The maintenance and repairs of transition zones pose significant challenges in the railways industry due to their accelerated degradation rates in comparison to free tracks. These zones, characterized by track property variations, amplify their response when a source travels along the tracks. The resulting amplifications in stress and strain fields lead to differential settlements, affecting both track's stability and passenger comfort. This study investigates the influence of incorporating active control forces and moments at the interface of transition zones to mitigate the excessive degradation of soft domains.

Three 1-dimensional models are developed, which include active control forces and moments as a novel method to minimize the amplification of the response in the soft domain of transition zones, as well as, the derivation of these forces. The purpose of these three models is to give the reader an inside view of the method to derive these active control forces with models that increase in complexity.

The first model involves an Euler-Bernoulli beam resting on a piece-wise inhomogeneous Winkler foundation. The second model extends this by including a shear beam and a second layer of foundation, with the first layer being homogeneous and the second layer piece-wise inhomogeneous (Kerr foundation). The third model is a hybrid model between the first two, on which the soft domain is represented by the description of the second model, and the rigid domain by the description of the first model. Numerical solutions in the time-domain were applied to these models, and the study focused on a transition zone subjected to a constant amplitude moving load with constant velocity, traveling from a soft to stiff domain. The purpose of the first model is to give the reader a general idea on the derivation of a very simplistic model. The second model's purpose is to better represent the different elements of a railway structure, on which the shear beam and the lower layer of springs represent the mobilised soil under the tracks, while the top layer of springs and the Euler-Bernoulli beam represent the ballast, the sleepers and the rail. Finally, the third model was made to represent a transition zones, on which the soil is discontinued due to a man-made structure, e.g. a concrete bridge, which leads the structure under the ballast, in the rigid domain, to be consider infinitely stiff and to be represented just by an Euler-Bernoulli beam on a Winkler foundation.

Findings reveal that the active control forces and moments are capable of fully mitigating the dynamic amplification in soft domains of transition zones, however, they increase the dynamic amplifications in the stiff domain. Moreover, the shape that these forces take over time is dictated by the interaction between both domains of the transition zone, when the interface of the transition zone has continuous elements, the forces take a similar shape to the eigenfield of the system, while when there is discontinuous elements over the interface, the forces take a 'flipping' shape. Furthermore, of the two parameters studied (velocity of the moving load and vertical stiffness), the dominating parameter in the response of the system depends upon the regime that the system is being subjected to. For relatively low and extremely high velocities of the moving load, the system is dominated by the vertical stiffness ratio, while for medium velocities of the moving load, the system is dominated by the velocity of the moving load. Finally, transition zones with discontinuous elements require significantly more energy to be absorbed and added into the system by the active control forces to mitigate the dynamic amplifications in the soft domain of the system.

These thesis offer valuable insights for preliminary designs of active control forces aimed at diminishing the dynamic amplification of soft domains of transition zones railway.