The mini-conical slump flow test: Analysis and numerical study
Introduction
Fresh concretes are constituted by a matrix which is a cement paste and by fine and coarse aggregates. To cast a given element, the concrete must be sufficiently fluid to fill the formwork. Consequently, the concrete design for a specific application and its performances are controlled by its rheological properties. Rheological properties must be evaluated scientifically for real predictability to be achieved. The rheology of concrete is governed by the fluidity and the packing density of the cement paste and by the particle size distribution of the aggregates [1], [2]. Some authors [3] considered the matrix as the association of coarse aggregates and mortar which could act as a continuous phase. Nevertheless, the rheology of mortar is partially controlled by the rheology of the cement paste and the properties of the fine aggregates. Although aggregates play an important role on the concrete flow characteristics [4], it can be assumed that any change in the concrete flow properties is, mainly, due to changes in the cement paste rheology. The rheological parameters characterizing the workability of the cement paste are the yield stress “τ0” which corresponds to the stress required to initiate flow and the plastic viscosity “μ” which describes the paste resistance to flow under external stress. Several models allow to relate these two parameters and to represent the rheological behavior of fresh paste mixtures: the pseudo-plastic model, Bingham or Herschel–Bulkley [5]. The Herschel–Bulkley model, described by Eq. (1), seems to be very effective for cement paste applications.
In Eq. (1)τ0, represent respectively the yield shear stress (Pa) and the shear rate (s− 1) while n is a material parameter giving indications on the degree of the fluid dilatancy (n ≻ 1, the fluid is dilatants and n ≺ 1 is attributed to pseudo plastic fluid). The Bingham model is recovered for n = 1 while the Newtonian model is deduced for n = 1 and τ0 = 0. The identified values of these rheological parameters vary according to the used measurement techniques. Different kinds of rheometers are developed in order to quantify rheological behavior of fresh pastes. However, such apparatus are relatively expensive, require a careful experimental procedure and are not practical when they must be used on construction sites. Mini-slump and Marsh cone tests are, then, used to evaluate the workability of fresh paste mixtures. These equipment are widely used throughout the world and were approved as standard techniques to assess the workability of pastes and grouts [6], [7]. The simplicity of use of these equipment in construction sites is at the origin of several investigations focusing on the establishment of relationships expressing the yield stress “τ0” and the plastic viscosity “μ” from the obtained experimental results [8].
The mini-slump test is the most common method for quality control in characterizing the pastes and grouts. The apparatus is a metallic truncated cone opened at both ends and placed on a metallic plate. When vertically lifting the filled cone, the gravity induces the paste to slump down. This phenomenon occurs if the yield stress is exceeded and will stop when the local stress is below such yield stress. Therefore, the slump test observations are related to the yield stress [8]. With the development of self-compacting concretes the slump height value “S” is very important and is difficult to be appreciated accurately. On the other hand, for the low yield stresses the viscous forces and inertia will play a significant role in conjunction with gravitational force at the end of slumping as suggested by Saak [9].
Several analytical models have been developed to relate the height slump values to the material yield stress and density by adopting the assumption that the only stress acting on the material is associated with the material's own weight [9], [10], [11], [12], [13]. Moreover these authors show that the size and the geometry of the cone do not affect the obtained results. For paste mixtures derived from self compacting concretes (characterized by low yield stress values or low viscosity), Okado et al. [14] proposed Eq. (2) to relate the yield stress to the mini-cone volume “Vc” and to the slumped paste final diameter named the final spread “Df = SF”. The developed model is based on the assumption that only the material's own weight is considered and controlling the phenomena.where ρ, g, Vc and Df are: the paste density, the gravity, the conical volume and the final spread diameter respectively.
Roussel et al. [15] showed that the model suggested by Okado et al. [14] (Eq. (2)) does not allow predicting low yield stresses. They propose to improve it by introducing the surface tension effect:where λ is a coefficient function of both the unknown tested fluid surface tension and contact angle.
