In this paper, we investigate the response of a cavity embedded in an elastic half-plane (2D) subjected to a harmonic SH wave. In previous work, the method of conformal mapping and the indirect boundary element method (indirect BEM) were employed to solve the 3D wave scattering from a cylindrical tunnel embedded in a half-space. Inaccurate results were obtained particularly at high frequencies (method of conformal mapping). Therefore, in this study we focus on a comparison of the two methods with the method of images, which serves as a benchmark solution. Through a systematic evaluation, we confirm that the two methods accurately work within the complete considered ranges of the dimensionless frequency and the embedded cavity depth. This suggests that representing the waves scattered from the free surface by cylindrical waves in the method of conformal mapping is the cause of the inaccuracies at high frequency in the 3D problem; the cylindrical waves are probably not able to fully capture all wave conversions taking place at the free surface. The presented results reveal significant effects of the system parameters on the responses. The system's response curves display nearly equally spaced resonances, which is in line with those of the 1D shear layer subject to bedrock motion, while similar response curves for the 3D case do not have this feature.

The study of periodic systems under the action of moving loads is of high practical importance in railway, road, and bridge engineering, among others. Even though plenty of studies focus on periodic systems, few of them are dedicated to the influence of a local inhomogeneous region, a so-called transition zone, on the dynamic response. In railway engineering, these transition zones are prone to significant degradation, leading to more maintenance requirements than the rest of the structure. This study aims to identify and investigate phenomena that arise due to the combination of periodicity and local inhomogeneity in a system acted upon by a moving load. To study such phenomena in their purest form, a one-dimensional model is formulated consisting of a constant moving load acting on an infinite string periodically supported by discrete springs and dashpots, with a finite domain in which the stiffness and damping of the supports is larger than for the rest of the infinite domain; this model is representative of a catenary system (overhead wires in railway tracks). The identified phenomena can be considered as additional constraints for the design parameters at transition zones such that dynamic amplifications are avoided.

This article presents a set of close approximations to model an elastic half-space supporting an embankment, which are evaluated in the context of phase velocity spectra, i.e. in terms of the normal wave propagation modes of the embankment-half-space system. The ultimate, intended target of these approximations is in the modeling of vertically-acting loads that may travel over the embankment with some prescribed, constant longitudinal speed. The proposed approximations are analogous to the well-known paraxial approximations that closely mimic a half-space terminating at a plane boundary, but differ from these in that the approximations herein aim at properly modeling not the waves with near normal incidence to the half-space, but waves which propagate at shallow, grazing angles along the longitudinal direction of load motion. Thus, these can be referred to as paralongitudinal approximations. The resulting expressions allow for a very effective simulation of the system at hand for loads moving with subcritical speed and solved in the context of a 2.5D solution method. Such 2.5D formulation considers a continuous model in the longitudinal direction and a discrete model in transverse planes.

This paper investigates the instability of vertical vibrations of an object moving uniformly through a tunnel embedded in soft soil. Using the indirect Boundary Element Method in the frequency domain, the equivalent dynamic stiffness of the tunnel-soil system at the point of contact with the moving object, modelled as a mass-spring system or as the limiting case of a single mass, is computed numerically. Using the equivalent stiffness, the original 2.5D model is reduced to an equivalent discrete model, whose parameters depend on the vibration frequency and the object's velocity. The critical velocity beyond which the instability of the object vibration may occur is found, and it is the same for both the oscillator and the single mass. This critical velocity turns out to be much larger than the operational velocity of high-speed trains and ultra-high-speed transportation vehicles. This means that the model adopted in this paper does not predict the vibrations of Maglev and Hyperloop vehicles to become unstable. Furthermore, the critical velocity for resonance of the system is found to be slightly smaller than the velocity of Rayleigh waves, which is very similar to that for the model of a half-space with a regular track placed on top (with damping). However, for that model, the critical velocity for instability is only slightly larger than the critical velocity for resonance (of the undamped system), while for the current model the critical velocity for instability is much larger than the critical velocity for resonance due to the large stiffness of the tunnel and the radiation damping of the waves excited in the tunnel. A parametric study shows that the thickness and material damping ratio of the tunnel, the stiffness of the soil and the burial depth have a stabilising effect, while the damping of the soil may have a slightly destabilising effect (i.e., lower critical velocity for instability). In order to investigate the instability of the moving object for velocities larger than the identified critical velocity for instability, we employ the D-decomposition method and find instability domains in the space of system parameters. In addition, the dependency of the critical mass and stiffness on the velocity is found. We conclude that the higher the velocity, the smaller the mass of the object should be to ensure stability (single mass case); moreover, the higher the velocity, the larger the stiffness of the spring should be when a spring is added (oscillator case). Finally, in view of the stability assessment of Maglev and Hyperloop vehicles, the approach presented in this paper can be applied to more advanced models with more points of contact between the moving object and the tunnel, which resembles reality even better.

