Two raw clayey soils were used for the manufacture of bricks. The first one was obtained by crushing termite Cubitermes spp. mounds (CMS) collected in the savanna around NGO (2˚29'14"S; 15˚45'20"E). They are at most 50 cm high and 30 cm large and are usually used to build floors in traditional houses or as rural road pavement. The crushed soil was sieved and only grains smaller than 2 mm were retained to manufacture bricks. The characteristics of this soil have been published [18] and are recalled in Table 1.

The second soil used is the lateritic soil (LS) from Mouyami (4˚27'34"S; 14˚42'48"E). It has been sieved to retain only the grains smaller than 2 mm. Its

geotechnical characteristics have been determined as described in [18] , that is, the particle size analysis was carried out in accordance with the NF 94 056 [19] and NF 94 057 [20] standards, and the Atterberg limits, the dry density, and the optimal moisture content were measured in accordance with the NF 94 051 [21] and NF P94-093 [22] standards, respectively. The organic matter content was determined by chemical route using the Walkley and Black method [23] . The results of these analyses are reported in Table 1.

For the stabilization of the bricks, five alkaline solutions were prepared (1.5%; 2.5%; 5%; 7.5% and 10% by weight) by dissolving sodium hydroxide pellets with a purity of 98% in distilled water. These NaOH solutions were used instead of the usual tap water for the manufacture of the bricks, at the content of the optimum moisture content determined through the Proctor test. The bricks have been molded by using a mechanical press with a pressure of 6 MPa. A whitish powder appeared on the surface of the stabilized bricks for 7.5% and 10% NaOH solutions. This powder is probably due to the reaction of sodium hydroxide with the air carbonic gas [13] .

The volumetric shrinkage rate of bricks at the instant t, λ(t), is equal to the difference between the initial volume V(0) and the volume at the instant t, V(t) divided by the initial volume.

The monitoring of the drying kinetics of the bricks was carried out as described in [18] , i.e., the mass of the bricks was recorded until its stabilization. The brick is assumed dry when its mass variation during three consecutive days is less than 2%. For each NaOH solution and soil type, three tests were conducted to check the reproducibility of the results.

Five parametric models have been tested to simulate the drying kinetics of the bricks: the Page-Avrami model [24] [25] , the diffusion model [18] [26] , the Khazaei’s model [27] [28] , the Peleg’s model [29] [30] and the Yong’s model [18] [31] . The meaning of their parameters has been recalled in [18] and their values are determined by minimizing the reduced chi-square using the origin Pro 8 software. The goodness of the fit is estimated through the value of its coefficient of determination R², the root mean square of the error (RMSE) and the Akaike’s Information Criterion (AIC). The models’ expressions are reported in Table 2.

The evaporable water content of the brick at the time t (the reduced mass) M_r(t) is calculated according to the formula:

M r ( t ) = M ( 0 ) − M ( t ) M ( 0 ) − M f

where M(t) is the brick’s mass at the time t and M_f the mass at the end of the drying.

The drying kinetics curves of earthen bricks made with Cubitermes spp. mound soil and lateritic soil activated with hydroxide sodium solutions are reported in Figure 1(a) and Figure 1(b), respectively.

These curves did not show the constant drying rate phase (a straight line at the start of the curve), but a steady variation of the drying rate, that is, there is almost no free water in the bricks. In other words, these drying kinetics are governed by the diffusion of moisture from the interior to the surface of bricks [25] . This behavior could be linked to the fact that the moisture content used to make bricks is the optimum moisture content (OMC) of the soil determined by the Proctor test. Indeed, the OMC diminishes the friction between soil grains, allowing the soil to have the highest density during its compaction, without being liquid [22] . The drying duration and the initial drying rate deduced from these curves are represented versus the activator content in Figure 2(a) and Figure 2(b), respectively. It appears that the difference between the clay contents of the two soils used has not a significant effect on the drying kinetics of the bricks. On the other hand, the activation of soils with NaOH increases the drying duration from about 23 days for non-stabilized bricks to about 28 days for the stabilized

bricks with the 10% NaOH solution. For the means values and by linear regression, the following relationship was found between the drying duration (D) and the NaOH content (α):

