Numerical Modeling of Self-Compacting Mortar Flow Using Discrete Element Method

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1 Nuerical Modeling of Self-Copacting Flow Using Discrete Eleent Method - Technical Paper - Miansong HUANG *1, Xuehui AN *, Takayuki OBARA *3 and Masahiro OUCHI *4 ABSTRACT A nuerical odeling of Self-Copacting (SCM) flow, based on the 3D Discrete Eleent Method (DEM), was presented in this paper. SCM was odeled as a set of spherical eleents and the shear strength and daping coefficient between ortar eleents were proposed as DEM paraeters, which odeled the yield stress and the plastic viscosity of SCM, respectively. After setting up appropriate set of paraeters, SCM with different properties can be successfully siulated, and the feasibility of the siulation was validated by the observed different types of SCM flows. Keywords: self-copacting ortar, siulation, three-diensional discrete eleent ethod, paraeter 1. INTRODUCTION Since Self-Copacting Concrete (SCC) was first developed in 1988 [1], it has been used all over the world and has been recognized as potentially the greatest developent in concrete technology. However, as forworks becoe ore and ore coplex and reinforceents becoe denser and denser, one of its ain probles during application is the risk of iproper for filling []. Nowadays, such probles can only be predicted by experiental siulations, which are always tie-expensive and oney-consuing. Therefore, it is iportant to develop soe effective nuerical tool to predict such behavior of SCC before actual construction. Moreover, as an integral part of SCC, Self-Copacting (SCM) serves as a basis for the design of the concrete, and the workability properties of SCC could be assessed by SCM [3]. With these regards, this paper, as the first step, ainly focused on the nuerical odeling of the flow behaviors of Self-Copacting. Though the SCM is usually considered as a kind of continual aterial, it was siulated by the eployent of three-diensional Discrete Eleent Method (DEM) in this study, in order to take the aggregate into account in the following SCC siulation. DEM was first proposed by Cundall and Strack [4] for siulating rock and granular flow, analyzing icroechanical behavior of granular edia. Then it grown rapidly to becoe an effective tool to siulate the dynaics in any other scopes of scientific and industrial, such as, silo discharge and process of ixing. Recently, DEM has been adopted in the area of concrete siulation, and the concrete is assued to be represented by a collection of discrete eleents. However, so far, the research has been liited to qualitative siulation because of the difficulty of defining appropriate DEM paraeters of ortar [5]-[9]. In this study, the shear strength f s and daping coefficient h between ortar eleents were proposed as the DEM paraeters to siulate the flow behaviors of SCM. And the feasibility of the proposed DEM siulation was validated by the observed different types of SCM flows. In this paper, the DEM siulation principle and the nuerical odeling of SCM are introduced at first. Then, the effects of the proposed paraeters on prediction of flow behaviors of SCM and the ethod of paraeters selection are described. Finally, the coparison between experient results and nuerical siulations are presented and soe conclusions of this research were drawn.. NUMERICAL MODELING.1 Basic siulation principle of DEM DEM is a tool with great capacity of odeling the oveent including the separation and autoatic contact detection of granular edia. In DEM siulations, prototypes are assued as discrete rigid balls. The contact echanis between SCM eleents is using sets of basic rheological eleents, such as spring, dashpot and slider, for both the noral and shear direction. And as shown in Fig.1, in order to siulate the adhesive and cohesive behaviors, a set of joints for both the noral and shear direction were also added as failure criterions in this study, which would be explained later. Based on the siulation principle, the code prograing work has been finished and the *1 Dept. of Hydraulic & Hydropower Engineering, Tsinghua University, PhD Candidate, JCI Meber * Prof., Dept. of Hydraulic & Hydropower Engineering, Tsinghua University, Dr. E. *3 Vice-president, Maeda (Beijing) Business Consulting Co., Dr. E. *4 Associate Prof., Dept. of Infrastruct. Syst. Eng., Kochi University of Technology, Dr. E., JCI Meber

