Research Article Simulation on the Self-Compacting...

Research ArticleSimulation on the Self-Compacting Concrete by an EnhancedLagrangian Particle Method

Jun Wu1 Xuemei Liu2 Haihua Xu3 and Hongjian Du4

1School of Urban Railway Transportation Shanghai University of Engineering Science Shanghai 201620 China2School of Civil Engineering and Built Environment Queensland University of Technology BrisbaneQLD 4000 Australia3Deepwater Technology Keppel Offshore amp Marine Technology Centre Singapore 6281304Department of Civil and Environmental Engineering The National University of Singapore Singapore 117576

Correspondence should be addressed to Xuemei Liu x51liuquteduau

Received 10 June 2016 Accepted 14 July 2016

Academic Editor Robert Cerny

Copyright copy 2016 Jun Wu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The industry has embraced self-compacting concrete (SCC) to overcomedeficiencies related to consolidation improve productivityand enhance safety and quality Due to the large deformation at the flowing process of SCC an enhanced Lagrangian particle-based method Smoothed Particles Hydrodynamics (SPH) method though first developed to study astrophysics problems withits exceptional advantages in solving problems involving fragmentation coalescence and violent free surface deformation isdeveloped in this study to simulate the flow of SCC as a non-Newtonian fluid to achieve stable results with satisfactory convergenceproperties Navier-Stokes equations and incompressible mass conservation equations are solved as basics Cross rheological modelis used to simulate the shear stress and strain relationship of SCCMirror particlemethod is used for wall boundariesThe improvedSPH method is tested by a typical 2D slump flow problem and also applied to L-box test The capability and results obtained fromthis method are discussed

1 Introduction

Industrialization of construction is the main trend in sci-entific and technical progress in construction includingthe extensive use of prefabricated factory-finished elementsand the conversion of production into a mechanized andcontinuously flowing process of assembly and installation ofbuildings and structures made of prefabricated assembliesand elements It will lead to higher-quality materials andmore cost-effectiveness and energy efficiency for infrastruc-ture construction Self-consolidating concrete (SCC) is athixotropic mixture created by tailoring different materialsand securing excellent deformability and adequate resistanceto segregation to insure the exceptional rheology behavior ofconcrete [1] The industry has embraced SCC to overcomedeficiencies related to consolidation improve productivityand enhance safety and quality To follow up the demandingfor the exceptional flowability of SCC to further improve

its filling behavior and improve the performance of SCCit is essential to fully understand its flow behavior and theinfilling characteristics Such understanding could furtherimprove the prediction of the infilling behavior of SCC withthe presence of reinforcing steel distributed with high densityor formwork in complex and irregular shapes To achievesuch purpose simulation may serve as an effective tool in theunderstanding as well as determining the desired rheologicalperformance of SCC

While simulation is a mature science in homogeneousfluids simulation of the flow of SCC is difficult because ofthe need to track the boundaries between the liquid and solidphases Few previous studies have focused on finding the rhe-ological material model for certain paste or concrete [2ndash4]

In considering the large deformation nature of SCC flowand great complexity of concrete-infilling behavior the con-ventional methods such as discrete element method (DEM)andfinite elementmethod (FEM)have two critical drawbacks

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016 Article ID 8070748 11 pageshttpdxdoiorg10115520168070748

2 Advances in Materials Science and Engineering

including the limitations in modeling free surfaces andnonguaranteed conservation of massThe recently developedSmoothed Particles Hydrodynamics (SPH) method offersa glimpse of the future of fresh concrete flow simulationAlthough SPH was first developed to study astrophysicsproblems [5 6] it has exceptional advantages in enablingthe simulation of flow and infilling behavior It has beenused to study wave-structure interactions for Newtonianflow [7ndash9] It has also been successfully used to simulatenon-Newtonian flow such as in metal forming [10] theimpacting droplet [11] blood-vessel interaction [12] andCouette flow [13] In one case it was employed to simulate theslump of concrete [14] In comparison with other methodsthe SPH method can solve the two issues encountered inDEM and FEM The SPH method has advantages in solvingproblems involving fragmentation and coalescence and vio-lent free surface deformation and has the potential to linkrheology and the infilling behavior of concrete Thereforethe particle-based Lagrangian technique-SPH method is apromisingmethod to simulate the flow of SCC as a non-New-tonian

However the existing SPH still has limitations whenapplied to non-Newtonian fluid Firstly it cannot measurethe velocity divergence and pressure gradient accurately Sec-ondly it cannot treat the nonslip boundary condition exactlywhich is an issue for SSC Hence further enhancement ofthe existing SPH method will be the focus of this studyfluid to achieve accurate and stable results with satisfactoryconvergence properties And the improved SPH algorithmis tested by a typical 2D slump flow problem and thenapplied for an L-box flow problem The SCC is modeledusing Cross rheological model The capability and resultsobtained from this method are discussed The simulationprovides reasonable good agreement with available data fromthe literature The findings may be of engineering interests inview of the flowability and pressure caused by fresh SCC onstructures

2 Mathematical Model and SPH Formulation

21 Governing Equation In the current study the SCC isassumed as viscous non-Newtonian fluid which is governedby the Navier-Stokes (NS) equationThe 2D Lagrangian formis [14 17]

nabla sdot u = 0 (1)

119863u119863119905

= minus1

120588nabla119901 + g + 1

120588nablasdotrArr

120591 (2)

where120588 is fluid density 119905 is time u = (119906 V) is velocity vector119901is pressure g = (119892

119909 119892119910) is gravitational acceleration119863(sdot)119863119905

is Lagrangian operator which is the total time derivative nablais gradient operator and rArr120591 is shear stress tensor The shearstress tensor is related to the strain tensor rArr120574 as

