Strain partitioning between the Suruga Trough and the Zenisu Thrust: Neogene to present tectonic evolution in the onland and offshore Tokai district, Japan

The Tokai district in central Japan is located close to the convergent boundary between the Philippine Sea and Eurasian plates, and has experienced not only repeated large interplate earthquakes but also intense aseismic movement. In this paper, the spatial and temporal tectonic evolution of the Tokai district, particularly around the Omaezaki area, is discussed to assess whether the district has been and will be active or inactive. According to a geological survey, the horizontal crustal shortening strain can imply the hypothetical tectonic model that the area has been getting less active and the strain rate since the Neogene can be calculated as 12% and 2×10⁻⁶%/year, respectively. The present interseismic horizontal crustal strain and strain rate around the Omaezaki area are approximately 4×10⁻⁷% and 4×10⁻⁹%/year. By comparing these rates, the decrease since Neogene can imply the hypothetical tectonic model that the area has been getting less active influenced by the strain partitioning between the Suruga Trough and the Zenisu Thrust.     

P-wave velocity and gradient images beneath the Okinawa Trough

To investigate the influence of spatial change of viscosity on postseismic deformation associated with the interplate 1946 Nankai earthquake (M 8.0) at the Nankai Trough, southwest Japan, we newly constructed a realistic viscoelastic structure model, taking into account temperature- and depth-dependent viscosity of materials. For this purpose, we first compiled leveling and triangulation data during postseismic periods and clarified characteristics of the amount and spatial patterns of postseismic vertical displacement and principal strain fields. Then, we calculated the spatial distributions of viscosity from temperature and flow fields, which were obtained from 2D subduction models. By incorporating the obtained viscosity structure into 3D viscoelastic finite element models, we constructed a temperature- and depth-dependent viscosity structure model (MODEL P2). Based on MODEL P2, we constructed a viscoelastic structure model, taking into account Poisson's ratio for the oceanic plate and low-velocity regions and the existence of low-viscosity materials beneath the Shikoku and Chugoku districts (MODEL P3), which were revealed from seismic tomography. We also constructed a conventional layered viscoelastic structure model (MODEL L1) and plate subduction model (MODEL P1) with constant viscosity for each region and evaluated the effects of different viscoelastic structures on postseismic surface deformations, using the coseismic slip distribution obtained by inversion analyses of geodetic data. We also compared the calculated surface deformations with the observed postseismic crustal deformations in and around Shikoku. The results show that postseismic surface deformation fields for the newly constructed MODEL P2 are rather different from those for MODELs L1 and P1. Landward horizontal displacements for MODEL P2 are smaller than those for MODELs L1 and P1, seaward horizontal displacements are negligible, and vertical displacement is characterized by small subsidence over Shikoku. The postseismic horizontal principal strain field for MODEL P2 is characterized by contractions in the N–S to NW–SE directions at amounts smaller than those for MODELs L1 and P1. Postseismic surface deformations for MODEL P3 are almost the same as those for MODEL P2. The observed postseismic vertical displacement and horizontal principal strain fields could not be explained by the viscoelastic response for the realistic viscoelastic structure models P2 and P3. This indicates that the effects of elastic and viscoelastic responses due to interplate coupling on the plate interface, after-slip at the extension of the coseismic slipped region, and poroelasticity should be taken into account to precisely estimate postseismic surface deformation. This also suggests that, in order to evaluate postseismic crustal deformations derived from a large interplate subduction zone earthquake, it is essential to use realistic temperature- and depth-dependent viscoelastic structure models.     

