Prestress Field Research Articles

Fault geometry, rupture dynamics and ground motion from potential earthquakes on the North Anatolian Fault under the Sea of Marmara

SUMMARY Using the 3-D finite-element method, we develop dynamic spontaneous rupture models of earthquakes on the North Anatolian Fault system in the Sea of Marmara, Turkey, considering the geometrical complexity of the fault system in this region. We find that the earthquake size, rupture propagation pattern and ground motion all strongly depend on the interplay between the initial (static) regional pre-stress field and the dynamic stress field radiated by the propagating rupture. By testing several nucleation locations, we observe that those far from an oblique normal fault stepover segment (near Istanbul) lead to large through-going rupture on the entire fault system, whereas nucleation locations closer to the stepover segment tend to produce ruptures that die out in the stepover. However, this pattern can change drastically with only a 10° rotation of the regional stress field. Our simulations also reveal that while dynamic unclamping near fault bends can produce a new mode of supershear rupture propagation, this unclamping has a much smaller effect on the speed of the peak in slip velocity along the fault. Finally, we find that the complex fault geometry leads to a very complex and asymmetric pattern of near-fault ground motion, including greatly amplified ground motion on the insides of fault bends. The ground-motion pattern can change significantly with different hypocentres, even beyond the typical effects of directivity. The results of this study may have implications for seismic hazard in this region, for the dynamics and ground motion of geometrically complex faults, and for the interpretation of kinematic inverse rupture models.

Deformation of compliant fault zones induced by nearby earthquakes: Theoretical investigations in two dimensions

[1] Using spontaneous rupture models with off-fault elastoplastic material response, we investigate the deformation of compliant fault zones induced by nearby earthquake ruptures in a two-dimensional plane-strain framework. We find that dynamic stresses from nearby ruptures can produce inelastic strain along some portions of a fault zone that experience dilatational stress changes, if the fault zone rock is close to failure in the prestress field. Accumulation of inelastic strain causes dramatic variations in particle velocity across the fault zone, reversing the sense of fault-parallel relative motion from retrograde (opposite to the long-term geologic slip) to sympathetic (consistent with the long-term slip) during the dynamic process. In the static displacement field of a roughly parallel strike-slip fault system, the inelastic response of a fault zone results in sympathetic motion, while the elastic response generally gives rise to retrograde motion. Our theoretical investigations reveal that some deficiencies may exist in applying an elastic inhomogeneity model to infer fault zone properties in previous studies, including the assumption of negligible fault-normal motion and ignorance of changes in some components of the stress tensor. These deficiencies and possible constraints on the in situ stress state by inelastic strain signals in the static displacement field call for a reexamination of existing observations of fault zone deformation induced by recent large earthquakes.

MODEL AND EXPERIMENTAL STUDY OF GIANT MAGNETOSTRICTIVE POWER GENERATION

A mathematical model of vibration power generation (VPG) with the giant magnetostrictive material (GMM) is proposed on the basis of the magneto-mechanical coupling model, Jiles-Atherton model and electromagnetic induction law. According to the model, the output voltage of a giant magnetostrictive power generator has been calculated under the condition of different vibration frequency, pre-stress and bias magnetic field. The calculating results show that the model can reveal the relationship between the input vibrating stress and output voltage. The experiment of a giant magnetostrictive power generator has been carried out, and the experimental results agree well with the calculating results.