2 developed progra was used in this research as a basic progra. In this progra, each calculation cycle of DEM includes two steps. Firstly, the differential equations for the otion of particles are applied to all particles to calculate the oveents and update the particles positions. Then, the contacts between eleents are autoatically detected and the constitutive law is applied to calculate the forces between eleents.. Rheological paraeters of SCM in DEM SCM, as well as SCC, in its fresh stage, can be considered as a kind of Bingha fluid [10]. The rheology at a esoscale can be written as a relation of the shear stress and the shear strain rate and there are two rheological constants naely the yield stress and the plastic viscosity in the relationship. In nuerical odeling, it is also regarded that the SCM behaves as Bingha odel. The constitutive law [Obara [11] ], which uses rheological paraeters in DEM siulation, has been adopted in this study. The spring rates is calculated with the consideration of spring cobination in series between eleents, and the daping coefficient are calculated by the differential equation of daping vibration, which are given in the following equations: k k c c n s fn k n c n 3 E 3 = 4 r 3 G 3 = 4 r = h k n n = h k s s Slider k n : noral stiffness k s : shear stiffness c n : noral viscous daping ratio c s : shear viscous daping ration f n : noral bond strength f s : shear bond strength Fig.1 Contact odel used for SCM 1 G = E (1 + ν ) where, E : elastic odulus of ortar eleent G : shear odulus of ortar eleent h : daping coefficient : ass of ortar eleent ν : poisson s ratio of eleent c s f s k s (1) () (3) (4) (5) Since the ortar is treated as a perfectly incopressible aterial in this study, the poisson s ratio of ortar eleent ν is set to be 0.5 and the elastic odulus of ortar eleent E should be enorous. However, generally speaking, the higher the E, the saller tie step is required, the larger CPU tie is consued. With this consideration, the E is set to be 10,000Pa based on the trial calculation. In addition, in order to siulate the tensile properties of SCM, the tensile strength f n and shear strength of eleents f s were also under consideration. And the strength properties of eleent could be forulated as follows: knδ n A fn (6) ksδs A fs (7) f = f (8) n s where, δ n : overlap in noral direction δ s : displaceent in shear direction A : contact area between eleents Here, the tensile strength f n was proposed as twice as the shear strength f s according to the Mohr-Coulob Theory. With these considerations, two rheological paraeters of SCM eleents, shear strength f s and daping coefficient h, should be input to siulate the flow behaviors of SCM, and the two paraeters odeled the two rheological constants of SCM, the yield stress and the plastic viscosity, respectively. It should be noted that, as shown in Fig., if the noral tensile stress carried by contact forces equals or exceeds the tensile strength, all the contact forces becoe zero and the particles detach fro each other independently. While, if shear stress reaches up to the shear strength, the slider works to allow slip between Separate τ f s (a) σ f n Contact Under tension Noral direction δ n Contact Under copression δ s (b) Shear direction Fig. Failure criterions of SCM odel

3 eleents, and the eleents still contact with each other until the failure happens in tensile direction..3 DEM odel of SCM In DEM siulation, the saller the particle sizes, the larger CPU tie is consued. It is iportant to choose a appreciate odel of SCM to finish the siulation in an acceptable coputation tie. In this study, the SCM was odeled as single sized ortar eleents with a diaeter of 5. since the ortar eleent siulates the behavior of the cobined water, powder and sand particles, and the axiu diaeter of these aterials is 5 in the real SCM. Though SCM is discrete at soe levels, it shows continuity as a part of SCC. While after packing the SCM eleents into a container, the eleents cannot fill all the space of the whole volue. In order to odel the SCM eleents have the sae weight with the SCM prototype, the eleents should have a greater density than the SCM. According to Obara [11], as shown in Fig.3, orthorhobic body center structure confors well of the arrangeent of the discrete eleents with the stiffness given above after rando packing. The void ratio was and the density of SCM was chosen as 3.67 g/c 3 in this study. The contact area A between eleents with the radius of r could be calculated with the following equation: d d 0 : 100 d 1 60 Fig.4 flow test Fig.5 funnel test Relative flow area Γ = (d 1 d ー d 0 )/d 0 Relative flow tie R = 10/t A 3 3 r = (9) 3. EVALUATION OF THE PARAMETERS flow cone 3.1 Basic description of experiental devices Since the ortar flow test and ortar funnel test have been being proposed for testing the workability properties of SCM for any years, these two types of tests have also been used in this research to study the effects of the proposed paraeters on prediction of flow behaviors of SCM. As show in Fig.4 and Fig.5, the ortar flow test is used to evaluate the deforability of ortar and the ortar funnel test is used to evaluate the viscosity of ortar. The indices for deforability and viscosity are defined as relative flow area Γ and relative funnel speed R. [1] ( d1 d d0) Γ = i (10) d 0 d / Fig.6 DEM siulation of flow test V-funnel Siulate 5 Actual ortar DEM odel of ortar Fig.3 SCM odel in DEM siulation Fig.7 DEM siulation of funnel test

