Automatic substepping integration of the subloading tij model with stress path dependent hardening

This paper discusses the numerical integration of the subloading tij model. This is an elastoplastic model with stress path dependent hardening, which can predict the behaviour of normally consolidated clays or loose sands, as well as of over-consolidated clays or dense sands, with a small number of material parameters. Three features distinguish the subloading tij model from the conventional ones: (a) the use of a modified stress space given by tensor t_ij; (b) the split of the plastic strain increments in two components leading to a stress path dependent hardening; and (c) the use of two yield surfaces (subloading yield surface and normal yield surface). This last feature is based on the concept of sub-yielding stress states and adds an extra internal strain-like hardening variable, related to the relative density state, which demands its own evolution law. The three characteristics above greatly improve the prediction capabilities of the model, with respect to those of the well-known Cam clay model, at the cost of only two additional parameters. Nonetheless, the numerical integration of the constitutive equations of subloading tij model is a bit challenging, mainly due to the stress path dependent hardening. In order to integrate the equations of subloading tij model in the same way as for any conventional model, the authors reformulated its equations in a simpler and direct manner. Here, these equations are integrated using multi-step explicit schemes, such as modified-Euler and Runge–Kutta–Dormand–Price, with automatic error control. Simple forward-Euler scheme is also used for the sake of comparison. The results show that the modified-Euler scheme is more accurate as well as faster than the other schemes analysed over a wide range of error tolerance. Besides, the automatic feature of these schemes is a great convenience for the users of numerical codes.     

Zircon U–Pb sensitive high mass-resolution ion microprobe dating of granitoids in the Ryoke metamorphic belt, Kinki District, Southwest Japan

Abstract Zircon U–Pb sensitive high mass-resolution ion microprobe dating was carried out on three types of granitic rock (gneissose biotite granodiorite, biotite granite and two-mica granite) from the Cretaceous Ryoke belt of the Kinki district, Southwest Japan. The results give the ages of granitic magmatism in the Shigi-san area of between 87 and 78 Ma and suggest extensive melting of the Cretaceous Ryoke granitic crust to form the two-mica granite, probably at ca 80 Ma. Discrimination into older and younger granites based on development of gneissosity does not appear to represent the sequence of magma generation, although there is some scope in the interpretation of the zircon U–Pb data that would allow all three granites to form at 83 Ma. Compilation of chemical Th-U-total Pb isochron dating method ages, whole rock Rb–Sr isotope ages and U–Pb isotope ages indicates that most Ryoke plutonism occurred from ca 70 Ma to ca 100 Ma. Younger (85 Ma–70 Ma) plutonism with the formation of two-mica granite occurred only in the eastern sector of the Ryoke belt, including the Kinki District.     

Non-hypersingular boundary integral equations for two-dimensional non-planar crack analysis

We derive a set of non-hypersingular boundary integral equations, both elastodynamic and elastostatic, for the analysis of arbitrarily shaped 2-D anti-plane and in-plane cracks located in an infinite homogeneous isotropic medium, rendered in a unified nomenclature for all cases. The hypersingularities that appear in the usual formulations for the dynamic cases, existent both at the source point and at the wavefront, are removed by way of a regularization technique based on integration by parts. The equations for the in-plane cases are presented in terms of a local Cartesian coordinate system, one of the axes of which is always held locally tangential to the crack trace. The expressions for the elastic field at any point on the model plane are also given.
Our formulations are shown to yield accurate numerical results, as long as appropriate stabilization measures are taken in the numerical scheme. The numerical applicability of our method to non-planar crack problems is illustrated by simulations of dynamic growth of a hackly crack which has small off-plane side-branches. The results imply that the branching of a crack brings about a significant decrease in the crack-tip stress concentration level and consequently may play an essential role in the arrest of earthquake rupturing.     

Crustal structure and tectonics of the Hidaka Collision Zone, Hokkaido (Japan), revealed by vibroseis seismic reflection and gravity surveys

This study is the first integrated geological and geophysical investigation of the Hidaka Collision Zone in southern Central Hokkaido, Japan, which shows complex collision tectonics with a westward vergence. The Hidaka Collision Zone consists of the Idon'nappu Belt (IB), the Poroshiri Ophiolite Belt (POB) and the Hidaka Metamorphic Belt (HMB) with the Hidaka Belt from west to east. The POB (metamorphosed ophiolites) is overthrust by the HMB (steeply eastward-dipping palaeo-arc crust) along the Hidaka Main Thrust (HMT), and in turn, thrusts over the Idon'nappu Belt (melanges) along the Hidaka Western Thrust (HWT). Seismic reflection and gravity surveys along a 20-km-long traverse across the southern Hidaka Mountains revealed hitherto unknown crustal structures of the collision zone such as listric thrusts, back thrusts, frontal thrust-and-fold structures, and duplex structures. The main findings are as follows. (1) The HMT, which dips steeply at the surface, is a listric fault dipping gently at a depth of 7 km beneath the eastern end of the HMB, and cutting across the lithological boundaries and schistosity of the Hidaka metamorphic rocks. (2) A second reflector is detected 1 km below the HMT reflector. The intervening part between these two reflectors is inferred to be the POB, which is only little exposed at the surface. This inference is supported by the high positive Bouguer anomalies along the Hidaka Mountains. (3) The shallow portion of the IB at the front of the collision zone has a number of NNE-dipping reflectors, indicative of imbricated fold-and-thrust structures. (4) Subhorizontal reflectors at a depth of 14 km are recognized intermittently at both sides of the seismic profile. These reflectors may correspond to the velocity boundary (5.9–6.6 km/s) previously obtained from seismic refraction profiling in the northern Hidaka Mountains. (5) These crustal structures as well as the back thrust found in the eastern end of the traverse represent characteristics of collisional tectonics resulting from the two collisional events since the Early Tertiary.     