Nb3Sn Quadrupoles Designs For The LHC Upgrades

NB 3 SN QUADRUPOLES DESIGNS FOR THE LHC UPGRADES H. Felice, LBNL, Berkeley, CA 94720, USA Abstract In preparation for the LHC luminosity upgrades, high field and large aperture Nb 3 Sn quadrupoles are being studied. This development has to incorporate all the relevant features for an accelerator magnet like alignment and cooling channels. The LARP HQ model is a high field and large bore quadrupole that will meet these requirements. The 2-layer coils are surrounded by a structure based on key and bladder technology with supporting iron yoke and aluminum shell. This structure is aimed at pre-stress control, alignment and field quality. We present here the magnetic and mechanical design of HQ, along with recent progress on the development of the first 1-meter model. efficiency will have to be combined with mechanical efficiency. The mechanical structure will have to withstand large Lorentz forces while remaining compact enough to fit within the LHC tunnel. The cable design is also a very important step for the design: to reach high field and to manage mechanical stress in the coil, the use of a 15mm wide cable is necessary. The windability and the cabling degradation have to be watched closely. HQ aperture is not yet determined but apertures ranging between 114 and 134 mm have been considered. We summarize here the results for a 114 mm aperture. MAGNETIC DESIGN Conductor The strand is 0.8 mm in diameter with a copper/non copper ratio of 0.87. The cable is made of 35 strands. The keystone of the cable is of the order of 0.75. Some cable optimization is in progress in order to reduce current degradation due to cabling. The cable dimensions used to design the magnetic cross-section are summarized in Table 1: Table 1: Conductor parameters Dimensions Width Mid thickness Insulation Units mm mm mm Values INTRODUCTION The main objective of LARP is to demonstrate the feasibility of the Nb 3 Sn technology for the LHC upgrades. The increase of the baseline luminosity requires IR quadrupoles with high performing gradients. Although NbTi solutions are considered, Nb 3 Sn remains the best candidate to achieve the performance required for the LHC Upgrade Phase 2. In this context, LARP has developed several series of Nb 3 Sn magnets: - The SQ series (Subscale Quadrupole) provided a gradient of 90 T/m in 110 mm aperture using subscale Nb 3 Sn racetrack coils and included alignment [1,2]. - The TQ series (Technologic Quadrupole) consists of 1-meter long, 90 mm aperture cosine theta quadrupole magnets with a peak field of the order of 12 T and a measured gradient between 200 and 220 T/m [3,4]. - The LR magnet (Long Racetrack in a common coil arrangement) relied on two 3.6 m Nb 3 Sn racetrack coils assembled in a shell-based structure to demonstrate the scalability of Nb 3 Sn racetracks [5]. - The LQ series (Long Quadrupole) is a scale up of the TQ series aiming at demonstrating the scalability of Nb 3 Sn cosine theta quadrupole [6]. In order to meet the requirements for Phase 2, the next series of magnet will have to reach 14-15 T at 1.9 K in a large aperture (above 110 mm) with alignment features (to provide field quality), cooling channels and LHe containment. The objective of the HQ series (High gradient, high field Quadrupole) is to address these requirements [7]. This leads to technical challenges: in terms of coil design and mechanical structure design. The magnetic Magnetic Cross-section For the same aperture, several magnetic cross-sections have been studied and compared in terms of: gradient peak field field quality pole angle in order to facilitate the windability maximum mechanical stress in the coil for a given mechanical structure. This study brought to light the importance of combining the magnetic design with the mechanical design. Two different 134 mm aperture cross-sections are presented in Figure 1. The mechanical stresses induced by the Lorentz forces are compared for a gradient of 200 T/m. In both cases, the mechanical structure is infinitely rigid and the coil layers can slide one with respect to the other. This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, High Energy Physics Division, U.S. Department of Energy, under contract No. DE-AC02- 05CH11231. H.Felice is with Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA (e-mail: HFelice@lbl.gov).

Design of HQ—A High Field Large Bore ${\rm Nb}_{3}{\rm Sn}$ Quadrupole Magnet for LARP

In support of the Large Hadron Collider luminosity upgrade, a large bore (120 mm) Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn quadrupole with 15 T peak coil field is being developed within the framework of the US LHC Accelerator Research Program (LARP). The 2-layer design with a 15 mm wide cable is aimed at pre-stress control, alignment and field quality while exploring the magnet performance limits in terms of gradient, forces and stresses. In addition, HQ will determine the magnetic, mechanical, and thermal margins of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn technology with respect to the requirements of the luminosity upgrade at the LHC.