4 R 10 t = (11) where, d 1 & d : easured flow diaeter d 0 : botto diaeter of ortar flow cone t : easured tie (sec) for ortar to flow through the funnel 3. DEM siulations As shown in Fig.6 and Fig.7, the DEM odels of ortar flow test and ortar funnel test are set up, respectively. Both odels are siulated as one quarter of the real apparatus to reduce the enorous nuber of particles. Then, in order to evaluate the effects of paraeters, various cases have been perfored on ortar flow test and ortar funnel test. The paraeters of these cases are shown in Table1. The Relationship between Γ and R of SCM in DEM siulation are shown in Fig.8. According to Okaura and Ouchi [1], the range of Γ and R of SCM for achieving self-copactability of fresh concrete is Γ of.5 to 6 h Relative Funnel Speed R Table1 Paraeters sets of siulations fy / Pa Relative Flow Area Γ Fig.8 Relationship between flow area and funnel speed of SCM h=0.5 h=1.0 h=.0 h=3.0 and of 0.75 to 1.5, which is also illustrated as the box in Fig.8, and it is shown that by given appropriate set of paraeters, SCM with different workability properties can be successfully siulated with the developed progra. The effects of paraeters of siulation of ortar flow test and ortar funnel test are shown in Fig.9 and Fig.10, respectively. It shows that Γ is ainly doinated by f s than h, and the R is deterined by both f s and h. It is siilar to say, the shear strength f s was shown to possess significant influence on the deforability and velocity of SCM flow, while, the daping coefficient h ainly influence the velocity of SCM flow. 3.3 Paraeter selection ethod With the goal of predicting the SCM flow behaviors during actual application, an appropriate set of paraeters has to be defined at first. According to the effect of paraeters on prediction of flow behaviors of SCM obtained above, the ortar flow test and ortar funnel test were proposed as the standard tests for the quantitative selection of the DEM paraeters of SCM in this research. And the procedure of paraeters selection were proposed and shown in the flow chart in Fig.11. At first, daping coefficient was set to be 0.5, and f s was adjusted to satisfy the deforability condition in the siulation of ortar flow test. Then, using the selected f s, h was calibrated to satisfy the viscosity Relative Funnel Speed R Fig Shear Strength of fs (Pa) h=0.5 h=1.0 h=.0 h=3.0 Siulation results of ortar funnel tests Start: Set Daping coefficient as 0.5 Relative Flow Area Γ Shear Strength of fs (Pa) h=1.0 h=0.5 h=.0 h=3.0 Fig.9 Siulation results of ortar flow tests No Define Shear strength Siulation of Flow test Fig.11 Agree with experient? Yes Define Daping Coefficient Siulation of Funnel test Agree with experient? End Yes Procedure of paraeters selection No

5 condition in the siulation of ortar funnel test. And according to the relationship shown in Fig.8, the DEM paraeters of SCM could be easily fixed after ~3 trial siulations. Finally, the appropriate set of paraeters could be selected to proceed the SCM flow siulations. Soe exaples of SCM flow siulations will be presented in the following. 1# Pipe cone SIMULATIONS OF SCM FLOWS After the DEM paraeters of SCM could be selected by eans of the siulation of ortar flow test and ortar funnel tests, a series of SCM flow tests were carried out both experientally and nuerically Description of experient In order to siulate the flow behaviors of SCM after puping during actual application, four types of pipe cone with different size were used in this study. The size of the pipe cones are Φ107*300, Φ107*600, Φ56*300, Φ56*600, which are defined fro 1# to 4#, respectively. An exaple of the pipe cone flow test is shown in Fig.1. The results of four types of pipe cone flow tests as well as ortar cone flow test are shown in Table. 