Shear Prestress Research Articles

Scale Dependence of Earthquake Rupture Prestress in Models With Enhanced Weakening: Implications for Event Statistics and Inferences of Fault Stress

AbstractDetermining conditions for earthquake slip on faults is a key goal of fault mechanics highly relevant to seismic hazard. Previous studies have demonstrated that enhanced dynamic weakening (EDW) can lead to dynamic rupture of faults with much lower shear stress than required for rupture nucleation. We study the stress conditions before earthquake ruptures of different sizes that spontaneously evolve in numerical simulations of earthquake sequences on rate‐and‐state faults with EDW due to thermal pressurization of pore fluids. We find that average shear stress right before dynamic rupture (aka shear prestress) systematically varies with the rupture size. The smallest ruptures have prestress comparable to the local shear stress required for nucleation. Larger ruptures weaken the fault more, propagate over increasingly under‐stressed areas due to dynamic stress concentration, and result in progressively lower average prestress over the entire rupture. The effect is more significant in fault models with more efficient EDW. We find that, as a result, fault models with more efficient weakening produce fewer small events and result in systematically lower b‐values of the frequency‐magnitude event distributions. The findings (a) illustrate that large earthquakes can occur on faults that appear not to be critically stressed compared to stresses required for slip nucleation; (b) highlight the importance of finite‐fault modeling in relating the local friction behavior determined in the lab to the field scale; and (c) suggest that paucity of small events or seismic quiescence may be the observational indication of mature faults that operate under low shear stress due to EDW.

“Volume collapse” instabilities in deep-focus earthquakes: A shear source nucleated and driven by pressure

Symmetry-breaking instabilities in high-pressure phase transformation produce the counterintuitive phenomenon of “volume collapse” producing only shear radiation, with little, or no, volumetric component, even under conditions of full isotropy, and explain the mystery of the long-standing observations in deep-focus earthquakes (400–700 km). Due to instability, at a critical “nucleation pressure”, an arbitrarily small densified region in the shape of a “pancake-like” flattened ellipsoidal Eshelby inclusion, grows self-similarly as a “lacuna” (zero particle velocity) with the phase transformation occurring under conditions of equilibrium in uniform strain/stress and at constant potential energy (at the vanishing of the M integral, when the radius-expanding driving force pεkk∗ overcomes the radius-shrinking self-force). The symmetry-breaking flattened shape favors minimization of the energy needed for the boundary to grow large, while for the accommodation of the large collapsing volume in the very thin inclusion deviatoric stresses are developed to avoid openings and overlaps. It is shown that, if an arbitrarily small flattened densified region is generated planarly, and the pressure exceeds the critical nucleation value, then it will necessarily produce a shear seismic source, with little or no, volumetric component, nucleated and driven to propagate by the pressure. The ellipsoid of phase change forms in the direction that minimizes the interaction energy with the pre-stress field and will be close to the direction of max shear pre-stress in the mantle. The obtained stress/deformation fields of a densified 2D flattened elliptical inclusion constitute a new defect that models the “anticrack” in geophysics and densified shear bands. The instability analysis can be extended to the nucleation and growth of the phase transition from water to a solid ice phase under high pressure, with the discovered instabilities providing insight to other phenomena of dynamic phase transformations, such as failure waves, amorphization, planetary impacts, etc.

Micro-mechanical prediction of UD laminates behavior under combined compression up to failure: influence of matrix degradation

This article aims to model the behavior of carbon fiber-reinforced polymer laminates up to failure and predict the corresponding energy absorption, under mixed loadings involving compression. In Guimard JM, Allix O, Pechnik N and Thévenet P. [Statistical energy and failure analysis of CFRP compression behavior using a uniaxial microbuckling model. J Compos Mater 2007; 41: 2807–2828], a simplified 2D micro-model has been used in order to assess the influence of the fiber misalignment parameters on the micro-structural compression behavior, both in terms of critical stresses and dissipated energies. This article goes further by introducing the influence of a shear pre-stress and by considering an inelastic and damageable constitutive behavior for the matrix and not only an inelastic one as it is done in the literature. Together with fiber waviness, these three parameters are proven to be critical for the simulation of the kinking phenomenon. Particularly, the main effect of the damageable behavior of the matrix is to avoid unrealistically high hardening of the epoxy. This affects the results significantly and allows a better correlation of the model with experimental data. It is shown, by a statistical analysis, that failure stresses are sensitive to both shear pre-stresses and fiber waviness. Dissipated energies and kink-band size are found to be affected by a shear pre-stress as well but rather less sensitive to fiber waviness.

