An NUMERICAL MODELLING OF SELF COMPACTED CONCRETE

V.VIGNESHKUMAR 1, DIVYA ANUSHA NAIDU 2, Dr. DUMPA VENKATESWARLU3

1 Post Graduate Student, Department Of Civil Engineering Godavari Institute Of Engineering & Technology, Assistant Professor, Department Of Civil Engineering Godavari Institute Of Engineering & Technology 2 ,Professor and Head of the department Department Of Civil Engineering Godavari Institute Of Engineering & Technology3

ABSTRACT With the appearance of Self-Compacting Concrete (SCC) that streams uninhibitedly, under the sole impact of gravity, the desire for issue free and unsurprising castings even in complex cases, spurged the recreation of solid stream as a way to demonstrate and anticipate solid functionality. To accomplish total and dependable structure loading up with smooth surfaces of the solid, the fortified formwork geometry must be perfect with the rheology of the new SCC. Anticipating stream conduct in the formwork and connecting the required rheological parameters to stream tests performed on the site will guarantee an improvement of the throwing procedure. In this theory, numerical reproduction of solid stream is explored, utilizing both discrete just as constant approaches. A future converging of the homogeneous liquid model with the molecule way to deal with structure particles in the liquid will highlight the progression of concrete as the physical suspension that it speaks to. One single ellipsoidal molecule falling in a Newtonian liquid was considered as an initial step. Keywords: Self-Compacting Concrete, SCC, Fresh solid stream, Numerical recreation

1. INTRODUCTION Cement is one of our most normal structure materials, it comprises of totals binded by concrete glue. The compressive quality of cement is to a huge degree subject to the water to bond proportion (w/c). Concrete is a pressure driven fastener, which means it solidifies by a response with water to something that isn't water solvent. The littlest particles of the solid glue are in the scope of micrometers (or even nanometers), the biggest particles, the totals, are going a few centimeters. The sorts and extents of the solid constiuents impact cement's hard properties, yet in addition its new properties. From 1687 beginning with the production of Isaac Newton's 'Principia' until the mid-1960s, liquid mechanics has depended on the two old style instances of unadulterated examination and unadulterated hypothesis as it were. The synergistic blend of spearheading trials and hypothetical investigations, regularly utilizing improved models of the stream, generally prompted numerous advances in the field of liquid mechanics. The original of computational liquid unique arrangements showed up during the 1950s and mid 1960s, impelled by the need to explain the high speed, high-temperature reemergence body issue of an intercontinental ballistic rocket or of a climatic passage vehicle for orbital or lunar return missions. Today, Computational Fluid Dynamics, CFD, supports and supplements both unadulterated analysis and unadulterated hypothesis. With the appearance of the highspeed computerized PC, numerical recreation of stream will remain a third measurement in liquid elements, Wendt (1992).PC speed has been said to twofold consistently, officially known as Moore's law. In 1965, Gordon Moore, prime supporter

of Intel, anticipated the quantity of transistors per square inch to twofold every year inside a not so distant. This forecast has hindered a bit, with information thickness presently multiplying at regular intervals. Most specialists, including Moore himself, anticipate that this pace should hold for an additional two decades. Self-Compacting Concrete, SCC, called Self-Consolidated Concrete in North America, is a solid that is compacted exclusively affected by gravity. Its stream qualities characterize the SCC functionality, and simply like there are various sorts and families for traditional cement, there are additionally a wide range of sorts of SCC. New SCC might be depicted as a molecule suspension, which means particles disseminated in a fluid. The accompanying three properties characterize the usefulness prerequisites for SCC: (i) filling capacity, (ii) passing (capacity to course through limited openings without blocking) and (iii) resistance to segregationas can be found in Concrete Report No. 10(E) (2002).History of SCC

So as to improve sturdiness and unwavering quality of solid structures, and to empower structure filling even with convoluted basic plan subtleties, Japanese analysts thought of the idea of another, self leveling concrete in the late 1980s. The importace of the high deformability of the material, and the requirement for high isolation obstruction are two highlights that are among the most hard to accomplish, since they are all in all negating properties. By utilization of substance admixtures, a stable SCC model was created in 1988. Ozawa, Maekawa and Okamura called their recently imagined solid High Performance Concrete, to push its high filling limit, Ozawa et al. (1992). SCC may spare work expenses and wounds, it totally disposes of the union clamor of the vibration pokers and it might prompt imaginative development frameworks. By 1996, SCC was being utilized for the moorings of Akashi-Kaikyo Bridge in Japan, the world's longest suspension connect. For this specific assignment, a SCC with a most extreme coarse total size of 40 mm was created and as much as 1900 m3 of cement was put in one single day, as portrayed by Okamura and Ozawa (1996). Development time was abbreviated with a sum of a half year, 120 000 m3 SCC in all were thrown. The advancement of SCC in Sweden authoritatively began in 1993 with a workshop at the Swedish Cement and Concrete Research Institute, CBI, with temporary workers and makers welcomed. A CBI blend configuration model was created and the principal connect altogether cast with SCC was done in January 1998, propably being the first outside Japan, Billberg (1999). Starting today, SCC is broadly utilized and acknowledged, particularly for passage linings of intensely fortified structures, where regular cement would not round out the formwork. The precast business has exploited the conceivable outcomes given by throwing with SCC. The solidified properties of SCC show proof of improved microstructure, this demonstrates an expansion in thickness, quality and toughness, Skarendahl (2003).