Surface displacements due to batter piles driven in cross‐anisotropic media

This article derives the closed‐form solutions for estimating the vertical surface displacements of cross‐anisotropic media due to various loading types of batter piles. The loading types include an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The planes of cross‐anisotropy are assumed to be parallel to the horizontal ground surface. The proposed solutions are never mentioned in literature and can be developed from Wang and Liao's solutions for a horizontal and vertical point load embedded in the cross‐anisotropic half‐space. The present solutions are identical with Wang's solutions when batter angle equals to 0^°. In addition, the solutions indicate that the surface displacements in cross‐anisotropic media are influenced by the type and degree of material anisotropy, angle of inclination, and loading types. An illustrative example is given at the end of this article to investigate the effect of the type and degree of soil anisotropy (E/E′, G′/E′, and ν/ν′), pile inclination (α), and different loading types (a point load, a uniform skin friction, and a linear variation of skin friction) on vertical surface displacements. Results show that the displacements accounted for pile batter are quite different from those estimated from plumb piles, both driven in cross‐anisotropic media. Copyright © 2007 John Wiley & Sons, Ltd.     

Is the plastic flow uniformly distributed below the seismogenic region?

We compared the cutoff depth of seismicity in and around the Nojima fault broken by the 1995 Kobe earthquake occurring in intraplate Japan with the brittle–ductile transition depth of the widely accepted strength profile model of the crust. We successfully determined the temperature profile from borehole measurements, since almost the same geothermal gradients were observed at two boreholes located about 4 km apart from each other, and the thermal conductivity and heat production were also measured by taking numerous core samples. We found that the cutoff depth was much deeper than the transition depth under the assumption that wet granite is deformed at a strain rate of 3×10⁻¹⁵ s⁻¹. This small strain rate implies, however, that plastic flow is uniformly distributed below the seismogenic region. When the strain rate is assumed to be greater than 10⁻¹³ s⁻¹, the cutoff depth can be attributed to the transition depth. This suggests that deformation is localized in a narrow fault zone below the seismogenic region, even in the intraplate region.     

Lithospheric flexure, uplift and expected horizontal strain rate in the Pannonian Carpathian region

The Apuseni Mountains are located between the Pannonian Basin and the Transylvanian Basin along a direction of SE convergence with the Carpathian belt. A flexural model based on the cylindrical bending of a semi-infinite, isostatically supported, thin elastic plate is here examined with the Apuseni playing the role of flexural bulge, and under the assumption that the plate is deforming under the action of a vertical shear force and a bending moment applied at the end of the plate, beneath the Carpathians. The model yields estimates of the plate thickness ranging between 13 and 14.5 km, depending on the assumed density contrast between crust/sediments and mantle providing buoyancy. The vertical shear force which is necessary to bend the plate is in the range between 60 and 300 × 10¹¹ N m^− 1, depending on the assumed density contrast. This force is shown to be modelled by a gravitational ‘slab pull’ force, using model parameters derived from seismic tomography. If the height of the flexural bulge, after correction for erosion, is allowed to increase, the model yields an estimate of the horizontal strain rate at the top of the bulge. For example, 5 mm/yr vertical change of the flexural bulge of a 14 km thick plate results in a horizontal deformation rate of approximately 7 nanostrain/yr at the top of the bulge, a value which is at the threshold of sensitivity of continuous GPS measurements. Different vertical rates will change the horizontal strain rate almost proportionally.     

Strain measurements and tectonics of New Zealand

Measurements of shear strain from triangulation data have been made at 30 locations in New Zealand. The standard error of measurement in terms of strain rate is about ±1 · 10⁻⁷ y⁻¹ and values of up to 7 · 10⁻⁷ y⁻¹ are observed. Together with 22 fault-plane solutions for crustal earthquakes the measurements indicate broad-scale patterns of deformation. Between the Hikurangi and Flordland active margins is a 100-km-wide belt, the axial tectonic belt, with shear strain rate averaging 5 ± 1 · 10⁻⁷y⁻¹ and an azimuth of the principal axis of compression of 114 ± 8°. The rate of movement (45 mm y⁻¹) and direction (085°) between the Pacific and Indian plates from the Minster et al. pole can be accounted for by the measured strain in the axial tectonic belt through simple shear parallel to, and compression normal to, the belt. The similarity in the rates determined from triangulation data averaged over 20–100 years and from plate movement averaged over 5 m.y. indicates plate movement to be uniform in time. West of the axial tectonic belt in Nelson and Fiordland are two zones in which movement is highly oblique to plate movement, and can be explained by slip line deformation analogous to the deformation of Asia. The azimuth of the principal axis of compression in the Taupo rift and East Cape region is NE—SW, perpendicular to its direction in the axial tectonic belt, suggesting extension in the rift and East Cape region normal to the subduction zone.     

