- Article
- Open Access

# Prediction of Concrete Pumping Using Various Rheological Models

- Myoung Sung Choi
^{1, 2}Email author, - Young Jin Kim
^{1}and - Jin Keun Kim
^{2}

**8**:84

https://doi.org/10.1007/s40069-014-0084-1

© The Author(s) 2014

**Received:**26 March 2014**Accepted:**9 June 2014**Published:**8 July 2014

## Abstract

When concrete is being transported through a pipe, the lubrication layer is formed at the interface between concrete and the pipe wall and is the major factor facilitating concrete pumping. A possible mechanism that illustrates to the formation of the layer is the shear-induced particle migration and determining the rheological parameters is a paramount factor to simulate the concrete flow in pipe. In this study, numerical simulations considering various rheological models in the shear-induced particle migration were conducted and compared with 170 m full-scale pumping tests. It was found that the multimodal viscosity model representing concrete as a three-phase suspension consisting of cement paste, sand and gravel can accurately simulate the lubrication layer. Moreover, considering the particle shape effects of concrete constituents with increased intrinsic viscosity can more exactly predict the pipe flow of pumped concrete.

## Keywords

- concrete pumping
- lubrication layer
- shear-induced particle migration
- multimodal viscosity model
- particle shape

## 1 Introduction

Since concrete pumping was firstly introduced in 1930s, it has been a most common technique to transport fresh concrete in the real construction sites as it allows access to hard to reach region and reduces casting process duration and allows for a continuous casting. It has mostly been conducted not based on a quantitative estimation but based on hand-on experience or qualitative estimation for the pumpability through simple material tests such as slump test and bleeding test. However, a methodology for the quantitative predictions of the concrete pumping such as pumpable height or distance, pressure level, and flow rates are necessary to control the casting speed and to determine the total duration of the construction period, which is directly related to the construction cost.

A possible mechanism that illustrates to the formation of its layer is shear-induced particle migration (Choi et al. 2013b; Phillips et al. 1992; Jo et al. 2012; Wallevik 2008; Koehler et al. 2006). When concrete is pumped, a redistribution of particles occurs near the wall of the pipe due to the gradient of the shear stress. This is a common feature of particle suspensions, and initially well-mixed particles in concentrated suspension flows undergo migration from regions of higher shear stress to those of lower shear stress. The concrete pumping can therefore be considered in most cases as the shearing of an annular layer that is a few millimeters thick and has much lower viscosity than the concrete itself. Phillips et al. (1992) verified that the shear-induced particle migration can be a formative mechanism for the formation of the layer. Choi et al. (2013b) and Jo et al. (2012) tried to simulate the formation of the layer in the concrete pipe flow with the shear-induced particle migration.

When conducting the shear-induced particle migration analysis, the rheological parameters of materials are a paramount factor to predict the lubrication layer and the pumping conditions. Various rheological models (Hafid et al. 2010; Chateau and Trung 2008; Liu 2000; Krieger 1959; Chong and Baer 1971; Farris 1968) were suggested to describe the rheological behavior of suspension. However, very few studies have been performed to establish comprehensive prediction methodology for concrete pumping, that is, there have been few studies investigating the role of these rheological models on determining the pipe flow of pumped concrete, more specifically, for the formation and material properties of lubrication layer.

The objectives of this study are therefore investigating the pipe flow of pumped concrete depending on the various rheological models. The calculated results were compared with the 170 m full-scale pumping tests (Choi et al. 2013a). From the comparison, it was found that the multimodal suspension model representing concrete as a three-phase materials consisting of cement paste, sand and gravel with the effects of the particle shape can accurately predict the properties of lubrication layer and the pipe flow of pumped concrete.

## 2 Analysis Method for the Pipe Flow of Pumped Concrete

### 2.1 Shear-Induced Particle Migration

As stated in the introduction, to predict the pipe flow of pumped concrete, the lubrication layer should be carefully investigated. Several possible mechanisms illustrating the formation of its layer could be found in existing studies (Kaplan et al. 2005; Kwon et al. 2013; Choi et al. 2013b; Phillips et al. 1992; Jo et al. 2012; Wallevik 2008; Koehler et al. 2006). In this study, the shear-induced particle migration which demonstrated that particles in suspension migrate across the streamlines from a region of a higher shear rate to a region of a lower shear rate was considered as a major possible mechanism that contributes to the formation of the lubrication layer. Leighton et al. (Leighton and Acrivos 1987a, b) suggested phenomenological models for particle migration in non-homogeneous shear flows that typically result from spatial variation in irreversible interaction frequency and effective viscosity. Phillips et al. (1992) adapted the scaling arguments of Leighton and Acrivos (1987a, b) and proposed a diffusive flux equation to describe the time evolution of the particle concentration based on a two-body interaction model. In this study, the particle diffusive model proposed by Phillips et al. (1992), combined with general flow equations, was extended to solve the flow of concrete and predict the particle concentration distribution of suspensions in a pressure driven pipe flow.

