## 2 Materials and Methods
### Visco-Elastic Behavior  
The governing equations of the visco-elastic part are  
\[s =2\eta^{K}\varepsilon^{\text{\dot{K}}}_{s}+2G^{K}\varepsilon^{K} _{s}, \tag{2}\] \[\dot{p} =K^{M}\varepsilon^{\text{\dot{M}}}_{v},\] (3) \[\dot{\varepsilon}^{\text{\dot{M}}}_{s} =\frac{\dot{s}}{2G^{M}},\] (4) \[\dot{\varepsilon}^{\text{\dot{e}}x} =\dot{\varepsilon}^{K}_{s}+\dot{\varepsilon}^{M}_{s},\] (5) \[\varepsilon^{\text{\dot{e}}v} =\frac{\varepsilon^{M}_{v}}{3}I+\varepsilon^{\text{\dot{e}}v}_{ s}, \tag{6}\]  
where \(s\) and \(\varepsilon_{s}\) are, respectively, the deviatoric stress and strain tensor, and \(p\) and \(\varepsilon_{v}\) are, respectively, the spherical stress (scalar) and the volumetric strain (scalar). The parameters in the equations are the Kelvin viscosity \(\eta^{K}\) and shear modulus \(G^{K}\), as well as the Maxwell bulk and shear modulus: \(K^{M}\) and \(G^{M}\). The dot \((\ast)\) defines the derivative with respect to time. From the equation above, it is clear that the Maxwell viscosity is not considered and that the Kelvin module is relevant only for the deviatoric stress-strain relationship. Regarding the latter, by using (2), (4), and (5) together, after differentiating once with respect to time, the solution for \(\varepsilon^{\text{ve}}_{s}\) in the case of constant stress field \((\dot{s}=0)\) is found:  
\[\varepsilon^{\text{ve}}_{s}=\varepsilon^{M}_{s}+\varepsilon^{K}_{s}=\frac{s} {2}\Bigg{[}\frac{1}{G^{M}}+\frac{1}{G^{K}}\Bigg{(}1-e^{-\frac{G^{K}}{v^{K}}t} \Bigg{)}\Bigg{]}. \tag{7}\]  
From Equation (7), it holds that the Maxwell stiffness is linked to the instantaneous deviatoric strain, and the Kelvin stiffness is linked to the time-dependent strain, with the parameter \(\alpha_{c}=\frac{G^{K}}{\eta^{K}}\) controlling the rate of the creep. It has to be highlighted that \(\alpha_{c}\) can vary in a very wide range, because it depends on the factors that affect the breakage phenomenon (i.e., the failure at particle contacts) at the local scale (REV, Representative Elementary Volume) and at the dam scale (macro-scale). The first set of factors includes the gradation of rockfill, its water content, the segregation during the poring, and the compaction effectiveness. The second set comprises the magnitude of the stress with respect to the rock strength. Thus, it is clear that \(\alpha_{c}\) is not a property of the rockfill and should be assessed considering the conditions as close as possible to those in the field. Thisis the reason why, in general, the values from tests tend to differ from those obtained by physical scaled models or by back-analyses from constructed dams. Similarly, the final visco-elastic deviatoric strain due to the Kelvin module \(\varepsilon_{s,f}^{K}\) is dependent on the breakage phenomenon, so rather than calculate it as the ratio between the shear stress and the shear modulus like in (7), it seems more reasonable to link it to a measure of the stress-strength ratio:  
\[D=\frac{\left|\left(\sigma_{min}-\sigma_{max}\right)\right|}{\left|\left( \sigma_{min}-\sigma_{max}\right)_{y}\right|}, \tag{8}\]  
where \(\sigma_{min}\) and \(\sigma_{max}\) are, respectively, the minimum and the maximum principal stress (compressive stress is negative), the subscript \(y\) states the yielding, and the explicit expression of \(D\) depends on the choice of the yield surface. In the present case, the Mohr-Coulomb yield surface has been chosen, and the strength parameter is the friction angle, as rockfill can be considered to be a cohesionless material. As it will be discussed below, the friction angle is, in turn, dependent on (1) the uniaxial compressive strength of the rock, \(\sigma_{c}\); (2) the particle size with 50% passing--\(d_{50}\); (3) the degree of particle roundness--\(r_{i}\); and (4) the porosity after compaction \(n\)--which is dependent of the compaction energy and water content, as per the Proctor test [27; 28]. Thus, the friction angle and, in turn, \(D\) include all parameters that define the rockfill at the meso-scale and the stress field at the macro-scale.