abstract

The formwork pressure exerted by a given self-compacting concrete (SCC) depends on its thixotropic behavior, pouring speed and formwork shape. In addition, it can be expected that these steel bars should also play a role in the case of formwork containing steel bars. In the first part, the concrete situation of cylindrical formwork containing a single cylindrical steel bar is studied. In the second part, after the stress corrosion cracking of casting, the theoretical predicted value of pressure drop is compared with the experimental measured value, and the proposed model is verified. Finally, it is suggested that the proposed method be extended to the case of rectangular formwork with a given horizontal section reinforcement, which can predict the formwork pressure during pouring.

Keywords: fresh concrete; Rheology; Commutability; Template pressure; thixotropy

1. Introduction

In most current building codes or technical recommendations [1], [2], [3] and [4], the main parameters that affect the formwork pressure in the pouring process are concrete density, formwork size, concrete pouring speed, temperature and binder type.

However, recent research shows that the thixotropic behavior of materials plays a major role in SCC [5] P. Bilberg, the pressure generated by self-compacting concrete, proceedings of the third international RILEM seminar on self-compacting concrete, RILEM PRO33, Reykjavik, Iceland (2003), p. 271–280. [5], [6], [7] and [8]. It can be noted that this influence is actually indirectly considered in the above-mentioned empirical technical suggestions through the influence of temperature and adhesive type, which are closely related to the ability of materials to build structures at rest [9], [10] and [1 1].

During the pouring process, the material does behave as a fluid, but if the pouring speed is slow enough or at rest, it will form an internal structure that can bear the load of concrete poured on it without increasing the lateral stress of the formwork. [7] and [8] prove that for SCC confined in the formwork and only subjected to gravity, the lateral stress (also called pressure) at the wall may be less than the hydrostatic pressure, because some shear stress τ walls are supported by the wall. It is also proved that the shear stress reaches the value of yield stress, and the yield stress itself increases with time due to thixotropy. Finally, if the interface between the material and the formwork does not slip [8], the yield stress (neither too much nor too little) is fully mobilized on the wall, and a part of the material weight is supported by the formwork (vertically). The pressure exerted by the material on the wall is lower than the value of hydrostatic pressure.

Based on these results, the model proposed by Ovarlez and Rousseau [7] predicts that the relative lateral pressure σ ′ (the ratio of pressure to hydrostatic pressure) at the bottom of formwork and at the end of pouring is equal to:

(1) and the pressure drop δ σ′ (t) after casting are equal to:

(2) in the formula, h is the height of concrete in the formwork, with the unit of m, Athix is the structuring rate, with the unit of Pa/s [10], r is the pouring rate, with the unit of m, e is the width of the formwork, with the unit of m, g is gravity, t is the time after pouring, and ρ is the density of concrete.

As can be seen from the above, the key point of pressure reduction is that the shear stress on each vertical boundary of the formwork is equal to the static yield stress of the material. Then it can be expected that in the case of formwork containing steel bars, the stress on the surface of steel bars should also play a role. The purpose of this paper is to extend the model developed by Ovarlez and Ro ussel [7] to the case of steel formwork. Because steel bars should have a positive impact on the formwork design (that is, reduce the formwork pressure), this can further reduce the formwork size.

In the first part, the concrete situation of cylindrical formwork containing a single cylindrical steel bar is studied. In the second part, after the stress corrosion cracking of casting, the theoretical predicted value of pressure drop is compared with the experimental measured value, and the proposed model is verified. Finally, it is suggested that the proposed method be extended to the case of rectangular formwork with a given horizontal section reinforcement, which can predict the formwork pressure during pouring.