2. LITERATURE REVIEW PC Aided Modeling and Simulation of Self-Compacting Concrete Flow The stream conduct of SCC is right now being examined as a progressing PhD venture. This paper exhibits an advancement of the Distinct Element Method utilizing the business programming

PFC3D to show the progression of SCC. A decent correspondence was acquired between the research center test and numerical outcome for the droop stream test. A molecule based technique including molecule contact powers characterizing the rheological conduct of the displayed cement is quickly exhibited and the twofold layered molecule (delicate glue layered covering a hard total part) is presented. The Bingham contact model is portrayed regarding mechanical apparatuses: a spring, dashpot and slip work. The power reliance of molecule size is expressed. Molecule size circulation was chosen as per the real sifter bend and glue content, which further improves the aftereffects of the numerical reproduction. PC Simulation of SCC Flow Beginning in 1993, Sweden was, propelled by Japanese research in the solid field, the principal European nation to build up the progressive material called Self Compacting Concrete (SCC). The Swedish Cement and Concrete Research Institute (CBI) was one of the pioneer investigate situations on SCC in Europe; for example the main European extensions were thrown in Sweden in 1998. Moreover, a SCC stream recreation undertaking was begun in 2000 at CBI. The utilized molecule based programming is called Particle Flow Code (PFC) and depends on the Distinct Element Method (DEM). Numerical Simulation of Fresh SCC Flow - Applications Numerical reenactment of Self-Compacting Concrete (SCC) stream demonstrates incredible potential and quick advancement transforming into a useful asset for expectation of SCC structure filling. Numerical reenactment is likewise of intrigue with regards to displaying little scale material phenomenology. This paper presents three distinct applications helpful for demonstrating various marvels on various scales: (I) Particles, each speaking to a total in the solid. (ii) Fluid, displaying concrete as a homogeneous fluid and (iii) Particle in Fluid, considering subtleties of stream. The strategies are contrasted and assessed all together with give the peruser a snappy direction into the universe of potential outcomes that open up with numerical reproduction. Connecting Numerical Simulation of Self-Compacting Concrete Flow to onSite Castings There is still opportunity to get better before the development part will most likely exploit Self-Compacting Concrete, SCC. This paper demonstrates one method for displaying solid stream by numerical recreation with Computational Fluid Dynamics (CFD). PC supported numerical reproduction of solid stream is a youthful science, forming into an incredible asset for expectation of SCC throwing. Displaying new solid stream adds to a structure of higher quality and advanced throwing techniques. The introduced model is contrasted with an expository case demonstrating an exact understanding. Further, a similar material stream model for cement reproduced as a Bingham material is likewise connected to full scale tests. An area of a precast twofold tee section and the structure filling of a full-scale divider throwing were examined. The correspondence among numerical and estimated qualities is promising.

3.1 Mix DesignThe blend structure of coarse and fine totals in the solid is significant both for the new and solidified solid properties. Right proportioning outcomes in better functionality of the crisp concrete just as expanded sturdiness for the solidified cement. Around 1900 a Frenchman, Feret, was the first to state logical standards for proportioning mortar. As can be perused in Meininger (1982), he created connections between the amounts of bond, air and water voids. In 1907, Fuller and Thompson distributed their 'Laws of Proportioning Concrete', including the wellknown 'Fuller Curve' for total reviewing of greatest thickness. By and large, a superior (yet not really denser) pressing arrangement of totals, is accepted to bring about a solid result of higher quality.

