Coupled Simulation of Seismic Wave Propagation and Failure Phenomena by Use of an MPS Method

The failure of brittle materials, for example glasses and rock masses, is commonly observed to be discontinuous. It is, however, difficult to simulate these phenomena by use of conventional numerical simulation methods, for example the finite difference method or the finite element method, because of the presence of computational grids or elements artificially introduced before the simulation. It is, therefore, important for research on such discontinuous failures in science and engineering to analyze the phenomena seamlessly. This study deals with the coupled simulation of elastic wave propagation and failure phenomena by use of a moving particle semi-implicit (MPS) method. It is simple to model the objects of analysis because no grid or lattice structure is necessary. In addition, lack of a grid or lattice structure makes it simple to simulate large deformations and failure phenomena at the same time. We first compare analytical and MPS solutions by use of Lamb’s problem with different offset distances, material properties, and source frequencies. Our results show that analytical and numerical seismograms are in good agreement with each other for 20 particles in a minimum wavelength. Finally, we focus our attention on the Hopkinson effect as an example of failure induced by elastic wave propagation. In the application of the MPS, the algorithm is basically the same as in the previous calculation except for the introduction of a failure criterion. The failure criterion applied in this study is that particle connectivity must be disconnected when the distance between the particles exceeds a failure threshold. We applied the developed algorithm to a suspended specimen that was modeled as a long bar consisting of thousands of particles. A compressional wave in the bar is generated by an abrupt pressure change on one edge. The compressional wave propagates along the interior of the specimen and is visualized clearly. At the other end of the bar, the spalling of the bar is reproduced numerically, and a broken piece of the bar is formed and falls away from the main body of the bar. Consequently, these results show that the MPS method effectively reproduces wave propagation and failure phenomena at the same time.     

Galerkin boundary integral equation method for spontaneous rupture propagation problems: SH-case

We develop a Galerkin finite element boundary integral equation method (GaBIEM) for spontaneous rupture propagation problems for a planar fault embedded in a homogeneous full 2-D space. A 2-D antiplane rupture propagation problem, with a slip-weakening friction law, is simulated by the GaBIEM. This method allows one to eliminate the strong singularities from the integral representation of the traction, and to separate explicitly the expression for the traction into an instantaneous component; static and time-dependent components with weakly (logarithmic) singular kernels; and a dynamic component and a quasi-static component, with continuous, bounded, kernels. Simulated results throw light into the performance of the GaBIEM and highlight differences with respect to that of the traditional, collocation, boundary integral equation method (BIEM). Both methods converge with a power law with respect to grid size, with different exponents. There is no restriction on the CFL stability number for the GaBIEM since an implicit, unconditionally stable method is used for the time integration. The error of the approximation increases with the time step, as expected, and it can remain below that of the BIEM.     

Distribution of boulders at Miyara Bay of Ishigaki Island,Japan: A flow characteristic indicator of tsunami and storm waves

This study investigates the distribution of boulders at Miyara Bay of Ishigaki Island, Japan. These boulders were deposited on a reef flat extending approximately 400–1300 m in width. Most boulders were rectangular to ellipsoidal, without sharp broken edges. They are reef and coral rock fragments estimated as <335 m³ (<633 t). Locally in the bay, the relationship between the boulder weight and position shows that boulders of a given weight have a clear limit on seaward distribution on the reef flat. For example, more than 1, 10, and 100 tons of boulders were deposited, respectively, more than 500, 300, and 100 m from the reef edge. The line is consistent with the possible landward transport limit by maximum storm waves at the Ryukyu Islands, suggesting that the line was formed by the reworking of some boulders by maximally strong storm waves, although we can not exclude the possibility that the line was formed by tsunamis. Furthermore, 68% of boulders at the bay are deposited beyond this line. Therefore, the presence of these boulders at their present positions is difficult to explain solely by storm waves, implying the possible tsunami origin of these boulders. The boulders are characteristically concentrated along the high‐tide line, suggesting the drastic reduction of the tsunami hydraulic force along the line. Previous studies using radiocarbon age dating, as well as our study, imply that at least 69 boulders at Miyara Bay were probably deposited at their present positions by the 1771 Meiwa tsunami, although some of these boulders might have been emplaced and displaced on the reef flat by prior tsunami or storm surges.     

