Analogue simulation by dem of material structure for property estimation of cementitious materials

ANALOGUE SIMULATION BY DEM OF M A T E R I A L STRUCTURE

F O R P R O P E R T Y ESTIMATION OF CEMENTITIOUS MATERIALS

Piet S T R 0 E V E N \ Huan HE^ and N g h i L , B . L E '

'Faculty o f C i v i l Engineering and Geosciences, Delft University o f Technology, Stevmweg 1, PO Box 5048, 2600 G A Delft, the Netherlands, e-mail: P.Stroeven@tudelft.nl

^GeMMe, Minerals Engineering-Materials-Enviromnent, University o f Liège, Chemrn des Chevreuils 1, 4000 Liège, Belgium.

A B S T R A C T

Realistic simulation of particulate materials like concrete on meso- as well as micro-level is nowadays possible by fast developments in computer technology. This would be a more economic way than by physical experiinents, which are more time-consuming, laborious and thus expensive. This concern the production o f t h e aggi'egate sti'ucture or of the fi'esh binder material pocketed between aggi'egate gi-ains. In the latter case, it should be followed by hydration to get the matured material. A subject of major relevance is porosimetry. This requires techniques of delineating the capillary pore network structure for the assessment of topological and geometric properties. By combining such features with hydraulic properties, a model could be designed for estimating transport properties of concrete. Influences o f technological parameters on packing characteristics are of interest for optimum packing, strength and durability of cementitious composites. The paper w i l l concentrate on packing problems and the resulting pore network structure. Some results w i l l be presented for illustrative purposes.

Keywords

Concrete, aggregate, particle packing, D E M , hydration, pore network.

INTRODUCTION

Packing capacity o f aggregate in concrete is obviously o f engineering and o f economic iirterests. Although ample research data are available, developments i n concrete technology -particularly in the high performance range - ask f o r additional research. This can now easier, but still reliably and m a more economical way be performed by the discrete element method ( D E M ) . The versatile H A D E S system is used f o r that pui-pose. This is a dynamic concurrent algoritlmi-based system [1,2]. I t renders possible considering arbitrarily shaped packed particles fi-om the dilute to the dense random state [2]. The particle packing problem is among the oldest topics i n mathematics and physics. So, additional mformation is available, although mostly dealing w i t h spheres. M o r e recently, also D E M has been employed for pacldng o f ellipses i n 2D [3] and ellipsoids in 3D [4]. The fundamental difference w i t h concrete tech-nology is the matrix. I n physics, the densest packing is pursued. I n concrete teclmology, however, the gravel grains are embedded i n a cementitious matrix w i t h a certain consistence, which upon hydration binds the aggregate grains together. Packing density is thus inevitably lower than found in such physics studies. Coordination number w i l l be reduced as well. Nevertheless, we are mterested to see whether particle shape w i l l exert similar effects on packing density and coordination number as found in physics.

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Studies o f cement paclcing in the fiesh state are performed rn a similar way. The loose random packing density is about the maximum level required for such binder packing, Hydration algoritlmis are requii'ed for studies o f hardened micro stmctures and porosimetry. We have covered spherical particles as w e l l as ellipsoidal ones w i t h various aspect ratios and polyhedral grams o f different types. The two categories could represent aggregate o f fluvial origin or o f cmshed rock, respectively. Moreover, they could represent cement particles, which were experimeirtally revealed to be non-spherical [5]. The fresh material is hydrated by the cement hydration model CemHydSim. Herein, the Integrated Particle Kinetics M o d e l ( I P K M ) for simulating hydration o f C3S grains [6] is upgraded to a multi-compound hydration model. Moreover, the hydration process can also consider grains o f incinerated, silica-rich fine-grained vegetable waste ( i n particular rice husk ash). Hydrating particle's expansion i n the complicated situation o f iiiterfering grains is assessed by a new numerical approach. Also, the micro sti'ucture o f hydrated cementitious material is stored and visualized by a 3D voxel system ( c f pixels i n digital image), whereby each voxel represents a particular phase.

