Stress Drop Rate Research Articles

Effect of displacement loading rate on dynamic mechanical characteristics of fault stick-slip under constant normal stiffness conditions

The role of the displacement loading rate in fault activation and evolution is of utmost importance, yet most existing studies have primarily focused on its effect under constant normal load (CNL) conditions. However, in reality, the rock mass surrounding the earthquake source at the deep part of the fault provides normal stiffness conditions. Therefore, the influence of the displacement loading rate on the dynamic mechanical characteristics of fault stick-slip under constant normal stiffness (CNS) conditions remains uncertain. To bridge this research gap, we conducted an experimental investigation on simulated faults in granite under constant normal stiffness (CNS) conditions. Our analysis focused on the influence of the displacement loading rate on the spatial and temporal evolution of local stresses along the fault and the size of the fault nucleation zone. The findings revealed the following: Under the CNS condition, the equivalent shear stress is larger compared to the CNL condition, while the shear stress drop is smaller. The recovery of normal stress under CNS conditions depends more on the displacement loading rate. The nucleation location of the fault is influenced by the normal boundary conditions, with a larger nucleation zone observed in the CNS condition than in the CNL condition. In the early stage of friction, the local stress and stress drop of the fault exhibit a positive correlation with the displacement loading rate, whereas in the later stage, they display a negative correlation. Moreover, at the same location, the order of local stress drop rates for the fault is v3 > v1 > v2, where v1 represents the local normal stress drop rate, v2 represents the local shear stress drop rate and v3 represents the local friction coefficient drop rate. These research results contribute to a further understanding of the deep fault-slip mechanical behavior.

Power law dependence of unstable slip velocity on decreasing shear loading stiffness

Shear loading stiffness plays a critical role in conditioning the stability of slip on reactivated faults. However, a relationship linking peak slip velocities and shear loading stiffness is lacking. To explore this, we shear granite faults in double direct shear with shear loading stiffnesses spanning two orders to define the effects of shear loading stiffness in conditioning the transition from stable to unstable slip. Our results show that peak slip velocity and acceleration decrease as power law relationships with respect to the shear loading stiffness ratio, with identical exponent, and with a linear relationship between the peak slip velocity and acceleration. The maximum acceleration occurs during the velocity weakening process that limits the peak slip velocity. The power law exponent increases linearly with increasing normal stress. Experimental results also indicate that slip magnitude, stress drop and recurrence time of unstable slip events increase, and slip durations decrease with decreasing stiffness ratios. The spans of limit cycles of velocity versus shear stress decrease, and their shapes evolve from triangular to semicircular with increasing loading stiffness ratio. Stress drops mostly occur during deceleration. The deceleration phase dominates the unstable slip duration that decreases as peak slip velocity increases. Our results indicate that the average stress drop rates over a slip duration increase as a power law relationship with reducing shear loading stiffness, which also contributes to a lower shear loading stiffness producing increased slip velocities and accelerations. Our findings highlight that loading stiffness ratio is an underlying mechanism defining unstable slip behaviors with the normal stress merely conditioning the exponent. The present relationship of unstable slip velocity with shear loading stiffness suggests a way to evaluate hazard of an impending instability event based on the initial shear loading stiffness ratio that can be calculated through the linear-elastic behaviors at the early quasi-static phase.

Mechanical parameter evolutions and deterioration constitutive model for ductile–brittle failure of surrounding rock in high-stress underground engineering

The deep surrounding rock is usually in the true triaxial stress state, and previous constitutive models based on the understanding of uniaxial and conventional triaxial test results have difficulty characterizing the degradation and fracture process of rock ductile–brittle failure under true triaxial stress state. Therefore, this study conducted a series of true triaxial tests to obtain the understanding of the ductile–brittle behaviour of rock, and then combined the test results and the Mogi–Coulomb strength criterion, and proposed calculation methods for the elastic modulus E, cohesion c and internal friction angle φ and the evolution functions of E, c and φ of rock under true triaxial stresses. With the decreasing of the minimum principal stress σ3 or increasing of the intermediate principal stress σ2, the marble post-peak stress drop rate gradually increases, the ductility gradually weakens, and the brittleness significantly strengthens. The calculation method and evolution function of rock E, c and φ under true triaxial stress were proposed. E decreased at first and then tended to remain stable with the increasing of equivalent plastic strain increment dεp. c and φ slowly increased at first and then rapidly decreased. With a method of parameter degradation rate to realize post-peak stress drop rate to reflect the ductile–brittle characteristics, a new three-dimensional ductile–brittle deterioration mechanical model (3DBDM) was established. The proposed model can accurately characterize the influence of σ2 and σ3 on mechanical parameters, the ductile–brittle behaviour of rock under true triaxial stresses, and the asymmetric failure characteristics of surrounding rock after excavation of deep underground engineering. The proposed model can be reduced to elastic–perfectly plastic, elastic–brittle, cohesion weakening friction strengthening (CWFS), Mohr–Coulomb, and Drucker–Prager models.

