pores by spheres o f
• !rMsinE sizes has been proven biased. . A far better altemative has been developed by Le. T w o parallel methods start f r o m the rapidly
vnlnrin- random tree (RRT) mediod used in robotics and are denoted DRaMuTS (double random l l t i p l e ' t r e e structuring) [6] and RNS (random node structuring) [7], By starting f r o m a arge
mher o f "seeds" trees consisting o f nodes and vertices are generated into the pore system. When d r e l o p i n g in the same pore, neighbouring frees w i l l merge. Also trees in isolated pores can be generated When frees span the f u l l height o f a specimen, they are effective as to fransport through
" T h e s e main trunks o f t h e trees run predominantly in the so called I T Z , however branches o f such main channels in neighbouring ITZs f o r m connection, so that die bulk zone between the ITZs i , also connected to the outside worid. Nevertheless, volume o f continuous pores is larger m the 11Z in asrreement w i d i experimental fmdings. Since the efficiency o f t h e delineation process is enlianced by violatmg the randomness o f t h e nodes in DRaMuTS. a second random point system is necessary for measuring pore dimensions.
-Fig 2 Pore system in hydraled PC at the left (3-30 PC particles: w/c-0.3) with 10.000 tree edges. Second uniformly random poim system at the right: only points inside pores are displayed.
A l l the points inside the pores are therefore provided w i t h a "star". Hence, pikes run f r o m the nucleus m systematic directions to the nearest pore surface (length / , ) . This star volume method ( S V M ) is used in medical research where it is applied to sections, however. Local pore size (i.e. the
diameter o f tlie representative sphere) is estimated by dj = 2 ^ . The ensemble oï dj for all j can be used f o r the consfinaction o f a volume based pore size distribution, PoSD. Ahematively, a 2 D version o f the star is positioned i n a section through a nucleus to derive the size o f t h e representative circle. The section w i t h the smallest circle is called die local pore throat. Finally, the tree structure can be "smoothened" by mathematical operators to yields proper information on pore length. Length and diameter distribution along its length define pore geometty between successive nodes in a tube network model. Non-circular cross-section o f die tube reflects the (by S V M ) assessed actual ratio o f perimeter length over area.
The observed shape o f the PoSD curve is supported by experimental evidences, but pores are somewhat too large. This is obviously f r o m the imposed limitations by the computer.
To simulate all particles involved in the Rosin-Rammler particle size distribution would be impossible; so, the smaller particle fractions were so far ignored. Therefore, die new upgraded version considers all particles in a two-stage prbcess. To that end, the relatively fast hydrating small PC particles are supposed randomly distributed i n the pore space between the larger hydrating particles. Some o f the smaller ones w i l l be embedded in the deposited hydration products o f these larger particles. The rest w i l l finally move w i d i die reducing amount o f water towards the surface o f the larger particles ("covering diem like a layer o f snow"). The resulting surface roughness reduces the cross section o f the pore. Generally, the pore diameter is reduced witin twice the surface roughness (the RMS value op surface topology).
Porosimetry on nano-level
Observadons have revealed that the hydration products are not deposited evenly on the hydrating particle's surface as modeled by die vector approach. After the hydrating PC particles have replaced their loss in volume due to hydration by the deposition o f high-density (HD) hydration products (so called CSH-in), experimental observations reveal the development o f a low density fibrous ( L D ) struc-mre on nano-scale (CSH-out), see by Fig. 3. It w i l l have its highest density near die surface o f die hydrating PC particle. Such L D structures around the hydrating cement particles w i l l leave open space for the capillary pores. This w i l l be snnulated in the near future by H A D E S . The hydrating cement particles can also be realistically shaped, like octahedrons, as we showed earlier. O f course, the pore network topology and geometry can be assessed by die earlier described pore delineation methods.
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ConcIiisioBS
The micro-poroshnetry methodology based on particle packing simulation by D E M system H A D E S , hydration simulation by vector-based X I P K M , pore delineation by DRaMuTS/RNS and topology and geometry assessment by S V M , is insttumental for smdying effects o f shuctural parameters on liydrau-lic properties governing fransport dirough die pore system. A s an example, Fig. 4 displays the effect o f blending the PC w i t h a fine-grained R H A on PoSD [8] and on permeability K [9]. Nano-porosimetry has the potential o f even closer simulating the real material and thus optimizing porosimetry.
10 15 Pore size (|mi)
6 B 10
Median partido size (nm)
Fig. 4. (left) Volume-based PoSD for plain (PC2) and blended PC (BPC2) for JTZ and middle zone (MZ); (right) Permeability Kvs. median particle size of PC and PC+RHA samples (w/b=0.4).
R e f e r e n c e s
[1] He, H . (2010) Computational modeling of particle packing in concrete. PhD Thesis, D e l f t University o f Technology, Ipskamp Drukkers, D e l f t
[2] Garboczi, E.J. and Bullard, J.W. (2004), Shape analysis o f a reference cement. Cem. Concr. Res. 34: 1933-1937,
[3] hltrr.'/'visiblecemenl. nisi, sov/cemenl. html
[4] Ye, G., van Breugel, K . and Fraaij, A . L . A . (2003). Three-dimensional microstructure analysis o f numerically simulated cementitious materials. Cem. Concr Res. 33: 215-222.
[5] Le, L . B . N . , Sfroeven, M . , Sluys, L.J. , Sttoeven, P. (2013) A novel numerical muhi-component model for sunulatlng hydration o f cement. Comp. Mat. Sci., 78:12-21
[6] Stroeven, P., Le, L . B . N . , Sluys, L.J. and He, H . (2012) Porosimetiy by double random muhiple free sfructuring. Image Analysis & Stereology, 31 -.55-63.
[7] Stroeven, P., Le, L . B . N . , Sluys, L.J. and He, H . (2012) Porosimetiy by random node stiiictiiring in virmal concrete. Image Analysis & Stereology, 31:79-87.
[S] Le, L . B . N . , Sttoeven, P. (2012) Porosity o f green concrete based on a gap-graded blend. Proc.
Int. Symp. Brittle Matrix Composites 10. I F T R and Woodhead Publ., Warsaw, pp. 315-324.
[9] L i , IC, Le, L . B . N . , Sfroeven, P., Sfroeven, M . (2014) Sfrategy for predicting fransport-based durability properties o f concrete based on D E M approach. RJLEMInt. workshop on