*ϕ*is the particle concentration,

*t*is the time,

*u*

_{ z }is the velocity component in the flow direction,

*a*is the particle radius,

*z*is the flow direction,

*r*is the radial direction,

*η*is the apparent viscosity of the concentrated suspension, and

*K*

_{ c }and

*K*

_{ η }are dimensionless phenomenological constants.

In the pipe flow of pumped concrete, the shear stress is the highest at the wall of the pipe and linearly decreases as the position moves to the center of the pipe. The stress gradient is a driving force to move particles toward the center of the pipe as described in the first term of the right side in Eq. (1). The increase of the particle concentration due to the migration may increase the viscosity and the yield stress, which hinder the additional migration of the particles as described in the second term of the right side in Eq. (1). As a result, the concentration of the particle inside the pipe is determined by the balance between the two actions, namely, the migration due to the stress gradient and the hindrance due to the increased rheological properties.

*u*= 0) and no particle flux through the wall as expressed below:

*ϕ*

_{0}is the initial concentration of particles. The parameters,

*K*

_{ c }and

*K*

_{ η }should be independent of the particle size, concentration, and shear rate. The values of these parameters were set to 0.3 and 0.6, respectively (Phillips et al. 1992).

### 2.2 Effects of Particle Concentration and Particle Shape on Rheological Properties

*η*which is a rheological parameter of materials should be carefully determined. The apparent viscosity

*η*for the Bingham fluid model can be expressed as follows:

*η*

_{ p }and

*τ*

_{0}are the plastic viscosity and yield stress of Bingham fluid model, respectively. The particle concentration variation due to particle migration might cause a considerable change in the rheological characteristics of the mixtures. For the yield stress

*τ*

_{0}, one possible model that was presented in the literature was used (Hafid et al. 2010; Chateau and Trung 2008)

*ϕ*

_{ s }and

*ϕ*

_{ g }are the volume fraction of sand and gravel and

*ϕ*

_{s,max}and

*ϕ*

_{g,max}are the maximum concentration of sand and gravel, respectively.

Through the preliminary investigation on the effects of the rheological properties on the concrete pumping (Choi et al. 2013a), the yield stress causes a minor effect on the pipe flow compared to the effects of the plastic viscosity, that is, above single yield stress model is sufficient to analyze the concrete flow. On the other hand, the plastic viscosity *η*_{
p
} is greatly influencing on flow rates and pump pressure so that it should be carefully determined to investigate the concrete pumping.

There have been various studies to illustrate the behavior of suspensions and suggested some viscosity models (Liu 2000; Krieger 1959; Chong and Baer 1971; Farris 1968). When taking into account the concrete, suggested viscosity models can be divided into two categories depending on the scale-level of constituents: unimodal suspension model and multimodal suspension model. From a unimodal suspension point of view, concrete can be considered as a two-phase material consisting of mortar and gravel. In this approximation, mortar is the suspending medium and gravel is an only particle considered. In this study, three unimodal viscosity models were investigated.

*a*is a constant which was determined from the (1 −

*η*

_{ r }) −

*ϕ*relationship.

This model takes into account the concentration, size distribution, and shape of the particles within the suspension. Ideally, the Krieger–Dougherty model is much better suited to evaluate the viscosity of a cement paste or concrete.

*ϕ*

_{ s }and

*ϕ*

_{ g }of each mode is determined separately according to the mix proportion and

*ϕ*

_{s,max}and

*ϕ*

_{g,max}is the maximum solid fraction of sand and gravel, respectively. Through the Liu model (Liu 2000), the maximum solid fractions of each mode were determined as 0.675 and 0.645, respectively, for this study condition. Where

*η*

_{ s }and

*η*

_{ g }are the intrinsic viscosity of the sand and gravel, respectively, and it represents the effects of individual particle shape on viscosity. It is defined as follows:

*η*

_{ r }is determined by Eq. (9). Therefore, in case of multimodal viscosity model, the effects of individual particle shape should be carefully determined in calculating the viscosity.

### 2.3 Effects of Particle Shape

*A*is the cross sectional area of particle, and

*P*is the perimeter of particles. In this study, to find out the parameters of circularity, the digital image processing technique was used and more details information could be found in earlier works (Choi et al. 2013b).