The H A D E S system is a dynamic concurrent algoritlmi-based D E M , i n which particle interference is an integral part. I n a dynamic system, this is accomplished by having the particles "moving around". The procedure is such that the grain mixture i n which the particles have a desired shape is dilute dispersed in a container. Hence, in this stage a random sequential addition (RSA) algorithm can be o f profitable use. For generation o f the densely packed aggregate stmcture, this approach yields a biased solution, despite being quite popular in concrete teclmology [ 7 ] . Next, grains are provided w i t h a thin guard zone and are set to move according to a Newtonian system for linear and rotational motions. Surfaces o f the grains are tessellated into a triangular system. Upon overlap o f guard zones o f colliding grains, interaction forces between the associated tessellated surface elements develop. Tliis force is a fimction o f penetration distances and areas o f the segments and is integrated for the activated part o f the surface. Such forces can be spring-like (leading to repulsion), cohesive (leading to attraction) or representations o f damping (due to energy losses i n the system) and fi'iction effects.

The grains also similarly interact w i t h the mould o f t h e container, whereby the container boundaries can be periodic, rigid, or a combination. During this dynamic stage, the container sliriiilcs in size until the desii'ed volume fi-action o f the grains is attained. The guard zones lead to small boundary gaps between the grains (Fig. 1). This has been at least partly compensated by a growth process o f the grains. M a x i m u m packing density could have been obtained by application o f randomized shifts and rotations i n places where overlap is f o u n d such as

G E N E R A T I O N OF P A R T I C U L A T E S T R U C T U R E

Fig. 2. Paclted structures o f arbitrary octalredra (maximum size about 5 mm) w i t h rough surface area texture at different growth levels o f 0.1, 0.2, 0.3 and 0.4 nmi, respectively. performed i n a static D E M . However, i n concrete teclmology this would be an iiTclevant action, because o f the presence o f the cement matrix between the aggregate, while the highest density in the binder would be that o f the loose random packing state. A n example o f loose random packed crushed rock aggregate stmcture represented by polyhedra subjected to gro\vth is shown in Fig. 2.

I n physics experiments similar stmcture generation procedures pertain. I n [ 3 ] , ellipses are generated by RSA procedures, whereby the perimeter is discretized (leading to polygons). Thereupon, growth is step-wise applied. Next, they locally shift and rotate the polygons in the static D E M approach for elimination o f overlap. These growth steps are applied until total overlap is exceeding a pre-fixed level. [ 3 ] . I n our research we also stop when overlap is exceeding a certain limit.

H Y D R A T I O N G E N E R A T I O N

Bislmoi and Scrivener [8] distinguish the discretization approach developed b y Bentz [9] from the vector approach fnst used by Jeimmgs and Jolmson [10]. The latter approach is also used by N a v i and Pignat and denoted Integrated Particle Kinetics Model ( I P K M ) [6], The fii'st approach is resolution-dependent and the second is more time-consuming in solving the complicated particle interference situations. Presently iir our studies, the fu-st hydration part is accomplished by the I P K M approach, whereas volume-pixels (voxels) are employed i n the second stage to represent the microstructure. The method is denoted CeinHydSim and is described m [ 1 ] . Recently, the method is extended to cover the two major compounds o f Portland cement (PC), i.e. C3S and C 2 S . See, Fig. 3. Intelhgent algoritlmis {e.g., for neighborhood definition) are employed for reducmg computer time. Also particles o f a silica-rich mineral admixture (Rice Husk A s h ( R H A ) ) are included. Finally, inert particles w i l l be added to the system.

SHAPE R E P R E S E N T A T I O N

The economy o f the experiment requir-es selecting a "representative" shape for a type o f aggregate particles, as shown i n Fig. 4. For aggregate o f fluvial origin, ellipsoidal grains are selected, whereas for crushed rock aggregate, polyhedra are taken. I n both cases, more than one type o f grain shape can be selected, o f course. For cement grains, sinfilar shape representation is accomplished, so that surface area to volume o f the grains is i n agreement w i t h experimental fmdings [ 5 ] . This is shown for polyhedra i n Fig. 5 [ I I ] . For ellipsoids, see [2].

