This contribution presents the results of numerical simulations in which a high-pier viaduct under lateral and vertical non-stationary spatially variable seismic ground motions is crossed by an articulated high-speed train at several speeds. The spectral representation method is employed to generate the required number of acceleration time-history series at each support location of the railway viaduct studied. Wave passage, local soil conditions and loss of coherency effects have been accounted for in the simulated ground-motion time histories, with several peak ground accelerations. Train and bridge responses have been obtained by means of a non-linear dynamic interaction multibody and finite element model. An analysis of train running safety indices has been carried out. The properties of earthquakes and train speeds which may cause problems to traffic safety are detailed, as is the train derailment probability. The numerical simulation outcomes show that it is not safe for the train to travel over the studied viaduct in earthquakes with peak ground acceleration equal to 0.03 g and for train speeds above 280 km/h.

This paper presents research work in which an innovative didactic proposal was designed for the study of 3D metric geometry in the second year of A-level courses (secondary education) in the specialty of the sciences. The designed didactic proposal has the format of a workshop of geometry practices and is framed in the Didactic Situations Theory and in the Anthropological Theory of the Didactic. Although the mentioned theories, which the French school has developed since the seventies, are widely known and studied by secondary school mathematics teachers during their training in pedagogy, especially in Spanish- and French-speaking countries, their innovative approach has not been fully implemented in the field of algebraic geometry. Mathematics textbooks follow the traditional approach in which the teacher simply provides the contents and instructs the student, who captures these concepts and reproduces them as they have been supplied. In the presented didactic proposal, the approach proposed by Brousseau is followed, in which three fundamental elements take part: student, teacher, and the didactic environment. The teacher is the one who facilitates the environment in which the student builds his knowledge. In the proposal the didactic contract is stablished, the didactic situations are designed, and the means and didactic variables for the study of 3D metric geometry are chosen. The methodology followed in this study consisted of identifying educational problems; describing the theoretical framework; developing the didactic proposal; and analysis, reflection, and criticism of this training product. The contextualization of the geometry workshop in the field of the construction of structures and the use of deductive reasoning techniques that are applied in synthetic geometry and also in the building information modeling (BIM) methodology may be a way of showing the use of analytical geometry in the industries of engineering and architecture; they also serve as an opportunity for students to better understand this mathematical work.