Surface strain accumulation and the seismic moment tensor

1997 ◽  
Vol 87 (5) ◽  
pp. 1345-1353
Author(s):  
J. C. Savage ◽  
R. W. Simpson
Keyword(s):  
Strain Rate ◽  
Accumulation Rate ◽  
Moment Tensor ◽  
Surface Strain ◽  
Seismogenic Zone ◽  
Strain Accumulation ◽  
Average Strain ◽  
Average Strain Rate ◽  
Double Couple ◽  
Scalar Moment

Abstract Although the scalar moment accumulation rate within the seismogenic zone beneath a given area is sometimes deduced from the observed average surface strain accumulation rate over that same area (e.g., Working Group on California Earthquake Probabilities, 1995), the correspondence between the two is very uncertain. The equivalence between surface strain accumulation and scalar moment accumulation is based on Kostrov's (1974) relation between the average strain rate over a volume and the moment-rate tensor for that volume. The average strain rate over the volume is replaced by the average strain rate measured at the free surface to deduce an approximate moment-rate tensor. Only in exceptional circumstances will that moment-rate tensor correspond to a double-couple mechanism, a mechanism that can be represented by a scalar moment accumulation rate. More generally, the moment tensor must be resolved into the superposition of two or more double-couple mechanisms, and that resolution can be done in many ways, each with its own scalar moment rate. Thus the resolution is not unique. This is demonstrated by deducing scalar moment accumulation rates for a GPS network that covers most of California south of San Francisco. It is shown that resolutions into different double-couple mechanisms lead to scalar moment accumulation rates differing by factors of ∼2. We suggest that the minimum scalar moment rate equivalent to principal surface strain rates ɛ1 and ɛ2 acting over the area A is M0(min) = 2μHA Max (¦ɛ1¦, ¦ɛ2¦, ¦ɛ1 + ɛ2¦), where μ is the rigidity and H the depth of seismogenic zone, and the function Max is equal to the largest of its arguments. Within the uncertainites of measurement, the scalar moment accumulation rate in southern California based on that approximation is in balance with the average historic seismic moment release rate so that no current earthquake deficit need be accumulating.

Evaluation of Fatigue Damage on Operating Plant Components in LWR Water

2004 ◽  
Author(s):  
Makoto Higuchi ◽  
Takashi Hirano ◽  
Katsumi Sakaguchi
Keyword(s):  
Strain Rate ◽  
Fatigue Damage ◽  
Austenitic Stainless Steels ◽  
Strain Range ◽  
Average Strain ◽  
Simple Method ◽  
Detailed Method ◽  
Class 1 ◽  
Average Strain Rate ◽  
Fatigue Life Reduction

The effects of LWR water environments on fatigue life reduction of LWR component materials have been evaluated quantitatively. The environmental correction factor Fen, which is determined by strain rate, temperature and dissolved oxygen content has been proposed for assessing this reduction in the case of carbon, low alloy and austenitic stainless steels. Equations to calculate Fen have been established based on fatigue data derived under constant test conditions but strain rate and temperature in actual transients are usually not constant. A method for calculating Fen under conditions of continuously changing strain rate and temperature was established in this study for use in assessing fatigue damage on actual transients, with due consideration to the effects of LWR water environments. The method should be found applicable to Class 1 vessels. It should be possible to determine the stress cycle and fatigue usage factor in air in accordance with the ASME B&PV Code Section III NB-3200. Fatigue damage in LWR water may be found by linear summation of the products of Fen and partial fatigue usage factor in stress cycles. The method is consisted of simple and detailed methods. The evaluation of Fen must be applied for the strain range in which the strain increases continuously. In the simple method, the entire range of stain increasing is used as one segment and the average strain rate and the highest temperature in it are used for computing Fen. In the detailed method, the strain increasing range should be divided into small segments and average strain rate and highest temperature in it are used for finding Fen and Fens in all segments are subsequently averaged by weighting with strain increment in it. The Fen by this latter procedure was found much less than with the former under a condition of considerable temperature change.

