## 4 Some Possible Reasons to Explain the Strength Recovery upon Reactivation
### Transition from Static to Kinetic Strength: The Role of Viscosity  
In the framework of the friction theory, the transition from static to kinetic conditions is described in terms of static friction at detachment and the subsequent kinetic friction during the sliding phase at a constant rate of displacement. For low sliding speeds, the former kind of friction is usually greater than the latter and is the result of both interlocking and adhesion of the shared micro-roughness between the surfaces in contact. Referring to the case of soil, the reactivated strength, \(\tau_{\text{reac}}\), plays a role analogous to that of static friction at detachment, whereas that of the steady residual strength, \(\tau_{\text{r}}(\
u)\), is analogous to kinetic friction. However, the frictional mechanism in soil may be quite different: the reactivation starts with the deformation of the soil fabric, which then dislocates as soon as the relative displacement increases. The previous ageing phase causes some increase in the density of the particle-to-particle contacts along the shear band: the strong viscosity of the absorbed water at the particle contacts (edge-to-face hinge) may explain the initial reaction at the start of displacement. In order to explain the strength decrease following reactivation, it should be kept in mind that the displacement occurring along the shear band is orthogonal to the direction along which the volumetric creep occurs during ageing; therefore, the initial aged fabric may become destructurated as the displacement increases and the strength may quickly decay towards \(\tau_{\text{r}}(\
u)\). In this mechanism, the reactivation speed may play an important role: as shown in Figure 8, the reactivated strength increases with the displacement speed and conversely decreases if the reactivation speed is low. If the displacement speed approaches zero, the reactivated shear strength could approach the reference value, \(\tau_{0}\). This latter circumstance  
Figure 12: Strength angle increment at reactivation after one month of ageing, \(\varphi_{\text{reac}}-\varphi_{\text{r}}(\
u)\), versus CF: reactivation speed of 0.089 mm/min. may occur irrespective of the amount of time spent in the previous ageing phase, and could be explained if the increase in strength at reactivation depended only on the viscous properties of the edge-to-face hinge so that \(\Delta\tau_{1}\) may be imperceptible if the reactivation speed is almost null. The strength increment upon reactivation may be expressed in terms of the viscous properties of soil:  
\[\tau_{\text{reac}}-\tau_{0}=c_{\text{reac}}\
u \tag{1}\]  
with \(c_{\text{reac}}\) being the viscous constant of soil at reactivation. Similarly, the strength mobilised in the steady condition may be expressed as:  
\[\tau_{\text{r}}(\
u)-\tau_{0}=\text{cv} \tag{2}\]  
with \(c\) being the viscous constant of soil in the residual steady condition. The shear strength, \(\tau\)(s,\(\
u\)), mobilised during the transition from the reactivation up to the residual steady condition, may be modelled with a softening law which takes into account both the cumulated displacement, s, and the reactivation speed, \(\
u\):  
\[\tau(s,\
u)=[\tau_{\text{reac}}-\tau_{\text{r}}(\
u)]e^{(-\beta s^{\delta})}+ \tau_{\text{r}}(\
u) \tag{3}\]  
with \(\beta\) and \(\delta\) being soil constants depending on both the vertical stress, \(\sigma_{\
u}\), and the time of ageing, \(t_{\text{agg}}\). Recalling the relationships (1) and (2), Equation (3) may be rewritten in terms of the viscous coefficients of soil:  
\[\tau(s,\
u)=(c_{\text{reac}}-c)\text{ve}^{(-\beta s^{\delta})}+\text{cv}+\tau_ {0} \tag{4}\]  
where the frictional strength component is provided by \(\tau_{0}\).