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SCC formwork pressure: Influence of steel rebars　　Abstract　　The formwork pressure exerted by a given Self Compacting Concrete (SCC) depends on its thixotropic behavior, on the casting rate and on the shape of the It can moreover be expected that, in the case of a formwork containing steel rebars, these should also play a In first part, the specific case of a cylindrical formwork containing a single cylindrical steel rebar is In second part, a comparison of the theoretical predictions to the experimental measurements of the pressure drop, after the end of casting SCC, was determined and the proposed model was Finally, an extrapolation is suggested of the proposed method to the case of a rectangular formwork containing a given horizontal section of steel rebars, which could allow the prediction of the formwork pressure during 　　Keywords: Fresh concrete; Rheology; Workability; Formwork presure; Thixotropy　　 Introduction　　In most of the current building codes or technical recommendations [1], [2], [3] and [4], the main parameters affecting formwork pressure during casting are the density of concrete, the formwork dimensions, the pouring rate of concrete, the temperature, and the type of 　　However, it was recently demonstrated that, in the case of SCC, the thixotropic behaviour of the material played a major role [5] P Billberg, Form pressure generated by self-compacting concrete, Proceedings of the 3rd International RILEM Symposium on Self-compacting Concrete, RILEM PRO33 Reykjavik, Iceland (2003), 271–[5], [6], [7] and [8] It can be noted that this influence is in fact indirectly taken into account in the above empirical technical recommendations via the effect of temperature and type of the binder, which are both strongly linked to the ability of the material to build up a structure at rest [9], [10] and [11]　　During placing, the material indeed behaves as a fluid but, if is cast slowly enough or if at rest, it builds up an internal structure and has the ability to withstand the load from concrete cast above it without increasing the lateral stress against the It was demonstrated in [7] and [8] that, for a SCC confined in a formwork and only submitted to gravity forces, the lateral stress (also called pressure) at the walls may be less than the hydrostatic pressure as some shear stress τwall is supported by the It was also demonstrated that this shear stress reached the value of the yield stress, which itself increased with time because of Finally, if there is no sliding at the interface between the material and the formwork [8], the yield stress (not less or not more) is fully mobilized at the wall and a fraction of the material weight is supported (vertically) by the The pressure exerted by the material on the walls is then lower than the value of the hydrostatic 　　Based on these results, the model proposed by Ovarlez and Roussel [7] predicts a relative lateral pressure σ′ ( ratio between pressure and hydrostatic pressure) at the bottom of the formwork and at the end of casting equal to:　　(1)and a pressure drop Δσ′(t) after casting equal to:　　(2)where H is the height of concrete in the formwork in m, Athix the structuration rate in Pa/s [10], R is the casting rate in m/s, e is the width of the formwork in m, g is gravity, t is the time after the end of casting and ρ is the density of the 　　As it can be seen from the above, the key point for the pressure decrease is that the shear stress on each vertical boundary of the formwork equals the static yield stress of the It can then be expected that, in the case of a formwork containing steel rebars, the stress at the surface of the rebars should also play a It is the objective of this paper to start from the model developed by Ovarlez and Roussel [7] and extend it to the case of reinforced As the steel rebars should have a positive effect on formwork design ( decreasing the formwork pressure), this could allow for a further reduction of the formwork 　　In first part, the specific case of a cylindrical formwork containing a single cylindrical steel rebar is In second part, a comparison of the theoretical predictions to the experimental measurements of the pressure drop, after the end of casting SCC, is determined and the proposed model is Finally, an extrapolation is suggested of the proposed method to the case of a rectangular formwork containing a given horizontal section of steel rebars, which could allow the prediction of the formwork pressure during 　　 Influence of a vertical steel bar on the pressure decrease inside a cylindrical formwork　　In this paper, SCC is considered as a yield stress material (in first step, thixotropy is neglected), and, for stresses below the yield stress, SCC behaves as an elastic material [7] In the following, cylindrical coordinates are used with r in the radius direction; the vertical direction z is oriented downwards (see F 1) The top surface (upper limit