120591119894119895= 120591119895119894= 120583eff120574119894119895 (3)

where 120583eff is effective viscosity 120591119894119895and 120574119894119895are the components

of rArr120591 and rArr120574 respectively and 120574119894119895is defined as

120574119894119895=1

2(120597119906119894

120597119909119895

+

120597119906119895

120597119909119894

) (4)

For non-Newtonian fluid the relationship of shear stressand strain is nonlinear which means the effective viscosityis not a constant This relationship may be modeled bymany numerical models including the Cross model [14] theBingham-plastic model [18ndash20] and the power-law model[17] In the current study the Cross model is used which canbe expressed as follows [14]

120583eff =1205830+ 119870120583119861

1 + 119870 (5)

where 120583119861is plastic viscosity 120583

0= 1000120583

119861 119870 = 120583

0120591119861 and 120591

119861

is yield stress is the strain rate and generally defined as thesecond invariant of the shear strain as

= radic1

2sum

119894

sum

119895

120574119894119895120574119894119895 (6)

In 2D case

= radic1

2((

120597119906

120597119909)

2

+ (120597V120597119910)

2

+1

2(120597119906

120597119910+120597V120597119909)

2

) (7)

22The Solution Algorithm The SCC flow is the incompress-ible flow and (1) and (2) can be solved by the explicit three-step projection scheme [17] At the first step (2) is solved byonly considering the body force and neglecting other forcesAn intermediate velocity is computed as

ulowast119899+1

= ulowast119899+ gΔ119905 (8)

where the subscript 119899 denotes the time step At the secondstep the computed intermediate velocity is used to computethe strain rate the effective viscosity and the divergence ofthe shear stress

1

120588nabla sdotrArr

120591 = S (9)

At the end of the second step the second intermediatevelocity is computed by

ulowastlowast119899+1

= ulowast119899+1

+ SΔ119905 = ulowast119899+ (g + S) Δ119905 (10)

The position is updated as

rlowastlowast119899+1

= r119899+ ulowastlowast119899+1Δ119905 (11)

where r = (119909 119910) is the position vectorThe following pressurePoisson equation is solved to get the pressure which is needed

Advances in Materials Science and Engineering 3

to enforce the incompressibility [21]

nabla sdot (1

120588nabla119901) =

nabla sdot ulowastlowast119899+1

Δ119905 (12)

At the third step the computed pressure is added to (2) to geta divergence-free velocity field at time 119899 + 1

u119899+1

= ulowastlowast119899+1

minus (1

120588nabla119901)Δ119905 (13)

The position at 119899 + 1 time step is computed as

r119899+1

= r119899+1

2(u119899+ u119899+1) Δ119905 (14)

23 The SPH Formulation The SPH is an interpolationmethod which transforms the Partial Difference Equation(PDE) to integration form and allows any function to beexpressed in terms of the value at a set of disordered particlesFollowing Gingold and Monaghan [5] a function119891(r) atlocation r can be defined by

119891 (r) = intΩ

119891 (r1015840)119882(10038161003816100381610038161003816r minus r101584010038161003816100381610038161003816 ℎ) 119889r

1015840

(15)

where the integration is computed over the entire domainΩ|r minus r1015840| is the scalar distance between r and r1015840 ℎ is smoothinglength and119882 is interpolation kernel or kernel (smoothing)function

The SCC domainmay be represented by discrete particlesand (15) can in turn be converted to the discretized formusingthe properties of all the particles inside the support domainas

119891 (r119886) = sum

119887

119891 (r119887)119882 (119903

119886119887 ℎ) 119881119887= sum

119887

119891119887119882119886119887119881119887 (16)

where 119887 represents the particle inside the support domain 119891119887

is the value of function 119891(r) at location r119887 119903119886119887= |r119886119887| = |r119886minus

r119887| is the distance between particle 119886 and 119887119882

119886119887is the kernel

value or contribution and 119881119887is the volume of particle 119887

In the current study the quintic kernel function [22] isused and can be expressed as

119882(119902) = 120572119863(1 minus

119902

2)

4

(2119902 + 1) 0 le 119902 le 2 (17)

where 120572119863= 7(4120587ℎ

2) 119902 = 119903

119886119887ℎ and ℎ is the smoothing

lengthThe order of quintic kernel function is higher than thewidely used cubic spline kernel function [14 17 23] Henceit has smoother kernel value and the first derivate which isimportant for kernel interpolation and derivate computation

Many forms have been proposed to evaluate the gradientanddivergence in the SPH literatures In the current study thevelocity divergence is computed by the antisymmetric form to

improve the accuracy [23 24]

nabla sdot u119886=

119873

sum

119887=1

(u119887minus u119886) sdot997888997888997888997888997888rarrnabla119886119882119886119887119881119887 (18)

where 997888997888997888997888997888rarrnabla119886119882119886119887

= ((r119886minus r119887)119903119886119887)(120597119882119886119887120597119903119886119887) = minus

997888997888997888997888997888rarrnabla119887119882119886119887

is the kernel gradient The pressure gradient is evaluatedby the symmetric form to conserve the linear and angularmomentum [14 17 18]

nabla119901119886= 120588119886

119873

sum

119887=1

119898119887(119901119886

1205882119886

+119901119887

1205882

119887

)997888997888997888997888997888rarrnabla119886119882119886119887 (19)

The Laplacian operator in the pressure Poisson equation isformulated as a hybrid of a standard SPH first derivative witha finite difference approximation for the first derivative [1720]

nabla sdot (1

120588nabla119901) = sum

119887

119898119887

8

(120588119886+ 120588119887)

