Statistics for Spatial Data.

[1] Field observations of mature crustal faults suggest that slip in individual events occurs primarily within a thin shear zone, <1–5 mm, within a finely granulated, ultracataclastic fault core. Relevant weakening processes in large crustal events are therefore suggested to be thermal, and to involve the following: (1) thermal pressurization of pore fluid within and adjacent to the deforming fault core, which reduces the effective normal stress and hence also the shear strength for a given friction coefficient and (2) flash heating at highly stressed frictional microcontacts during rapid slip, which reduces the friction coefficient. (Macroscopic melting, or possibly gel formation in silica-rich lithologies, may become important too at large enough slip.) Theoretical modeling of mechanisms 1 and 2 is constrained with lab-determined hydrologic and poroelastic properties of fault core materials and lab friction studies at high slip rates. Predictions are that strength drop should often be nearly complete at large slip and that the onset of melting should be precluded over much (and, for small enough slip, all) of the seismogenic zone. A testable prediction is of the shear fracture energies that would be implied if actual earthquake ruptures were controlled by those thermal mechanisms. Seismic data have been compiled on the fracture energy of crustal events, including its variation with slip in an event. It is plausibly described by theoretical predictions based on the above mechanisms, within a considerable range of uncertainty of parameter choices, thus allowing the possibility that such thermal weakening prevails in the Earth.

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Heating and weakening of faults during earthquake slip

To simulate numerically the microstructure of shear bands, the distinct element method was modified such that the effect of rolling resistance at contacts could be taken into account. To this end, the relative movement by rolling is related to the relative rotation between two particles with a common contact, which makes it possible to generalize the conservation law of angular momentum for a more general case than the moments can be transmitted through contacts. Not only the generation of large voids inside a shear band but also the high gradient of particle rotation along the shear band boundaries can be reproduced, in a manner quite similar to those of natural granular soils, when the rolling resistance at contacts is considered. The development of columns is a common feature that appears in the strain hardening process, and buckling of the columns parallels the development of shear bands. The generation of large voids and the high gradient of particle rotation are produced as a result of the buckling of the columns.

Rolling Resistance at Contacts in Simulation of Shear Band Development by DEM

In this paper, intergranular (\Ie\dc\N) and interfine (\Ie\df\N) void ratios and confining stress are used as indices to characterize the stress-strain response of gap-graded granular mixes. It was found that at the same global void ratio (\ie) and confining stress, the collapse potential (fragility) of silty sand increases with an increase in fines content (FC) due to a reduction in intergranular contact between the coarse grains. Beyond a certain threshold fines content (FC\Dth\N), with further addition of fines, the interfine contact friction becomes significant. The fragility decreases and the soil becomes stronger. The value of FC\Dth\N depends on \ie and the characteristics of fines and coarse grains. At FC FC\Dth\N), fine grain friction plays a primary role and dispersed coarse grains provide a beneficial, secondary reinforcement effect. At the same \Ie\df\N, the collapse potential decreases with an increase in sand content. Beyond a certain limiting fines content, the soil behavior is controlled by \Ie\df\N, the collapse potential decreases with an increase in sand content. Beyond a certain limiting fines content, the soil behavior is controlled by \Ie\df\N only. An intergranular matrix diagram is presented that delineates zones of different behaviors of granular mixes as a guideline to determine the anticipated behavior of gap-graded granular mixes. New equivalent intergranular contact void ratios, (\Ie\dc\N)\Deq\N and (\Ie\df\N)\Deq\N, are introduced to characterize the behavior of such soils at FC FC\Dth\N, respectively.