of the formwork) is the plane z = 0; the formwork walls are at r = R The bottom of the formwork is located at z = H An elastic medium of density ρ is confined between the cylindrical formwork and an internal cylindrical steel rebar defined by the boundary (r = rb) For the boundary condition, the Tresca conditions are imposed everywhere at the walls ( it is assumed that the shear stress at the walls is equal to the yield stress τ00 as argued by Ovarlez and Roussel [7] and demonstrated in [8]) In order to compute the mean vertical stress σzz(z) in the formwork, the static equilibrium equation projected on the z axis on an horizontal slice of material confined between two coaxial rigid cylinders can be written:　　 Evaluation of the structuration rate of SCC at rest　　 The vane test　　The yield stress of the studied SCC was measured using a concrete rheometer equipped with a vane The vane geometry used in this study consisted of four 10 mm thick blades around a cylindrical shaft of 120 mm The blade height was 60 mm and the vane diameter was 250 The gap between the rotating tool and the external cylinder was equal to 90 mm which is sufficiently large to avoid any scaling effect due to the size of the gravel (Dmax = 10 mm here)　　Tests were performed for four different resting times after mixing on different samples from the same Of course, working with the same batch does not allow for the distinction between the non-reversible evolution of the behavior due to the hydration of the cement particles and the reversible evolution of the behavior due to thixotropy [9] and [10] It can however be noted that the final age of the studied system ( from the beginning of the mixing step to the last vane test measurement) was of the order of 70 Although Jarny et [13] have recently shown, using MRI velocimetry, that a period of around 30 min exists, for which irreversible effects have not yet become significant compared to reversible ones, the final age of the system in the present study was over this However, no strong stiffening nor softening of the sample was visually spotted nor measured as it will be shown Finally, the data analysis proposed by Estellé et [14] was used for the yield stress 　　 The plate test　　The plate test appears to be a very convenient method to monitor the apparent yield stress evolution of a thixotropic material with It was first developed and used in [8] but more details about its application to other materials than cement can be found in [15]　　The device is composed of a plate rigidly attached below a The plate is lowered into a vessel containing the SCC ( F 2) The apparent mass of the plate is continuously monitored versus time by recording the balance output with a The balance measurements have an uncertainty of ± 01 The vessel was made of smooth PVC and was cylindrical with a diameter of 200 mm and 200 mm in The plate was placed along the cylinder During the tests, the vessel was filled with material to a height of 200 The plate used was 3 mm thick, 75 mm wide and 100 mm It was covered with sand paper with an average roughness of 200 µ The sand paper was used to avoid any slippage between the material and the plate [8] The distance between the plate and the vessel walls was large enough compared to the size of the constitutive particles that the material can be considered as homogeneous [16] and [17] The height H of the immersed portion of the plate was measured before the start of the To ensure that all tests start with the suspension in similar condition, vibration was applied (frequency of 50 Hz, amplitude of 5 mm) for 30 This step is critical in order to ensure tests Variations between tests performed on the same material in the same experimental conditions were then less than 5%　　--------------------------------------------------------------------------------　　Full-size image (22K)　　F Schematic of the plate 　　View Within Article　　The plate test analysis is based on the fact that the slight deformation of the cement paste under its own weight allows for the transfer of a part of this weight to the plate by the mobilization of a shear stress on the This shear stress is equal to the maximum value physically acceptable, which is the yield stress (more details were given in [8], [15], [16] and [17]) The variation in apparent yield stress with time can then be calculated from the measured apparent mass evolution of the plate with time using the following relation:　　(9)Δτ0(t)=gΔM(t)/2Swhere ΔM(t) is the measured variation in the apparent mass of the plate and S is the immerged 　　 Laboratory cylindrical formworks　　Two columns were simultaneously filled with the studied SCC The columns were made of the same PVC covered with the same sand paper as the plate The columns inner diameters were equal to 100 Each column was 1300 mm The thickness of the plastic wall was 3 A 25 mm diameter steel bar was introduced in the second column (F 3)

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