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Multiscale Computational Modeling of Cementitious Materials Krakow, Poland, 2012

1>Q _ \ C3S ^ C2S SiOz ineit T] CSH-in U CSH-oiit CH

F i g . 3. Particle models o f cement, pozzolanic a d m i x t u r e and h y d r a t i o n product.

Crushed rock Polyhedra

Fig. 4. Representation o f river gravel and crushed rock aggregates by ehipsoids and polyhedra, respectively [2].

Fig. 5. H A D E S simulation o f 1000 packed muhi-size polyhedra in 10-50 [im size range; experimental regression results (right) and visualized structure o f compacted grains (left).

E F F E C T OF GRAIN SHAPE ON PACKEVG

l u the 2D physics expermients on multi-size ellipses in the "janmied state", authors in [3] found a volume density o f 0.84 for cuxles w i t h a polydisperse distribution. A t declining value o f t h e aspect ratio the density increased to about 0.9 f o r A~0.7, whereupon it declined again. For /l<0.25, the packing density was even below that o f t h e cir-cles. A t the proper sensitivity level for the assessment o f contacts between ellipses, the average contact number increased from 4 f o r cir-cles to a plateau value o f 5.7 that was reached at 2-0.6 (6 being the theoretical value f o r the average number o f contacts o f janmied ellipses). Donev et al. [4] presented data m 3D on mono-size ellipsoids and spheroids obtained by a dynamic concurrent algoritlnn-based D E M . I n both cases, the volume fraction at random dense packing o f spheres o f 0.64 mcreased to 0.71 for spheroids at an aspect ratio o f about 0.6, and for ellipsoids to only a shghtly higher volume fraction at an aspect ratio o f about 1.5. Average number o f contacts per particle mcreased i n both cases from about 6 (spheres) to 10, approxmiately. A l l those simulations use periodic boundaries for exclusion o f wall effects. Comparison w i t h experiments in real contamers (lüce those w i t h M & M s , M i l k Chocolate Candies) is therefore not straight forward.

I n our 2D smmlations we also employed partly periodic boundaries. Loose as well as dense random states were explored (the latter tluough compaction on the top surface o f the "contamer"). Fig. 6 shows the density differences m 2 D f o r both regunes at different particle elongation (=reciprocal o f aspect ratio) o f the ellipses. The cuive for compacted grams is quite similar to that in Donev et al. [4] on a slightly lower level. Average coordmation number o f circles is about 4 and somewhat higher f o r the ellipses in loose packing; m general lower than i n Delaney et al. [3]. This is due to different algorithms as well as different particle samples bemg used. Delaney et al. [3] used a polydisperse particle size distribution to avoid the ordered stmcture, which could obviously have increased the coordmation number.

A similar procedure but w i t h the rigid boundaries is followed m the case o f the 3D packing o f mono-size standard polyhedra ( w i t h facet number 4 to 8) and an iiTcgularly-shaped particle. 864 particles w i t h sieve size 10 n m i were used for each simulation. Fig. 7 visually illustrates some loose packed structures w i t h several typical shapes. As facet number and sphericity are the sensitive parameter for these shapes, loose pacldng density is presented i n Fig. 8 as fimction o f these parameters. Sphericity is defined as surface area ratio o f the equivalent sphere and the particle (both having equal volume). Loose random packing density is generally increased w i t h increasmg facet number and sphericity as similarly found in case

E l o n g a t i o n C o o r d i n a t i o n n u m b e r

g. 6. Packmg density o f ellipses as a fimction o f elongation (left) and frequency distribution for the coordination number o f the ckcles as a fiinction o f t h e reguiie

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Multiscale Computational Modeling of Cementitious Materials _{Krakow, Poland, 2012}

pentahedron heptahedron octahedron arbitrary shape Fig. 7. Mono-size random loose packing states o f particles w i t h some typical shapes.

4.0 6.0

Facet n u m b e r

0.4 0.6 0.8

Sphericity

Fig. 8. Random loose packmg density as fonction o f (left) facet number and (right) sphericity o f particles.