The Influence of Strain Rate on the Passive and Stimulated Engineering Stress–Large Strain Behavior of the Rabbit Tibialis Anterior Muscle

1998 ◽  
Vol 120 (1) ◽  
pp. 126-132 ◽  
Author(s):  
B. S. Myers ◽  
C. T. Woolley ◽  
T. L. Slotter ◽  
W. E. Garrett ◽  
T. M. Best
Keyword(s):  
Strain Rate ◽  
Tibialis Anterior ◽  
High Speed ◽  
Large Strain ◽  
Strain Rates ◽  
Average Strain ◽  
Stress Strain ◽  
Engineering Stress ◽  
Average Strain Rate ◽  
Strain Responses

The passive and stimulated engineering stress–large strain mechanical properties of skeletal muscle were measured at the midbelly of the rabbit tibialis anterior. The purpose of these experiments was to provide previously unavailable constitutive information based on the true geometry of the muscle and to determine the effect of strain rate on these responses. An apparatus including an ultrasound imager, high-speed digital imager, and a servohydraulic linear actuator was used to apply constant velocity deformations to the tibialis anterior of an anesthetized neurovascularly intact rabbit. The average isometric tetanic stress prior to elongation was 0.44 ± 0.15 MPa. During elongation the average stimulated modulus was 0.97 ± 0.34 MPa and was insensitive to rate of loading. The passive stress–strain responses showed a nonlinear stiffening response typical of biologic soft tissue. Both the passive and stimulated stress–strain responses were sensitive to strain rate over the range of strain rates (1 to 25 s−1). Smaller changes in average strain rate (1 to 10, and 10 to 25 s−1) did not produce statistically significant changes in these responses, particularly in the stimulated responses, which were less sensitive to average strain rate than the passive responses. This relative insensitivity to strain rate suggests that pseudoelastic functions generated from an appropriate strain rate test may be suitable for the characterization of the responses of muscle over a narrow range of strain rates, particularly in stimulated muscle.

scholarly journals Estimation of crustal deformation parameters and strain build-up in Northwest Himalaya using GNSS data measurements

2021 ◽  
Vol 51 (3) ◽  
pp. 225-243
Author(s):  
Abhishek YADAV ◽  
Suresh KANNAUJIYA ◽  
Prashant Kumar CHAMPATI RAY ◽  
Rajeev Kumar YADAV ◽  
Param Kirti GAUTAM
Keyword(s):  
Seismic Hazard ◽  
Strain Rate ◽  
Accumulation Rate ◽  
Himalayan Region ◽  
Compression Rate ◽  
Strain Accumulation ◽  
Gps Measurements ◽  
Baseline Method ◽  
Maximum Shear Strain ◽  
Continuous Gps

GPS measurements have proved extremely useful in quantifying strain accumulation rate and assessing seismic hazard in a region. Continuous GPS measurements provide estimates of secular motion used to understand the earthquake and other geodynamic processes. GNSS stations extending from the South of India to the Higher Himalayan region have been used to quantify the strain build-up rate in Central India and the Himalayan region to assess the seismic hazard potential in this realm. Velocity solution has been determined after the application of Markov noise estimated from GPS time series data. The recorded GPS data are processed along with the closest International GNSS stations data for estimation of daily basis precise positioning. The baseline method has been used for the estimation of the linear strain rate between the two stations. Whereas the principal strain axes, maximum shear strain, rotation rate, and crustal shortening rate has been calculated through the site velocity using an independent approach; least-square inversion approach-based triangulation method. The strain rate analysis estimated by the triangulation approach exhibits a mean value of extension rate of 26.08 nano-strain/yr towards N131°, the compression rate of –25.38 nano-strain/yr towards N41°, maximum shear strain rate of 51.47 nano-strain/yr, dilation of –37.57 nano-strain/yr and rotation rate of 0.7°/Ma towards anti-clockwise. The computed strain rate from the Baseline method and the Triangulation method reports an extensive compression rate that gradually increases from the Indo-Gangetic Plain in South to Higher Himalaya in North. The slip deficit rate between India and Eurasia Plate in Kumaun Garhwal Himalaya has been computed as 18±1.5 mm/yr based on elastic dislocation theory. Thus, in this study, present-day surface deformation rate and interseismic strain accumulation rate in the Himalayan region and the Central Indian region have been estimated for seismic hazard analysis using continuous GPS measurements.