. METHODOLOGY3

Figure 3.1: Particle paste layersThe danger of isolation diminishes as τ0 holds a high worth and as the thickness distinction between the molecule and the encompassing liquid abatements. Since a high estimation of τ0 brings about less deformability, one ought to choose as low (ρs − ρf) as could be expected under the circumstances. Smaller scale particles gliding in water that help little particles shaping a mortar stage holding considerably greater totals. Clearly, an advanced evaluating of the totals guarantees legitimate usefulness.3.1.1 Mix Design of SCCThe first Japanese methodology of blending SCC, created in the late 1980s, was adjusted during the 1990s by severeral nations in Europe, Sweden being one of them.ConstituentsLike some other cement, SCC comprises of bond, totals, sand and may hold fly slag, silica smolder, air entraining operators or different added substances. To accomplish the high ease of the solid, without causing isolation by including water, alleged super plasticizers are utilized. There are three ages of superplasticizers. The original is Lignin based. The subsequent age depends on Melamine/Naphtalene and the third era plasticizers are polycarboxylates, Ljungkrantz et al. (1994). Superplasticizers of the third era are water solvent anionic polymers, that are adsorbed onto concrete particles. They decline or stifle the interparticle fascination and increment molecule streamThe Japanese Design MethodThis blending strategy is a cyclic element enhancement of the glue, mortar and last the solid stage. Powder is here characterized as particles underneath 90 µm, sand is littler than 5 mm and the coarse total is < 20 mm, Grünewald (2003), see Figure 3.2 for a flowchart of the enhancement cycle.To err on the side of caution, one could state, that powder limits a measure of water equal to its very own volume. Moreover, the volume proportion of bond, sand and coarse total ought to be approximaterly 1:1.5:1.5, a further increment of the coarse total would offer ascent to issues identified with blocking, which increments radically if the thickly stuffed coarse total volume surpasses half of the strong substance. The volume of particles bigger than 90µm ought to be set to 40% of the all out mortar volume.

FR = πr2 · τ0

FB = ρf · g · (4/3)πr3

FW = ρs · g · (4/3)πr3

with r being the particle radius, ρf and ρs being the density of the fluid and the solid particle respectively, g is the gravitational acceleration acting on the system. The yield stress, τ0, defines the deformability of the surrounding fluid, in this case the concrete, Wüstholz (2006). For a non-segregating SCC, the following criterion is valid:

FW 6 FB + FR3.1.1 Mix Design of SCCConstituentsLike some other cement, SCC comprises of bond, totals, sand and may hold fly slag, silica smolder, air entraining operators or different added substances. To accomplish the high ease of the solid, without

Distance between Particles Distance between Particles Distance between Particles Distance between Particles Distance between Particles Distance between Particles Distance between Particles Distance between Particles Distance between Particles Distance between Particles Distance between Particles Distance between Particles Distance between Particles

causing isolation by including water, alleged super plasticizers are utilized. There are three ages of superplasticizers. The original is Lignin based. The Japanese Design MethodThis blending strategy is a cyclic element enhancement of the glue, mortar and last the solid stage. Powder is here characterized as particles underneath 90 µm, sand is littler than 5 mm and the coarse total is < 20 mm, Grünewald (2003), see Figure 3.2 for a flowchart of the enhancement cycle..

Figure 3.2: Japanese Design Method, from Okamura and Ozawa (1994)The CBI Mix Design MethodAlso to the Japanese strategy, the blend structure technique created at CBI isolates the advancement of the glue and the totals. A mimimum void volume decided exactly from pressing tests decides the base glue volume. In light of work from Van Bui (1994) and Tangtermsirikul and Van Bui (1995), likewise, a blocking rule is presented. Elements affecting blocking are recognized as total reviewing, clear dispersing between rebars the properties of the fluid stage. Underneath appeared in Figure 3.3, blocking is pictured for various rock to add up to total proportions. The base void is plotted in a similar diagram, indicating distinctive structure criteria for squashed and normally adjusted rock.3.1.2 Particle Shape

When considering the exessive paste required to make the concrete flowable, one should take into account the shape of the particles. Coming from one and the same quarry and passing the 16 mm sieve, the following aggregates are an example of different shapes and sizes found. They may be elongated, crushed and flaky or rounded. The textures vary from rough to smooth, the size can be approximately defined using a ratio a:b:c of the thickness, hight and length of each aggregate The aggregates shown in the photo (Figure 3.4) are of the following dimensions, going from left to right always measuring the largest width, lentgh and hight (in mm)

15.2 16.5 14.0 12.3 14.210.1

::::::

19.7 20.2 16.1 14.3 17.816.0

::::::

31.9 26.1 41.4 43.0 21.229.8

Since the mesh of the sieve consists of squares, an extremely flaky particle measuring a width of 22.6 mm could theoretically pass through, Figure 3.6.