Bridge Girder Heavily Damaged by Impact Vehicle Load: A Case Strategy for Structure Assessment and FRP Strengthening

Episodes like impact of traffic vehicles on existing bridges occur very frequently manly due to the increase of traffic volume and vehicles dimensions respect of actual roads and overpass geometry. An interesting case of FRP strengthening on existing deck bridge has been applied to one overpass of state road SS36 (Lecco, Italy). Heavy damage at both intrados and webs of I girder prestress beams was caused by impact of a vehicle higher then the vertical clear dimension between main road and crossing overpass. Extensive damage to concrete, subject to spalling and cracking, and complete failure of ordinary reinforcement and prestress tendons was recognized by detailed inspection. Main concern of strengthening strategy was driven by absence of original detail design project, because lack of project documents as drawings or calculation reports from road owner and maintenance office. For this reason it was necessary to apply “back analysis” strategy of strengthening, assessing original strength contribution (both in flexure and shear) of each bridge girder portion which showed evident damage or failure. After repairing of damaged concrete by specific mortar, to recover original element geometry and inertia, carbon FRP sheets was designed and applied at free surface to increase both flexure and shear prestress concrete girder capacity. Main advantages of this strengthening application were shown by minimize time and cost of repairing without closing of main road.

Rupture modes in laboratory earthquakes: Effect of fault prestress and nucleation conditions

Seismic inversions show that earthquake risetimes may be much shorter than the overall rupture duration, indicating that earthquakes may propagate as self‐healing, pulse‐like ruptures. Several mechanisms for producing pulse‐like ruptures have been proposed, including velocity‐weakening friction, interaction of dynamic rupture with fault geometry and local heterogeneity, and effect of bimaterial contrast. We present experimental results on rupture mode selection in laboratory earthquakes occurring on frictional interfaces, which were prestressed both in compression and in shear. Our experiments demonstrate that pulse‐like ruptures can exist in the absence of a bimaterial effect or of local heterogeneities. We find a systematic variation from crack‐like to pulse‐like rupture modes with both (1) decreasing nondimensional shear prestress and (2) decreasing absolute levels of shear and normal prestress for the same value of nondimensional shear prestress. Both pulse‐like and crack‐like ruptures can propagate with either sub‐Rayleigh or supershear rupture speeds. Our experimental results are consistent with theories of ruptures on velocity‐weakening interfaces, implying that velocity‐weakening friction plays an important role in governing the dynamic behavior of earthquake ruptures. We show that there is no measurable fault‐normal stress decrease on the fault plane due to the nucleation procedure employed in experiments, and hence, this is not a factor in the rupture mode selection. We find that pulse‐like ruptures correspond to the levels of nondimensional shear prestress significantly lower than the static friction coefficient, suggesting that faults hosting pulse‐like ruptures may operate at low levels of prestress compared to their static strength.

Pulse-like and crack-like dynamic shear ruptures on frictional interfaces: experimental evidence, numerical modeling, and implications

Destructive large earthquakes occur as dynamic frictional ruptures along pre-existing interfaces (or faults) in the Earth’s crust. One of the important issues in earthquake dynamics is the local duration of relative displacement or slip. Seismic inversions show that earthquakes may propagate as self-healing pulse-like ruptures, with local slip duration being much shorter than the overall rupture duration. Yet many classical models produce crack-like ruptures, with local slip durations comparable to the overall rupture duration. We study rupture modes in an experimental set up designed to mimic a fault prestressed both in compression and in shear. Our experiments demonstrate systematic variation from crack-like to pulse-like rupture modes as nondimensional shear prestress is decreased. The results of our experiments are consistent with theories of ruptures on interfaces with velocity-weakening friction. To consider the possibility that slip-weakening friction can also result in such rupture mode transition in the presence of the dynamic nucleation procedure employed by the experimental setup, we conduct numerical simulations with linear slip-weakening friction. In the simulations, we use the parameter regimes that were shown in previous studies to reproduce supershear transition distances obtained in the same experimental setup. We find that simulations with linear slip-weakening friction are unable to reproduce pulse-like ruptures, even in the presence of the dynamic initiation procedure. Our experimental results and simulations imply that velocity-weakening friction plays an important role in dynamic behavior of shear ruptures and needs to be included in earthquake models.

