Proceedings of the International rilem conference Materials, Systems and Structures in Civil Engineering 2016

387

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

rejected for several reasons, the main one being the difficulty of limiting the forced 

convection on the faces subjected to drying, and of ensuring the uniformity of this 

phenomenon on all sides. The requirements of the storage bin are similar to those of a 

desiccator.  It must be able to contain saline and be impermeable to air and moisture. In order 

to enable placing several temperature and relative humidity sensors inside the storage bin, 

sealing plugs were installed. The concrete samples were placed on a plastic honeycomb 

duckboard allowing maximized interaction between the salt solution and the ambient air. This 

setup is shown in Figure 1. The saturated salt solution was made using potassium carbonate in 

order to reach an ambient RH of close to 45%. The room temperature was controlled at 25°C. 

The concrete samples were prevented from drying until the test started. The samples were 

submitted to drying more than two months after mixing. Due to the high w/c ratio of the B11 

concrete, it can therefore be considered that the hydration reactions were completed, and that 

the auto-desiccation phenomenon could be neglected [3]. 

 

 

Figure 1: Experimental setup linked to the continuous measurement of RH and T sensors 

 

2.3. Test setup 

The experimental measurements consisted in mass loss measurements at regular intervals and 

in the continuous measurement of the internal relative humidity in concrete samples at various 

distances from the drying interface. Four sample geometries were considered:  

- G1: 70x70x280mm prism, drying on the two opposite lateral faces, 

- G2: 70x70x110mm prism, drying on the two opposite lateral faces, 

- G3: 70x110mm cylinder, radial drying, 

- G4: 70x70x110mm prism, drying on the four longitudinal faces. 

For each of these geometries, the average drying radius (r

d

) was computed as the ratio 

between the drying surface and the sample volume. This resulted in r

d

 of 0.14, 0.055, 0.0275 

and 0.0175m for geometries G1, G2, G3 and G4 respectively. 

The mass loss measurements were performed on 3 samples for G1, 2 samples for G2 and G3, 

and on 1 sample for G4. This study focuses on the first weeks after drying was initiated. The 

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388

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

relative humidity was measured at various distances from the drying interface on geometries 

G1, G2 and G3 according to the distribution shown in Figure 2.  

 

Figure 2: layout plan of RH sensors (sides submitted drying displayed in red) 

 

 

3. Drying 

model 

 

The drying model used in this study assumes that two mechanisms are at the origin of the 

water transport in the concrete: the diffusion of water vapour and the permeation of liquid 

water. If the concrete porous network is saturated, the latter mechanism is the predominant 

one, whereas for a low degree of saturation, the movement of water in the form of vapour 

diffusion cannot be neglected. 

The liquid water flow can be expressed through Darcy's law, which relates the fluid mass flow 

through a medium to the pressure gradient of this fluid as expressed in the equation (1), where 

K

eff

 is the concrete effective permeability (s), p

c

 the capillary pressure (Pa), and J

l

 is the rate 

of liquid water flow (kg.m

-2

.s

-1

). 

 

(1)

According to the Kelvin equation, the relationship between the capillary forces and the 

relative humidity in concrete can be expressed as shown in equation 2, where M

w

 is the 

molecular mass of water (kg/mol), 

l

 is the liquid water density (kg/m

3

), R is the gas constant 

(J.K

-1

.mol

-1

) and T is the temperature (K). 

 

(2)

In order to take into account the dependency of the water permeability to the degree of 

saturation, equation 3 can be used, where K

0

 is the intrinsic water permeability of concrete in 

saturated conditions, 

l

 is the water dynamic viscosity , and k

rl

 is the relative permeability. 

This latter term can be determined through the Mualem empirical relationship [4] shown in 

equation 4, where S

l

 is the saturation degree, p

krl

 is a fitting parameter. The relationship 

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389

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

between the degree of saturation and relative humidity is given by the van Genuchten 

equation [5] (equation 5), where a

vg

 and b

vg

 are two parameters that can be obtained by fitting 

experimental results of the desorption isotherm for the tested material. 

 

(3)

 

(4)

 

(5)

Thus, equations 1-2 can be re-written as equation 6, while equations 3-5 allow to solve this 

equation for any given relative humidity. 

 

(6)

On the other hand, when the saturation degree decreases, pores are progressively not filled 

with water. This leaves space for a flow of water vapour (J

v

, expressed in kg.m

-2

.s

-1

) due to 

the gradient of vapour pressure (p

v

) between the inside of concrete and the ambient conditions 

according to Fick's law, as shown in equation 7. 

 

(7)

The effective diffusion coefficient in a porous medium (D

eff

, expressed in m².s

-1

) can be 

related to the degree of saturation, to the porosity ( ) and to the diffusion coefficient of water 

in air (D

0

) through the empirical Millington and Quirk relationship [6] expressed in equation 

8. In equation 9, the relative humidity is related to the saturation vapour pressure p

vs

 and to 

the vapour pressure of water p

v

. 

 

(8)

 

(9)

 

The saturation vapour pressure is temperature dependent and can be determined by the 

Clausius-Clapeyron relationship (equation 10), where L

v

 is the heat of vaporisation of water 

(J/kg), T

0

 is the reference temperature (273 K) and T is the air temperature (K). In the same 

way, the dependency of D

0

 to temperature can be taken into consideration by equation 11. 

 

(10)

 

(11)

From combining equations 6, 7 and 9, to the continuity equation, the equation that has to be 

solved for the moisture transport can be expressed as equation 12.  

 

(12)

The modelling of drying requires the definition of adapted boundary conditions. Indeed, 

imposing the ambient relative humidity directly at the air-concrete interface is a possibility [1, 

7]. However, such methodology does not take into account the presence of a boundary layer 

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