Research on Concrete Vertical Precompressive Stress Field at Webs of Box Girder Bridge

Based on Fourier series, an analytic formula for analyzing the prestress in the web of box girder with single bar was deduced through simplifying the action of single vertical prestress bar as a couple of concentrated forces with equal value but opposite direction acting on a thin rectangular board with infinite length. The vertical compress stress distribution in the web gotten from the analytic solution basically agrees with that from the ANASYS finite element solution. The analysis result indicates that the vertical compressive stress distribution in the webs meets the normal distribution and small tensile stresses are created aside the tendons. Field tests on a real bridge also demonstrate that the analytic formula is adaptable to the solution of the superposition of vertical prestress in the web. Furthermore, the feature of the vertical prestressing field along the height of the web was analyzed and modifying formula was presented by introducing a compensation factor K. In addition, the μ-K curves of the webs under the action of prestressing tendons with different spacing intervals were presented.

Pre-stressing effect on DC breakdown in low-density polyethylene

Polyethylene is widely used in electrical wires and power cables. The pre-stressing effect, which restricts the applications of polyethylene, has not yet been investigated in depth. We studied the breakdown of low-density polyethylene (LDPE) films pre-stressed by direct current (DC) electric field. The results showed some conformity, as reported in many other papers, that the DC breakdown strength E B+ with the same polarity to that of the pre-stressing field was higher than the DC breakdown strength E B of thin LDPE films without pre-stressing, while the DC breakdown strength E B − with the opposite polarity was lower than E B. Such phenomena could be explained by the hetero effects of accumulating space charges, which enhanced the electrical field when the polarity was reversed. However, as a further increase in pre-stressing electrical field, both E B+ and E B − were found higher than E B. We investigated the space charge behavior in LDPE films and found that when applied with a higher electrical field, space charge packet initialized and traveled through the specimen. The results suggest that the space charge packet behavior may contribute to the pre-stressing effects on electrical breakdown in LDPE films.

The influence of pre-stressing on breakdown characteristics in liquid silicone rubber

Liquid silicone rubber (LSR) has increasingly been used as one kind of inner insulating material. Studies of space charge and its effect during pre-stressing and breakdown (BD) process in LSR were carried out. DC electrical breakdown field (BDF) of LSR specimens before and after DC electrical pre-stressing was measured. The space charge characteristics of LSR specimens under different DC electrical pre-stressing fields and that during the BD processes were measured by a pulsed electro-acoustic (PEA) method. It was found that the amount of homo space charges near electrodes increases obviously as a rising electric field is applied. Whether the polarity of BDF is the same as that of the pre-stressing field or not, the DC BDF of pre-stressed specimens is higher than that of specimens without pre-stressing. However, the pre-stressing does not show monotone and saturation effects, as generally occurs in the literature. In hetero BD experiments for example, with an increasing pre-stressing field, the DC BDF first increases up to 14.5% at the pre-stressing field of 25 kV/mm and then decreases. The influence of pre-stressing on the BD processes in LSR are discussed. The relationship between space charge and the DC BDF was related to the microstructure of nano-silica and LSR molecules.

Stress distribution around a circular cylindrical cavity in a prestressed plate

A system of equilibrium equations for nonthin transversely isotropic plates with a uniform prestress field is derived by expanding the unknown functions into Fourier-Legendre series. A method of finding the general solution of this system is expounded and used to determine the stress state of a plate with a circular cylindrical cavity

Off‐fault damage patterns due to supershear ruptures with application to the 2001 Mw 8.1 Kokoxili (Kunlun) Tibet earthquake

We extend a model of a two‐dimensional self‐healing slip pulse, propagating dynamically in steady state with slip‐weakening failure criterion, to the supershear regime in order to study the off‐fault stressing induced by such a slip pulse and investigate features unique to the supershear range. Specifically, we show that there exists a nonattenuating stress field behind the Mach front that radiates high stresses arbitrarily far from the fault (practically this would be limited to distances comparable to the depth of the seismogenic zone), thus being capable of creating fresh damage or inducing Coulomb failure in known structures at large distances away from the main fault. We allow for both strike‐slip and dip‐slip failure induced by such a slip pulse. We show that off‐fault damage is controlled by the speed of the slip‐pulse, scaled stress drop, and principal stress orientation of the prestress field. We apply this model to study damage features induced during the 2001 Kokoxili (Kunlun) event in Tibet, for which it has been suggested that much of the rupture was supershear. We argue that an interval of simultaneous induced normal faulting is more likely due to a slip partitioning mechanism suggested previously than to the special features of supershear rupture. However, those features do provide an explanation for otherwise anomalous ground cracking at several kilometers from the main fault. We also make some estimates of fracture energy which, for a given net slip and dynamic stress drop, is lower than for a sub‐Rayleigh slip pulse because part of the energy fed by the far‐field stress is radiated back along the Mach fronts.

