Application of a SPH depth-integrated model to landslide run-out analysis

Hazard and risk assessment of landslides with potentially long run-out is becoming more and more important. Numerical tools exploiting different constitutive models, initial data and numerical solution techniques are important for making the expert’s assessment more objective, even though they cannot substitute for the expert’s understanding of the site-specific conditions and the involved processes. This paper presents a depth-integrated model accounting for pore water pressure dissipation and applications both to real events and problems for which analytical solutions exist. The main ingredients are: (i) The mathematical model, which includes pore pressure dissipation as an additional equation. This makes possible to model flowslide problems with a high mobility at the beginning, the landslide mass coming to rest once pore water pressures dissipate. (ii) The rheological models describing basal friction: Bingham, frictional, Voellmy and cohesive-frictional viscous models. (iii) We have implemented simple erosion laws, providing a comparison between the approaches of Egashira, Hungr and Blanc. (iv) We propose a Lagrangian SPH model to discretize the equations, including pore water pressure information associated to the moving SPH nodes

Online games for the teaching of mathematics

In this article we present a didactic experience developed by the GIE (Group of Educational Innovation) “Pensamiento Matemático” of the Polytechnics University of Madrid (UPM), in order to bring secondary students and university students closer to Mathematics. It deals with the development of a virtual board game called Mate-trivial. The mechanics of the game is to win points by going around the board which consists of four types of squares identified by colours: “Statistics and Probability”, “Calculus and Analysis”, “Algebra and Geometry” and “Arithmetic and Number Theory ”. When landing on a square, a question of its category is set out: a correct answer wins 200 points, if wrong it loses 100 points, and not answering causes no effect on the points, but all the same, two minutes out of the 20 minutes that each game lasts are lost. For the game to be over it is necessary, before those 20 minutes run out, to reach the central square and succeed in the final task: four chained questions, one of each type, which must be all answered correctly. It is possible to choose between two levels to play: Level 1, for pre-university students and Level 2 for university students. A prototype of the game is available at the website “Aula de Pensamiento Matemático” developed by the GIE: http://innovacioneducativa.upm.es/pensamientomatematico/. This activity lies within a set of didactic actions which the GIE is developing in the framework of the project “Collaborative Strategies between University and Secondary School Education for the teaching and learning of Mathematics: An Application to solve problems while playing”, a transversal project financed by the UPM.

Stability Analysis of a Run-of-River Diversion Hydropower Plant With Surge Tank And Spillway in the Head Pond

Run-of-river hydropower plants usually lack significant storage capacity; therefore, the more adequate control strategy would consist of keeping a constant water level at the intake pond in order to harness the maximum amount of energy from the river flow or to reduce the surface flooded in the head pond. In this paper, a standard PI control system of a run-of-river diversion hydropower plant with surge tank and a spillway in the head pond that evacuates part of the river flow plant is studied. A stability analysis based on the Routh-Hurwitz criterion is carried out and a practical criterion for tuning the gains of the PI controller is proposed. Conclusions about the head pond and surge tank areas are drawn from the stability analysis. Finally, this criterion is applied to a real hydropower plant in design state; the importance of considering the spillway dimensions and turbine characteristic curves for adequate tuning of the controller gains is highlighted