3.2 Rheology 3.2.1 Rheological Model

They may comprise of the accompanying analogies portraying a material, here as mechanical models found in Figure 3.8.The spring capacity complying with Hooke's Law gives the connection beween a power and a misshapening. As expressed by Robert Hooke in 1678, 'The intensity of any spring is in a similar extent with the strain thereof.', Macosko (1994). For a one-dimensional case we get: F = G • xThe dashpot, likewise, depicts the connection between a power and the speed of the misshapening, from Macosko (1994). Newton depicts a thick fluid in 'Principia Mathematica' by the accompanying in 1687: 'The opposition which emerges from the absence of trickiness starting in a liquid, different things being equivalent, is corresponding to the speed by which the pieces of the liquid are being isolated from one another.' By 'obstruction' is implied the nearby pressure and 'speed by which the pieces of the liquid are being isolated' can be perused as the speed inclination or the difference in speed. The proportionality between them is the consistency, the 'absence of dangerous'. For an instance of one measurement, this can be composed as τ = ηγ˙.Outer powers following up on a material may bring about twisting, that can be either versatile, just like the instance of a spring (the distortion is totally recoverable when the power is discharged) or plastic, as given by the dashpot, (disfigurement does not recuperate).The shear stream of a Newton material, for example, water, nectar or oil, might be imagined as a dashpot, the pressure being relative to the shear rate,The material moves according to the viscosity η of the dashpot. The stress to shear rate ratio, the slope of the function, is the viscosity3.2.2 Prediction of Workability

So far, the apparent and the plastic viscosity was mentioned. As can be read in Macosko (1994), Einstein studied the increase in viscosity adding to a Newtonian fluid a perfect sphere, as discussed in his papers dating back to 1906 and 1911. For an incrompressible Newtonian liquid subjected to creeping flow a density neutral (ρf = ρs) particle increases viscosity byη = ηf(1 + 2.5φ) (2.1)

This holds true for a sufficiently small particle volume fraction, φ, with no interaction of particles. The value 2.5 accounts for particle shape characteristics, it is the so called intrinsic viscosity [η] for spherical particles. The relative viscosity ηr is defined as

with subscript f being the fluid without particles. whereas the specific viscosity is

The intrinsic viscosity is written

Einstein’s equation, Equation 2.1 can now be rewritten as η = ηf(1 + [η]φ) or ηsp = [η]φ. Also note that the particle radius does not affect the viscosity, as long as the liquid volume is of an adequate amount. Analogously to the relative viscosity, the relative yield stress can be defined as:

In order to taylor both fresh and hardened concrete properties, a prediction of the properties would be convenient before the actual mixing takes place. Prediction of concrete workability is a useful tool for mix design of SCC. In the fresh state, it is of particular interest to ensure good workability, eliminate the risk of blocking, to ensure interaction of the concrete layers during casting and proper filling of the formwork.

Years after Einstein’s definition of the relation for viscosities of dilute suspensions, Mooney (1951) published a relation introducing a self crowding factor to account for particle interactions of more concentrated suspensions. The crowding factor is today commonly replaced by the maximum solid fraction:

Mooney’s relation is hence written

(2.2) Krieger and Dougherty’s relation states that, for any kind of particle shape, the relation from Barnes et

al. (1989)

(2.3)3.3 BlockingIt is important to recognize physical sticking of totals and obstructing of the solid blend because of poor usefulness (fragmented structure fillling).Blocking may happen essentially because of the way that the totals are too enormous to even think about passing the obstacleThis curve shaped by a few totals will square further totals from passing.Yield pressure τ0 decides spread, though plastic thickness µpl is a parameter identified with speed of stream. For this situation, he droop stream breadth of the ordinary stream test for SCC with the Abram's cone is considered. The breadth at stream stoppage SF is picked to check the yield pressure τ0 of the solid as indicated by Kokado et al. (1997), and Roussel and

Coussot (2005): (2.5). When the thickness and last spread of the solid are known, the yield pressure can be resolved, here approximated for a 6 liter example to be:

2/s2] (2.6) with c = 2805.4 [m and l0 = 0.01 [m]

for 0.45 m ≤ l ≤ 1.20 m, where l is the final spread length in the box and ρ is the material density [kg/m3].3.5 Numerical MethodsThis segment is limited to the hypothesis of the Distinct Element Method, and Computational Fluid Dynamics, CFD, which were utilized to show mortar and solid stream by the creator. For the two sorts of numerical strategies, it remains constant that in the framework determined,

I) vitality is rationed,ii) mass is preserved andiii) Newton's subsequent law: F = m • an is relevant.

For a general audit of strategies and research in the field of numerical recreation of solid stream, if it's not too much trouble see section 3 for a concise introduction of some past work.3.5.1 The Distinct Element Method, DEM. The removals and pivots of the particles are determined by the accompanying administering conditionFi = m(x¨i − gi) Mi = H˙

i

where Mi is the resultant minute following up on the molecule and H˙ I is the precise energy, included by the snapshot of inactivity and the rakish speeding up and speed of the molecule. These conditions of movement are incorporated utilizing a focused limited contrast methodology. Speeds and points are determined part of the way through the time venture at t ± ∆t/2, ∆ being the size of the progression. Relocations, increasing speeds, rakish speeds, powers and minutes are figured at the essential interims of t ± ∆t. The increasing speeds are determined as

Inserting the above expressions into the governing equations for particle displacements and rotation we get:

Finally the obtained velocities are updated according to:

