Fully Dynamic Earthquake Cycle Simulations on a Nonplanar Fault Using the Spectral Boundary Integral Element Method (sBIEM)

ABSTRACT One of the most suitable methods for modeling fully dynamic earthquake cycle simulations is the spectral boundary integral element method (sBIEM), which takes advantage of the fast Fourier transform (FFT) to make a complex numerical dynamic rupture tractable. However, this method has the serious drawback of requiring a flat fault geometry due to the FFT approach. Here, we present an analytical formulation that extends the sBIEM to a mildly nonplanar fault. We start from a regularized boundary element method and apply a small-slope approximation of the fault geometry. Making this assumption, it is possible to show that the main effect of nonplanar fault geometry is to change the normal traction along the fault, which is controlled by the local curvature along the fault. We then convert this space–time boundary integral equation of the normal traction into a spectral-time formulation and incorporate this change in normal traction into the existing sBIEM methodology. This approach allows us to model fully dynamic seismic cycle simulations on nonplanar faults in a particularly efficient way. We then test this method against a regular BIEM for both rough-fault and seamount-fault geometries and demonstrate that this sBIEM maintains the scaling between the fault geometry and slip distribution.

An axisymmetric problem for a penny-shaped crack under the influence of the Steigmann–Ogden surface energy

A problem for a nanosized penny-shaped fracture in an infinite homogeneous isotropic elastic medium is considered. The fracture is opened by applying an axisymmetric normal traction to its surface. The surface energy in the Steigmann–Ogden form is acting on the boundary of the fracture. The problem is solved by using the Boussinesq potentials represented by the Hankel transforms of certain unknown functions. With the help of these functions, the problem can be reduced to a system of two singular integro-differential equations. The numerical solution to this system can be obtained by expanding the unknown functions into the Fourier–Bessel series. Then the approximations of the unknown functions can be obtained by solving a system of linear algebraic equations. Accuracy of the numerical procedure is studied. Various numerical examples for different values of the surface energy parameters are considered. Parametric studies of the dependence of the solutions on the mechanical and the geometric parameters of the system are undertaken. It is shown that the surface parameters have a significant influence on the behaviour of the material system. In particular, the presence of surface energy leads to the size-dependency of the solutions and smoother behaviour of the solutions near the tip of the crack.

Molecular Dynamics-Based Cohesive Zone Model for Mg/Mg17Al12 Interface

The fracture of the Mg/Mg17Al12 interface was investigated by molecular dynamics simulations. The interface crack extends in a brittle manner without noticeable plasticity. The distributions of normal stress and separation along the interface were examined to render a quantitative picture of the fracture process. A normal traction–separation curve was extracted from simulation and compared with three cohesive zone models, i.e., cubic polynomial cohesive zone model, exponential cohesive zone model, and bilinear cohesive zone model. The exponential cohesive zone model exhibits the best agreement with simulation results, followed by the bilinear cohesive zone model.

Nonlinear Rheology at Shallow Depths with Reference to the 2016 Kumamoto Earthquakes

Strong S waves produce dynamic stresses, which bring the shallow subsurface into nonlinear inelastic failure. We examine implications of nonlinear viscous flow, which may be appropriate for shallow muddy soil, and contrast them with those of Coulomb friction within a shallow reverberating uppermost layer with low‐seismic velocities. Waves refract into essentially vertical paths at the shallow layers and produce tractions on horizontal planes. The Coulomb ratio of shear traction to lithostatic stress for S waves equals the resolved horizontal acceleration normalized to the acceleration of gravity. The ratio of dynamic vertical normal traction to lithostatic stresses is the vertical normalized acceleration from P waves. The predicted viscous inelastic strain rate in muddy soil begins at low normalized accelerations and then increases mildly and nonlinearly with increasing normalized acceleration. Failure is unaffected when P waves decrease the vertical normal traction. Seismic waves recorded at KiK‐net station KMMH16 for the 2016 Kumamoto mainshock and strong foreshock show these effects. Inelastic deformation commences at a normalized horizontal acceleration of ∼0.25 and reduces S‐ and P‐wave velocities within the uppermost ∼15 m reverberating layer. Normalized horizontal accelerations and the Coulomb stress ratio reach ∼1.25. Strong S waves arrived even when strong P waves produced vertical tension on horizontal planes. In contrast, inelastic Coulomb failure commences at a normalized horizontal acceleration equal to the effective coefficient of friction; rapid inelastic strain precludes even higher accelerations. Furthermore, horizontal planes should fail from the stresses of strong S waves during the tensional cycle of strong P waves.

A double-Hertz model for adhesive contact between cylinders under inclined forces

A generalized double-Hertz (D-H) model has been proposed to consider the adhesive contact between an elastic cylinder and an elastic half space under inclined forces. The normal traction is exactly the same as that in the conventional D-H model. The shear traction of finite value is distributed into a slipping zone and a non-slipping zone. In the slipping zone, the shear traction is proportional to the compressive pressure. With the model, adhesive contact behaviour between cylinders has been numerically illustrated. The shear-induced peeling has been demonstrated. The value of the ratio for shear traction to normal traction larger than friction coefficient has been found in part of the non-slipping zone. Those altogether are consistent with experiments.

Field Investigations on Rolling Stock Components Designed to Overcome Low Adhesion Related Problems

The tangential force that a braking or tractive wheel can exert on a rail is limited by the friction coefficient available at the surfaces in contact for a given normal load. In clean steel-on-steel contacts the friction coefficient is known to be higher than the adhesion requirements of the majority of the existent rolling stock. However, in the presence of contamination (e.g. leaves, water, grease, and rust) the friction level can decrease to values far below those required in normal traction and braking operations. In particular, fallen leaves have been identified by many railways to cause considerable low adhesion problems in autumn. Despite the available countermeasures the adhesion problems still seem to persist in the majority of the affected networks. This could to a large extent be due to the lack of fundamental understanding on the effectiveness of the countermeasures used under different operating conditions. In this paper, the effectiveness of two rolling stock components, namely locomotive sanders and permanent magnetic track brakes, in leaf contaminated contacts is investigated by means of full-scale tests in a stabling yard. An electrical locomotive has been used to asses the performance of the sanders, whereas the tests with permanent magnetic track brakes have been carried out with an electrical multiple unit.

Slip event propagation direction in transition region of low surface slope

The base of the ice in the transition zone between an ice stream and an ice shelf is likely to be well lubricated by broadly distributed water, a condition which should permit fast sliding motion. It has been observed that motion takes place not smoothly but by localized stick–slip events that propagate in the downstream direction towards the ice shelf and at velocities approximately that expected for shear wave velocity of the basal till. Thus slip packets of gliding edge dislocations are likely to move at the base. I show here that subsonic dislocations should move upstream, rather than downstream, if frictional resistance is determined by normal traction stress change at the base. Transonic dislocations are expected to move in the downstream direction. However, if frictional resistance is lowered by hydrostatic pressure reduction at the base, the subsonic dislocation should move downstream.