119875119886119887r119886119887

119903119886119887

2 + 1205782sdot997888997888997888997888rarrnabla119882119886119887119881119887 (20)

where 119875119886119887

= 119875119886minus 119875119887and 120578 = 001ℎ is a small number

introduced to keep the denominator no-zeroThe gradient of shear stress is computed similar to the

pressure gradient and can be expressed by

1


120591 = nabla119898119887(119886

1205882119886

+119887

1205882

119887

) sdot997888997888997888997888rarrnabla119882119886119887 (21)

The smoothing length is an important parameter for SPHsimulation which influences the accuracy of SPH interpo-lation For particles near the free surface which has lessneighboring particles due to the absence of particles abovethe free surface the number of neighboring particles is lessthan the inner particles This may cause the accuracy of SPHinterpolation to be reduced In this paper the smoothinglength of the particle changes depended on the neighboringparticle number (eg 119899min = 40) and the smoothing lengthexpands with the following scheme for each step

(1) The particle assigns the initial smoothing lengthℎ = 2Δ where Δ is the particle size The particlecomputes the number of neighboring particles (119873)using smoothing length ℎ

(2) If 119873 gt 119899min the particlersquos smoothing length forcurrent step is ℎ = 2Δ

(3) If119873 lt 119899min the particle increases the smoothing withℎnew = ℎ+Δℎ = ℎ+Δ100 and computes the numberof neighboring particles119873

(4) The particle will continue to increase the smoothinglength until the smoothing length becomes largerthan 3Δ or the number of neighboring particlesbecomes larger than119873

The abovementioned algorithm has two advantages The firstis that the particles especially those near the free surfacehave more neighboring particles and the accuracy of the


01 m

03m

02m

Figure 1 The initial configuration of the placement for slump flow

kernel interpolation will be increased The second is thatthe smoothing length is linearly distributed and only 101smoothing lengthswere used It is easy to construct the kerneltable and each particle saves the index of the kernel table bythe smoothing length In the simulation the kernel properties(120572119863in (17)) can be easily gotten by indexing the smoothing

table

24 The Boundary Condition There are several methods tomodel the boundary condition including the virtual forcemethod [14] the fixed wall particle method [9 14 17] andthe mirror particle method [21 24ndash26] Compared with thevirtual force method the mirror particle method can predictaccurate pressure near the wall boundary and it can furtherreduce the pressure oscillation [25] Compared with the fixedwall particle method the mirror particles are mirrored fromthe fluid particles instead of solving the NS equations Hencethe number of particles in the NS equation is less than thefixed wall particle method and can save the simulation timeBy considering the advantages of mirror particle method itis adopted in current study to treat the wall boundary Theposition of the mirror particles is computed by mirroring theSCC particlesThe volume density and effective viscosity areset equal to their reference SCC particles The velocity of themirror particle is set to zero to simulate the partial slip ofwall boundary condition The pressure of the mirror particleis computed by 119901

119898= 119901119904+ 120588119904r119898119904sdot g where the subscripts 119898

and 119904 denote the mirror and SCC particle respectively

3 Applications in SCC Modeling

In this section the improved SPH model is applied to abenchmark slump test model to simulate the slum flow ofSCC to demonstrate the capability of the proposed model inSCC flow modeling And the model is also used to simulatethe filling ability of SCC by using the L-box test

31 Slump Test Figure 1 illustrates the configuration of theslump cone which is used for slump testing according to BSEN 12350-8 Numerical simulation of the SCC flow is carriedout in two-dimensional configurations

The SCC is a high performance mix and the densityand rheological properties of SCC used for slump test arepresented in Table 1 [16] The mixture has a plastic viscosity

Table 1 Density and rheological properties of SCC for simulation[16]

Density (kgm3) Plastic viscosity (Pa s) Yield stress (Pa)SCC 2380 484 563

at 4 Pasdots and yield stress at 200 Pa with the density at2380 kgm3

The simulation domain is discretized by particles withsize Δ = 2mm in total 11268 particles are involved inthe simulation The particle size was selected after the con-vergence study was done The time step size is dynamicallyadjusted according to the CFL number (equal to 02 inthis study) The slump cone movement is important for thesimulation results In order to keep the consistency with BSEN 12350-8 standard and considering the numerical stabilitythe slump cone is initially located 001m above the bottomAs the simulation starts the slump cone is fixed at the first01 s At 119905 = 01 s it starts to move upward with fixed speedof 01ms until the simulation finishes It is important for theslump cone to keep the 001mdistance from the bottom If theslump cone put on the bottom there will be no free surface inthe domain and the Poisson equation is difficult to solve Theslump cone starts to move at 01 s as assumedThat means theslump cone initially located at the bottom and in 01 s it moves001m to compensate the difference with the standard

Figures 2ndash4 show the various stages of the 2D flowprofile during the numerical simulations of slump test ofSCC including the contour of the distribution of the velocitypressure and the shear strain rate respectively It is evidentfrom the results that the improved SPH method is able tocharacterize the flow of SCC at different stages It shouldbe also noted that the initial profiles of the free surfaces areaffected by themotion of the slump conewith its fast removalThe available experimental test data from literature [21] isused for comparison The model is capable of capturing allthe key characteristics of the SCCflow including the pressurevelocity shear strain rate and viscosity at different locationsHowever only the spread value is available for comparisonBy comparing the spread value from the simulation resultswith the test value the simulation provides reasonable agree-ment with the experimental results with less than 20 ofdiscrepancies

32 L-Box Test In order to understand the filling ability inaddition to the flow characteristics of SCC the classic L-box filling test is also simulated by using the improved SPHmethod Figure 5 illustrates the configuration of the physicalL-box test and its dimension The apparatus consists ofrectangular section box in the shape of an ldquoLrdquo with a verticaland horizontal section separated by a movable gate in frontof which vertical lengths of reinforcement bar are fitted Thevertical section is filled with concrete and then the gate waslifted to let the concrete flow into the horizontal sectionThistest is to measure the filling and passing ability of concreteto flow through tight obstructions without segregation orblocking


