Influence of coarse aggregate settlement induced by vibration on long-term chloride transport in concrete: a numerical study

Abstract

High-frequency vibration helps to improve the compactness of concrete, but also causes the settlement of coarse aggregates (CAs) and then affects the durability of hardened concrete. In this paper, a numerical study combining multi-phase CA settlement model and multi-component ionic transport model is performed to understand the influence of vibration-induced settlement on long-term chloride transport in concrete. Through parametric analysis, the influence mechanism of relevant factors on both chloride profile distribution and reinforcement corrosion initiation is discussed in detail. The results indicate that with the increase of vibration time, a decrease of chloride concentration appears in the bottom part of concrete specimen and a significant increase in the top part, because more CAs deposit in the bottom layer. Due to sedimentation, a more obvious fluctuation of chloride concentration along the height direction can be observed in the concrete mixed with a larger density and particle size of CAs. According to the model prediction, the corrosion of the top steel bar initiates 1.03–1.80 years earlier than that of the bottom steel bar under the same parameters. In practical engineering, special attention should be paid on the stability of fresh concrete and vibrating procedures to avoid obvious CA settlement.

Appendices

Appendix 1

The acceleration of CA movement (a) is expressed as:

$$a = \frac{{g\left( {\rho_{a} - \rho_{m} } \right)}}{{\rho_{a} }} - \frac{{18\eta_{pl} }}{{d^{2} \rho_{a} }} \cdot v$$

(20)

Assumptions:

$$M = \frac{{g\left( {\rho_{a} - \rho_{m} } \right)}}{{\rho_{a} }}$$

(21)

$$N = \frac{{18\eta_{pl} }}{{d^{2} \rho_{a} }}$$

(22)

Equation (20) can be further expressed as:

$$\frac{{{\text{d}}v}}{{{\text{d}}t}} = M - N \cdot v$$

(23)

The expression of v can be obtained by solving Eq. (23):

$$v = \frac{M}{N} - \frac{M}{N} \cdot \exp \left( { - N \cdot t} \right)$$

(24)

Through integral calculation, the CA settlement height is expressed as:

$$\Delta h = \frac{M}{N} \cdot t - \frac{M}{{N^{2} }} + \frac{M}{{N^{2} }} \cdot \exp \left( { - N \cdot t} \right)$$

(25)

Bring Eqs. (21) and (22) into Eq. (25), that is:

$$\Delta h = \frac{{d^{2} g\left( {\rho_{a} - \rho_{m} } \right)}}{{18\eta_{pl} }} \cdot \left\{ {t - \frac{{d^{2} \rho_{a} }}{{18\eta_{pl} }} \cdot \left[ {1 - \exp \left( { - \frac{{18\eta_{pl} }}{{d^{2} \rho_{a} }} \cdot t} \right)} \right]} \right\}$$

(26)

Appendix 2

See Fig. 

Fig. 13

Particle size distribution of CAs

13.