1.0

of rairdom dense packing [12]. Both cases o f pacldng density have revealed particle shape as an extremely important factor m particle packing. It seems that polyhedra w i t h larger sphericity can be packed to Irigher density. Similar tendencies are found for dense packing o f the same standard mono-size polyhedra, shown in Fig. 9.

Coordmation number is an important parameter for evaluatmg packmg efficiency. As i n 2D space, a numerical method is estabhshed for calculation o f coordination number o f a packed system o f arbitrary-shaped particles. Certain additional mesh and evaluation pomts are applied to surface o f particles for the assessment purpose. Its precision is related to the

1.0 0.6 S.0.4 Ë •S 0.2 0.0 4 6 Facet n u m b e r 10 1.0 = O.E '0.6 ™ 0.4 0 0.2 •a 1 0.0 0.0 0.2 0.4 0.6 0.1 Sphericity 1.0 1.2

Fig. 9. Random dense packing density o f 3D tetrahedra and a spherical particle versus facet number (left) and as a fonction o f sphericity (right).

T e t r a h e d r o n P e n t a h e d r o n I P e n t a h e d r o n II H e x a h e d r o n H e p t a h e d r o n I H e p t a h e d r o n II O c t a h e d r o n I O c t a h e d r o n II Cube 0 5 10 15 C o o r d i n a t i o n n u m b e r

Fig. 10. Frequency distributions o f coordination irumber o f dense randomly packed polyhedra o f differeirt types

fineness o f the evaluation mesh. Selectmg a coarse mesh speeds up the calculation, but leads to biased results. Therefore, a refmed mesh should be applied f o r calculation o f coordination irumber. The resultmg distributions o f coordmation number w i t h different shapes are presented m Fig. 10. So, coordination numbers m polyhedra packing are also not only related to packmg density, but also related to shape.

P O R O S I M E T R Y IN MATURED S T A T E

Pore delineation stage

A random point system is superimposed on the virtual material. Only those points inside the pores are considered. A path plaimmg algoritlmi mspii-ed by the rapidly exploruig random tree (RRT) approach developed m robotics is applied to the pomts resultmg i n the growth o f tree-lüce structures consistmg o f the points and coimectiiig lines. The efficiency o f the RRT approach is unproved at the expense o f violating randomness. Moreover, multiple trees are growing suiiultaneously from randomly chosen or selected "seeds", whereupon comiected trees w i l l merge. I n the measuring stage, another random point system is superimposed, which led to the name: Double Random Multiple-Tree Structurmg (DRaMuTS). Details o f the methodology are described in [13,14]. B y increasing the number o f points, the coimectivity i n the pore system is eiilianced approaching a plateau value dependmg on the fineness o f the capillary pore system between about lO'* and 10^ tree edges. Since the finest pores probably do not contribute significantly to the transport mechanism, a lower sensitivity level could be selected f o r practical purposes making the approach even more economic. Fig. 11 shows tree structures f o r PC and f o r gap-graded blended PC f o r all detected pores (left) and for the main trunlcs o f t h e pore network coimectmg the outer surfaces o f the specimen (right).

Pore measuring stage

The second stage starts by the aforementioned generation o f the second random system o f points o f which the ones outside pore space are removed. The point fi-action associated w i t h the chaimels equals its volume fi-action or continuous pore fi-action. So, volume fi-action o f pores branching o f f the main chaimels and volume fi-action o f t h e isolated pores are similarly determined. W i t h a developed algoritlmi that fmds all ends o f pores, the f u l l pore topology is assessed. The effect o f t h e aggregate grain surface on the distribution o f total pore volume can

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Multiscale Computational Modeling of Cementitious Materials Krakow, Poland, 2012

thus easily be displayed. This gradient structure can be studied as fonction o f interesting techirological paraiueters. As an example, the effect o f gap-gradmg by a mineral admixture

{i.e., R H A ) has been studied. I t could be demonstrated this way that the pore peak value zone

inside the I T Z was narrowed due to blending, as Fig. 12 (left) convmcingly demonstrates.