0

06

02

04

z(m

)Time = 0100 s

04020 06minus06 minus04 minus02

x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(a) 119905 = 01 sec


x (m)

0

06

02

04

z(m

)

Time = 0500 s

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 4050 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(f) Final spread

Figure 2 The velocity distribution during slump flow

The same SCC mix properties as presented in Table 1 areused for L-box model The mixture has a plastic viscosityat 4 Pasdots and yield stress at 200 Pa with the density at2380 kgm3 Figures 6ndash8 present the distribution of velocitypressure and strain rate during the flow of SCC in an L-boxat 02 s 06 s 15 s and 10 s respectively It can be observed

that due to the friction between the SCC and the wall theparticles very close to the wall surfaces take longer time toflow The flowing and filling ability of the SCC can be wellcaptured by this model

The simulation domain is discretized by particles withsize Δ = 2mm in total 18000 particles are involved in


0

06

02

04

z(m

)Time = 0100 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(a) 119905 = 01 sec

0

06

02

04

z(m

)


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

Time = 0500 s

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 5230 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(f) Final spread

Figure 3 The pressure distribution during slump flow

the simulation The particle size was selected after the con-vergence study was done The time step size is dynamicallyadjusted according to the CFL number (equal to 02 in thisstudy)

4 ConclusionsDue to the large deformation at the flowing process ofSCC an enhanced Lagrangian particle-based methodmdashanimproved SPH methodmdashwith its exceptional advantages


0 1 2 3 4 5 6 7 8 9 10Shear strain rate


x (m)

0

06

02

04

z(m

)Time = 0100 s

(a) 119905 = 01 sec



x (m)

0

06

02

04

z(m

)

Time = 0500 s

(b) 119905 = 05 sec



x (m)

0

06

02

04

z(m

)

Time = 1000 s

(c) 119905 = 10 sec



x (m)

0

06

02

04z

(m)

Time = 1200 s

(d) 119905 = 12 sec



x (m)

0

06

02

04

z(m

)

Time = 1500 s

(e) 119905 = 15 sec



x (m)

0

06

02

04

z(m

)

Time = 4810 s

(f) Final spread

Figure 4 The shear strain rate distribution during slump flow


Initial concrete level

Slidingdoor

Rebars

600200

100 600

150

(mm)

H2

H1

Figure 5 The configuration of the L-box test for SCC [15]

06

05

0

03

04

01

02

z(m

)

Time = 0200 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(b) 119905 = 06 sec06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(d) 119905 = 10 secFigure 6 Simulation of L-box testing for SCC with velocity distribution


06

05

0

03

04

01

02

z(m

)Time = 0200 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(b) 119905 = 06 sec

06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(d) 119905 = 10 sec

Figure 7 Simulation of L-box testing for SCC with pressure distribution

in solving problems involving fragmentation coalescenceand violent free surface deformation is developed in thisstudy to simulate the flow of SCC as a non-Newtonianfluid to achieve stable results with satisfactory convergenceproperties Navier-Stokes equations and incompressiblemassconservation equations are solved as basics Cross rheolog-ical model is used to simulate the shear stress and strainrelationship of SCC Mirror particle method is used forwall boundaries The improved SPH method is tested by atypical 2D slump flow problem and also applied to L-boxflowing problem The results obtained from this method

are reasonably agreeing with the experimental data Thisenables the modeling of the flow of SCC by enhancing thecurrent particle method and also provides an efficient tool toestimate the lateral pressure of the SCC exerted on structuresMoreover it will benefit the industry and practical concreteapplications by using this method to estimate the flowabilitythe mould filling performance of concrete and also theinteractions between the concrete and mould during castingThe proposedmethod could also become an efficient methodto study the mix design to optimize the workability of theconcrete


06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

1 2 3 4 5 6 7 8 9 10Shear strain rate

Time = 0200 s

(a) 119905 = 02 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 0600 s


(b) 119905 = 06 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 1500 s


(c) 119905 = 15 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 9970 s


(d) 119905 = 10 sec

Figure 8 Simulation of L-box testing for SCC with shear strain rate distribution

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

Grateful acknowledgment ismade to ECARDResearchGrantscheme from Queensland University of Technology and theNational Natural Science Foundation of China (Project no51508294) to collectively support this project

References

[1] K H Khayat ldquoWorkability testing and performance of self-consolidating concreterdquo ACI Materials Journal vol 96 no 3pp 346ndash353 1999

[2] J E Wallevik ldquoRheological properties of cement pastethixotropic behavior and structural breakdownrdquo Cement andConcrete Research vol 39 no 1 pp 14ndash29 2009

[3] A Ghanbari and B L Karihaloo ldquoPrediction of the plasticviscosity of self-compacting steel fibre reinforced concreterdquoCement and Concrete Research vol 39 no 12 pp 1209ndash12162009

[4] N Roussel G Ovarlez S Garrault and C Brumaud ldquoThe ori-gins of thixotropy of fresh cement pastesrdquoCement and ConcreteResearch vol 42 no 1 pp 148ndash157 2012

[5] R A Gingold and J J Monaghan ldquoSmoothed particle hydrody-namics theory and application to non-spherical starsrdquoMonthlyNotices of the Royal Astronomical Society vol 181 no 3 pp 375ndash389 1977


[6] L B Lucy ldquoA numerical approach to the testing of the fissionhypothesisrdquoThe Astronomical Journal vol 82 no 12 pp 1013ndash1024 1977

[7] J J Monaghan ldquoOn the problem of penetration in particlemethodsrdquo Journal of Computational Physics vol 82 no 1 pp1ndash15 1989