Test study on failure and energy supply characteristics of rock under different loading stiffness

Based on the stiffness theory, the stiffness difference and energy supply of surrounding rocks are important inducing factors for rock burst. However, due to the lack of multi-level low stiffness testing machine, there are few experimental studies on rock failure mechanism under the influence of loading stiffness. Aiming at the above problems, this paper improved the rock mechanics testing machine, and developed several sets of low stiffness flexible rings, which realized laboratory test under five different loading stiffness in the range of 0.07 ∼ 0.615GN/m. Based on low stiffness loading device, the mechanical behavior of sandstone specimens was studied. With the decrease of the loading stiffness, the post-peak stage of the stress–strain curve of the specimen changes from step shape to oblique linear shape, and the specimen changes from progressive shear failure to brittle splitting failure. There is a power function positive correlation between the specimen’s post-peak failure duration and stiffness ratio of the testing machine and the specimen, and a power function negative correlation between stress drop rate and stiffness ratio. When the specimen is damaged and the stress is dropped, the deformation of low stiffness testing machine rebounds with high-speed, resulting in an obvious dynamic load behavior. The loading stiffness has little effect on the energy storage and energy dissipation characteristics of the specimen, while the release energy of the testing machine increases as the stiffness ratio decreases, which is the key factor affecting the failure mode of the specimen. According to the test results, a rock burst mechanical model considering the stiffness is established, and the energy supply mechanism of rock burst is quantitatively explained.

Source time functions of earthquakes based on a stochastic differential equation

Source time functions are essential observable quantities in seismology; they have been investigated via kinematic inversion analyses and compiled into databases. Given the numerous available results, some empirical laws on source time functions have been established, even though they are complicated and fluctuated time series. Theoretically, stochastic differential equations, including a random variable and white noise, are suitable for modeling complicated phenomena. In this study, we model source time functions as the convolution of two stochastic processes (known as Bessel processes). We mathematically and numerically demonstrate that this convolution satisfies some of the empirical laws of source time functions, including non-negativity, finite duration, unimodality, a growth rate proportional to t^3, omega ^{-2}-type spectra, and frequency distribution (i.e., the Gutenberg–Richter law). We interpret this convolution and speculate that the stress drop rate and fault impedance follow the same Bessel process.

Reduction of Brittleness of Fine Sandy Soil Biocemented by Microbial-Induced Calcite Precipitation

Microbial-induced calcite precipitation (MICP) is a sustainable soil improvement technology widely used in the biogeotechnical field. However, the high brittleness of calcium bonding in biomineralization has limited the application of MICP. The objective of this study was to find an efficient microbial treatment that reduces the brittleness of traditional MICP. An experiment was conducted in three stages in 2016 (MICP-B), 2018 (MICP-C), and 2020 (MICP-E). Unconfined compressive strength and triaxial compression tests were performed. Residual strength and failure and residual strain increased, the post-peak stress drop rate decreased, and the failure pattern changed from vertical through crack to oblique crack. Brittleness was substantially reduced. The cement between the sand particles was analyzed by SEM, EDS, and IR spectroscopy. It consisted of calcium carbonate plus glial extracellular polysaccharides and was mainly responsible for reducing MICP brittleness. The final MICP-E test was based on a highly effective microbial strain screened from the soil. This bacterium had good brittleness reduction efficacy and has excellent practical potential for MICP biocementation. The experimental results of the study provide theoretical and empirical foundations for brittleness reduction in MICP-treated soils. Ameliorated biocementation technology could be used for the microbial reinforcement of mechanically unstable soils.

A New Rock Brittleness Evaluation Method Based on the Complete Stress-Strain Curve

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.

Multicycle Simulation of Strike-Slip Earthquake Rupture for Use in Near-Source Ground-Motion Simulations

ABSTRACTRealistic 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.

