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Segmental tunnels cannot be considered as continuous rings due to the existence of joints. The mechanical behaviour of the segment joints is defined by the axial load in the joint. However, this load is not constant throughout the analysis, so it is necessary to make a series of iterations. A practical moment–rotation equation to represent the mechanical behaviour of typical planar joints without steel bolts is proposed. The advantage of the constitutive equation proposed in this paper is that the need for iteration is taken away because the eccentricity of the axial load remains constant during the loading process. This equation depends on the geometry of the joint, the elastic properties of the concrete and the eccentricity of the axial load in the joint. The equation was validated by means of (lab-based) experimental research on planar joints and was used in numerical models of single rings based on the finite-element method. It was concluded that this equation represents the mechanical behaviour of this type of joints correctly and, therefore, can be used to analyse single rings for segmental tunnels, reducing the computational effort spent in three-dimensional models. [ABSTRACT FROM AUTHOR]

Numerical estimation of Lyapunov exponents in non-linear dynamical systems results in a very high computational cost. This is due to the large-scale computational cost of several Runge-Kutta problems that need to be calculated. In this work we introduce a parallel implementation based on MPI (Message Passing Interface) for the calculation of the Lyapunov exponents for a multidimensional dynamical system, considering a weakly coupled algorithm. Since we work on an academic high-latency cluster interconnected with a gigabit switch, the design has to be oriented to reduce the number of messages required. With the design introduced in this work, the computing time is drastically reduced, and the obtained performance leads to close to optimal speed-up ratios. The implemented parallelisation allows us to carry out many experiments for the calculation of several Lyapunov exponents with a low-cost cluster. The numerical experiments showed a high scalability, which we showed with up to 68 cores.e [ABSTRACT FROM AUTHOR]