Slip Front Research Articles

Opening versus shearing of a fluid-driven fault reactivation

Geological injection of fluids plays a key role in addressing societal challenges such as renewable energy transition and climate crisis mitigation. However, frequent injection activities would disturb the stability of surrounding fault zones and furtherly induce seismicity. When fluid enters a fault, the competition among pressure front and slip front can play a role on the fault’s seismic behaviour. Fault’s stiffness as well as the rock’s Poisson’s ratio affects the shape of the slip and pressure front. In this study, the fault’s seismic behaviour has been extensively study through numerical modelling. The aim is to investigate the impact of deformable aperture and rock matrix’s Poisson’s ratio on the opening rupture and shear rupture of a pre-existing critically stressed fault. The parametric study shows that, with this initial stress state, the opening rupture grows slower than the shearing rupture, and the ratio between the front length is approximately 70%. A slip-weakening feature could boost this difference. Moreover, the variation between the front length along the y-direction and dip-direction of the fault increases with the increase of rock matrix’s Poisson’s ratio.

Geomechanical modelling of injection-induced seismicity: the case study of the Muara Laboh geothermal plant

SUMMARY In this work, we study the induced seismicity recorded during an injection operation at the Muara Laboh geothermal plant (Indonesia). The swarm, consisting of three bursts activating a normal fault zone, is characterized by rapid earthquake (km d−1) migration. We use a 2-D rate-and-state asperity model to better understand the physical mechanisms controlling the evolution of this induced swarm. The model suggests that the observed rapid seismic migration can be explained by the interaction among asperities through the expansion of slow post-seismic slip fronts. Also, it shows that the amount of seismicity generated by the fluid injection is strongly controlled by the background seismicity of the system, that is by the seismicity determined by the tectonic load charging the fault. This close correlation between natural and induced seismicity suggests that the injection in Muara Laboh principally stimulates critically stressed faults, which release the seismicity determined by their natural seismic cycle.

Control of Seismicity Migration in Earthquake Swarms by Injected Fluid Volume and Aseismic Crack Propagation

AbstractThe evolution of fluid injection‐induced seismicity, generally characterized through the number of events or their seismic moment, depends on, among other factors, the injected fluid volume. Migration of seismicity is observed during those sequences and might be caused by a range of mechanisms: fluid pressure diffusion, fluid‐induced aseismic slip propagating along a stimulated fault, interactions between earthquakes. Recent theoretical and observational developments underline the important effect on seismicity migration of structural parameters, like fault criticality, or injection parameters, like flow rate or pressurization rate. Here, we analyze two well‐studied injection‐induced seismic sequences at the Soultz‐sous‐Fôret and Basel geothermal sites, and find that the evolution of the seismicity front distance primarily depends on the injected fluid volume. Based on a fracture mechanics model, we develop new equations relating seismicity migration to injected fluid volume and frictional and structural properties of the fault. We find that the propagation of a fluid‐induced aseismic slip front along the stimulated fault, triggering seismicity, explains well the observations made on the two sequences. This model allows us to constrain parameters describing the seismicity front evolution and explains the diversity of migration patterns observed in injection‐induced and natural earthquake swarms.

Stress transfer outpaces injection-induced aseismic slip and triggers seismicity

As concerns rise over damaging earthquakes related to industrial activities such as hydraulic fracturing, geothermal energy extraction and wastewater disposal, it is essential to understand how subsurface fluid injection triggers seismicity even in distant regions where pore pressure diffusion cannot reach. Previous studies suggested long-range poroelastic stressing and aseismic slip as potential triggering mechanisms. In this study, we show that significant stress transfer far ahead of injection-induced aseismic slip can travel at much higher speeds and is a viable mechanism for distant earthquake triggering. It could also explain seismicity migration that is much faster than aseismic slip front propagation. We demonstrate the application of these concepts with seismicity triggered by hydraulic fracturing operations in Weiyuan shale gas field, China. The speed of stress transfer is dependent on the background stress level and injection rate, and can be almost an order of magnitude higher than that of the aseismic slip front.

Research on the impact of mandrels in titanium tubes during tube continuous rolling

Tube continuous rolling (TCR) is a beneficial method for the production of titanium pipes due to its high efficiency and shorter process, with the mandrel playing a crucial role. The present study delved into the mechanism of the mandrel and its impact on the TCR process, through comprehensive analyses that included numerical simulations and experimental tests. The following conclusions were drawn: as the mandrel diameter coefficient increases, the area of the front slip zone gradually expands, and the tension changes from tensile stress to compressive stress. Additionally, the temperature exhibited an overall downward trend, while the strain distribution at the groove vertex and taper became more uneven. Concerning metallographic structure, instances where the mandrel diameter coefficient increases led to elongated, recrystallized grains at the groove vertex. The twinning quantity at the groove taper increased initially and then decreased, indicating a deformation mechanism shift from twinning to slip.