Displacement and stress distributions under a uniform inclined rectangular load on a cross‐anisotropic geomaterial

In practical engineering, an applied rectangular area load is not often horizontally or vertically distributed but is frequently inclined at a certain angle with respect to the horizontal and vertical axes. Thus, the solutions of displacements and stresses due to such a load are essential to the design of foundations. This article yields the analytical solutions of displacements and stresses subjected to a uniform rectangular load that inclines with respect to the horizontal and vertical axes, resting on the surface of a cross‐anisotropic geomaterial. The planes of cross‐anisotropy are assumed to be parallel to the horizontal ground surface. The procedures to derive the solutions can be integrated the modified point load solutions, which are represented by several displacement and stresses elementary functions. Then, upon integrations, the displacement and stress integral functions resulting from a uniform inclined rectangular load for (1) the displacements at any depth, (2) the surface displacements, (3) the average displacements in a given layer, (4) the stresses at any depth, and (5) the average stresses in a given layer are yielded. The proposed solutions are clear and concise, and they can be employed to construct a series of calculation charts. In addition, the present solutions clarify the load inclinations, the dimensions of a loaded rectangle, and the analyzed depths, and the type and degree of geomaterial anisotropy profoundly affect the displacements and stresses in a cross‐anisotropic medium. Parametric results show that the load inclination factor should be considered when an inclined rectangular load uniformly distributed on the cross‐anisotropic material. Copyright © 2008 John Wiley & Sons, Ltd.     

Calculation of finite incremental deformations in ductile geological materials and structural models

Although the total continuous deformation of rocks can be the net result of several tectonic pulses (finite increments), it will be assumed that there are only two. It is further assumed that differential displacements are unknown, but that two generations of rotation gauges are available in a rock body, together with two respective generations of strain gauges. A mathematical procedure is outlined herein for calculating the first or second deformation increment in natural structures and putty models with elliptical markers. To illustrate their practical value, one set of equations is used to determine the pattern of large incremental strain associated with the lateral spreading of a mature model diapir. This model pattern may help to interpret igneous fabric patterns of undeformed granitoid plutons.     

Secular crustal deformation and interplate coupling of the Japanese Islands as deduced from continuous GPS array, 1996–2001