The role of friction in statistics and scaling laws of avalanches.

We investigate statistics and scaling laws of avalanches in two-dimensional frictional particles by numerical simulations. We find that the critical exponent for avalanche size distributions is governed by microscopic friction between the particles in contact, where the exponent is larger and closer to mean-field predictions if the friction coefficient is finite. We reveal that microscopic "slips" between frictional particles induce numerous small avalanches which increase the slope, as well as the power-law exponent, of avalanche size distributions. We also analyze statistics and scaling laws of the avalanche duration and maximum stress drop rates, and examine power spectra of stress drop rates. Our numerical results suggest that the microscopic friction is a key ingredient of mean-field descriptions and plays a crucial role in avalanches observed in real materials.

Dynamic rupture of subduction earthquakes located near the trench

We perform kinematic and dynamic source inversions of four interplate thrust earthquakes that occurred near the trench at the base of the continental wedge in Northern Chile and we compare them to deeper intraplate events. The magnitudes of these interplate events were between Mw 6.3 and Mw 6.5, with hypocentral depths varying between 17.8 km and 28 km. These earthquakes correspond to one foreshock and three aftershocks of the large 2014 Mw 8.2 Iquique earthquake. The geometry of the seismic rupture obtained from the kinematic and dynamic inversions were similar for the four earthquakes studied and their dynamic source parameters are in accordance with typical interplate earthquakes around Mw 6.5. We compare the dynamic rupture of these events with those of five intraplate, intermediate-depth earthquakes that occurred in Northern Chile, Japan, Argentina and Mexico with depths between 57 km and 250 km. We also compare these events with the Mw 6.9 Valparaiso earthquake that was also a shallow interplate thrust event. Results show that the main dynamic parameters of the interplate events (stress in the nucleation zone, overall stress drop and fracture energy rate) were smaller than those of the intraplate intermediate-depth earthquakes. Furthermore, we compare our results with those obtained with several methodologies commonly used to estimate values of stress drop, fault radius and corner frequency. We find some minor differences between them for most of the earthquakes analyzed. Finally, we infer from our results that the studied area, located in the subduction interface zone near the trench, is suitable for earthquake nucleation of small to moderate earthquakes and does not represent a barrier for a future large tsunamigenic rupture.

A New Rock Brittleness Index Based on the Characteristics of Complete Stress–Strain Behaviors

Rock brittleness is an essential mechanical property, which plays a significant role in rock classifications and rockburst risk evaluations. To overcome the problems associated with the traditional brittleness indexes not comprehensively charaterizing the rock strength and deformation behaviors, this study systematically summarized the existing rock brittleness indexes. Then, a novel brittleness index (BICSS) based on the complete stress–strain curves of rock under different confining pressures was proposed. Its advantages included innovatively considering the characteristic stresses and strains at the stage of crack initiation, the peak points, and residual points. The index also described the stress growth rates from the pre-peak crack-initiation stress to the peak stress points, as well as the stress drop rates from the peak stress to the residual stress points. This study conducted uniaxial and triaxial compression tests of metamorphic sandstone, granite, and gneiss obtained from a deeply buried long-line tunnel group. The aforementioned tests were combined with wave velocity tests and thin-section identification tests using polarizing microscopy techniques. The reliability and applicability of the index were then successfully verified. The results showed that the BICSS could not only quantify and classify the brittleness characteristics of different rock types and characterize the confining pressure inhibition behaviors of rock brittleness, but could also comprehensively express the influences of homogeneity, mineral compositions, and particle sizes on the rock brittleness. Finally, through the parameter sensitivity analysis of the BICSS, the influences of subjective errors in the results of the cracking initiation stress and strain values caused by the different selections during the linear elastic phase could be successfully excluded, resulting in the further verification of the stability of the BICSS.

