stress drop
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Author(s):  
Chen Ji ◽  
Ralph J. Archuleta

Abstract We investigate the relation between the kinematic double-corner-frequency source spectral model JA19_2S (Ji and Archuleta, 2020) and static fault geometry scaling relations proposed by Leonard (2010). We find that the nonself-similar low-corner-frequency scaling relation of JA19_2S model can be explained using the fault length scaling relation of Leonard’s model combined with an average rupture velocity ∼70% of shear-wave speed for earthquakes 5.3 < M< 6.9. Earthquakes consistent with both models have magnitude-independent average static stress drop and average dynamic stress drop around 3 MPa. Their scaled energy e˜ is not a constant. The decrease of e˜ with magnitude can be fully explained by the magnitude dependence of the fault aspect ratio. The high-frequency source radiation is generally controlled by seismic moment, static stress drop, and dynamic stress drop but is further modulated by the fault aspect ratio and the relative location of the hypocenter. Based on these two models, the commonly quoted average rupture velocity of 70%–80% of shear-wave speed implies predominantly unilateral rupture.


Materials ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 124
Author(s):  
Jun Ho Lee ◽  
Geon Young Lee ◽  
Jong-joo Rha ◽  
Ji Hoon Kim ◽  
Jae-Hyung Cho

Based on electron backscatter diffraction (EBSD), hollow structures of Ni foam struts fabricated by electroplating on a chemically removable template were observed. Three-dimensional (3D) pore structures of Ni foams were also obtained using X-ray computed tomography (CT), and microstructural features such as porosity, pore size and strut thickness were statistically quantified. Evolution of microstructure and mechanical properties during ex situ compression of open-cell Ni-foams was investigated based on X-ray CT, and experimental results were compared with predictions by the finite element method (FEM). 3D microstructures obtained by X-ray CT revealed that the stress drop started with the buckling of struts at the center of the Ni-foams. The flow stress increased after the buckling of the struts spreads to most of the regions. For effective simulation of the compressive deformation and determination of the microstructural evolution, small domains of interest were selected from the entire set of observed 3D microstructures based on X-ray CT, and struts of Ni foams with a hollow structure were simplified with relevant thin-solid struts. Numerical 3D modeling comprehensively disclosed that compression caused the transverse buckling of the struts, with the bending and buckling of struts thus reducing the stress. Thickness variation of the struts causes a change in the porosity of Ni-foams without a change in pore shape or connectivity. The overall range of strut thickness was from 59 to 133 μm, and the range of porosity values was from 80% to 93.7%. A stress drop was predicted with a decrease in the strut thickness or an increase in the porosity, as measured experimentally. It was also found that the stress drop contributed to an increase in the calculated energy absorption efficiency.


2021 ◽  
Author(s):  
Kazumasa Sueyoshi ◽  
Manami Kitamura ◽  
Xinglin Lei ◽  
Ikuo Katayama

Abstract The frequency characteristics of acoustic emission (AE) during triaxial compression of thermally cracked and unheated (“fresh”) granite samples were investigated with the aim of understanding the influence of pre-existing cracks on precursor information regarding macroscopic failure. The peak frequency during the damage process was the same for thermally cracked and fresh granites. Analysis of AE signals showed that signals with low peak frequency appeared before failure of the sample, implying the initiation of microfractures with progressive growth of cracks. The peak amplitude of the frequency spectrum recorded in the thermally cracked samples was much lower than that in the fresh samples. This result suggests two reasons for the difference in peak amplitude: reduction in shear modulus and the attenuation filtering phenomenon caused by thermal cracks. In particular, the maximum value of peak amplitude in the low-frequency band for the thermally cracked samples was smaller than that for fresh samples. This characteristic can be related to the stress drop and crack size. Assuming that pre-existing thermal cracks grow during the pre-failure stage, the events with low peak frequency and low peak amplitude in the heat-treated samples are interpreted as exhibiting a low stress drop because of the small rupturing area for individual events. Therefore, although AE signals with low frequency can be considered as precursors to rock failure, cracking behavior suggested by events with low frequency depends on the initial damage condition of the rock sample.


Lithosphere ◽  
2021 ◽  
Vol 2021 (Special 4) ◽  
Author(s):  
Chenyang Liu ◽  
Lizhi Du ◽  
Xiaopei Zhang ◽  
Yong Wang ◽  
Xinmin Hu ◽  
...  

