## 3 Results and Discussion
### Stability of the Macrostructure
Conversely, when the compaction energy increases, the structural stability (slow disaggregation) increases as well. Specimens with a dry density of 1.57 g/cm\({}^{3}\) still had around 10 wt.% in class interval 1 after 30 min of shaking (Figure 3b). In the case of the dry density of 1.74 g/cm\({}^{3}\), after 40 min of shaking, there was still about 25 wt.% of MU with a size equal to or larger than 10 mm (Figure 3c), which demonstrates the outstanding mechanical stability of the highly compacted specimens. Shaking times over 3000 s (50 min) were required in this case for the disaggregation patterns to exhibit a stationary distribution of the MU sizes. The differential MU size distribution curves (dMUSD) at the analyzed shaking times also explain the disaggregation evolution; see Figure 4, where frequencies are associated with the class marks defined in Table 3. With respect to dMUSD in uncompacted conditions, specimens with a higher degree of compaction showed slower time evolution of their dMUSD, as expected. Interestingly, as shown in Figure 4d, the dMUSD of all compacted specimens tended to conform to the uncompacted bentonite curves (both as received and with \(w\) = 10%) as shaking time increased. Figure 5 at t = 5 s compares for the nine class intervals the associated frequencies to the dry uncompacted material and the three dry densities. MUSD evolved during the compaction process. Even though initially the main class interval was number 7 (0.40 mm-0.16 mm), its predominance decreased as the compaction loading (and dry density) increased. Class intervals 6 to 9 (between 0.63 mm and <0.08 mm) showed analogous behavior, whereas number 1 (>10 mm) became progressively dominant. For the bentonite considered, compaction developed for growing MU sizes larger than 0.40 mm, the maximum size of interval 7, which prevailed in uncompacted conditions. Therefore, an aggregation index \(A\) is defined  
\[A=\sum_{i=1}^{n}F_{i}\cdot f\mathrm{i} \tag{1}\]  
where \(n\) = 9 are the class intervals considered, \(F_{\mathrm{i}}\) is the frequency associated with the \(i\)-th class, and \(f_{\mathrm{i}}\) is a function defined by  
\[f_{\mathrm{i}}=\left\{ \begin{array}{ll}1,&\mathrm{if}\,d_{\mathrm{min,i}} \geq d_{\mathrm{REF}}\\ 0,&\mathrm{otherwise}\end{array} \right. \tag{2}\]where \(d_{\rm min,i}\) is the minimum size of the \(i\)-th size interval (respectively equal to 10, 5, 2, 1.25, 0.63, and 0.40 mm) for class intervals 1 to 6, with classes with a minimum size larger or equal to \(d_{\rm REF}=0.40\) mm taken as the reference size. The ability of index \(A\) to summarize the increase in aggregation with compaction is illustrated in Figure 6.  
\(A\) is also a good estimator of the disaggregation process. This process, illustrated in Figure 3, is described in more detail in Figure 5, which shows for each dry density the evolution of the frequencies associated with the size intervals considered. The frequency of larger aggregates was reduced as shaking time advanced, eventually reaching a steady state. Remarkably, classes 2 to 5 (between 10 mm and 0.63 mm) showed low frequencies throughout the disaggregation process, which may be interpreted as metastable transition MU sizes. Figure 4: Differential aggregate size distribution, dMUSD (wt.% retained on sieve), for each shaking time and for each degree of compaction (average values) used in the bentonite studied: (**a**) 1.40 g/cm\({}^{3}\); (**b**) 1.57 g/cm\({}^{3}\); (**c**) 1.74 g/cm\({}^{3}\). Graph (**d**) compares the dMUSD for the maximum shaking time employed in each case with respect to the dMUSD of the samples before compaction, both as received and at moisture content \(w=10\) wt.%. The tendency of dMUSD to reach a stationary state around the initial size distribution in uncompacted conditions is depicted in Figure 7. The evolution of \(A\) during the shaking test is represented for each dry density, and the values of \(A\) for the uncompacted samples, dry and wet, are shown for reference. As the shaking progressed, \(A\) decreased.