More recently Tregger et al. [16] have studied the rheological properties of different paste compositions. They noted that experimental data follow the same trend as Eqs. (2), (3) but a great disparity is observed between the predicted and the measured values. They explained these discrepancies by the experimental protocol and the rheological parameter range. They suggested a relation between the measured yield stress, from a concentric cylinder rheometer, and the final diameter of slumped paste by a power law fit:
Moreover they showed that the viscosity is related to the final spread time Tf (time required to reach the final mini-slump spread, in seconds). They proposed an expression (Eq. (5)) for determining the plastic viscosity μ based on the knowledge of τ0 and Tf from mini-slump test, for a given paste mixture,
It should be noticed that the prediction of μ depends on the value of τ0 determined using the previous equations (Eqs. (2), (3), (4)) which does not give a satisfactory estimation of low yield stresses.
All these previous suggestions and corrections underline the importance of the cement paste dynamic flow behavior. They suggest that the final spread diameter is controlled by both the yield stress and viscosity. In addition the estimation of the yield stress on the basis of the measured values of Df is not precise. Based on these remarks, another question relating to the used paste volume (Eqs. (2), (3)) can be raised: what is the effect of the mini-conical height and shape on the final obtained equilibrium Df?
Domone and Jin [17] previously showed that two empirical tests must be used to determine the rheological parameters: the mini-slump and the Marsh cone tests, but the main question of the expression accuracy and validity remains. Ferraris and de Larrard [18] have tested different paste mixtures using a parallel plate rheometer and empirical tests. They have observed a correlation between final mini-slump spread and the yield stress while the plot of the obtained flow time from Marsh cone test versus the viscosity shows no correlation at all. As a matter of fact, the flow time reflecting the fluidity of the pastes and grouts depends on the viscosity and the yield stress [19].
From these previous works it is obvious that growth weight (ρ and Vc) and yield stress are not enough to characterize such materials. The spread dynamic must be included. Such improvement was proposed by including the final time spread [15]. However the proposed phenomenological correlation is not general as it was deduced from limited observation and do not incorporate the physical aspect and the nonlinear inertia effect.
In the present work we suggest to discuss the validity of Eqs. (2), (3) and to establish a more general and robust model allowing the prediction of low yield stresses using experimental results coming from empirical tests and numerical simulations. The first section deals with the experimental apparatus and test allowing the identification of the rheological parameters. The second section describes the model and the numerical approach used. It is followed by a section related to the obtained results and to the discussion.
Section snippets
Experimental procedure
Different tests were conducted on specimens made from CEM I 52.5N Portland cement, water and CIMFLUID 2002 superplasticizer. The cement pastes are manufactured using a water–cement ratio of 0.37 by weight and two dosages of superplasticizers 0% and 1.15%.
Two experimental procedures are used in this study to estimate the properties of the cement pastes, the mini-conical test in order to estimate the yield stress τ0 and the Marsh cone test to identify the plastic viscosity μ.
Model and numerical approach
The considered modeled geometry is represented in Fig. 3. For such geometry and under the assumption of homogeneous cement paste the resulting phenomena will present a vertical axial symmetry. So, by using the cylindrical coordinate a 2-D approach is possible.
The flow versus time will be analyzed from the initial trapezoid shape at final state, i.e. as initial condition, to the final state.
The shape of the free surface will change during time imposed by the resulting flow. In order to follow
Results and discussion
The previously presented model was resolved on a fixed grid using a commercial code COMSOL [24]. The set level method allows the interface tracking and the weighting technique makes available the use of a unique equation over the whole domain with an equivalent physical property function of the spatial existence phase (paste or air).
The Portland cement paste rheological properties, previously identified in Section 2 (cement paste no. 1 τ0 = 20 Pa and μ0 = 1.4 Pa s), were used to get numerical results.
Conclusion
The present work provides a general study on the paste flow. It focuses on the characterization of Portland cement paste rheological properties. Experiments are conducted in order to well define the viscous character and to get the global Portland Cement Paste flow ability. The numerical approach is used to reproduce the global flow behavior and to ensure the accuracy of the obtained viscosity. The computational modeling permits the access to local information in order to analyze the different
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