3.5.2 Computational Fluid Dynamics, CFDIn liquid mechanics, ordinarily the Reynold's number (Re) is utilized to describe the kind of stream. Stream might crawl stream around for example a circular item (Re << 1), it might be laminar, transient or violent. The Reynold's number must be equivalent for two cases with a similar powerful similitude in which thick impacts are significant, Kundu and Cohen (2004), just like the case for SCC stream. The Reynold's number is characterized as:

where U is the characterstic velocity, ν is the kinematic viscosity and l is the characterstic length. Further, for incompressible fluids (such as concrete), as are liquids in general, with fluid velocity vector

denoted u:∇ · u = 0 the (tensorial formulation of) Navier-Stokes equation for viscous flow reduces to

Du 2

ρ = −∇p + ρg + µ∇ uDt

Limited VolumesIn this bit of work, Volume of Fluid, VOF, strategy is utilized as the interface following technique for a multiphase model. VOF (Hirt and Nichols (1981)) tracks the interface utilizing a stage pointer marker γ with the end goal that in a control volume, γ = 0 just stage one is spoken to and γ = 1 just stage two is spoken to. 0 < γ < 1 speaks to an interface in the control volume. The scalar γ is the volume part moving, the liquid properties change in space as indicated by the volume portion of each stage:

ρ = ρ1γ + ρ2(1 − γ)µ = µ1γ + µ2(1 − γ)

Limited ElementsThe Finite Element Method, FEM, began from the requirement for understanding complex flexibility and auxiliary investigation issues in common and aeronautical designing. The strategy is a numerical method for investigating structures and continua. FE methodology are utilized to investigate issues of pressure examination, yet in addition of warmth move, liquid stream, oil, electric and attractive fields and so on. In FEM, a persistent space is discretized into a lot of discrete sub-areas called components, Cook et al. (1989). FEM is a decent decision for understanding PDEs

4.EXPERIMENTAL STUDTY 4.1 Laboratory

In the fresh concrete laboratory, the following methods were used to determine workability of paste, mortar and concrete: Camflow, ConTec-4, slump flow with Abram’s cone, J-ring, L-box, LCPC-box and Thixometer. They are briefly described in the following paragraphs.

Figure 4.1: Camflow equipment with Haegermann cone used for slump flow measurements, from Gram and Piiparinen (2005)

Figure 4.2: ConTec-4 SCC viscometer used for rheological evaluation of Bingham parameters

Slump flow test with the Abram’s cone:

Figure 4.3: The Abram’s cone is placed on a levelled metal base-plateThe filled Abram's cone is lifted to let the solid spread affected by gravity. Speed of stream was

recorded, just as the last droop stream width. J-ring For blocking tests, the J-ring (φ = 300 mm) might be put outside the Abram's cone before lift, so as to gauge how well the solid passes rebars. 18 mm thick rebars are symmetrically set on the ring (their number can be 16, 18 or even 22), the stature of the solid is estimated when the rebars, speed of stream just as conclusive droop stream breadth was recorded. The L-box was tried and recreated without rebars (Figure 4.4). A moveable entryway separates the vertical segment and the flat area. Subsequent to filling the vertical area with solid (stature = 600 mm, width = 200 mm, profundity = 100 mm) the door is opened for the solid to stream into the even segment. The stream is created by the static load of the new concrete in the segment. Stream speed was recorded and mimicked.

2

1

3

Figure 4.4: A hardwood L-box in the lab with its three removeable rebars mounted. The LCPC-box with dimensions height = 150 mm, width = 200 mm and length = 1200 mm

described and experimentally validated by Roussel (2007), 6 liters of concrete are slowly poured (during 30 seconds) at one end of the box. Once the density and final spread of the concrete are known, the yield stress can be determined according to Equation 2.6, see Figure 4.5.

Figure 4.5: Hardwood LCPC-box with a convenient transparent frontA numerical explanation for the connection of greatest torque Tm and yield pressure is set to be a direct connection between most extreme torque and yield worry as per:

τ0 = a Tm + bwith a = 53.96 [m−3] (4.1) and b = 18.3 [Pa] what's more, aligned for the specific thixometer arrangement utilized, steady a relating geometrically (for vane distance across = 100 mm and tallness = 100 mm) and b filling in as the 'mechanical' consistent. Droop stream estimations on the structure site (and the thereof gotten yield worry as indicated by Equation 2.5) are connected to the most extreme torque as per Figure 4.6.

mm 700

mm 200

mm 600

mm 100

0τ

mT

Measurementtau0

28,161,41,1,210,8 6,0 0,4 0,20

350

300

250

200

150

100

50

0

= 0,07762Ry = 53,961x + 18,296

rThixomete

4.2 Simulation4.2.1 PFCPFC3D by Itasca Consulting Group, Inc. (https://www.itascacg.com), models development and cooperation of circular particles by the Distinct Element Method. It is intended to be a productive instrument to show convoluted issues in strong mechanics and granular stream. Particles may append to each other through bonds (hard or delicate). Particles may likewise be amassed together, framing unbreakable purported super-particles to frame discretionary shapes as appeared in Figure 4.7.