Transition zones in railway tracks are locations with a significant variation of track properties (i.e. foundation stiffness) encountered near structures such as bridges and tunnels. Due to strong amplification of the track’s response, transition zones are prone to rapid degradation. To investigate the degradation mechanisms in transition zones, researchers have developed a multitude of models, some of them being very complex. This study compares three solution methods, namely an integral-transform method, a time-domain method, and a hybrid method, with the goal of solving these systems efficiently. The methods are compared in terms of accuracy, computational efficiency, and feasibility of application to more complex systems. The model employed in this paper consists of an infinite, inhomogeneous, and piecewise-linear 1-D structure subjected to a moving constant load. Although the 1-D model is not particularly demanding computationally, it is used to make qualitative observations as to which method is most suitable for the 2-D and 3-D models, which could lead to significant gains. Results show that all three methods can reach similar accuracy levels, and in doing so, the time-domain method is most computationally efficient. The integral-transform method appears to be efficient in dealing with frequency-dependent parameters, while the time-domain and hybrid methods are efficient in dealing with a smooth nonlinearity. For multi-dimensional models, if nonlinearities and inhomogeneities are considered throughout the depth, the time-domain method is likely to be most efficient; however, if nonlinearities and inhomogeneities are limited to the surface layers, the integral-transform and hybrid methods have the potential to be more efficient than the time-domain one. Finally, although the 1-D model presented in this study is mainly used to assess the three methods, it can also be used for preliminary designs of transition zones in railway tracks.

We introduce the open-source package MercuryDPM, which we have been developing over the last few years. MercuryDPM is a code for discrete particle simulations. It simulates the motion of particles by applying forces and torques that stem either from external body forces, (gravity, magnetic fields, etc.) or particle interactions. The code has been developed extensively for granular applications, and in this case these are typically (elastic, plastic, viscous, frictional) contact forces or (adhesive) short-range forces. However, it could be adapted to include long-range (molecular, self-gravity) interactions as well. MercuryDPM is an object-oriented algorithm with an easy-to-use user interface and a flexible core, allowing developers to quickly add new features. It is parallelised using MPI and released under the BSD 3-clause licence. Its open-source developers’ community has developed many features, including moving and curved walls; state-of-the-art granular contact models; specialised classes for common geometries; non-spherical particles; general interfaces; restarting; visualisation; a large self-test suite; extensive documentation; and numerous tutorials and demos. In addition, MercuryDPM has three major components that were originally invented and developed by its team: an advanced contact detection method, which allows for the first time large simulations with wide size distributions; curved (non-triangulated) walls; and multicomponent, spatial and temporal coarse-graining, a novel way to extract continuum fields from discrete particle systems. We illustrate these tools and a selection of other MercuryDPM features via various applications, including size-driven segregation down inclined planes, rotating drums, and dosing silos. Program summary: Program Title: MercuryDPM Program Files doi: http://dx.doi.org/10.17632/n7jmdrdc52.1 Licensing provisions: BSD 3-Clause Programming language: C++, Fortran Supplementary material: http://mercurydpm.org Nature of problem: Simulation of granular materials, i.e. conglomerations of discrete, macroscopic particles. The interaction between individual grains is characterised by a loss of energy, making the behaviour of granular materials distinct from atomistic materials, i.e. solids, liquids and gases. Solution method: MercuryDPM (Thornton et al., 2013, 2019; Weinhart et al., 2016, 2017, 2019) is an implementation of the Discrete Particle Method (DPM), also known as the Discrete Element Method (DEM) (Cundall and Strack, 1979). It simulates the motion of individual particles by applying forces and torques that stem either from external forces (gravity, magnetic fields, etc.) or from particle-pair and particle–wall interactions (typically elastic, plastic, dissipative, frictional, and adhesive contact forces). DPM simulations have been successfully used to understand the many unique granular phenomena – sudden phase transitions, jamming, force localisation, etc. – that cannot be explained without considering the granular microstructure. Unusual features: MercuryDPM was designed ab initio with the aim of allowing the simulation of realistic geometries and materials found in industrial and geotechnical applications. It thus contains several bespoke features invented by the MercuryDPM team: (i) a neighbourhood detection algorithm (Krijgsman et al., 2014) that can efficiently simulate highly polydisperse packings, which are common in industry; (ii) curved walls (Weinhart et al., 2016) making it possible to model real industrial geometries exactly, without triangulation errors; and (iii) MercuryCG (Weinhart et al., 2012, 2013, 2016; Tunuguntla et al., 2016), a state-of-the-art analysis tool that extracts local continuum fields, providing accurate analytical/rheological information often not available from experiments or pilot plants. It further contains a large range of contact models to simulate complex interactions such as elasto-plastic deformation (Luding, 2008), sintering (Fuchs et al., 2017), melting (Weinhart et al., 2019), breaking, wet and dry cohesion (Roy et al., 2016, 2017), and liquid migration (Roy et al., 2018), all of which have important industrial applications.