[8] A Colagrossi and M Landrini ldquoNumerical simulation ofinterfacial flows by smoothed particle hydrodynamicsrdquo Journalof Computational Physics vol 191 no 2 pp 448ndash475 2003

[9] H Xu Numerical simulation of breaking wave impact on struc-tures [PhD thesis] NationalUniversity of Singapore Singapore2013

[10] J Bonet and S Kulasegaram ldquoCorrection and stabilization ofsmooth particle hydrodynamics methods with applications inmetal forming simulationsrdquo International Journal for NumericalMethods in Engineering vol 47 no 6 pp 1189ndash1214 2000

[11] Y-P Chui and P-A Heng ldquoA meshless rheological model forblood-vessel interaction in endovascular simulationrdquo Progressin Biophysics ampMolecular Biology vol 103 no 2-3 pp 252ndash2612010

[12] X Xu J Ouyang B Yang andZ Liu ldquoSPH simulations of three-dimensional non-Newtonian free surface flowsrdquo ComputerMethods inAppliedMechanics and Engineering vol 256 pp 101ndash116 2013

[13] G Zhou W Ge and J Li ldquoSmoothed particles as a non-Newtonian fluid a case study in Couette flowrdquo ChemicalEngineering Science vol 65 no 6 pp 2258ndash2262 2010

[14] S Shao and E Y M Lo ldquoIncompressible SPH method forsimulating Newtonian and non-Newtonian flows with a freesurfacerdquo Advances in Water Resources vol 26 no 7 pp 787ndash800 2003

[15] F Carl Curling and strain monitoring of slabs strips in alaboratory environment [MS thesis] Universite Laval QuebecCity Canada 2005

[16] F Mukhtar Computer-aided modelling and simulation of flow ofself-compacting concrete [MS thesis] King Fahd University ofPetroleum and Minerials Dhahran Sudi Arabia 2011

[17] S M Hosseini M T Manzari and S K Hannani ldquoA fullyexplicit three-step SPH algorithm for simulation of non-Newtonian fluid flowrdquo International Journal of Numerical Meth-ods for Heat amp Fluid Flow vol 17 no 7-8 pp 715ndash735 2007

[18] S Kulasegaram B L Karihaloo and A Ghanbari ldquoModellingthe flow of self-compacting concreterdquo International Journal forNumerical and Analytical Methods in Geomechanics vol 35 no6 pp 713ndash723 2011

[19] H Lashkarbolouk A M Halabian and M R ChamanildquoSimulation of concrete flow in V-funnel test and the properrange of viscosity and yield stress for SCCrdquo Materials andStructures vol 47 no 10 pp 1729ndash1743 2014

[20] H Zhu N S Martys C Ferraris and D D Kee ldquoA numericalstudy of the flow of Bingham-like fluids in two-dimensionalvane and cylinder rheometers using a smoothed particle hydro-dynamics (SPH) based methodrdquo Journal of Non-NewtonianFluid Mechanics vol 165 no 7-8 pp 362ndash375 2010

[21] S J Cummins and M Rudman ldquoAn SPH projection methodrdquoJournal of Computational Physics vol 152 no 2 pp 584ndash6071999

[22] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash762010

[23] J J Monaghan ldquoSimulating free surface flows with SPHrdquoJournal of Computational Physics vol 110 no 2 pp 399ndash4061994

[24] A Colagrossi A Meshless Lagrangian Method for Free-Surfaceand Interface Flows with Fragmentation Universita di Roma LaSapienza Rome Italy 2003

[25] X Liu H Xu S Shao and P Lin ldquoAn improved incompress-ible SPH model for simulation of wave-structure interactionrdquoComputers amp Fluids vol 71 pp 113ndash123 2013

[26] E Y M Lo and S Shao ldquoSimulation of near-shore solitary wavemechanics by an incompressible SPH methodrdquo Applied OceanResearch vol 24 no 5 pp 275ndash286 2002

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


including the limitations in modeling free surfaces andnonguaranteed conservation of massThe recently developedSmoothed Particles Hydrodynamics (SPH) method offersa glimpse of the future of fresh concrete flow simulationAlthough SPH was first developed to study astrophysicsproblems [5 6] it has exceptional advantages in enablingthe simulation of flow and infilling behavior It has beenused to study wave-structure interactions for Newtonianflow [7ndash9] It has also been successfully used to simulatenon-Newtonian flow such as in metal forming [10] theimpacting droplet [11] blood-vessel interaction [12] andCouette flow [13] In one case it was employed to simulate theslump of concrete [14] In comparison with other methodsthe SPH method can solve the two issues encountered inDEM and FEM The SPH method has advantages in solvingproblems involving fragmentation and coalescence and vio-lent free surface deformation and has the potential to linkrheology and the infilling behavior of concrete Thereforethe particle-based Lagrangian technique-SPH method is apromisingmethod to simulate the flow of SCC as a non-New-tonian

However the existing SPH still has limitations whenapplied to non-Newtonian fluid Firstly it cannot measurethe velocity divergence and pressure gradient accurately Sec-ondly it cannot treat the nonslip boundary condition exactlywhich is an issue for SSC Hence further enhancement ofthe existing SPH method will be the focus of this studyfluid to achieve accurate and stable results with satisfactoryconvergence properties And the improved SPH algorithmis tested by a typical 2D slump flow problem and thenapplied for an L-box flow problem The SCC is modeledusing Cross rheological model The capability and resultsobtained from this method are discussed The simulationprovides reasonable good agreement with available data fromthe literature The findings may be of engineering interests inview of the flowability and pressure caused by fresh SCC onstructures