Abstract Brittleness is a crucial parameter of rock mass and the key indicator in rock engineerings, such as rockburst prediction, tunnelling machine borehole drilling, and hydraulic fracturing. To solve the problem of using present brittleness indexes, the existing rock brittleness indexes were firstly summarised in this paper. Then, a brittleness index (BL), which considers the ratio of stress drop rate and stress increase rate and the peak stress, was proposed. This new index has the advantage of simplifying the acquisition of key parameters and avoiding dimensional problems, as well as taking the complete stress-strain curves into account. While applying the BL, the peak strain is used to describe the difficulty of brittle failure before the peak point, and the ratio of stress drop to strain increase can reflect the stress drop rate without dimension problem. In order to verify the applicability of BL, through the PFC2D, the microparameters and confining pressure were changed to model different types of rock numerical specimens and different stress condition. The results show that the BL can well reflect and classify the brittleness characteristics of different rock types and characterise the constraint of confining pressure on rock brittleness. Moreover, the influence of microparameter on macroparameter was studied. In order to further verify the reliability of the brittleness index (BL), this study conducted uniaxial and triaxial compression tests (30 MPa) on marble, sandstone, limestone, and granite under different confining pressure.


Author(s):  
R. E. Abercrombie ◽  
D. T. Trugman ◽  
P. M. Shearer ◽  
X. Chen ◽  
J. Zhang ◽  
...  
Keyword(s):  

Author(s):  
John G. Anderson ◽  
Glenn P. Biasi ◽  
Stephen Angster ◽  
Steven G. Wesnousky

ABSTRACT We develop a self-consistent scaling model relating magnitude Mw to surface rupture length (LE), surface displacement DE, and rupture width WE, for strike-slip faults. Knowledge of the long-term fault-slip rate SF improves magnitude estimates. Data are collected for 55 ground-rupturing strike-slip earthquakes that have geological estimates of LE, DE, and SF, and geophysical estimates of WE. We begin with the model of Anderson et al. (2017), which uses a closed form equation for the seismic moment of a surface-rupturing strike-slip fault of arbitrary aspect ratio and given stress drop, ΔτC. Using WE estimates does not improve Mw estimates. However, measurements of DE plus the relationship between ΔτC and surface slip provide an alternate approach to study WE. A grid of plausible stress drop and width pairs were used to predict displacement and earthquake magnitude. A likelihood function was computed from within the uncertainty ranges of the corresponding observed Mw and DE values. After maximizing likelihoods over earthquakes in length bins, we found the most likely values of WE for constant stress drop; these depend on the rupture length. The best-fitting model has the surprising form WE∝logLE—a gentle increase in width with rupture length. Residuals from this model are convincingly correlated to the fault-slip rate and also show a weak correlation with the crustal thickness. The resulting model thus supports a constant stress drop for ruptures of all lengths, consistent with teleseismic observation. The approach can be extended to test other observable factors that might improve the predictability of magnitude from a mapped fault for seismic hazard analyses.


2021 ◽  
Vol 40 (9) ◽  
pp. 667-676
Author(s):  
Clay Kurison ◽  
Huseyin S. Kuleli

Microseismic events associated with shale reservoir hydraulic fracturing stimulation (HFS) are interpreted to be reactivations of ubiquitous natural fractures (NFs). Despite adoption of discrete fracture network (DFN) models, accounting for NFs in fluid flow within shale reservoirs has remained a challenge. For an explicit account of NFs, this study introduced the use of seismology-based relations linking seismic moment, moment magnitude, fault rupture area, and stress drop. Microseismic data from HFS monitoring of Marcellus Shale horizontal wells had been used to derive planar hydraulic fracture geometry and source properties. The former was integrated with associated well production data found to exhibit transient linear flow. Analytical solutions led to linear flow parameters (LFPs) and system permeability for scenarios depicting flow through infinite and finite conductivity hydraulic fractures. Published core plug permeability was stress-corrected for in-situ conditions to estimate average matrix permeability. For comparison, the burial and thermal history for the study area was used in 1D Darcy-based modeling of steady and episodic expulsion of petroleum to account for geologic timescale persistence of abnormal pore pressure. Both evaluations resulted in matrix permeability in the same picodarcy (pD) range. Coupled with LFPs, reactivated NF surface area for stochastic DFNs was estimated. Subsequently, the aforementioned seismology-based relations were used for determining average stress drops needed to estimate NF rupture area matching flow-based DFN surface areas. Stress drops, comparable to values for tectonic events, were excluded. One of the determined values matched stress drops for HFS operations in past and recent seismological studies. In addition, calculated changes in pore pressure matched estimates in the aforementioned studies. This study unlocked the full potential of microseismic data beyond extraction of planar geometry attributes and stimulated reservoir volume (SRV). Here, microseismic events were explicitly used in the quantitative account of NFs in fluid flow within shale reservoirs.