Nonuniform prestress from prior earthquakes and the effect on dynamics of branched fault systems

To examine the effects of branched fault geometry on the dynamics of fault systems in the long term, we perform multicycle simulations on generic faulting models. An explicit finite element algorithm is used to simulate spontaneous dynamic rupture of earthquakes. The fault stress during the interseismic period is evaluated by an analytical viscoelastic model. We find that the fault prestress field becomes highly nonuniform near the branch point and on the two branch segments over multiple earthquake cycles, owing to the branched fault geometry and stress interaction between the two segments. The principal prestress on faults rotates over multiple earthquake cycles and departs from the regional stress field significantly near the branch point. After a number of earthquake cycles, the branched fault systems evolve to a steady state in which several patterns of the fault prestress and earthquake rupture repeat. The nonuniform prestress developed from previous earthquakes has large effects on the rupture and slip patterns. Several different rupture scenarios can occur on a given branched fault system. In addition, backward branching can occur in the nonuniform prestress field, either driven by slip on the “stem” of the fault system or through a triggering mechanism. These modeling results may have important implications for understanding fault‐branching behavior observed in the 1992 Landers, the 1999 Hector Mine, and the 2002 Denali fault earthquakes and for seismic hazard analysis in the areas where branched fault systems exist.

Uniaxial electromechanical behavior of ferroelectric ceramic PZT-53

Effect of compressive pre-stress and biased electrical field on the uniaxial electromechanical behavior of a soft ferroelectric ceramic PZT-53 is investigated. The emphasis is on the effect of electric and mechanical loading history upon the response of PZT-53 to external loading and on the effect of pre-stress and biased electrical field upon the electro-mechanical coupling behavior. It is found that the uniaxial behavior of the PZT-53 is sensitive to the compressive pre-stress and biased electrical field, and is less sensitive to the loading history. Obtained results are expected to shed insightful light on developing reliable constitutive model for ferroelectric ceramics.

Dynamic shear rupture interactions with fault bends and off‐axis secondary faulting

On the basis of elastodynamic stress fields for singular crack and nonsingular slip‐weakening models of propagating rupture, we develop preliminary answers to such questions as follows: If a rupturing fault is intersected by another, providing a possible bend in the failure path, when will stressing be consistent with rupture along the bend? What secondary fault locations and orientations, in a damaged region bordering a major fault, will be stressed to failure by the main rupture? Stresses that could initiate rupture on a bend are shown to increase dramatically with crack speed, especially near the limiting speed (Rayleigh for mode II, shear for mode III). Whether a bend path, once begun, can be continued to larger scales depends on principal stress directions and ratios in the prestress field. Conditions should often be met in mode II for which bend paths encouraged by stressing very near the rupture tip are discouraged by the larger‐scale stressing, a basis for intermittent rupture propagation and spontaneous arrest. Secondary failure in the damage zone likewise increases markedly as the limiting speed is approached. Such may make the fracture energy much greater than for slip on a single surface. The extent of secondary faulting is strongly affected by prestress directions and the ratio of residual to peak strength. For mode II, prestress controls whether activation occurs primarily on the extensional side, which we show to be the typical case, or on the compressional side too. Natural examples are consistent with the concepts developed.