2 Mathematical Model and SPH Formulation

21 Governing Equation In the current study the SCC isassumed as viscous non-Newtonian fluid which is governedby the Navier-Stokes (NS) equationThe 2D Lagrangian formis [14 17]

nabla sdot u = 0 (1)

119863u119863119905

= minus1

120588nabla119901 + g + 1

120588nablasdotrArr

120591 (2)

where120588 is fluid density 119905 is time u = (119906 V) is velocity vector119901is pressure g = (119892

119909 119892119910) is gravitational acceleration119863(sdot)119863119905

is Lagrangian operator which is the total time derivative nablais gradient operator and rArr120591 is shear stress tensor The shearstress tensor is related to the strain tensor rArr120574 as

120591119894119895= 120591119895119894= 120583eff120574119894119895 (3)

where 120583eff is effective viscosity 120591119894119895and 120574119894119895are the components

of rArr120591 and rArr120574 respectively and 120574119894119895is defined as

120574119894119895=1

2(120597119906119894

120597119909119895

+

120597119906119895

120597119909119894

) (4)

For non-Newtonian fluid the relationship of shear stressand strain is nonlinear which means the effective viscosityis not a constant This relationship may be modeled bymany numerical models including the Cross model [14] theBingham-plastic model [18ndash20] and the power-law model[17] In the current study the Cross model is used which canbe expressed as follows [14]

120583eff =1205830+ 119870120583119861

1 + 119870 (5)

where 120583119861is plastic viscosity 120583

0= 1000120583

119861 119870 = 120583

0120591119861 and 120591

119861

is yield stress is the strain rate and generally defined as thesecond invariant of the shear strain as

= radic1

2sum

119894

sum

119895

120574119894119895120574119894119895 (6)

In 2D case

= radic1

2((

120597119906

120597119909)

2

+ (120597V120597119910)

2

+1

2(120597119906

120597119910+120597V120597119909)

2

) (7)

22The Solution Algorithm The SCC flow is the incompress-ible flow and (1) and (2) can be solved by the explicit three-step projection scheme [17] At the first step (2) is solved byonly considering the body force and neglecting other forcesAn intermediate velocity is computed as

ulowast119899+1

= ulowast119899+ gΔ119905 (8)

where the subscript 119899 denotes the time step At the secondstep the computed intermediate velocity is used to computethe strain rate the effective viscosity and the divergence ofthe shear stress

1


120591 = S (9)

At the end of the second step the second intermediatevelocity is computed by

ulowastlowast119899+1

= ulowast119899+1

+ SΔ119905 = ulowast119899+ (g + S) Δ119905 (10)

The position is updated as

rlowastlowast119899+1

= r119899+ ulowastlowast119899+1Δ119905 (11)

where r = (119909 119910) is the position vectorThe following pressurePoisson equation is solved to get the pressure which is needed



nabla sdot (1

120588nabla119901) =


Δ119905 (12)


u119899+1


minus (1

120588nabla119901)Δ119905 (13)


r119899+1

= r119899+1

2(u119899+ u119899+1) Δ119905 (14)


119891 (r) = intΩ

119891 (r1015840)119882(10038161003816100381610038161003816r minus r101584010038161003816100381610038161003816 ℎ) 119889r

1015840

(15)



119891 (r119886) = sum

119887

119891 (r119887)119882 (119903

119886119887 ℎ) 119881119887= sum

119887

119891119887119882119886119887119881119887 (16)







119882(119902) = 120572119863(1 minus

119902

2)

4

(2119902 + 1) 0 le 119902 le 2 (17)

where 120572119863= 7(4120587ℎ

2) 119902 = 119903





nabla sdot u119886=

119873

sum

119887=1


where 997888997888997888997888997888rarrnabla119886119882119886119887

= ((r119886minus r119887)119903119886119887)(120597119882119886119887120597119903119886119887) = minus

997888997888997888997888997888rarrnabla119887119882119886119887


nabla119901119886= 120588119886

119873

sum

119887=1

119898119887(119901119886

1205882119886

+119901119887

1205882

119887

)997888997888997888997888997888rarrnabla119886119882119886119887 (19)


nabla sdot (1

120588nabla119901) = sum

119887

119898119887

8

(120588119886+ 120588119887)

119875119886119887r119886119887

119903119886119887

2 + 1205782sdot997888997888997888997888rarrnabla119882119886119887119881119887 (20)

where 119875119886119887




1


120591 = nabla119898119887(119886

1205882119886

+119887

1205882

119887

) sdot997888997888997888997888rarrnabla119882119886119887 (21)








01 m

03m

02m



table















0

06

02

04

z(m

)Time = 0100 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(a) 119905 = 01 sec


x (m)

0

06

02

04

z(m

)

Time = 0500 s

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 4050 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(f) Final spread






0

06

02

04

z(m

)Time = 0100 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(a) 119905 = 01 sec

0

06

02

04

z(m

)


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

Time = 0500 s

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 5230 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(f) Final spread







x (m)

0

06

02

04

z(m

)Time = 0100 s

(a) 119905 = 01 sec



x (m)

0

06

02

04

z(m

)

Time = 0500 s

(b) 119905 = 05 sec



x (m)

0

06

02

04

z(m

)

Time = 1000 s

(c) 119905 = 10 sec



x (m)

0

06

02

04z

(m)

Time = 1200 s

(d) 119905 = 12 sec



x (m)

0

06

02

04

z(m

)

Time = 1500 s

(e) 119905 = 15 sec



x (m)

0

06

02

04

z(m

)

Time = 4810 s

(f) Final spread




Slidingdoor

Rebars

600200

100 600

150

(mm)

H2

H1


06

05

0

03

04

01

02

z(m

)

Time = 0200 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(b) 119905 = 06 sec06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03



06

05

0

03

04

01

02

z(m

)Time = 0200 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(b) 119905 = 06 sec

