## 3 Seismic Behavior of Micropiles
### Behavior of MPs in Association with Seismic Dampers  
As MPs are commonly used for retrofitting existing buildings, an enhancement of the seismic resilience can be obtained by associating MPs with seismic dampers. In this paragraph we are not treating the seismic damper aspects but the association MPs-seismic dampers, which is a quite new subject not fully treated in the literature. We further expand the discussion into the field of damping and seismic dampers, as damping in any structure is a combination of intrinsic, aerodynamic, hysteretic, and supplementary damping. Supplementary damping can be obtained by adding damping devices; these devices can help enhance the seismic response by increasing the damping value, decoupling the superstructure from the seismic motion, or combination of both ways [8; 22; 23; 24]. Related to this and returning to the introduction, two questions can arise. The first question is the ability of MPs to behave in a way that enhances the seismic behavior similar with the seismic dampers, meaning increasing the damping value (inertial interaction) and the effect on the kinematic interaction. It is expected that when using MPs, the stiffness of the system increases [6], but also the incoherence, as MP technology induce modifications to the surrounding soil, firstly during the drilling process, which is a symmetrical modification,and secondly due to the grouting process, which can be a simple (under gravity) or complicated process with asymmetrical modifications (in the two horizontal directions) and in terms of the vertical grouting profile. Thus, it is very interesting to study wave transformation and the coupling/decoupling of the applied forces with the system due to MPs. This can be done with the same procedure as for other types of piles, as in the work of [PERSON] et al. [25], who performed numerical analysis validated by shaking table tests; or analytically, as the in the work of [PERSON] et al. [26] who used an analytical solution to calculate the response of a structure (Q) as a function of several parameters, e.g., kinematic interaction factors and impedance functions. The same concept can be used for MPs, after investigating how these parameters can be suitable for each type of MP; for example, the impedance function that allows for soil stiffness and damping coefficient can be expanded to be \"unaffected\" by soil stiffness and damping coefficient, which are added to the \"affected\" by soil stiffness and damping coefficient due to MPs, and eventually the final matrix can be formed. \[K_{ij}=k_{ij}+ia_{\theta}c_{ij} \tag{1}\]  
\[K_{ij}=(k_{ij,us}+k_{ij,as})+ia_{\theta}(c_{ij,as}+c_{ij,as}) \tag{2}\]  
Equation (1) is the impedance function as presented in [26], with \(k_{ij}\) the soil stiffness and \(c_{ij}\) the soil damping coefficient. In Equation (2), \(k_{ij,as}\) and \(k_{ij,as}\) are the unaffected and affected soil stiffness values, respectively, while \(c_{ij,as}\) and \(c_{ij,as}\) are the unaffected and affected soil damping coefficients, respectively, as proposed; these values can be obtained from numerical models or by analytical equations. The second question is whether it is beneficial to combine seismic dampers with MPs; this combination might help in increasing the damping value, as not all damping devices increase the damping value sufficiently, as many of them mainly decouple the superstructure from the input motion [27]. Thus, adding MPs might combine these two enhancements in the behavior. Development and research on base isolator technologies to increase the damping value is an ongoing process and a subject of a great interest, with numerical studies being developed, for example, as for LRB (lead rubber bearing) and RRB (rubber bearing with steel rings) [28]. There are many other innovations for enhancing the performance of base isolators. [PERSON] et al. [29] studied the effect of increasing the number of the lead cores, and the effect of changing the shape of the base isolators; instead of circular, rectangular shapes were studied numerically.