Effects of Rock Damage on Seismic Waves Generated by Explosions

In studying the physical processes involved in the generation of seismic waves by explosions, it is important to understand what happens in the region of high stresses immediately surrounding the explosion. This paper examines one of the processes that takes place in this region, the growth of pre-existing cracks, which is described quantitatively as an increase in rock damage. An equivalent elastic method is used to approximate the stress field surrounding the explosion and a micro-mechanical model of damage is used to calculate the increase in damage. Simulations for a 1 kt explosion reveal that the region of increased damage can be quite large, up to ten times the cavity radius. The damage is initiated on a damage front that propagates outward behind the explosive stress wave with a velocity intermediate between that of P and S waves. Calculations suggest that the amount of increased damage is controlled primarily by the initial damage and the extent of the region of increased damage is controlled primarily by the initial crack radius. The motions that occur on individual cracks when damage increases are converted to seismic moment tensors which are then used to calculate secondary elastic waves which radiate into the far field. It is found that, while the contribution from an individual crack is small, the combined effect of many cracks in a large region of increased damage can generate secondary waves that are comparable in amplitude to the primary waves generated by the explosion. Provided that there is asymmetry in the damage pattern, this process is quite effective in generating S waves, thus providing a quantitative explanation of how S waves can be generated by an explosion. Two types of asymmetry are investigated, a shear pre-stress and a preferred orientation of cracks, and it is found that both produce similar effects.

A first estimation of prestress in so-called circularly fibered osteonic lamellae

The existence and role of prestress in the various hierarchical structures of long bone are long standing questions. In this study, the prestress and associated strain that exist in a component of human bone microstructure, circularly fibered osteonic lamella, are estimated. Such estimates allow the formulation of hypotheses on prestress formation and lamellar stiffness. Dimensional measurements were obtained for eight fully calcified lamellae. These dimensions, before isolation from the surrounding alternate osteon and after strain relief by isolation and axial sectioning, furnish data upon which a geometric lamellar model is constructed. A material model is based on the most likely hypothesis as to lamellar structure. This geometric-material model allows estimation of the preexisting strain. The largest strains occur in shear circumferential–axial and normal axial strain directions, averaging 0.08 and 0.05, respectively. The geometric-material model expresses prestress in terms of as yet unknown elastic moduli. The average prestress magnitude is the largest in shear circumferential–axial direction, compensating for alternate osteon weakness in this direction. The estimated axial prestress confirms long hypothesized alternate osteon precompression, which impedes fractures of areas of collagen bundles transverse to the osteon axis at low stresses. The results of the model support the formulation of the following biological hypotheses: (a) lamellar prestress occurs at a supra-molecular level, namely through collagen bundles which are themselves likely to be prestressed; (b) collagen bundles oblique to the lamellar axis are responsible for shear prestress; (c) prestress ranges up to 0.11 GPa; and (d) the lamella is less stiff than alternate osteon.

Near-field waveforms from an arbitrarily expanding, transparent spherical cavity in a prestressed medium

A simple, approximate (‘transparent’) solution is derived for the near-field radiation emitted by a spherical cavity expanding in an initial pure shear prestress field. Near-field terms, their propagation and decay are discussed for a variety of growth histories, and are shown to be rather insensitive to the detailed variations of rupture velocity. The transparency approximation is shown to be adequate in the near field as well as in the far field; the main effect is a slight narrowing of far-field pulses. Time domain moment estimators at close range are more reliable for the S wave than for the P wave since transverse pulses are not as strongly contaminated by near-field effects.

Elastic relaxation coefficients for a spherical cavity in a prestressed medium of arbitrary orientation

Archambeau gave elastic relaxation coefficients for a spherical cavity introduced into a pure shear prestress field. The technique is generalized to a stress field for which only the trace of σ_(ij)^(0) is zero. The coefficients are given for a general deviatoric prestress field of arbitrary orientation. They are then specialized to the case of a pure shear stress expressed in terms of the orientation angles commonly used in fault plane descriptions, i.e. dip and slip angle. The extension of this technique to an arbitrary homogeneous prestress field and its limitations are discussed.