Figure 4.7: Forming so called super-particles with unbreakable bonds to the left, regular particle bonds can break once stress/strain exceeds their strength,

to the rightA unique COMMAND language installed in supposed PFC FISH capacities is utilized to produce particles, dividers, start speeds, characterize bonds, and so forth. For the particular Bingham model utilized here, a User Defined Model (UDM) was actualized. While the first code of the product stays murky, the client may get to C++ pointers to modifiable PFC capacities for rubbing, bonds, contact powers and speeds just as molecule positions. This permits the production of for example pressing calculations and contact models.So as to acquire a satisfactorily free pressing, the particles are created indiscriminately positions inside a predefined territory. Affected by gravity, the particles can be guided to their holder through a channel or comparative, Petersson and Hakami (2001). In the event of an example with monosized circles, cautious pressing could bring about crystallization of the molecule gathering, giving a structure that won't stream. Best outcomes are acquired with various molecule estimates, the size ought to vary at any rate ±25 %.No direct association between the rheological parameters of the displayed material and the bury molecule powers was found. Some connection between's estimations of the slip work and the dashpot could be watched. The majority of the material characterstics is controlled by the state of the non-straight spring capacity administering molecule to molecule contacts in the ordinary course, introduced in articles I and II (Figure 4.8).

Figure 4.8: Non-linear spring function governing particle to particle interaction in the normal direction

A steeper slope of the spring constant (higher inter-particle forces) results in a smaller slump flow. A qualitative analysis of the simulated slump seen in Figure 4.9 gives at hand that the particle

distribution seems equal to the particle distribution of slumps seen in the lab.

Figure 4.9: Final spread of slump flow simulation, top view4.2.2 OPENFOAMThe OpenFOAM (Field Operation And Manipulation) code is an item situated numerical reenactment toolbox for continuum mechanics written in C++, discharged by OpenCFD Ltd and accessible for nothing (https://www.opencfd.co.uk). It is a huge CFD library with various sorts of solvers running on Linux or Unix Operating Systems. This limited volume solver with polyhedral work backing ascertains the mass and force conditions in their discretized structure, which ensures the preservation of motions through the control volume. The code is straightforward and might be changed and upgraded with additional items by the client. The liquid reproduced speaks to a homogeneous material, for this situation the solid. Impacts of particles in the solid are not represented here. The solid is expected to carry on as a Bingham material during shear. To fit the Navier-Stokes conditions, the obvious thickness η is composed as:

(4.2) The speed of flow is governed by the plastic viscosity µpl, whereas the shape of the material at

flow stoppage is determined by the yield stress τ0, given that inertia effects can be neglected for the flow. As defined in most rheology books, e.g. Goldstein (1996), the shear rate is

√γ˙ = 2D : D

with D being the tensor of rate of deformation:(4.3)

(4.4) In this case, L represents the velocity gradient tensor of the flowing material. Equations (4.2), (4.3)

and (4.4) define the incompressible non-Newtonian viscosity model for the simulations of laminar flow.

The material model is verified and compared to analytical solutions (according to Equation 2.5 and Equation 2.6) for both the slump flow and the LCPC-box for two different levels of yield stress as seen in Figure 4.10.

Figure 4.10: Material model calibrated for two different geometries [cm]: the slump flow (radius vs height) and the LCPC box (length vs height)

At stream stoppage the numerical model and the investigative arrangement contrast close to 3 %, as depicted in articles III and IV. Solver for Two-Phase Flow Like the filling procedure with PFC3D, the solid might be filled from the top (Figure 4.11), similarly as, in actuality. OpenFOAM solvers are consistently 3D. A 2D case can be made utilizing void limits. The solver utilized 'with the expectation of complimentary surface stream' of cement called interFoam is explicitly custom fitted for incompressible (fluid) interface following of laminar liquid stream. The VOF strategy portrayed in segment 2.5.2 is really not a free surface technique, however a two liquid methodology. The standard limited volume discretization chose is Gaussian mix with a straight upwind insertion conspire. A purported PISO (Pressure Implicit with Splitting Operators) calculation is utilized for the estimations. It depends on the presumption that the energy discretization might be securely solidified through a progression of weight correctors, which is genuine just at little league steps. Hence, this calculation is touchy to work quality. To guarantee assembly of certain PDEs utilized by OpenFOAM, the purported Courant number, Co, ought to be underneath 1 consistently. It is characterized as

(4.5) where ∆t is the time step, |u| is the magnitude of the velocity through the element and ∆x is the size

of the element in the direction of the velocity. Since the flow varies across the domain, Co < 1 must be ensured everywhere, OpenFOAM (2008).