Undrained Fragility of Clean Sands, Silty Sands, and Sandy Silts

Experimental results are presented from the extensive program of drained plane strain compression tests on sand carried out in Grenoble over the last two decades. Systematic analysis of photographs of the deforming specimen allowed for measuring deformations and determining strain fields throughout the test, that is: prior to, at, and after the onset of strain localization. The principles, details and accuracy of the procedure are described, as well as its suitability to properly depict the patterns of deformation. Findings concerning the occurrence and progression of strain localization are discussed. The issues of shear band orientation and thickness are addressed, as well as temporary and persistent complex localization patterns, and the volumetric behaviour inside a band after its formation. The influence of such variables as initial state of the sand (effective stress and relative density), specimen size and slenderness, as well as grain size, is discussed. Copyright © 2004 John Wiley & Sons, Ltd

Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry

Experimental results are presented which characterize the behaviour of a loose, fine-grained, water-saturated sand tested under globally undrained and drained conditions in a plane strain apparatus. The objective of this investigation is to provide insight into the phenomenon of shear banding in loose sand. Together with local measurements of boundary forces and deformations, stereophotogrammetry is used to investigate the progression of strain localization in plane strain compression. Typical results and findings concerning the evolution of non-homogeneous deformation are presented in detail. Shear banding occurred in both undrained and drained experiments on loose masonry sand. In general, temporary modes of strain localization, observed during macroscopically ‘uniform’ deformations of a specimen, gave way to a single, persistent shear band. A clear pattern of onset of the formation of the persistent shear band, mobilization of the maximum effective friction and complete formation of the band was observ...

Shear bands in plane strain compression of loose sand

Experimental results are presented that characterize the behavior of a loose, fine-grained, water-saturated sand tested under globally undrained conditions is a plane strain apparatus. Together with local measurements of boundary forces and deformations, stereophotogrammetry is used to track the progressive localization of strain. The constitutive behaviors in the tests prior to localization can be characterized as either undrained local softening or undrained load softening and subsequent rehardening. In both cases, a consistent pattern of onset of the formation of the persistent shear band, mobilization of the maximum effective friction, and the complete formation of the band was observed. Conditions approximating steady state only were observed in the shear bands. The effect of strain localization on the conventionally derived steady state line was found to be minimal when undrained load softening behavior was observed, but significantly different steady-state lines were found from results of plane strain and axisymmetric tests. The differences between tests conducted under these two stress conditions assessed to evaluate the practical implications of the observed differences.

Closure of "Strain Localization and Undrained Steady State of Sand"

A field investigation was carried out with an instrumented vibratory roller compactor to explore the relationship between vibration characteristics and underlying soil properties, namely soil stiffness. The roller was outfitted with instrumentation to monitor drum and frame acceleration, as well as eccentric excitation force. Multiple consecutive passes were performed over six test beds on an active earthwork construction site to capture changes in roller vibration during compaction. Using lumped parameter vibration theory, soil stiffness was extracted from the roller data drum and frame acceleration and drum phase lag. Both drum acceleration and drum phase lag were found to be very sensitive to changes in underlying soil stiffness. The drum-soil natural frequency of the coupled roller-soil system varied considerably and increased with compaction-induced soil stiffening. Phase lag always decreased with increasing soil stiffness, whereas drum acceleration trends depended on whether the excitation frequency was less than or greater than resonance. Roller-determined soil stiffness was found to be a function of the eccentric force, and heterogeneity in moisture, lift thickness, and underlying stiffness has a considerable affect on roller vibration behavior. When used as a proof roller, the instrumented roller identified soft areas in the embankment that were not identified by a static proof roll test.

Field Monitoring of Roller Vibration during Compaction of Subgrade Soil

Strain Localization and Undrained Steady State of Sand

The development of localized strains (shear banding) in soils near peak stress levels and the subsequent continued deformation within shear bands during observed softening render important issues such as critical state difficult to investigate. The determination and overall validity of critical state behavior in sand is of considerable importance, as it provides the basis both for failure criteria/postfailure behavior of many constitutive models and for stability analysis. A series of drained plane-strain experiments on sand specimens with detailed local analysis was carried out to investigate the evolution of stress state and void ratio, as well as the uniqueness of critical state. Persistent shear bands form at the peak effective stress ratio; subsequent strain softening behavior occurs in concert with localized deformation with the shear band. A unique critical stress state was found to exist for a given confining stress; however, the test results indicate that there is no unique relationship between void ratio and confining stress at the critical state.

Michael A. Mooney

Papers

Shear bands in plane strain compression of loose sand

Closure of "Strain Localization and Undrained Steady State of Sand"

Field Monitoring of Roller Vibration during Compaction of Subgrade Soil

Strain Localization and Undrained Steady State of Sand

A Unique Critical State for Sand