06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(d) 119905 = 10 sec





06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp


Time = 0200 s

(a) 119905 = 02 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 0600 s


(b) 119905 = 06 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 1500 s


(c) 119905 = 15 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 9970 s


(d) 119905 = 10 sec


Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





nabla sdot (1

120588nabla119901) =


Δ119905 (12)


u119899+1


minus (1

120588nabla119901)Δ119905 (13)


r119899+1

= r119899+1

2(u119899+ u119899+1) Δ119905 (14)


119891 (r) = intΩ

119891 (r1015840)119882(10038161003816100381610038161003816r minus r101584010038161003816100381610038161003816 ℎ) 119889r

1015840

(15)



119891 (r119886) = sum

119887

119891 (r119887)119882 (119903

119886119887 ℎ) 119881119887= sum

119887

119891119887119882119886119887119881119887 (16)







119882(119902) = 120572119863(1 minus

119902

2)

4

(2119902 + 1) 0 le 119902 le 2 (17)

where 120572119863= 7(4120587ℎ

2) 119902 = 119903





nabla sdot u119886=

119873

sum

119887=1


where 997888997888997888997888997888rarrnabla119886119882119886119887

= ((r119886minus r119887)119903119886119887)(120597119882119886119887120597119903119886119887) = minus

997888997888997888997888997888rarrnabla119887119882119886119887


nabla119901119886= 120588119886

119873

sum

119887=1

119898119887(119901119886

1205882119886

+119901119887

1205882

119887

)997888997888997888997888997888rarrnabla119886119882119886119887 (19)


nabla sdot (1

120588nabla119901) = sum

119887

119898119887

8

(120588119886+ 120588119887)

119875119886119887r119886119887

119903119886119887

2 + 1205782sdot997888997888997888997888rarrnabla119882119886119887119881119887 (20)

where 119875119886119887




1


120591 = nabla119898119887(119886

1205882119886

+119887

1205882

119887

) sdot997888997888997888997888rarrnabla119882119886119887 (21)








01 m

03m

02m



table















0

06

02

04

z(m

)Time = 0100 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(a) 119905 = 01 sec


x (m)

0

06

02

04

z(m

)

Time = 0500 s

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 4050 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(f) Final spread






0

06

02

04

z(m

)Time = 0100 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(a) 119905 = 01 sec

0

06

02

04

z(m

)


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

Time = 0500 s

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 5230 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(f) Final spread







x (m)

0

06

02

04

z(m

)Time = 0100 s

(a) 119905 = 01 sec



x (m)

0

06

02

04

z(m

)

Time = 0500 s

(b) 119905 = 05 sec



x (m)

0

06

02

04

z(m

)

Time = 1000 s

(c) 119905 = 10 sec



x (m)

0

06

02

04z

(m)

Time = 1200 s

(d) 119905 = 12 sec



x (m)

0

06

02

04

z(m

)

Time = 1500 s

(e) 119905 = 15 sec



x (m)

0

06

02

04

z(m

)

Time = 4810 s

(f) Final spread




Slidingdoor

Rebars

600200

100 600

150

(mm)

H2

H1


06

05

0

03

04

01

02

z(m

)

Time = 0200 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(b) 119905 = 06 sec06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03



06

05

0

03

04

01

02

z(m

)Time = 0200 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(b) 119905 = 06 sec

06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(d) 119905 = 10 sec





06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp


Time = 0200 s

(a) 119905 = 02 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 0600 s


(b) 119905 = 06 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 1500 s


(c) 119905 = 15 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 9970 s


(d) 119905 = 10 sec


Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




01 m

03m

02m



table















0

06

02

04

z(m

)Time = 0100 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(a) 119905 = 01 sec


x (m)

0

06

02

04

z(m

)

Time = 0500 s

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 4050 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(f) Final spread






0

06

02

04

z(m

)Time = 0100 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(a) 119905 = 01 sec

0

06

02

04

z(m

)


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

Time = 0500 s

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 5230 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(f) Final spread







x (m)

0

06

02

04

z(m

)Time = 0100 s

(a) 119905 = 01 sec



x (m)

0

06

02

04

z(m

)

Time = 0500 s

(b) 119905 = 05 sec



x (m)

0

06

02

04

z(m

)

Time = 1000 s

(c) 119905 = 10 sec



x (m)

0

06

02

04z

(m)

Time = 1200 s

(d) 119905 = 12 sec



x (m)

0

06

02

04

z(m

)

Time = 1500 s

(e) 119905 = 15 sec



x (m)

0

06

02

04

z(m

)

Time = 4810 s

(f) Final spread




Slidingdoor

Rebars

600200

100 600

150

(mm)

H2

H1


06

05

0

03

04

01

02

z(m

)

Time = 0200 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(b) 119905 = 06 sec06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03



06

05

0

03

04

01

02

z(m

)Time = 0200 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(b) 119905 = 06 sec

06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(d) 119905 = 10 sec





06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp


Time = 0200 s

(a) 119905 = 02 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 0600 s


(b) 119905 = 06 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 1500 s


(c) 119905 = 15 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 9970 s


(d) 119905 = 10 sec


Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

06

02

04

z(m

)Time = 0100 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(a) 119905 = 01 sec


x (m)

0

06

02

04

z(m

)

Time = 0500 s

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 4050 s


x (m)

Vel (ms)0 005 01 015 02 025 03 035 04 045 05

(f) Final spread






0

06

02

04

z(m

)Time = 0100 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(a) 119905 = 01 sec

0

06

02

04

z(m

)


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

Time = 0500 s

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 5230 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(f) Final spread







x (m)

0

06

02

04

z(m

)Time = 0100 s

(a) 119905 = 01 sec



x (m)