Data from the nation-wide GPS continuous tracking network that has been operated by the Geographical Survey Institute of Japan since April 1996 were used to study crustal deformation in the Japanese Islands. We first extracted site coordinate from daily SINEX files for the period from April 1, 1996 to February 24, 2001. Since raw time series of station coordinates include coseismic and postseismic displacements as well as seasonal variation, we model each time series as a combination of linear and trigonometric functions and jumps for episodic events. Estimated velocities were converted into a kinematic reference frame [Heki, K., 1996. Horizontal and vertical crustal movements from three-dimensional very long baseline interferometry kinematic reference frame: implication for reversal timescale revision. J. Geophys. Res., 101: 3187–3198.] to discuss the crustal deformation relative to the stable interior of the Eurasian plate. A Least-Squares Prediction technique has been used to segregate the signal and noise in horizontal as well as vertical velocities. Estimated horizontal signals (horizontal displacement rates) were then differentiated in space to calculate principal components of strain. Dilatations, maximum shear strains, and principal axes of strain clearly portray tectonic environments of the Japanese Islands. On the other hand, the interseismic vertical deformation field of the Japanese islands is derived for the same GPS data interval. The GPS vertical velocities are combined with 31 year tide gage records to estimate absolute vertical velocity. The results of vertical deformation show that (1) the existence of clear uplift of about 6 mm/yr in Shikoku and Kii Peninsula, whereas pattern of subsidence is observed in the coast of Kyushu district. This might reflect strong coupling between the Philippine Sea plate and overriding plate at the Nankai Trough and weak coupling off Kyushu, (2) no clear vertical deformation pattern exists along the Pacific coast of northeastern Japan. This might be due to the long distance between the plate boundary (Japan trench) and overriding plate where GPS sites are located, (3) significant uplift is observed in the southwestern part of Hokkaido and in northeastern Tohoku along the Japan Sea coast. This is possibly due to the viscoelastic rebound of the 1983 Japan Sea (M_w 7.7) and the 1993 Hokkaido–Nansei–Oki (M_w 7.8) earthquakes and/or associated with distributed compression of incipient subduction there. We then estimate the elastic deformation of the Japanese Islands caused by interseismic loading of the Pacific and Philippine Sea subduction plates. The elastic models account for most of the observed horizontal velocity field if the subduction movement of the Philippine Sea Plate is 100% locked and if that of the Pacific Plate is 70% locked. However, the best fit for vertical velocity ranges from 80% to 100% coupling factor in southwestern Japan and only 50% in northeastern Japan. Since horizontal data does not permit the separation of rigid plate motion and interplate coupling because horizontal velocities include both contributions, we used the vertical velocities to discriminate between them. So, we can say there is strong interplate coupling (80%–100%) over the Nankaido subduction zone, whereas it is about 50% only over the Kurile–Japan trench.     

Finite strain analysis of nonuniform deformation inside shear bands in sands

A methodology has been developed to extend the incremental (Eulerian) Digital Image Correlation (DIC) technique to enable a Lagrangian‐based large‐strain analysis framework to examine the nature of strain and kinematic nonuniformity within shear bands in sands. Plane strain compression tests are performed on dense sands in an apparatus that promotes unconstrained persistent shear band formation. DIC is used to capture incremental, grain‐scale displacements in and around shear bands. The performance of the developed accumulation algorithm is validated by comparing accumulated displacements with two sources of reference measurements. A comparison between large and infinitesimal rotation is performed, demonstrating the nature of straining within shear bands in sands and the necessity of using a finite strain formulation to characterize ensuing behavior. Volumetric strain variation along the shear band is analyzed throughout macroscopic postpeak deformation. During softening, volumetric activity within the shear band is purely dilative. During the global critical state, the shear band material is seen on the average to deform at zero volumetric strain; however, locally, the sand is seen to exhibit significant nonzero volumetric strain, putting into question the current definition of critical state. At the softening‐critical state transition, a spatially periodic pattern of alternating contraction and dilation along the shear band is evidenced, and a preliminary evaluation indicates that the periodicity appears to be a physical phenomenon dictated only in part by median grain size. Copyright © 2011 John Wiley & Sons, Ltd.     

Long-term creep experiment of rock with small deviator of stress under high confining pressure and temperature

Long-term creep tests of gabbro which have been performed with a maximum bending stress (20 bar) under a high confining pressure (1 kbar) and various temperatures, are described. Methods and techniques used in the experiment are mainly similar to those reported previously by the same authors (Itô and Sasajima, 1980) except for the application of high pressure and temperature. The techniques include the bending system, size and preparation of the sample, and the determination of its deformation by use of interference fringes of Na-D light. In order to measure a very small deformation of creep, intermittent breaks of the application of loading, confining pressure and temperature are necessary, and the creep curve is constructed from the intermittent advance of permanent deformation.The experiment has revealed two strange phenomena : one is a sinuous progress of the creep curve, and the other is that the deformation recovery shows strange behavior after the unloading. These results are discussed in close connection with the mechanism of the “turn back of creep” denoted by Itô and Sasajima (1980). The mean creep curves, at 25°C. 95°C and 150°C, obtained so far lead to viscosities of 1.6 · 10²⁰, 1.9 · 10¹⁹ and 4.8 · 10¹⁸ poise, respectively and the maximum strain rates employed in the samples were 4.2 · 10⁻¹⁴, 3.6 · 10⁻¹³ and 1.4 · 10⁻¹²/sec, respectively, which cover the geological strain rate. Although we have only three data points, the logarithm of viscosity is linearly related to the reciprocal of absolute temperature (see Fig. 7), and an activation energy for creep of gabbro is found to be 7.6 kcal/mol. It should be noted that viscosities obtained are considerably smaller than those estimated for the crust and mantle, and that the activation energy is surprisingly smaller than those obtained by high-pressure experiments of rock deformation, which have been carried out under a strain rate larger than 10⁻⁸/sec.     