Non-linear constitutive relations for magnetostrictive materials

In this paper, non-linear deformation behavior of magnetostrictive materials is studied and three magnetoelastic coupling constitutive models are developed. The standard square (SS) constitutive model is developed by means of truncating the polynomial expansion of the Gibbs free energy. The hyperbolic tangent (HT) constitutive equations, which involve a hyperbolic tangent magnetic-field dependence, are proposed to model the magnetic-field-induced strain saturation of magnetostrictive materials in the region of intense magnetic fields. A new model based on density of domain switching (DDS) is established in terms of the basic truth that magnetic domain switching underlies magnetostrictive deformation. In this model, it is assumed that the relation between density of domain switching, defined by the quantity of magnetic domains switched by per unit magnetic field and magnetic field can be described by a density function with normal distribution. The moduli in these constitutive models can be determined by a material function that is proposed to describe the dependence of the peak piezomagnetic coefficient on the compressive pre-stress for one-dimensional cases based on the experimental results published. The accuracy of the non-linear constitutive relations is evaluated by comparing the theoretical values with experimental results of a Terfenol-D rod operated under both compressive pre-stress and bias magnetic field. Results indicate that the SS constitutive equations can accurately predict the experimental results under a low or moderate magnetic field while the HT model can, to some extent, reflect the trend of saturation of magnetostrictive strain under a high magnetic field. The model based on DDS, which is more effective in simulating the experimental curves, can capture the main characteristics of the mechanism of magnetoelastic coupling deformation of a Terfenol-D rod, such as the notable dependence of magnetoelastic response on external stress and the saturation of magnetostrictive strain under intense magnetic fields. In addition, the SS constitutive relation for a general three-dimensional problem is discussed and an approach to characterize the modulus tensors is proposed.

Large-signal characterization of prestressed PMN-PT-Ba and PMN-PT-Sr at various temperatures

Quasistatic (10-Hz) electromechanical measurements were made of two relaxor ferroelectrics, PMN–PT–Ba (90 mol% lead-magnesium-niobate, 10 mol% lead-titanate, doped with 3% barium) and PMN–PT–Sr (88 mol% lead-magnesium-niobate, 10 mol% lead-titanate, 2 mol% strontium, w/2500 ppm iron oxide) under high electric fields (0–1.5 MV/m) and high mechanical prestresses (0–41.4 MPa) over a temperature range (−5–40 °C). The measured quantities—the piezoelectric constant, d33, the permittivity, ε33T the Young’s modulus, Y33E the electromechanical coupling factor, k33, and the energy density, U—are found for both small and large ac signal conditions. These measurement conditions and material properties are of great interest for applications in high-power Navy sonar transducers to material manufacturers. Material property trends with increasing prestress, temperature, and electric field are identifieid. The PMN–PT–Sr is shown to have better properties for sonar transducers than the PMN–PT–Ba. Compared to Navy type-III PZT piezoelectric ceramic, the energy density of PMN–PT–Sr at 5°C and 41.4 MPa is nearly 11 dB higher and the coupling 23% lower.

The direct current pre-stress effect on electrical breakdown in oxidized polyethylene

The effects of direct current pre-stress on impulse electric strength Fb of oxidized polyethylene were investigated. For the sample oxidized for 50 h (heavy oxidation), Fb decreased with pre-stress field with both the same and opposite polarity to the subsequent impulse. These results were interpreted in terms of either deep penetration of home space charge injected from an electrode or thermal breakdown due to the large current increase caused by heavy oxidation. For oxidation time 25 h, Fb increased and decreased with field aiding and opposing pre-stress, respectively. The space-charge profile was also observed by the laser induced pressure pulse method. The relation between the pre-stress effect and the space charge distribution can be quantitatively explained in terms of the electric field distortion due to the effect of home space charge formed during the pre-stress. The effects of pre-stress time and rest time following application of pre-stress on Fb were also investigated.

Nonlinear waves in a layer with energy influx

A nonlinear evolution equation is derived to study the propagation of deformation waves in an elastic layer in which energy is not conserved due to possible energy release from the prestress field within the layer. The approach is phenomenological and the influence of nonlinearity, geometrical dispersion and possible energy influx is all accounted for simultaneously. The corresponding KdV-type evolution equation with a r.h.s. is derived. An example is solved numerically for transient waves subject to pulse-type (soliton-type) and harmonic inputs. As a result it is demonstrated that stable solitary waves may form depending on the properties of the driving force.