Figure 4.11: Meshed geometry for tee described in article IV showing the filling procedure

The work appeared in Figure 4.11 was checked for skewness by the OpenFOAM programming before running the case. The geometry demonstrated was discretized in 2 x 4480 components. Solver for Multiphase Flow The solver utilized for more than two-stage stream is called multiphaseInterFoam and comes up short on the solidness that has been executed into interFoam. Cautious time-venturing and

cross section is prompted so as to get numerical union. A few layers of liquid were mimicked with a modest quantity of water trickling from a stature of 120 mm onto a couple of 5 mm layers of (lightweight) concrete, ρ = 2000 kg/m3. The impact of various viscosities of the reproduced cements can be found in Figure 4.12.

Figure 4.12: Multiphase flow simulation captured at t = 0.2 s for three differentcases - left: water dripping on hardened concrete, middle picture: fresh concrete, and to the right: two layers of fresh concrete

In spite of the way that volume and properties of the trickling water are the equivalent in each of the three cases, water drops appear to be exceptionally unique in the event that 2 and 3 whenever contrasted with the drops from case 1 hitting the hardended concrete. This is accepted to be because of the way that the multiphase solver does not completely deal with time-reliance. Since the model depicted and utilized in article IV isn't thickness based and is unsensitive to time-reliance, results are as yet satisfactory. 4.2.3 FEMLEGO Falling of a chamber in an incrompressible Newtonian fluid (oil) was reenacted with an in-house programming from the Mechanics Department at The Royal Institute of Technology (KTH) in Stockholm, called femLego, Amberg et al. (1999). Limited Element Method was utilized in 2D with a uniform quadratic work with 91 x 451 hubs. This FEM application depends on a discretization technique which is of first request in existence. The work is uniform and couldn't be subducted to changes locally. Subsequently, to improve the exactness of the calculations, a streamline dispersion was presented. Streamline dissemination has a similar thought as fake thickness, which spreads out (diffuses) the enormous inclination, subsequently giving a smooth arrangement, Wendt (1992). Remembering that the technique is of the main request, the estimation of the cycle venture in the calculations was kept very low, ∆ = 10−4.

Figure 4.13: Simulation of a falling cylinder An object immersed in liquid is being dropped from zero velocity to free fall (Figure 4.13),

eventually reaching its so called terminal velocity, which can clearly be identified in the simulations. The computations also show that the terminal verlocity depends on the diameter of the object. Simulation of object in liquid with the same non-dimensional density function

(4.6) and shape shows that a larger cylinder falls faster than a small one. A comparison of the terminal

verlocity obtained with cylinders of non-dimensional diameters d = 0.5 and d = 0.25 is shown in Figure 4.14.

Figure 4.14: Different terminal velocity of two cylinders with different diameters, clearly showing a lower terminal velocity for the smaller particle

Also, it was shown that elliptical cylinders of the same size that were dropped at different angles quickly align their long axis of the ellipse with the direction of flow, and all quickly reach the same terminal velocity corresponding to the cross section of their frontal area, with a characteristic length corresponding to the smallest diameter of the ellipse.

5. RESULTS AND DISCUSSION

DEM particle simulation showing the height difference of the concretebefore and after passing the rebars

5.2 Comparisons between Lab Tests and SimulationsFigure 5.2: Slump flow propagation of a concrete with measured τ0 = 30 Pa and µpl =71

Pa·s

Simulated value

Laboratory value5432 1 0

5

4

3

2

1

0

600 L-box t

6.CONCLUSION AND FUTURE RESEARCHThe first supposition that it is conceivable to numerically recreate the progression of Self-Compacting Concrete (SCC) still holds. An end that can be drawn is the significance of scaling and decision of technique when choosing a model. There is still to come a widespread material model that completely covers every one of the wonders that assume a significant job during stream and throwing of SCC. Diverse recreation models are useful for clarifying and anticipating various marvels. SCC test techniques (for example droop stream, J-ring, L-box) were performed and recorded in the research center before the reenactment. Stream of cement in a particlularly clogged area of a twofold tee chunk just as two lifts of a multi-layered full scale divider throwing were effectively demonstrated. A molecule approach (DEM) will almost certainly clarify phenomenology of powers following up on circular or non-round totals during blending, pressing or streaming. DEM additionally permits a subjectively right reenactment of blocking and the development of granular curves in clogged territories, given molecule shape and rubbing is incorporated into the model. This technique is most sufficient in the investigation of subtleties and phenomenology. A homogeneous methodology (CFD) is more PC effective. It might serve to show huge volumes of solid stream just as deficient structure filling (in any case, no isolation or framing of granular curves) because of poor compatability between the geometry of the formwork and the rheology of the solid. It might well fill in as a useful asset direct in the in advance determination of formwork and rheological parameters of the solid for an upgraded match.

mix No.