## 3 Experimental Programs

### 3.1 Materials and Mix Proportions

^{3}. The sand was natural river sand with density 2,590 kg/m

^{3}and fineness modulus of 2.81. Sand particle size ranges from 0.08 to 5 mm with water absorption capacity 2.43 %. The maximum coarse aggregate size was 25 mm. It was a limestone aggregate with water absorption capacity 0.8 %, density 2,610 kg/m

^{3}, and fineness modulus 6.72. The amount of mixing water was corrected to take into account the water absorbed by sand and coarse aggregates. A polycarboxylate-based high range water reducing admixtures (HRWRA) was also used. Its dosage is shown in Table 1 marked as % HRWRA, meaning the percentage of admixture relative to binder content which is the sum of cement, fly ash and blast furnace slag (in weight). The mix proportion has 4.5 % air content.

Mix proportions.

Materials | Design strength |
---|---|

Series name | C50 |

Cement CEM I 52.5 N (kg/m | 225 |

Fly ash class F (kg/m | 50 |

Blast furnace slag (kg/m | 225 |

| 0.33 |

Sand (kg/m | 736 |

Coarse aggregate (kg/m | 871 |

% Polycarboxylate-based HRWRA | 0.9 |

Slump flow (mm) | 620 ± 20 |

### 3.2 Measurement of Rheological Properties

### 3.3 Full Scale Pumping Test

^{3}reservoirs, which were connected to a linear variable differential transformer (LVDT). As the pump cylinder volume is known, the filling rate was computed from the LVDT length variation with designated stroke times. Through these experiments, the averaged filling rate was found to be around 85 %.

### 3.4 Ultrasonic Velocity Profiler (UVP)

Experimental UVP parameters.

Item | Content |
---|---|

Frequency (MHz) | 8 |

Cycles per pulse | 2–32 |

No. of profiles | 1,024 |

Sound velocity (m/s) | 2,680 ± 200 |

Doppler angle (°) | 85 ± 0.5 |

Spatial resolution (mm) | Min. 0.20 |

## 4 Numerical Simulation for the Pumping Test

### 4.1 Intrinsic Viscosity for Sand and Gravel

In case of multimodal viscosity model, the modified intrinsic viscosity for sand and gravel should be determined for the shear-induced particle migration analysis. To determine an optimum intrinsic viscosity considering the particle shape effects, the circularity was quantified using digital image processing technique (Kwan et al. 1999; Mora and Kwan 2000; Otsu 1979). Through the relationship between the intrinsic viscosity and the circularity in Fig. 2, the calculated intrinsic viscosity of sand and gravel are determined as 3.5 and 6, respectively, which are the averaged values of representative samples of each aggregate which are selected randomly (Choi et al. 2013b).

### 4.2 Pipe Modeling and Analysis Conditions

Input values for the analysis of shear-induced particle migration.

Parameters | Values |
---|---|

Rheological properties of cement paste | |

Plastic viscosity (Pa s) | 1.0 |

Yield stress (Pa) | 10.0 |

Rheological properties of mortar | |

Plastic viscosity (Pa s) | 2.5 |

Yield stress (Pa) | 10.0 |

Maximum solid fraction | |

| 0.675 |

| 0.645 |

Volume fraction | |

| 0.458 |

| 0.349 |

Intrinsic viscosity | |

| 3.5 |

| 6.0 |

## 5 Results and Discussion

### 5.1 Shear Rate and Velocity

### 5.2 Flow Rates

Through these comparison results, multimodal suspension approximation for concrete is right method to simulate the concrete flow in pipe and taking into account the particle shape effects would provide better insight to predict the pipe flow of pumped concrete.

## 6 Conclusion

- 1.
When concrete is being pumped, the lubrication layer which is formed at the interface between the concrete and the wall of the pipe plays a dominant role to facilitate the concrete pumping.

- 2.
The shear-induced particle migration which demonstrated that particles in suspension migrate across the streamlines from a region of a higher shear rate to a region of a lower shear rate is a major possible mechanism that illustrates to the formation of the lubrication layer.

- 3.
Regarding the shear-induced particle migration, the rheological parameters are a paramount factor to predict the pipe flow. Among four viscosity models used in this study, the multimodal viscosity model representing concrete as a three-phase material consisting of cement paste, sand and gravel can accurately simulate the lubrication layer and flow condition of pumped concrete.

- 4.
When calculating the multimodal viscosity model, the increased intrinsic viscosity reflecting the particle shape effects of concrete constituents, especially the sand and the gravel should be considered to predict more exactly the real velocity profile and the flow rates of pumped concrete.

- 5.
From this study, a comprehensive prediction methodology for the pipe flow of pumped concrete was established.

## Declarations

### Acknowledgments

This research was supported by a Grant from the Construction Technology Innovation Program (08CTIPE01-Super Long Span Bridge R&D Center) funded by Ministry of Land, Transportation and Maritime Affairs (MLTM) of Korean government.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

## Authors’ Affiliations

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