Comparative Study of Element Formulation on Simulation of Superplastic Forming

2007 ◽  
Vol 551-552 ◽  
pp. 281-286 ◽  
Author(s):  
X.F. Xu ◽  
L.M. Tang ◽  
G.Q. Tong
Keyword(s):  
Finite Element ◽  
Comparative Study ◽  
Strain Rate ◽  
Rate Control ◽  
Superplastic Forming ◽  
Control Algorithms ◽  
Average Strain ◽  
Pressure Time ◽  
Average Strain Rate ◽  
Forming Characteristics

A comparative study of different element formulations in simulating superplastic forming with the MARC finite element code is performed in the paper. Simulations were accomplished with solid, shell, membrane elements to predict forming characteristics and pressure-time curves. Finite element analysis (FEA) predictions of SPF pressure-time curves were found to be greatly affected by the element type and the strain rate control algorithms. Two strain rate control algorithms were applied in the present study: an algorithm based on limiting the rate of deformation with the average strain rate of all the elements, i.e. the build-in method in MARC, and a second algorithm which limits the rate of deformation based on the average strain rate of the elements with the 20 highest strain rates. The resulting pressure-time curves for each of these formulations were compared with respect to each type of element. Under the guide of the analysis, the die was fabricated and the AA5083 bracket was successfully manufactured. Good agreement was obtained between predicted and measured thickness in the part.

scholarly journals Ice Flow along the Byrd Station Strain Network, Antarctica

1979 ◽  
Vol 24 (90) ◽  
pp. 15-28 ◽  
Author(s):  
I. M. Whillans
Keyword(s):  
Strain Rate ◽  
Isotopic Ratio ◽  
Accumulation Rate ◽  
Ice Core ◽  
Ice Sheet ◽  
Surface Strain ◽  
Rate Data ◽  
Progressive Development ◽  
Bed Form ◽  
Oxygen Isotopic

AbstractThe flow of the Antarctic ice sheet near Byrd Station is modeled using surface net accumulation-rate data, surface strain-rate data, and core-hole tilting results. The model empirically allows for the progressive development of ice fabric and for values of the vertical strain-rate nearer to zero at depth, and adjusts the strain-rates according to the effect of the climatic warming at the beginning of the Holocene.The validity of the model is supported by the agreements between calculated bed form and that measured by radar sounding, and between calculated and measured present-day ice-sheet thinning-rates. The ice was about 200 m thicker before thinning.The depth-age relationship for the Byrd Station ice core shows that the climatic change represented by the oxygen isotopic ratio of the ice began some 5000 years sooner than in north Greenland (Hammer and others 1978), but ended at about the same time.

Research on the Mechanical Behavior of Styropor Concrete at High Strain Rates

2010 ◽  
Vol 168-170 ◽  
pp. 2086-2091
Author(s):  
Ze Bin Hu ◽  
Jin Yu Xu ◽  
Jie Zhu ◽  
Qiang He ◽  
Gang Li ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Strain Rate ◽  
Mechanical Behavior ◽  
High Strain ◽  
Dynamic Strength ◽  
Strain Rates ◽  
Average Strain ◽  
High Strain Rates ◽  
Average Strain Rate ◽  
The Impact

Mechanical behavior of Styropor concrete(EPSC) added with various volumetric fractions of EPS subjected to high strain rates were studied by using the Large-Diameter-SHPB. The infection of volumetric fractions and average strain rate to dynamic properties of EPSC were investigated. The experimental results show that under high strain rate condition, the dynamic strength, dynamic strength increase factor(DIF) and limit strain of EPSC are strain rate dependent, the strain rate effect can be expressed by linear approximations, and the relationship between elastic modulus and average strain rate is independent.With the addition of volumetric fractions of EPS, the impact compressive strength and elastic modulus of EPSC declines, and the toughness of EPSC is reinforced.