GPS rotation and strain rates in the Baikal–Mongolia region

Current deformation in Pribaikalia, Western and Central Mongolia, and Tuva has been studied from measured horizontal GPS velocities and respective computed strain and rotation rates using 1994–2007 data of the Baikal–Mongolian GPS triangulation network.The GPS velocity field shows two main trends: an NE trend within Jonggaria, the Mongolian Altay, and the Great Lakes Valley and an SE trend in the Hangayn and eastern Gobi Altay mountains, and in the Transbaikalian block of the Amur plate. The velocity magnitudes and vectors are consistent with an SE motion of the Amur plate at a rate of ～2 mm/year.The derived strain pattern includes domains of crustal contraction and extension recognized from the magnitudes of relative strains. Shortening predominates in the Gobi and Mongolian Altay and in the Khamar-Daban Range, where it is at ?₂ = (19.2 ± 6.0)×10^?9 yr^?1 being directed northeastward. Extension domains exist in the Baikal rift and in the Busiyngol–West Hangayn area, where the crust is stretching along NW axes at ?₁ = (22.2 ± 3.1) × 10^–9 yr^–1. The eastern Hangayn dome and the Gobi peneplain on its eastern border show low and unstable strain rates. In central and northern Mongolia (Orhon–Selenge basin), shortening and extension are at similar rates: ?₂ = (15.4 ± 5.4)×10^?9 yr^?1 and ?₁ = (18.1 ± 3.1)×10^?9 yr^?1. The strain pattern changes notably in the area of the Mogod earthquake of 1967.Most of rotation throughout Central Asia is clockwise at a low rate of about Ω = 6×10^?9 deg·yr^?1. High rates of clockwise rotation are observed in the Hangayn domain (18.1 ± 5.2)×10^?9 deg·yr^?1, in the Gobi Altay (10.4 ± 7.5)×10^?9 deg·yr^?1, and in the Orhon–Selenge domain (11.9 ± 5.2)×10^?9 deg·yr^?1. Counterclockwise rotation is restricted to several domains. One is in western Tuva and northwestern Great Lakes Valley of Mongolia (Ω = 3.7×10^?9 deg·yr^?1). Two more counterclockwise rotation regions occur on both flanks of the Baikal rift: along the craton edge and in basins of Transbaikalia on the rift eastern border, where rotation rates are as high as (13.0 ± 3.9)×10^?9 deg·yr^?1, while rotation within the Baikal basin does not exceed the measurement error. Another such domain extends from the eastern Hövsgöl area to the Hangayn northern foothills, with the counterclockwise rotation at a highest rate of (16.3 ± 2.8)×10^?9 deg·yr^?1.     

Surface displacements in Japan before the 11 March 2011 M9.0 Tohoku-Oki earthquake

Daily resolution data retrieved from the 1243 ground-based Global Positioning System (GPS) stations in Japan are utilized to expose surface displacements before the destructive M9 Tohoku-Oki earthquake (March 11, 2011). Variations in the residual GPS data, in which effects of the long-term plate movements, short-term noise and frequency-dependent variations have been removed through a band-pass filter via the Hilbert–Huang transform, are compared with parameters of the focal mechanism associated with the Tohoku-Oki earthquake for validation. Analytical results show that the southward movements, which were deduced from the residual displacements and agree with the strike of the rupture fault, became evident on the 65th day before the Tohoku-Oki earthquake. This observation suggests that the shear stress played an important role in the seismic incubation period. The westward movements, which are consistent with the angle of the maximum horizontal compressive stress, covered entire Japan and formed an impeded area (142°E, 42°N) about 75 km away from the epicenter on the 47th day prior to the earthquake. The horizontal displacements integrated with the vertical movements from the residual GPS data are very useful to construct comprehensive images in diagnosing the surface deformation from destructive earthquakes along the subduction zone.     