Propagation of weak waves in elastic-plastic solids

Wave fronts admitting discontinuities only in the derivatives of the dependent variables are by convention called ‘weak’ waves. For the special case of discontinuous first-order derivatives, the fronts are customarily called ‘acceleration’ waves. If the governing equations are quasi-linear, then the weak waves are necessarily characteristic surfaces. Sometimes, these surfaces are also referred to as ‘singular surfaces’ of order r ⩾ 1, where r stands for the order of the first discontinuous derivatives. This latter approach is adopted in this paper and applied to governing equations which form a set of first-order quasi-linear hyperbolic equations. When these equations are written in terms of singular surface coordinates, simplification occurs upon differencing equations written on the front and rear sides of the surface: a set of algebraic (‘connection’) equations is generated for the discontinuities in the normal derivatives of the dependent variables across the surface. When a similar operation is performed on the governing equations written for second-order derivatives, a set of first-order differential (‘transport’) equations is generated. This paper treats the problem of the propagation of acceleration waves in an elastic-plastic strain-hardening rate-independent solid. The homogeneous connection equations provide an expression for the wave speeds, and the transport equations are integrated for the case of plane wave propagation in a homogeneously pre-stressed medium to obtain a solution for the change in the strength of the discontinuity. For particular examples of uniaxial and pure shear pre-stress, it is found that the second derivative of the effective-stress, effective-strain function plays a significant role in the attenuation of the wave, the decay being more pronounced as the derivative increases. Combined geometrical and material attenuation effects are found for weak waves which propagate cylindrically outward into a medium which is homogeneously pre-stressed along the cylinder axis. It is found that geometrical effects dominate until the wave has propagated a distance greater than ten times the radius of the cylinder.

Seismic radiation from explosions in prestressed media and the measurement of tectonic stress in the Earth

The radiation field from explosions in a prestressed medium can be theoretically predicted on the basis of a dynamical theory of stress relaxation in the vicinity of the shock‐induced fracture zone created by an explosion. The field consists of the normal compressional wave field resulting from the conversion of the shock wave to an elastic wave plus an anomalous part due to the release of strain energy. In this study we consider the nature of the radiation field to be expected from such a source in an inhomogenous earth and determine the stress field required to explain the observations from a large underground explosion. The field is described in terms of radiation patterns as functions of frequency or alternately as the amplitude and phase spectrums at particular distances. These theoretical predictions are compared to the Love‐ and Rayleigh‐wave radiation patterns and spectra from the nuclear explosion Bilby. Using the known source parameters, we obtain agreement between the observed radiation patterns and the predicted patterns for a pure shear prestress field equivalent to a shear couple oriented approximately N10°W. Using the amplitude spectrum of the observed field adjusted for propagational effects, we find that the prestress was 70 ± 20 bars in the source area. We conclude that this approach can be utilized as a means of systematically measuring the stress field of the earth.

DYNAMIC PHOTOELASTIC STUDIES OF P AND S WAVE PROPAGATION IN PRESTRESSED MEDIA

The occasional existence of very pronounced, anomalous, horizontally polarized seismic waves from underground nuclear bomb blasts has been reported by several investigators. In order to further understanding of this phenomenon and the processes of mechanical radiation from explosions, particularly in prestressed media, a model study has been undertaken. Experimental apparatus has been developed which permits the generation and propagation of body waves from explosions in transparent plate models prestressed to various two‐dimensional stress configurations. High‐speed framing camera sequences are presented showing the explosion process and the resulting plate compressional and shear wave propagation in prestressed models. These are compared to theoretical calculations of isochromatic and [Formula: see text] isoclinic fringe patterns associated with the wave propagation in stressfree plates and plates prestressed in tension and shear. The following distinctive optical phenomena were predicted theoretically and observed in the high‐speed photoelastic patterns: a [Formula: see text] discontinuity between P and S wave isoclinics for the unstressed case; a tendency for the isoclinics to broaden and envelope the isochromatics in regions where the P and S waves are superimposed; development of serrations in the dynamic isoclinics in the presence of a prestressing field (yielding a pseudo‐isochromatic appearance to isoclinics when viewed monochromatically); and finally, a general similarity between the dynamic optical effects in media under tensile and shear prestress.