τ0

[Pa]µpl

[Pa·s]ρ [kg/m3]

LAB: t600

[s]

SIM: t600

[s]1 53.03 23.94 2305 2.0 1.742 29.85 40.46 2338 2.65 2.723 13.28 43.25 2338 2.8 2.764 43.09 40.81 2331 2.8 2.925 47.16 31.0 2331 2.1 2.26 19.0 27.96 2344 2.5 1.767 19.66 34.83 2344 2.4 2.268 99.87 11.02 2317 0.88 0.869 16.59 18.31 2327 1.6 1.06

10 77.96 26.48 2327 2.85 2.1811 93.63 15.23 2305 1.3 1.2812 17.49 21.47 2333 2.4 1.313 28.83 26.24 2333 2.4 1.714 20.56 23.38 2327 1.5 1.4615 23.53 29.51 2328 1.45 1.916 82.56 42.32 2328 3.6 3.6617 43.41 18.57 2242 2.7 1.2618 94.8 31.5 2242 4.3 3.14

CFD might be utilized for an enormous scale reproduction to get a diagram on conceivable issue regions, which could then promptly be displayed in detail with DEM. A simple available toolbox to use before giving and a role as criticism for quality control of the solid conveyed to the work site is a long haul objective.As PC speed and limit create, blending the two depicted methodologies, molecule and liquid, will frame another measurement in reproduction of suspension stream. This is doubtlessly the way taken later on. A basic instance of one single molecule in liquid was contemplated as a first little advance.

7.REFERENCES

ACI (Ed.), 1994. ACI 116R-90, Cement and concrete terminology. Materials and general properties of concrete, Part I.Amberg, G., Tonhardt, R., Winkler, C., 1999. Finite element simulations using symbolic computing. Mathematics and Computers in Simulation 49, 257–274.Bagi, K., 2007. On the concept of jammed configurations from a structureal mechanics perspective. Granular Matter 9, 109–134.Barnes, H., Hutton, J., Walters, K., 1989. An introduction to rheology. No. 3 in Rheology Series. Elsevier, Amsterdam, The Netherlands.Barrat, J.-L., de Pablo, J., 2007. Modeling deformation and flow of disordered materials. MRS Bulletin 32, 941–944.Bentur, 2002. Cementitous materials - nine millenia and a new century: Past, present and future. Journal of Materials in Civil Engineering 14:1, 2–22.Billberg, P., 1999. Self-compacting concrete for civil engineering structures - the Swedish experience. Tech. Rep. 2:99, Swedish Cement and Concrete Research Institute, SE-100 44 Stockholm, Sweden.

Cementa Research, 2004. Camflow users manual. Camflow 1.0.Christensen, G., 1991. Modelling the flow of fresh concrete: the slump test. Ph.D. thesis, Princeton University, USA.Chu, H., Machida, A., 1996. Numerical simulation of fluidity behaviour of fresh concrete by 2D distinct element method. Transactions of the Japan Concrete Institute 18, 1–8.Chu, H., Machida, A., 1998. Experimental evaluation and theoretical simulation of self-compacting concrete by the modified distinct element method (MDEM). In: Recent Advances in Concrete Technology, Fourth CANMET/ACI/JCI International Conference, Tokushima, Japan. pp. 691–714.Chu, H., Machida, A., Kobayashi, H., 1997. Verification of application of DEM to fresh concrete by sphere dragging ball viscometer. Transactions of the Japan Concrete Institute 19, 1–8.Clarke, B., 1967. Rheology of coarse settling suspensions. Trans, Inst. Chem. Eng. 45, 251–256.Concrete Report No. 10(E), 2002. Self-compacting concrete - recommendations for use. Tech. rep., Swedish Concrete Association, Stockholm, Sweden.Cook, R. D., Malkus, D. S., Plesha, M. E., 1989. Concepts and applications of finite element analysis. John Wiley & Sons, Inc., NY, USA.de Larrard, F., 1999. Concrete mixture proportioning, a scientific approach. E & FN SPON, London, Great Britain.De Schutter, G., Bartos, P., Domone, P., Gibbs, J., 2008. Self-Compacting Concrete. Whittles Publishing, Caithness, Scotland.

Dufour, F., Pijaudier-Cabot, G., 2005. Numerical modelling of concrete flow: Homogeneous approach. International Journal for Numerical and Analytical Methods in Geomechanics 29, 395–416.European Committee for Standardization, November 2007. Testing fresh concrete: Self-compacting concete. prEN12350-8,10,12.Fernlund, J., Zimmermann, R., Kragic, D., 2007. Influence of volume/mass on grainsize curves and conversion of image-analysis size to sieve size. Engineering Geology doi:10.1016/j.enggeo.2006.12.007.Ferraris, C., de Larrard, F., 1998. Testing and modelling of fresh concrete rheology.

NISTIR 6094, National Institute of Standards and Technology, Gaitherburg, USA.