Field-based description of near-surface crustal deformation in a high-strain shear zone: A case study in southern Kyushu,Japan

This study investigated geological evidence for near-surface crustal deformation in a high-strain shear zone that has been geodetically identified but which is not associated with obvious tectonic landforms. Fieldwork was conducted in the east–west-trending southern Kyushu high-strain shear zone (SKHZ), Japan, focusing mainly on occurrences of fracture zones, which are defined by a visible fracture density of >1 per 10 cm² and are commonly associated with cataclasite, fault breccia, and gouge. The area in which east–west-trending fracture zones are dominant is restricted to the east–west-trending, ~2-km-wide aftershock area of the 1997 Northwestern Kagoshima Earthquakes. Analysis of slip data from minor faults using the multiple inverse method, irrespective of whether the faults are in fracture zones, reveals that the area where the calculated main stress field is consistent with the current stress field estimated from focal-mechanism solutions of microearthquakes is restricted to the east–west-trending aftershock area. This finding for the SKHZ contrasts with the case of the Niigata–Kobe Tectonic Zone, which is a major strain-concentration zone with many exposed active faults in central Japan and for which the stress field estimated using fault-slip data is considered to be uniform and coincides with the current stress field. The cumulative amount of displacement estimated from the areal density of fracture zones in the SKHZ study area is smaller than that estimated from geodetically measured strain rates. Investigations based on slip data from minor faults and fracture-zone occurrence could help to identify concealed faults that are too small to generate tectonic landforms but which are sufficiently large to trigger major earthquakes.     

Storage-efficient reconstruction framework for planar contours

A storage-efficient reconstruction framework for cartographic planar contours is developed. With a smaller number of control points, we aim to calculate the area and perimeter as well as to reconstruct a smooth curve. The input data forms an oriented contour, each control point of which consists of three values: the Cartesian coordinates (x, y) and tangent angle θ. Two types of interpolation methods are developed, one of which is based on an arc spline while the other one is on a cubic Hermite spline. The arc spline-based method reconstructs a G¹ continuous curve, with which the exact area and perimeter can be calculated. The benefit of using the Hermite spline-based method is that it can achieve G² continuity on most control points and can obtain the exact area, whereas the resulting perimeter is approximate. In a numerical experiment for analytically defined curves, more accurate computation of the area and perimeter was achieved with a smaller number of control points. In another experiment using a digital elevation model data, the reconstructed contours were smoother than those by a conventional method.     

Impacts of nutrient management and decrease in paddy field area on groundwater nitrate concentration: a case study at the Nasunogahara alluvial fan,Tochigi Prefecture,Japan

In order to help evaluate the trends in the NO₃-N concentration in groundwater with a view to preventing further degradation in water quality in the future, a distributed groundwater quality model was constructed for the Nasunogahara basin. The best fit for the groundwater table elevations by the flow component of the model was achieved with average mean absolute errors (MAEs) of 0·92 m for the calibration period and 0·83 m for the validation period. Moreover, the best fit for the NO₃-N concentration by the water quality component was achieved with average mean relative errors (MREs) of 29·8% for the calibration period and 30·3% for the validation period. After developing a robust model, various change scenarios were tested; specifically, the effects of effluent load control and a decrease in paddy field area on the NO₃-N concentration in groundwater were predicted. The most intensively farmed area contributed about 40% of the total effluent load because of livestock farming in the basin. When the effluent load from this area was decreased by 50%, the average NO₃-N concentrations at sites S1, S2 and S3 were reduced by about 15%; however, the average concentrations at S4 and S5 were reduced by only 1%. Furthermore, when the total effluent load from the concentrated livestock area was removed completely, the average groundwater NO₃-N concentrations at S1, S2 and S3 were reduced by about 30% as compared with the original calculated results. In contrast, decreasing the area of the paddy fields in the basin did not greatly influence the groundwater NO₃-N concentration. In the case of a 70% reduction in paddy field area, average NO₃-N concentrations increased by about 7% at S1, S2 and S3. Copyright © 2008 John Wiley & Sons, Ltd.