D = 24 + 0.8 α − 0.04 α 2 ; R 2 = 0.91

This lengthening of the drying duration by the NaOH activation could be explained by the tendency of NaOH to form compounds with water, and/or by the formation of the zeolitic structure between the initial soil grains [13] [16] [17] . Indeed, for an alkaline activated mortar made with a natural soil, Kim and al. observed that the formation of zeolitic structure is coupled with the reduction of the mortar porosity [16] . For their part, Diop and Grutzeck reported microstructure transformations during the alkaline activation of a clayey soil [17] . Besides, the drying duration has a strong and negative correlation with the initial drying rate (−0.97). Thus, NaOH activation of soil and stabilization of soil with cassava starch or amylopectin have opposite effects on the drying duration [18] . This variation of the effect of stabilizers on the brick behavior justifies the necessity to evaluate each process to optimize it.

As for the drying kinetics, there is no significant difference between the volumetric shrinkage rate of Cubitermes spp. soil bricks and that of lateritic soil bricks (Figure 3(a) and Figure 3(b)), despite the difference in clay content. The NaOH activation reduces significantly the shrinkage rate of bricks from about 5% for non-activated soils to 3% for soil activated with the 10% NaOH solution. This reduction of the shrinkage rate could be due to the formation of the zeolitic structure [13] [16] [17] that reduces the brick porosity as above mentioned. Besides, manufactured earth bricks did not show visible cracks. In fact, the increasing of the drying duration combined with the shrinkage reduction would reduce the appearance of cracks in bricks, and therefore would contribute to the increase of their strength. Indeed, slower lost of water, and weaker shrinkage generate less internal stresses, and thus the appearance of cracks in the bricks.

The shrinkage decrease observed here is lower than that induced by the addition of lime [6] and plant fibers [32] [33] , while it is higher than that produced by the addition of cement [34] or polyethylene strap [35] . However, in average, the improvement of the earthen brick strength due to the addition of lime [6] [36] , or plant fibers [32] [33] is lower than that reported for the NaOH activated soils [16] [17] .

The reduced water contents predicted by the models are represented as functions of those measured in Figure 4. To evaluate the quality of these predictions,

the mean values of the coefficient of determination (R²), the root mean square error (RMSE), and the Aike’s information criterion (AIC) for all models tested are also reported on these figures. For each model and any drying kinetics curve, the coefficient of determination is greater than 0.992, and the RMSE is less than 0.03. Therefore, all these models could be considered suitable to simulate this drying kinetics. However, the Khazaei model has better results than the others (Table 3), for all statistical criteria. As it has already proved to be the best for simulating the drying kinetics of earthen bricks stabilized with other binders [18] , it seems very suitable for modeling the drying kinetics of compressed earth bricks.

The values of the parameter n (the exponent of the time) of the Page-Avrami model and those of the khazaei’s model (Table 4 and Table 5) are on average equal to 1. These values are consistent with the shape of the drying curves which shows a steady decrease of the drying rate. However, there is a slight increase in the value of n with the increase of NaOH content. All factors affecting negatively the drying rate could contribute to this increase, and in particular, the decrease of porosity by the formation of zeolitic structure, the appearance of the flour on the brick surface due to the NaOH-CO₂ reaction. Indeed, as we have already reported in the material and methods part, for the bricks activated with 7.5 and 10% NaOH solution, a whitish powder appeared on the surface of the bricks.

The values of the parameter k of the Page-Avrami model, those of 1/T of the Khazaei’s model, and the inverse of the parameter a of the Peleg’s model decrease when the NaOH content increases. This result is consistent with the fact that the first two parameters are directly related to the time after which 63.2% of water is evaporated, and the third with the initial drying speed.

The values of the parameter K of the diffusion model obtained here are larger than those obtained earlier [18] because the drying durations measured here are shorter than the previous ones.