Measurement of stress-time avalanches inside polypropylene fiber reinforced concrete beams during flexure

In this work, we studied stress variations of loading histories on polypropylene fiber reinforced concrete beams during flexure. A new experimental system was created to collect the stress-time curves at 100 kHz sampling rate to reveal temporal profiles of stress drops in high resolution. Concrete beams prepared at the early age of seven days with different fiber volume fractions were loaded at various rates during four-point bending tests. Stress drops induced by interactions between polypropylene fibers and cementitious matrices or matrix cracking were modeled as avalanches along the time history. We used the mean field model to predict statistics and dynamics of avalanches occurred inside polypropylene fiber reinforced concrete beams during flexure. Good agreement was obtained between measurements and predicted power law exponents and scaling functions from the mean field model. Two types of avalanches were observed for polypropylene fiber reinforced beams during flexure, i.e., small avalanches collapsed onto the scaling regime and large avalanches beyond the regime. Maximum stress drop rates of small avalanches were on the order of kPa/s, whereas maximum stress drop rates of large avalanches could reach the order of MPa/s. Observations of different avalanches revealed insights into the essential failure evolved during flexure concrete beams, i.e., small avalanches with limited plastic deformation and large avalanches with extended incubation periods. Findings from this study could help measure the evolved damage of concrete structural members under service loads, which provide valuable hints to improve the durability of reinforced concrete structures.

Study of Strength and Deformation Evolution in Raw and Briquette Coal Samples under Uniaxial Compression via Monitoring Their Acoustic Emission Characteristics

Briquette coals with different cement contents are frequently used to study the coal body’s properties. In this study, the deformation and strength of briquette coal samples with 0, 5, 10, and 20% cement contents were experimentally and theoretically investigated using the acoustic emission (AE) characteristics monitored during the uniaxial compression tests. The results show that the uniaxial compression process of raw coal and briquette coal samples can be subdivided into compaction, elastic, plastic (yield), and brittle failure stages. With an increase in cement content, briquette coal samples undergo the elastic and plastic stages, and their postpeak stress drop rate gradually grows, and their plastic deformation is followed by brittle failure. The uniaxial compressive strength and elastic modulus of briquette coal samples show a linearly increasing relationship with cement content, while their Poisson’s ratio decreases gradually. During the uniaxial compression, raw coal and briquette coal samples produce the AE signals. The overall AE signal of briquette coal samples is relatively low, and there are no obvious AE events in raw coal samples. The uniaxial compressive strength, elastic modulus, and Poisson’s ratio of briquette coal samples with a 20% cement content and their AE signal cumulative amplitude, count, and energy values are very close to the corresponding parameters of raw coal samples. Therefore, they can be used for simulating raw coal samples in laboratory tests.

Dynamics of deformation band formation investigated by high-speed techniques during creep in an AlMg alloy

Dynamics of the deformation band formation during creep in an Al–Mg alloy was investigated by simultaneous high-speed video recording of deformation bands with an extremely high time resolution of 40 μs and measurement of the concomitant acoustic emission. The results are consistent with the mechanism where the trigger of a strain step on the creep curve is the nucleation and rapid widening of a primary deformation band, generating an acoustic emission signal within 1 ms. Correlations between various stages of the deformation band formation, acoustic emission, and stress response are explored in detail. Notably, the stress drop rate and the amplitude of the acoustic emission signal are found to be linearly related. The mechanism of the acoustic emission associated with the initial rapid stage of the band development is discussed.

Rock Brittleness Evaluation Method Based on the Complete Stress-Strain Curve

Brittleness plays an important role in the brittle failure process of rocks, and is also one of the important mechanical properties of rocks and a key indicator in rock engineering such as hydraulic fracturing, tunnelling machine borehole drilling and rockburst prediction. Therefore, aiming at the applicability of the brittleness index, this paper summarizes and analyzes the existing brittleness indices based on different experimental methods. Through analysis, it is found that many of the existing methods have their limitations. On the other hand, the brittleness evaluation method based on the stress s-strain curve makes it easier to obtain key parameters and quantify them. Therefore, this paper also adopts this practically widely used method. It proposes a brittleness index based on the post-peak stress drop rate of the rock stress-strain curve and the difficulty of brittle failure, verifies by the traditional triaxial surrounding rock pressure test the accuracy and superiority of BL and further explores the differences between the brittleness indices B8, B11, B12 and BL. Finally, the brittleness index BL and B13 are further contrasted by the existing experimental data.