Domain observation and magnetostriction in Tb0.3Dy0.7Fe2 twinned single crystals

The ternary alloy Tb0.3Dy0.7Fe2 (Terfenol-D) exhibits the largest known magnetostriction to anisotropy ratio near room temperature. To better determine the interaction between the elastic and magnetic properties of this material, a stoichiometric twinned single crystal was grown by a free-standing float-zone technique. Observations using Scanning electron microscopy and energy dispersive spectroscopy confirmed that the sample was free of the normally present rare-earth (RE) eutectic phase and simultaneously free of Widmanstatten precipitate (RE Fe3). A bar with (111) and (11̄0) faces perpendicular to the [112̄] growth direction was examined. Also, a [111̄] slab was cut from the boule. This slab was studied along the [111̄] and [11̄0] directions with prestress applied along the [111̄]. This is the first report of the effects of applying prestress and magnetic fields in a direction not collinear with the [112̄] growth direction. From magnetization (M) and magnetostriction (λ) measurements as a function of field, prestress, and temperature, we determined the hysteresis and saturation parameters. These measurements do not indicate the [11̄0] λ and M behaviors found previously for RE-rich Terfenol-D. Domain observations with differential phase contrast and x-ray topography have shown different orientations in the twin and parent sections of the [111̄] specimen. The observed structures can be interpreted as arising from domains with magnetization components normal to the surface. The domain observations on the (111) and (11̄0) bar faces and on the [111̄] slab correlate with each other with respect to orientations and domain interpretations.

Variability in explosion body-wave magnitudes: An analysis of the RULISON/GASBUGGY anomaly

AbstractAn analysis of the RULISON/GASBUGGY mb anomaly is presented which encompasses comparative studies of near-regional, regional, and teleseismic data recorded from these two explosions, as well as theoretical simulation analyses of selected near-regional and teleseismic data sets. Previously proposed explanations for this mb anomaly, such as differences in explosive source coupling and variations in upper mantle attenuation beneath the two test sites, are critically examined and shown to be inconsistent with various aspects of the observed data. However, both long-period and short-period evidence is presented, which indicates that significant tectonic release accompanied the RULISON explosion. It is demonstrated that the short-period, near-regional SH observations from RULISON can be theoretically explained by an explosion-induced tectonic release equivalent to a 250 to 300 bar stress drop at the elastic radius of the explosion. The inferred prestress field is homogeneous to first order and oriented as a pure shear on planes dipping at about 45°, with normal, or dip-slip displacements occurring as a consequence of stress relaxation. Such a tectonic release mechanism would be expected to decrease the associated explosion mb value by more than 0.3 units and, therefore, can provide a quantitative explanation of the observed RULISON/GASBUGGY mb anomaly. We conclude that tectonic release can significantly affect the short-period teleseismic P waves from explosions, at least in cases where the tectonic stress is large and favorably oriented.

Impulse Breakdown of Prestressed Polyethylene Films in the Ns Range

This paper describes the effect of prestressing on the breakdown strength and time lag of lowdensity polyethylene films subjected to square pulses of 100 ns width. When prestress and impulse fields are opposite in polarity, the 50% breakdown strength Eb decreases from 4.9 to 3.4 MV/cm as the prestressing field is increased from 0 to 4.6 MV/cm. When prestress and impulse fields have the same polarity, Eb increases to 5.4 MV/cm as the prestress is increased to 4.1 MV/cm. The dc break-down strength is 5.8 MV/cm. The formative time lag tf decreases with increasing applied field. The value of tf is insensitive to the level of prestress within a given mode. The mode of opposite prestress yields considerably larger values of tf than the other two modesof no and same prestress, and at relatively low applied fields. The apparent electron mobility calculated from tf increases from 2.2×10-2 to 2.4×10-1 cm2/Vs as the total (prestress +pulse) applied field is changed from 3.0 to 6.0 MV/cm. The results are attributed to a modification of the field intensity near the electrodes due to space charge accumulation during the period of prestressing. The breakdown mechanism is discussed on the basis of an avalanche-streamertransition in the gaseous breakdown theories.