Author(s):  
Percy Galvez ◽  
Anatoly Petukhin ◽  
Paul Somerville ◽  
Jean-Paul Ampuero ◽  
Ken Miyakoshi ◽  
...  

ABSTRACT Realistic dynamic rupture modeling validated by observed earthquakes is necessary for estimating parameters that are poorly resolved by seismic source inversion, such as stress drop, rupture velocity, and slip rate function. Source inversions using forward dynamic modeling are increasingly used to obtain earthquake rupture models. In this study, to generate a large number of physically self-consistent rupture models, rupture process of which is consistent with the spatiotemporal heterogeneity of stress produced by previous earthquakes on the same fault, we use multicycle simulations under the rate and state (RS) friction law. We adopt a one-way coupling from multicycle simulations to dynamic rupture simulations; the quasidynamic solver QDYN is used to nucleate the seismic events and the spectral element dynamic solver SPECFEM3D to resolve their rupture process. To simulate realistic seismicity, with a wide range of magnitudes and irregular recurrence, several realizations of 2D-correlated heterogeneous random distributions of characteristic weakening distance (Dc) in RS friction are tested. Other important parameters are the normal stress, which controls the stress drop and rupture velocity during an earthquake, and the maximum value of Dc, which controls rupture velocity but not stress drop. We perform a parametric study on a vertical planar fault and generate a set of a hundred spontaneous rupture models in a wide magnitude range (Mw 5.5–7.4). We validate the rupture models by comparison of source scaling, ground motion (GM), and surface slip properties to observations. We compare the source-scaling relations between rupture area, average slip, and seismic moment of the modeled events with empirical ones derived from source inversions. Near-fault GMs are computed from the source models. Their peak ground velocities and peak ground accelerations agree well with the ground-motion prediction equation values. We also obtain good agreement of the surface fault displacements with observed values.


2021 ◽  
Vol 228 (1) ◽  
pp. 134-146
Author(s):  
Jian Wen ◽  
Jiankuan Xu ◽  
Xiaofei Chen

SUMMARY The stress drop is an important dynamic source parameter for understanding the physics of source processes. The estimation of stress drops for moderate and small earthquakes is based on measurements of the corner frequency ${f_c}$, the seismic moment ${M_0}$ and a specific theoretical model of rupture behaviour. To date, several theoretical rupture models have been used. However, different models cause considerable differences in the estimated stress drop, even in an idealized scenario of circular earthquake rupture. Moreover, most of these models are either kinematic or quasi-dynamic models. Compared with previous models, we use the boundary integral equation method to simulate spontaneous dynamic rupture in a homogeneous elastic full space and then investigate the relations between the corner frequency, seismic moment and source dynamic parameters. Spontaneous ruptures include two states: runaway ruptures, in which the rupture does not stop without a barrier, and self-arresting ruptures, in which the rupture can stop itself after nucleation. The scaling relationships between ${f_c}$, ${M_0}$ and the dynamic parameters for runaway ruptures are different from those for self-arresting ruptures. There are obvious boundaries in those scaling relations that distinguish runaway ruptures from self-arresting ruptures. Because the stress drop varies during the rupture and the rupture shape is not circular, Eshelby's analytical solution may be inaccurate for spontaneous dynamic ruptures. For runaway ruptures, the relations between the corner frequency and dynamic parameters coincide with those in the previous kinematic or quasi-dynamic models. For self-arresting ruptures, the scaling relationships are opposite to those for runaway ruptures. Moreover, the relation between ${f_c}$ and ${M_0}$ for a spontaneous dynamic rupture depends on three factors: the dynamic rupture state, the background stress and the nucleation zone size. The scaling between ${f_c}$ and ${M_0}$ is ${f_c} \propto {M_0^{ - n}}$, where n is larger than 0. Earthquakes with the same dimensionless dynamic parameters but different nucleation zone sizes are self-similar and follow a ${f_c} \propto {M_0^{ - 1/3}}$ scaling law. However, if the nucleation zone size does not change, the relation between ${f_c}$ and ${M_0}$ shows a clear departure from self-similarity due to the rupture state or background stress.


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