SR isotope geochemistry of voluminous rhyolite of the Tamagawa Welded Tuffs, related rocks and andesite of the young volcanics, in Hachimantai geothermal area, Northeast Japan

The volcanic rocks from the Hachimantai geothermal area, Northeast Japan, are divided into the following five groups: (1) rhyolite of the Tamagawa Welded Tuffs (about 500 km³, 2.0–1.4 Ma); (2) andesite related to the Tamagawa Welded Tuffs (about 10 km³, 1.5 Ma); (3) andesite of the Matsukawa Andesite (about 100 km³, 1.8-1.2 Ma); (4) dacite of the Kashinai Formation (about 100 km³, 1.1 Ma); and (5) andesite of the Young Volcanics (about 300 km³, younger than 1 Ma). ratios of less-altered samples of the five groups range from 0.7038 to 0.7046. There is no significant difference in ratios among the five groups in spite of differences in age and chemical composition. Therefore, fusion of or contamination by old acidic crust can be ruled out for the genesis of the voluminous acidic magma which produced the rhyolite of the Tamagawa Welded Tuffs and the dacite of the Kashinai Formation.The low ratios and the chemistry suggest two possibilities for the genesis of the acidic rocks. One is a low degree of partial melting of the basic crust, which has a low ratio, under high temperature. Another is a high degree of fractional crystallization from basic magma derived from the mantle.     

Slow slip generated by dehydration reaction coupled with slip-induced dilatancy and thermal pressurization

Sustained slow slip, which is a distinctive feature of slow slip events (SSEs), is investigated theoretically, assuming a fault embedded within a fluid-saturated 1D thermo-poro-elastic medium. The object of study is specifically SSEs occurring at the down-dip edge of seismogenic zone in hot subduction zones, where mineral dehydrations (antigorite, lawsonite, chlorite, and glaucophane) are expected to occur near locations where deep slow slip events are observed. In the modeling, we introduce dehydration reactions, coupled with slip-induced dilatancy and thermal pressurization, and slip evolution is assumed to interact with fluid pressure change through Coulomb’s frictional stress. Our calculations show that sustained slow slip events occur when the dehydration reaction is coupled with slip-induced dilatancy. Specifically, slow slip is favored by a low initial stress drop, an initial temperature of the medium close to that of the dehydration reaction equilibrium temperature, a low permeability, and overall negative volume change associated with the reaction (i.e., void space created by the reaction larger than the space occupied by the fluid released). Importantly, if we do not assume slip-induced dilatancy, slip is accelerated with time soon after the slip onset even if the dehydration reaction is assumed. This suggests that slow slip is sustained for a long time at hot subduction zones because dehydration reaction is coupled with slip-induced dilatancy. Such slip-induced dilatancy may occur at the down-dip edge of seismogenic zone at hot subduction zones because of repetitive occurrence of dehydration reaction there.     

Along-arc lateral variation of Rb−Sr and K−Ar ages of Cretaceous granitic rocks in Southwest Japan

Cretaceous granitic rocks were emplaced over a distance of 700 km along arc in Southwest Japan. Rb–Sr and K–Ar ages of a major group of these granitic rocks, with ilmenite series ore mineralogy, were examined. Rb–Sr whole rock ages of 92.8±4.0 Ma and Rb–Sr and K–Ar biotite ages of 80–88 Ma were obtained on one group of these granitic rocks from Kamo-Sera area of central Hiroshima Prefecture. The K–Ar ages of various minerals, combined with the Rb–Sr whole-rock age, give a smooth cooling curve, which suggests a 5 to 10 Ma time-lag between intrusion and cooling at 300° C for the Cretaceous granitic rocks. The Rb–Sr whole-rock and Rb–Sr/K–Ar biotite ages of these granitic rocks become younger eastward along the Southwest Japan arc, and the time-lag between the two systems remains constant at 5 to 10 Ma over the entire area. The along-arc age variation does not support the genetical relationship of the Cretaceous granitoids with steady-state subduction. The Cretaceous granitic province at the eastern margin of Eurasian continent was, at least partly, formed by an episodic event such as ridge subduction.