In this work we propose a model for the analysis of the dynamic behaviour of a ballasted track that combines discrete and continuous elements. The rail is modelled via an Euler-Bernoulli beam, the periodically spaced sleepers are represented with lumped masses, and the ballast is simulated using a lattice (regular network of elastically connected lumped masses). All elements are assumed to behave linearly, and the lattice can be supported by a flexible or a rigid foundation, simulating soil or a hard rock. The equations of motion of each component are presented and the coupled system is solved semi-analytically in the frequency domain. The time domain response can be calculated afterwards by means of a numerical inverse Fourier transform. Dispersion curves and time responses are produced for the case of a ballasted track on a stiff soil. These responses are compared with the scenario in which ballast is modelled as lumped supports, and the scenario in which the force is applied directly to the ballast (no superstructure). It is observed that the simpler models fail to capture the vibration modes in which energy is concentrated in the ballast, and that the superstructure significantly alters the response of the track, increasing its critical velocity and changing the deformed shape of the ballast. The model herein proposed can be used to assess the dynamic characteristics of the track (critical speeds, energy propagation, vehicle-track interaction, etc.) and will serve as framework for a development of a tool for assessment of the settlement behaviour of ballast.

A method is presented to accurately capture the 3D interaction phenomena of a foundation pile embedded in soil, in a computationally efficient non-local 1D model. It is shown how to extract the global stiffness kernels from simulations with the 3D inhomogeneous continuum, and implement them in a 1D non-local Winkler-type model that can subsequently serve as a stand-alone, condensed substructure. The presented method for obtaining the kernels removes the need to assume certain distributions for these functions. We show that the method is very versatile, and yields accurate results for a wide range of pile geometries and soil stiffness profiles, over the full depth of the embedded pile. For the dynamic case, the discretized global stiffness kernels (matrices) become complex-valued (they include soil stiffness, inertia and damping), and the 1D model proves to be capable of mimicking also the out-of-phase part of the response. The method being straightforward and fast, the engineering community is served the benefits of accuracy (3D model) and speed (1D model), without the need of empiric tuning.

In this paper the effect of a nearby, semi-infinite, level ice sheet on the frequency domain response of a thin, floating, rigid body is studied using a 2D model. The ice is modeled using a dynamic Euler-Bernoulli beam and the finite depth water layer is described with the Laplace equation and the linearized Bernoulli equation. Eigenfunction matching is used to resolve the interface between the ice covered and open water regions. The body is excited by external loads, generating waves. The waves are partially reflected by the ice edge and these reflected waves influence the body's response. It is this influence that this paper focuses on. Below a certain onset frequency the amplitude of the reflected waves is insignificant and consequently the body remains unaffected by the ice. This frequency is only sensitive to the ice thickness with thinner ice resulting in a higher onset frequency. Above the onset frequency the reflected waves cause quasi-standing waves between body and ice. For frequencies at which half the wavelength of the surface wave in the water is approximately an integer multiple of the gap length, the amplitude of the standing waves is greatly amplified. This can result in (anti-)resonance depending on the phasing between the reflected waves and the body's motion.