Theoretical and Numerical Modeling of Plastic Shrinkage in Concrete

by ce on December 14, 2011

There are several aspects of modeling that can be considered when dealing with plastic shrinkage cracking.  These aspects include bleeding, evaporation, cement hydration, capillary pressure development, volume contraction and crack formation.  Followings are some of studies that have been carried out to deal with some aspects of plastic shrinkage modeling.

Radocea developed a theoretical model of plastic shrinkage based on the idea that the concrete constituents are incompressible and thus the loss of water due to bleeding Ws can be related directly to volume contraction or shrinkage.  The model was derived by comparing two curves of capillary pressure, P, versus evaporated water, W, for materials with the same pore structures, one in which the bleeding is negligible (do not shrink) and the other in which the bleeding is significant (shrink). The evaporated water for material that shrinks consists of bleeding water, Ws, and an amount of water, (W- Ws), that depends on the geometry of the spaces between the outermost grains.  On the other hand, for material that does not shrink, the evaporated water comes only from water occupying pore spaces near the surface.  Since both materials have the identical pore structures, one can determine Ws by comparing both curves.

Josserand et al. developed a bleeding model based on an aging nonlinear model accounting for the sample size effect experimentally observed on the bleeding capacity.  The model is thus capable of capturing the convex nature of bleeding capacity versus the height of specimens curve.  Cement content and temperature were found to be the keys in the ageing kinetics.  More work is still needed to relate the model with mix design.

Kwak and Ha proposed a model to evaluate the plastic shrinkage was based on the balance between water evaporation and bleeding. The bleeding model based on the concept of self-weight consolidation of the cement paste.  The evaporation model takes into account the temperature variation due to cement hydration.  The model was then numerically implemented using finite difference method.  Several parameter studies, such water to cement ratio, slab thickness, wind velocity etc., can be investigated using the developed model.  One of the interesting results is that the bleeding capacity is proportional to slab thickness, which is contradicted with that of Josserand et al.

 

References

A. Rodecea, A model of plastic shrinkage, Mag. Concr. Res. 46(167) (1994) 125-132.

L. Josserand, O. Coussy, F. de Larrard, Bleeding of concrete as an ageing consolidation process, Cem. Concr. Res. 36(9) (2006) 1603–1608.

H.-G. Kwak, S.-J. Ha, Plastic shrinkage cracking in concrete slabs. Part I: a numerical model, Mag. Concr. Res., 58(8) (2006) 505–516.

H.-G. Kwak, S.-J. Ha, Plastic shrinkage cracking in concrete slabs. Part II: numerical experiment and prediction of occurrence, Mag. Concr. Res., 58(8) (2006) 517–532.

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