Evaluation of rock brittleness based on the ratio of stress drop rate to strain drop rate and peak strength

Evaluation of rock brittleness based on the ratio of stress drop rate to strain drop rate and peak strength

Characteristics of secondary slip fronts associated with slow earthquakes in Cascadia

We implement an algorithm to automatically detect migrations of low frequency earthquakes at time scales between 30 min and 32 h during the 2003, 2004 and 2005 slow slip events in Cascadia. We interpret these migrations of seismicity as a passive manifestation of secondary slip fronts (SSFs) that propagate faster than the main front. We identify the dominant features of 383 SSFs, including time, location, duration, area, propagation velocity and estimate: their moment, stress drop, slip, and slip rate. We apply the same algorithm to continuous tremor detection in Cascadia between 2009 and 2015 and characterize 693 SSFs at time scales between 4 h and 32 h. We identify — to our knowledge for the first time — numerous 11–22.5 h long SSFs that propagate at velocities intermediate between slow slip events and previously reported SSFs. The systematic detection of SSFs fills a gap between seismically and geodetically detectable slow earthquake processes. Analysis of SSF basic features indicates a wide range of stress drops and slip rates (with medians of 5.8 kPa and 1.1 mm/h) as well as an intriguing relationship between SSF direction and duration that was observed in other contexts and could potentially help discriminate between the different physical models proposed to explain slow slip phenomena.

A New Method to Evaluate Rock Mass Brittleness Based on Stress–Strain Curves of Class I

Brittleness is a key controlling parameter for rock engineering projects such as hydrocarbon production and other applications. In this paper, commonly used methods based on stress–strain curves of Class I for the calculation of rock brittleness are reviewed. In order to describe the rock brittleness more reasonable, the new index B i was proposed based on the stress drop rate obtained from post-peak stress–strain curve and the ratio of elastic energy released during failure to the total energy stored before the peak strength. Then the validity of B i is verified with experimental tests conducted on rock specimens drilled from the interlayer and oil layer through a well of Shengli Oilfield. Moreover, numerical simulation is performed to analyze the effects of primary mechanical parameters on the brittleness of rock masses. Based on experimental tests and numerical simulation results, the acoustic emission modes influenced by brittleness index B i are summarized. At last, correlation between acoustic emission mechanism and index B i is verified by comparing the acoustic emission modes of limestone under different levels of confining pressure and various types of coal.

Assessment of teleseismically-determined source parameters for the April 25, 2015 MW 7.9 Gorkha, Nepal earthquake and the May 12, 2015 MW 7.2 aftershock

On April 25, 2015 a major (MW 7.9) thrust earthquake ruptured the deeper portion of the seismogenic plate boundary beneath Nepal along which India is underthrusting Eurasia. An MW 7.2 aftershock on May 12, 2015 extended the eastern, down-dip edge of the rupture. These destructive events caused about 9000 fatalities and 23,000 injuries. The overall rupture zone is about 170km long and 40–80km wide. This region of the plate boundary previously experienced a large earthquake in 1833, and in 1934 a larger MS 8.0 event located to the east ruptured all the way to the surface. The Main Himalayan Thrust (MHT) on which slip occurred in 2015 has a very low dip angle of ~6°, and the depth of the mainshock slip distribution is very shallow, extending from ~7 to ~18km. The shallow dip and depth present challenges for resolving faulting characteristics using teleseismic data. We analyze global teleseismic signals for the mainshock and aftershock to estimate source parameters, evaluating the stability of various procedures used for remotely characterizing kinematics of such shallow faulting. Back-projection and finite-fault slip inversion are used to assess the spatio-temporal rupture history and evidence for frequency-dependent radiation along dip. Slip zone width constraints from near-field geodetic observations are imposed on the preferred models to overcome some limitations of purely teleseismic methods. Radiated energy, stress drop and moment rate functions are determined for both events.

Experimental evidence for both progressive and simultaneous shear during quasistatic compression of a bulk metallic glass

Two distinct types of slip events occur during serrated plastic flow of bulk metallic glasses. These events are distinguished not only by their size but also by distinct stress drop rate profiles. Small stress drop serrations have fluctuating stress drop rates (with maximum stress drop rates ranging from 0.3–1 GPa/s), indicating progressive or intermittent propagation of a shear band. The large stress drop serrations are characterized by sharply peaked stress drop rate profiles (with maximum stress drop rates of 1–100 GPa/s). The propagation of a large slip is preceded by a slowly rising stress drop rate that is presumably due to the percolation of slipping weak spots prior to the initiation of shear over the entire shear plane. The onset of the rapid shear event is accompanied by a burst of acoustic emission. These large slips correspond to simultaneous shear with uniform sliding as confirmed by direct high-speed imaging and image correlation. Both small and large slip events occur throughout plastic deformation. The significant differences between these two types require that they be carefully distinguished in both modeling and experimental efforts.