0

06

02

04

z(m

)

Time = 0500 s

(b) 119905 = 05 sec



x (m)

0

06

02

04

z(m

)

Time = 1000 s

(c) 119905 = 10 sec



x (m)

0

06

02

04z

(m)

Time = 1200 s

(d) 119905 = 12 sec



x (m)

0

06

02

04

z(m

)

Time = 1500 s

(e) 119905 = 15 sec



x (m)

0

06

02

04

z(m

)

Time = 4810 s

(f) Final spread




Slidingdoor

Rebars

600200

100 600

150

(mm)

H2

H1


06

05

0

03

04

01

02

z(m

)

Time = 0200 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(b) 119905 = 06 sec06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03



06

05

0

03

04

01

02

z(m

)Time = 0200 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(b) 119905 = 06 sec

06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(d) 119905 = 10 sec





06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp


Time = 0200 s

(a) 119905 = 02 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 0600 s


(b) 119905 = 06 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 1500 s


(c) 119905 = 15 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 9970 s


(d) 119905 = 10 sec


Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

06

02

04

z(m

)Time = 0100 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(a) 119905 = 01 sec

0

06

02

04

z(m

)


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

Time = 0500 s

(b) 119905 = 05 sec

0

06

02

04

z(m

)

Time = 1000 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(c) 119905 = 10 sec

0

06

02

04z

(m)

Time = 1200 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(d) 119905 = 12 sec

0

06

02

04

z(m

)

Time = 1500 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(e) 119905 = 15 sec

0

06

02

04

z(m

)

Time = 5230 s


x (m)

0 1000 2000 3000 4000 5000

P (Pa)

(f) Final spread







x (m)

0

06

02

04

z(m

)Time = 0100 s

(a) 119905 = 01 sec



x (m)

0

06

02

04

z(m

)

Time = 0500 s

(b) 119905 = 05 sec



x (m)

0

06

02

04

z(m

)

Time = 1000 s

(c) 119905 = 10 sec



x (m)

0

06

02

04z

(m)

Time = 1200 s

(d) 119905 = 12 sec



x (m)

0

06

02

04

z(m

)

Time = 1500 s

(e) 119905 = 15 sec



x (m)

0

06

02

04

z(m

)

Time = 4810 s

(f) Final spread




Slidingdoor

Rebars

600200

100 600

150

(mm)

H2

H1


06

05

0

03

04

01

02

z(m

)

Time = 0200 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(b) 119905 = 06 sec06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03



06

05

0

03

04

01

02

z(m

)Time = 0200 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(b) 119905 = 06 sec

06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(d) 119905 = 10 sec





06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp


Time = 0200 s

(a) 119905 = 02 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 0600 s


(b) 119905 = 06 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 1500 s


(c) 119905 = 15 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 9970 s


(d) 119905 = 10 sec


Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






x (m)

0

06

02

04

z(m

)Time = 0100 s

(a) 119905 = 01 sec



x (m)

0

06

02

04

z(m

)

Time = 0500 s

(b) 119905 = 05 sec



x (m)

0

06

02

04

z(m

)

Time = 1000 s

(c) 119905 = 10 sec



x (m)

0

06

02

04z

(m)

Time = 1200 s

(d) 119905 = 12 sec



x (m)

0

06

02

04

z(m

)

Time = 1500 s

(e) 119905 = 15 sec



x (m)

0

06

02

04

z(m

)

Time = 4810 s

(f) Final spread




Slidingdoor

Rebars

600200

100 600

150

(mm)

H2

H1


06

05

0

03

04

01

02

z(m

)

Time = 0200 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(b) 119905 = 06 sec06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03



06

05

0

03

04

01

02

z(m

)Time = 0200 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(b) 119905 = 06 sec

06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(d) 119905 = 10 sec





06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp


Time = 0200 s

(a) 119905 = 02 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 0600 s


(b) 119905 = 06 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 1500 s


(c) 119905 = 15 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 9970 s


(d) 119905 = 10 sec


Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Slidingdoor

Rebars

600200

100 600

150

(mm)

H2

H1


06

05

0

03

04

01

02

z(m

)

Time = 0200 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(b) 119905 = 06 sec06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010

Vel (ms)

x (m)

0 005 01 015 02 025 03



06

05

0

03

04

01

02

z(m

)Time = 0200 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(b) 119905 = 06 sec

06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(d) 119905 = 10 sec





06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp


Time = 0200 s

(a) 119905 = 02 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 0600 s


(b) 119905 = 06 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 1500 s


(c) 119905 = 15 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 9970 s


(d) 119905 = 10 sec


Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




06

05

0

03

04

01

02

z(m

)Time = 0200 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(a) 119905 = 02 sec

06

05

0

03

04

01

02

z(m

)

Time = 0600 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(b) 119905 = 06 sec

06

05

0

03

04

01

02

z(m

)

Time = 1500 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(c) 119905 = 15 sec

06

05

0

03

04

01

02

z(m

)

Time = 9990 s

02 03 0504 06 07010x (m)

500 1000 1500 2000 2500 3000

P (Pa)

(d) 119905 = 10 sec





06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp


Time = 0200 s

(a) 119905 = 02 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 0600 s


(b) 119905 = 06 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 1500 s


(c) 119905 = 15 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 9970 s


(d) 119905 = 10 sec


Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp


Time = 0200 s

(a) 119905 = 02 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 0600 s


(b) 119905 = 06 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 1500 s


(c) 119905 = 15 sec

06

05

0

03

04

01

02

zp

02 03 0504 06 07010xp

Time = 9970 s


(d) 119905 = 10 sec


Competing Interests


Acknowledgments


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials
































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Research Article Simulation on the Self-Compacting...

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Transcript of Research Article Simulation on the Self-Compacting...