Abstract:

In this note, it is proposed a joint initiative between the areas of Applied Mathematics and of Continuum Mechanics to reinforce the mathematical skills of the students, in such a way that a better understanding of both the engineering and mathematical concepts can be achieved. To this end we have integrated a lecture subject that combines the analysis of soil strain in a raw materials storing zone during the different phases of a civil engineering work with the basic ideas related with first order differential equations. The aim is two-fold: on the one hand, it allows the students focusing their attention in the development of the technological methods, without feeling overwhelmed by the mathematical arsenal employed.

On the other hand, it reinforces the basic explicit Mathematical curriculum of Civil Engineering that has as a fundamental part a proper knowledge of the topic of ordinary differential equations. It also develops the capability of the student of modelling a realistic, or quasi-realistic, problem. As it is pointed out by the European Society for Engineering Education (SEFI) “the ability to formulate a mathematical model of a given physical situation, to solve the model, interpret the solution and refine the model is a key aspect of the mathematical development of an engineer”.

The material corresponding to the lecture “Rheologic models application in Civil Engineering” is presented. This lecture can be tackled within the first two years of the degree. In particular, it is considered the instantaneous and delay strain in quasi-static loading system for a determined period of execution of the works (2 years). To model this situation, the instantaneous strain is represented by a spring whereas the delay strain is a combined system of spring and dashpot (viscoelastic model) both in a serial mode. We will consider two different kinds of soil: clay and gravel, analyzing the distinct responses along the time accordingly with the different types of charges. From a mathematical point of view, that is translated into the establishment of a first order differential equation, whose solution allows determining the movement of the soil, including the negative effects during the distinct phases of the work. In this way, the student can analyze the behaviour of the soil, understanding the relationship between the model and the real case (rheology). Finally, an analysis of the possible benefits of carrying out these kinds of methods in the learning process of the future engineer will be performed, discussing some recommendations in order to improve the integration between the Engineering and Mathematics approaches

Keywords:

experiences in education, transferring disciplines, civil engineering, mathematics.