## 4 MP Modeling by Experimental and Numerical Methods
The importance of this study is that as many parameters were considered in the numerical analysis, parameters which directly concern the soil and affect CM inputs. Soil nonlinearity, plasticity, and soil internal friction angle were all considered. The behavior that was found is in accordance with what was discussed before and the usual behavior of other types of piles [11]. [PERSON] et al. [36; 37] performed a numerical study on the performance of MPed rafts in sand and clay; the study was calibrated with a centrifuge test. The CM used in the analysis was MC, linear elastic perfectly plastic, with interface elements to model the interaction between MPs and the soil; the interface elements also adopted MC criterion, and according to paper's authors, the results of the numerical analysis showed good agreement when they had been calibrated with the centrifuge test results [36; 37]. [PERSON] et al. [38] performed a numerical study validated and calibrated with a model test device. The aim of the study was to investigate the effectiveness of several installation methods of MPs that can affect the bearing capacity by modifying the failure mechanism. Several installation methods were tested, inclination angles or lengths of MPs, and the failure mechanism was monitored for each case, both in the numerical study and for the model test device [38]. The numerical analysis was able to replicate the failure mechanism and the changes occurred when modifying the installation method. The soils used in the study were medium dense sand and clayey silt, for which the MC failure criterion was used. According to the authors, the results showed agreement with classical soil mechanics, as general shear failure occurred in the sandy soil (Figure 17), while punching shear occurred in the clayey silt (Figure 18) and the modifications in the failure mechanism were based on these two concepts. Not only the ability of the numerical model to accurately simulate the failure mechanism is interesting, but also the ability to model the confinement effect, which has a large influence on the seismic performance of MPs and the superstructure, since the size, depth, and location of soil which is contributing to the failure mechanism can affect the soil stiffness, which in turn can affect the seismic performance [38]. More examples of experimental methods can be found in the works of [PERSON] et al. [39], [PERSON] et al. [40], and [PERSON] et al. [41]. [PERSON] et al. [39] performed field tests on full scale MPs of type E (self-drilling); the aim of the study was to evaluate the bond strength of grouting/ground; the outcome of the study showed that the value usually taken from FHWA [1] is less than the actual value of the bond strength that can be developed. From the numerical analysis point of view, the test results showed the importance of performing a nonlinear analysis when analyzing MPs that are excited by cyclic loads, as head movement can accumulate, and the existing possibility of a gap creation between the MP and the surrounding soil. These are well-known phenomena with other types of piles, but there is no coherent study as in the case of other types of piles. The outcome of such a study can be important for the inertial interaction. [PERSON] et al. [40] studied the load sharing between the existing piles and newly installed MPs through a model test; two types of MPs were studied, a waveform MP (WF), which is a new type of MP, and a conventional MP (type A). The outcome showed that the waveform MPs are always contributing more to the load sharing as a percentage vs. the conventional MPs used in the experiment; according to the authors this is due to the fact that the waveform MPs have a higher stiffness than the conventional MPs used. This is true for the MPs used in this particular test, but other type of MPs can potentially have a higher stiffness due to the grouting technology. [PERSON] et al. [41] performed a model test and a numerical study on the load capacity of MPs embedded in rocks.