4. Siulation of experient The sae SCM pipe cone flow tests have also been siulated, as shown in Fig.13. First, according to the paraeter selection ethod proposed above, the shear strength f s and daping coefficient h were selected as 10Pa and 0.5, respectively. The siulated ortar cone flow test was 47, which was close to the experient value of 46. Then, the four types of pipe cone flow tests have been siulated with the sae paraeters obtained above. The results of siulations are also shown in Table, and the coparison between the results of experients and siulations are illustrated in Fig.14. It is found that four types of SCM pipe cone flows have been successfully siulated. The axiu relative difference between the results of siulations and experients is only 5%, which eans that the nuerical odeling proposed in this study is quite capable of predicting the flow behaviors of SCM. 4.3 Typical procedures of SCM flow siulation Finally, based on the siulation results of this study, the typical procedures of SCM flow prediction could be suarized in two steps: (1) Paraeter selection The flow behaviors of SCM should be observed in the laboratory by eans of ortar flow test and ortar funnel test. Then, an appropriate set of DEM paraeters, shear strength and daping coefficient, of the SCM, can be selected with the procedures Table 1#Pipe_ cone Ф107*300 Fig.1 Pipe cone flow test 1#Pipe cone Experiental and nuerical results of different types of ortar flow tests #Pipe_ 3#Pipe_ 4#Pipe_ Ф107*600 Ф56*300 Ф56*600 Experients % % % % % Siulations % % % 35 10% % 300 Fig.13 Diaeter of Flow area /() Fig.14 R53.5 DEM siulation of the pipe cone flow Paraeters selection cone Pipe_Ф107*300 Pipe_Ф107*600 Pipe_Ф56*300 Pipe_Ф56*600 Types of FLows Experients Siulations Coparison between experients and siulations

6 illustrated in Fig.11. () SCM flow siulation Based on the strength and daping coefficient obtained above, the siulation of SCM flow is started. And the flow behaviors of SCM could be predicted fro the final results. 5. CONCLUSIONS DEM is a very potential tool for SCM flow siulation. A nuerical odeling of SCM, based on the three-diensional DEM, has been presented herein, and the following conclusions can be ade fro this part of research of siulation of SCM flow. (1) The feasibility of the siulation with the proposed rheological paraeters, the shear strength f s and the daping coefficient h, have been validated. () The flow behaviors of SCM, with the relative flow area Γ of and relative funnel speed R of , have been successfully siulated. (3) In DEM siulation, the results of ortar flow test are ainly controlled by the shear strength, while, the results of ortar funnel flow test are controlled by both the shear strength and daping coefficient. (4) The appropriate DEM paraeters of SCM with certain workability could be easily defined by using the presented ethod. (5) The typical procedures of SCM flow siulation have been proposed, and the behaviors of SCM pipe cone flow can be well predicted. Ongoing work ainly focuses on finding out the relationship between the rheological paraeters used in this study and the rheological constants of actual SCM, and the influence of the size of ortar eleents. The study on nuerical odeling of coarse aggregates using DEM is also currently in process with the goal of providing tools which are capable to predict possible segregation and blocking of aggregates during casting of SCC. REFERENCES Technology, Vol. 1, Issue 1, pp. 5-15, 003 [] N. Roussel, M. R. Geiker, F. Dufour, L. N. Thrane and P. Szabo: Coputational Modeling of Concrete Flow: General Overview, Ceent and Concrete Research, Vol. 37, Issue 9, pp , 007 [3] K. Ozawa, K. Maekawa and H. Okaura: Developent of High Perforance Concrete, Journal of The Faculty of Engineering, Uinv. of Tokyo, Vol. 41, Issue 3, pp ,199 [4] P. A. Cundall and O. D. L. Strack: A Discrete Nuerical Model for Granular Asseblies, Geotechnique, Vol. 9, pp , 1979 [5] H. Chu, A. Machida and N. Suzuki: Experiental Investigation and DEM Siulation of Filling Capacity of Fresh Concrete, Transactions of the Japan Concrete Institute, Vol. 18, pp. 9-14, 1996 [6] U. C. Puri: Nuerical Siulation of Shotcrete by Distinct Eleent Method, PhD Thesis,Uinv. of Tokyo, 1999, Tokyo [7] M. A. Noor and T. Uooto: Three-Diensional Discrete Eleent Model for Fresh Concrete, Nuerical Siulation of Fresh Concrete IIS Journal, Vol. 51, Issue 4, pp. 5-8, 1999 [8] Ö. Petersson: Siulation of Self-Copacting Concrete Laboratory Experients and nuerical odeling of Testing Methods, Jring and L-box Tests, Proc. of the 3 rd Int. Syp. on SCC, pp. 0-07, August 003, Reykjavik, Iceland [9] V. Mechtcherine and S. Shyshko: Virtual Concrete Laboratory Continuous Nuerical Modeling of Concrete fro Fresh to The Hardened State, Advances in Construction Materials 007, Springer Berlin Heidelberg, pp , 007 [10] M. Ouchi and T. Tsuchitani: A Syste for Modification of s Mix Proportion of Self-Copacting Concrete, Proceedings of the Japan Concrete Institute Vol. 18, Issue, pp ,1996 [11] T. Obara: Developent and Application of Discrete Eleent Siulation Syste For Mixing Materials, PhD Thesis,Tsinghua University, 007, Beijing [1] H. Okaura and M. Ouchi: Self-Copacting Concrete. Journal of Advanced Concrete