Micromechanics of vortices in granular media: connection to shear bands and implications for continuum modelling of failure in geomaterials

Recent analysis of data from triaxial tests on sand and discrete element simulations indicate the final pattern of failure is encoded in grain motions during the nascent stages of loading. We study vortices that are evident from grain displacements at the start of loading and bear a direct mathematical connection to boundary conditions, uniform continuum strain and shear bands. Motions of three grains in mutual contact, that is, 3‐cycles, manifest vortices. In the initial stages of loading, 3‐cycles initiate a rotation around a region Ω^* where the shear band ultimately develops. This bias sets a course in 3‐cycle evolution, determining where they will more likely collapse. A multiscale spatial analysis of 3‐cycle temporal evolution provides quantitative evidence that the most stable, persistent 3‐cycles degrade preferentially in Ω^*, until essentially depleted when the shear band is fully formed. The transition towards a clustered distribution of persistent 3‐cycles occurs early in the loading history—and coincides with the persistent localisation of vortices in Ω^*. In 3D samples, no evidence of spatial clustering in persistent 3‐cycle deaths is found in samples undergoing diffuse failure, while early clustering manifests in a sample that ultimately failed by strain localisation. This study not only delivered insights into the possible structural origins of vortices in dense granular systems but also a tool for the early detection of the mode of failure—localised versus diffuse—a sample will ultimately undergo. Copyright © 2014 John Wiley & Sons, Ltd.     

Deformation of an elastic layer coupling in different ways to a base due to a very long vertical strike-slip dislocation

The closed-form analytic expressions for the displacement and stresses at any point of an elastic layer lying over a base due to a very long vertical strike-slip dislocation are obtained. The interface between the layer and the base is assumed to be either ‘smooth-rigid’ or ‘rough-rigid’ or ‘welded’. The variations of displacement and stresses with the horizontal distance from the fault for different types of coupling of the layer with the base have been studied. It is found that the displacement for ‘welded interface’ lies between the displacements due to ‘smooth rigid’ and ‘rough-rigid’ interfaces for different positions of the observer and different values of the ratio of rigidities of the layer and half-space.     

Computing Displacements in Transversely Isotropic Rocks Using Influence Charts

Summary  This paper presents a simple graphical method for computing the displacement beneath/at the surface of a transversely isotropic half-space subjected to surface loads. The surface load can be distributed on an irregularly-shaped area. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. Based on the point load solutions presented by the authors, four influence charts are constructed for calculating the three displacements at any point in the interior of the half-space. Then, by setting z=0 of the derived solutions, another four influence charts for computing the surface displacements can also be proposed. These charts are composed of unit blocks. Each unit block is bounded by two adjacent radii and arcs, and contributes the same level of influence to the displacement. Following, a theoretical study was performed and the results showed that the charts for interior displacements are only suitable for transversely isotropic rocks with real roots of the characteristic equation; however, the charts for surface displacements are suitable for all transversely isotropic rocks. Finally, to demonstrate the use of the new graphical method, an illustrative example of a layered rock subjected to a uniform, normal circular-shaped load is given. The results from the new graphical method agree with those of analytical solutions as well. The new influence charts can be a practical alternative to the existing analytical or numerical solutions, and provide results with reasonable accuracy.     