. 4 o C i '^-S 2 o

1

^ 1 —W40Pc " W 4 0 P o 2 0 25 10 20 30 40 50 60 70 80 90 100

Distance f r o m lef=t r i g i d w a l l (|.im)

20 15 u a

|io

—W40PC-MZ ' -W40PC-ITZ — W40Po20-MZ[ / / w ^ 1

/

f' \ \

///

\

— W40Po20-ITZ / / w ^ 1

/

f' \ \

///

\

\

\ \

//'''

I I <

/

6 8 10 Pore size ( | i m ) 12 14

Fig. 12. Gradient sti-uctures o f total porosity as influenced by gap-graded blendmg w i t h R H A (left). Pores are coarser inside the I T Z zone m PC, however disproportionately refmed b y gap-graded blending (right). Note that M Z is middle zone, between ITZs; Pc=Portland cement;

Next, the random pomts are provided w i t h a star, i.e. f r o m each porirt lines run i n random or systematic directions to the nearest surface o f the pore, formmg the stars' pilces. Length /, o f all pikes are measured per point, cubed and averaged. Twice the tlirrd root value is an estimate o f the local pore diameter, d-,. Heirce, c/, = 2-^// . The method is called star volume measuring and is developed basically f o r estimating pore size f r o m 2D sections [ 1 5 ] . However, in the 3D reality o f the virtual material it can be directly applied. The collected volumes o f all such representative spheres can be used for the construction o f a volume-based pore size distribution f u n c t i o n (PoSD), w h i c h renders possible studymg the effects o f teclmological measures on the PoSD. As an example, the favorable effect o f blendmg by a gap-graded mineral admixture {i.e., R H A ) on the PoSD could be revealed this way (Fig. 12) [16]. W i t h the eye on use o f pore size characteristics m a transport-based model, it seems more logic determming the local pore tluoat. This is defined as the smallest pore area o f random plain sections tlu'ough a random point. A 2D star is defmed i n such a section by a random or systematic set o f pilces i n the section plane. Püce lengths /,- are determined per point, squared and averaged; cross section area is nl'^ . The area-based pore tlu-oat size distribution function is obtamed by collecting all local pore tliroat area measurements. Curves are not fimdamentally differeirt fi-om PoSD. A final operation could be smoothenmg o f the zigzag lures in chaimels to get a more appropriate measure for then tortuosity. This is being executed at the moment. Relevance is derived f r o m the expectation that pore size (tliroat distribution) and pore tortuosity w o u l d be the major parameters i n a transport model.

D E M by H A D E S is a reliable and economic way to simulate particle packing on both levels o f the microstructure m concrete. For aggregate, at least the dense random packing state should be produced; for the binder, the loose pacldng state could be appropriate at low water to binder ratios representative for High Performance Concretes.

HADES renders possible simulating arbitrarily-shaped particles. For economic reasons, however, a limited number o f standard shapes o f ellipsoidal and polyhedron categories should be selected. The research dealmg with shape effects on packing are qualitatively in agreement w i t h physics studies i n 2D and 3 D . This approach therefore renders possible studymg effects o f aggregate grain shape (river gravel versus crushed rock) on packing density both i n combination w i t h variations iir relevant teclmological parameters.

The non-spherical nature o f cement grains can be captured m packing studies in the fi'esh state as weh. The far more complicated hydration algoritlmis as compared to those for spherical grams have still to be developed. They w i l l make it possible performing porosimetry studies on an even more realistic virtual representation o f concrete.

The completed methodology o f HADES-CeiiiHydSim-DRaMuTS is available for elaborating in an economic way comprehensive studies on influences o f teclmological para-meters on geometrical and topological pore characteristics. H A D E S simulation w i l l produce information superior in reliability as compared to such mformation coming fi'om application of popular RSA systems [17].

The favorable strength experiences w i t h gap-graded blending by R H A m real concrete [18] are supplemented i n the present virtual experiments as to porosity. This w i l l exert also positive effects on durability.

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