Measurement of the average strain rate of thin aluminum deformation under laser shock

2013 ◽  
Vol 52 (5) ◽  
pp. 054302
Author(s):  
Hongbing Yao ◽  
Zhusheng Zhou ◽  
Yanqun Tong ◽  
Jie Ping ◽  
Liangwan Li ◽  
...  
Keyword(s):  
Strain Rate ◽  
Laser Shock ◽  
Average Strain ◽  
Thin Aluminum ◽  
Average Strain Rate

Use of Average Temperature in Fen Calculations

2020 ◽  
Author(s):  
W. F. Weitze
Keyword(s):  
Strain Rate ◽  
Rise Time ◽  
Water Environment ◽  
Constant Strain Rate ◽  
Temperature Response ◽  
Threshold Temperature ◽  
Average Strain ◽  
Linear Temperature ◽  
Average Temperature ◽  
Average Strain Rate

Abstract The effect of the light reactor water environment on fatigue damage is referred to as environmentally assisted fatigue (EAF). This effect is accounted for by applying an environmental fatigue correction factor, Fen, to calculated fatigue usage. In providing guidelines for calculation of Fen, Revision 0 of NUREG/CR-6909 [1] permits temperature averaging for the case of a constant strain rate and linear temperature response, and permits it in other cases as well, but only if the average temperature used produces results that are consistent with the modified rate approach [1, p. A.5]. Revision 1 of NUREG/CR-6909 [2] modifies this slightly, requiring that the threshold temperature be used in averaging instead of the minimum if the minimum is below the threshold [2, p. A-6]. In both cases, the benchmark for accuracy is the modified rate approach [2, Section 4.4]. In this paper, we use real world examples to compare Fen values based on the modified rate approach with those using average strain rate and temperature. We also examine how to select the rise time used to calculate average strain rate in those cases where it is not obvious. We find that temperature averaging is conservative if rise time and other parameters are correctly selected.

scholarly journals Coupled Static-Dynamic Tensile Mechanical Properties and Energy Dissipation Characteristic of Limestone Specimen in SHPB Tests

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Qi Ping ◽  
Zhaohui Fang ◽  
Dongdong Ma ◽  
Hao Zhang
Keyword(s):  
Mechanical Property ◽  
Tensile Strength ◽  
Strain Rate ◽  
Dynamic State ◽  
Average Strain ◽  
Absorbed Energy ◽  
Dynamic Tensile Strength ◽  
One Dimensional ◽  
Average Strain Rate ◽  
Dissipation Characteristic

To investigate the dynamic splitting tensile mechanical property of limestone under coupled static and dynamic state, the dynamic split tensile tests of limestone under one-dimensional coupled static and dynamic load with different strain rates were performed with the help of modified split Hopkinson pressure bar (SHPB) equipment. The dynamic splitting tensile mechanical property and energy dissipation characteristic under two stress states were also compared in this research. Test results indicated that the dynamic tensile strength of the limestone specimen increased with the increase of average strain rate, exhibiting an obvious strain rate effect. In addition, dynamic tensile strength under uniaxial state was higher than that under one-dimensional coupled static and dynamic load state under the same test condition. Moreover, the deformation modulus increased with increasing average strain rate under uniaxial state, while it decreased with increasing average strain rate under coupled static and dynamic state. Both the reflected energy and absorbed energy linearly increased with increasing incident energy. The preload in the radial direction could increase the reflected energy and decrease the absorbed energy. Moreover, the transmitted energy with preload state was slightly lower than that under uniaxial state. Finally, the dynamic tensile strength of limestone specimen increased as a power function with increasing absorbed energy.

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