2. Influence of vertical reinforcement on internal pressure drop of cylindrical formwork

In this paper, SCC is regarded as a yield stress material (thixotropy is ignored in the first step), and SCC behaves as an elastic material for stresses below the yield stress [7]. Hereinafter, cylindrical coordinates are used, and r is in the radial direction; The vertical direction z is downward (see figure 1). The top surface (template upper limit) is plane z = 0；; The formwork wall is located at r = R The bottom of the template is located at z = h. The elastic medium with density ρ is confined between the cylindrical formwork and the internal cylindrical steel bar defined by the boundary (r = rb). For boundary conditions, the Tresca condition is applied anywhere on the wall (that is, it is assumed that the shear stress on the wall is equal to the yield stress τ00, as described by Ovarlez and Rousseau [7] and proved in [8]). In order to calculate the average vertical stress σzz(z) in the template, the static equilibrium equation can be projected on the z axis of the horizontal material slice between two coaxial rigid cylinders:

3.2. Assessment of SCC Structural Rate at Rest

3.2. 1. Vane test

The yield stress of SCC studied was measured by using a concrete rheometer equipped with blade tools. The blade geometry used in this study consists of four blades with a thickness of 10 mm around a cylindrical shaft with a diameter of120 mm. The blade height is 60mm and the blade diameter is 250mm. The clearance between the rotary tool and the outer cylinder is equal to 90 mm, which is enough to avoid any scaling effect caused by gravel size (here Dmax = 10 mm).

Different samples of the same batch were mixed and tested at four different standing times. Of course, using the same batch can't distinguish the irreversible behavior evolution caused by hydration of cement particles from the reversible behavior evolution caused by thixotropy [9] and [10]. However, it can be noted that the final age of the studied system (that is, from the beginning of the mixing step to the last blade test measurement) is on the order of 70 minutes. Although Jarny et al. [13] recently used MRI velocimeter to show that there is a period of about 30 minutes, and the irreversible effect has not become significant compared with the reversible effect, the final age of the system in this study exceeded this period. However, the strong hardening or softening of the sample was neither found nor measured visually, which will be shown later. Finally, the data analysis [14] proposed by Estellé et al. is used to calculate the yield stress.

3.2.2. Plate test

Plate test seems to be a very convenient method to monitor the apparent yield stress of thixotropic materials with time. It was originally developed and used in [8], but more details about its application in materials other than cement can be found in [15].

The device consists of a flat plate rigidly connected below the balance. Place the board in a container containing SCC (see Figure 2). By recording the output of the balance with a computer, the apparent quality of the plate is continuously monitored with respect to time. The n uncertainty of balance measurement is 0.01g. The container is made of smooth PVC and is cylindrical with a diameter of 200 mm and a height of 200 mm. The plate is placed along the axis of the cylinder. During the test, the container was filled with material to a height of 200 mm The plate used is 3 mm thick, 75 mm wide and 100 mm long. It is covered with sandpaper with an average roughness of 200? Sandpaper is used to avoid any slippage between the material and the board [8]. Compared with the size of the constituent particles, the distance between the plate and the container wall is large enough, so it can be considered that the material is uniform [16] and [17]. Before the test begins, measure the height h of the immersed part of the board. In order to ensure that all tests start from the suspension under similar conditions, vibration (frequency 50 Hz, amplitude 5 mm) is applied for 30 seconds. This step is very important to ensure the reproducibility of the test. The difference between the tests on the same material under the same experimental conditions is less than 5%.

-

Full-size image (22K)

Figure 2. Schematic diagram of plate test.

View in the article

The plate test analysis is based on the fact that the slight deformation of cement slurry under its own weight allows a part of the weight to be transferred to the plate by moving the shear stress on the plate. The shear stress is equal to the physically acceptable maximum value, namely the yield stress (see [8], [15], [16] and [17] for more details). Then, the change of apparent yield stress with time can be calculated by measuring the change of apparent mass of plate with time, using the following relationship:

(9) Δ τ 0 (t) = gΔ m (t)/2s where Δ m (t) is the measured change of the apparent mass of the plate and s is the submerged surface.

3.2.3. Laboratory cylindrical template

Both columns were filled with SCC under study. The column is made of the same PVC as the plate test and covered with the same sandpaper. The inner diameter of the column is equal to 100 mm. The height of each column is1300mm. The thickness of the plastic wall is 5.3 mm. A steel bar with a diameter of 25mm was introduced into the second column (Figure 3).