Terrestrial heat flow around the aseismic front of the Japanese Island Arc

Very few data on heat flow are available in the area around the aseismic front of the Japanese Islands. In order to remedy this situation, measurements of the terrestrial heat flow were made at three locations in the eastern part of Fukushima Prefecture, northeastern Honshu, Japan. The observed values of heat flow were 37 mW/m² (0.88 μcal/cm²·s) at Soma, 52 mW/m² (1.25 μcal/cm²·s) at Kashima and 19 mW/m² (0.46 μcal/cm²·s) at Naraha, respectively. These data partially fill the gaps in the terrestrial heat flow data on land in northeastern Honshu, Japan. These values are considerably lower than the average heat flow over the world, but agree well with the previous estimation for the area.     

Active faults and magnitudes of left-lateral displacement along the northern margin of the Tibetan Plateau

The northern margin of the Tibetan Plateau (NMTP) is a major intracontinental Cenozoic transpressional zone that comprises a series of active strike-slip faults and thrust faults. It is important to document cumulative horizontal displacements along the NMTP in order to understand quantitatively strain partitioning in East Asia since the India–Eurasia collision. Based on an analysis of horizontal slip along major active faults, the total amount of horizontal displacements is estimated up to 700 km between the Tibetan Plateau and the Tarim Basin since the convergence of India and Eurasia. Along the western and middle segment of the Altyn Tagh fault to the northern margin of the Qaidam Basin, there are abundant evidence that show that the net displacement is 400 km since 40–35 Ma, and along the Shulenan Shan and southeast of middle Qilian Shan since 25–17 Ma, the amount of offset is 150 km. The largest horizontal slip in Qilian Shan–Hexi Corridor to the northeast of the Altyn Tagh fault is also 150 km since late Oligocene to early Miocene. It decreases to only 60 km along the Haiyuan fault (since late Miocene) and to 25 km along the Zhongwei–Tongxin fault since the Pliocene (about 5.3–3.4 Ma), at the northeast margin of the Tibetan Plateau. This clearly implies northeastward diminishing of the total horizontal displacement and temporal getting younger of the fault slip along the NMTP. However, this tendency is very complicated at different times and different segments as a result of the uplift, growth and rotation of different segments of the NMTP at different stages during the convergence of India and Eurasia.     

A new approach for calculating strain for particulate media

Discrete element modelling is a viable alternative to conventional continuum‐based analysis for analysing problems involving localized deformations of particulate media. However, to aid in the interpretation of the results, it is useful to express the results of discrete element analyses in terms of the continuum parameters of stress and strain. A number of homogenization methods have been proposed to calculate strain in discrete systems; however, two significant limitations of these methods remain. First, none of these methods incorporate particle rotation effects satisfactorily, although significant particle rotation occurs in shear bands in both physical tests and numerical simulations of granular materials. Additionally, observations of the particle displacement fields in shear bands in granular materials indicate that the displacements within the localizations are erratic. Consequently, existing linear, local interpolation approaches produce substantial variations in the strain values calculated in adjacent elements in the region of localization, hindering clear visualization of the strain localization as it evolves. A new method of domain discretization for calculating strain is proposed. This method is capable of capturing particle rotation and employs a non‐local meshfree interpolation procedure capable of smoothing the erratic displacements in strain localizations, which better defines their evolution. The proposed method is validated for problems involving both two and three dimensions. A number of methods are compared with the proposed method and pertinent insights are made. Copyright © 2003 John Wiley & Sons, Ltd.     

Horizontal soil stress changes around displacement piles

A simplified analysis of the problem of horizontal soil stress changes around circular displacement piles, caused by pile placement, is presented. Pile installation is assumed to cause soil displacements in the horizontal direction only, thus yielding an axisymmetric problem. The soil surrounding the pile is modelled as a weightless non-linear elastic material. Material non-linearity is handled in a simplified manner by adopting secant shear moduli defined in terms of a proportionality coefficient and a softening factor. The resulting equilibrium equation is solved analytically and an expression is obtained which is also conveniently presented in graphical form. The derived expression can be used to estimate horizontal soil stress changes and is incorporated into a simple procedure to estimate the ultimate load or the efficiency of pile groups. Comparisons are made between efficiencies calculated according to this procedure and efficiencies measured in full-scale group load tests in sand.