Influence of Creep Compaction and Dilatancy on Earthquake Sequences and Slow Slip

AbstractFluids influence fault zone strength and the occurrence of earthquakes, slow slip events, and aseismic slip. We introduce an earthquake sequence model with fault zone fluid transport, accounting for elastic, viscous, and plastic porosity evolution, with permeability having a power‐law dependence on porosity. Fluids, sourced at a constant rate below the seismogenic zone, ascend along the fault. While the modeling is done for a vertical strike‐slip fault with 2D antiplane shear deformation, the general behavior and processes are anticipated to apply also to subduction zones. The model produces large earthquakes in the seismogenic zone, whose recurrence interval is controlled in part by compaction‐driven pressurization and weakening. The model also produces a complex sequence of slow slip events (SSEs) beneath the seismogenic zone. The SSEs are initiated by compaction‐driven pressurization and weakening and stalled by dilatant suctions. Modeled SSE sequences include long‐term events lasting from a few months to years and very rapid short‐term events lasting for only a few days; slip is ∼1–10 cm. Despite ∼1–10 MPa pore pressure changes, porosity and permeability changes are small and hence fluid flux is relatively constant except in the immediate vicinity of slip fronts. This contrasts with alternative fault valving models that feature much larger changes in permeability from the evolution of pore connectivity. Our model demonstrates the important role that compaction and dilatancy have on fluid pressure and fault slip, with possible relevance to slow slip events in subduction zones and elsewhere.

Deriving the slip-front propagation velocity with slip-dependent and slip-velocity-dependent friction laws via the use of the linear marginal stability hypothesis.

We investigate analytically and numerically the determining factors of the slip front propagation (SFP) velocity. The slip front has two forms characterized by an intruding or extruding front. We assume a one-dimensional viscoelastic medium on a rigid and fixed substrate, and we employ the friction law depending on the slip and slip velocity. Despite this dependency potentially being nonlinear, we use the linear marginal stability hypothesis, which linearizes the governing equationfor the slip, to investigate the intruding and extruding front velocities. The analytically obtained velocities are found to be consistent with the numerical computation where we assume the friction law depends nonlinearly on both the slip and slip velocity. This implies that the linearized friction law is sufficient to capture the dominant features of SFP behavior.

Laboratory evidence for slip evolution of granite fractures due to chemical stimulation in geothermal reservoirs

Understanding the mechanisms of injection-induced seismicity is critical for managing the anthropogenic geohazard, which recently hinders the development of geothermal energy. Here we reanalyzed the seismic data recorded during the acid fluid injection at the geothermal field of Soultz-sous-Forêts (France) in 2005 and conducted a series of water injection experiments on granite fractures treated with dilute hydrochloric acid. We aimed to provide laboratory evidence for slip transition of the chemically treated fractures in geothermal reservoirs. We found that the amount of induced seismic events is promoted by the acid treatment, and the distribution of these seismic events is expanded in the post-acid water injection. Our experimental study demonstrated non-linear distributions of water pressure and frictional strength over the fracture during the water injection. The ratio of the shear stress variation to the fluid pressure variation reduces with a larger aseismic slip front amplification factor, which reflects the transition from the aseismic to seismic slip. The study revealed that the acid treatment potentially causes an increase in seismic event amount but a reduction in moment magnitude in the chemically treated region. The aseismic slip in the treated region may promote shear stress gradient along the fracture and result in the seismic events expanding in untreated regions. Additionally, the moment magnitude may be amplified when the fracture dictates neighboring fractures beyond the treated region.

Foreshock Activity Promoted by Locally Elevated Loading Rate on a 4‐m‐Long Laboratory Fault

AbstractWe report laboratory experimental results to reveal the factors that control the occurrence and magnitude of foreshocks. We conducted rock friction experiments using an apparatus that can shear 4‐m‐long rock specimens. We observed many stick‐slip events, as well as very slow (several tens of μm/s) but long‐lasting slips between those main events. These long‐term slow slips individually initiated from both the leading and trailing edges of the fault, and kept propagating steadily toward each other. Such steady slips did not immediately trigger any seismic events, regardless of the accumulated slip amount. After the coalescence of the two long‐term slow slip fronts, a second phase of slow slip with higher slip rate (several hundreds of μm/s)—called precursory slow slip, began at the central area and was accompanied by the occurrence of small seismic events (foreshocks). Subsequently, the main fast rupture eventually developed. We propose that the asperities that hosted foreshocks had similar size to the local critical nucleation length; the asperities slipped stably when the local loading rate was low, but could also slip unstably and radiated seismic waves when the local loading rate became high. We further found a clear positive correlation between foreshock magnitude and local slip rate. These results suggest that local loading rate has a significant influence on the occurrence and magnitude of foreshocks. Therefore, its effect should be taken into account during the studies of earthquake nucleation process and other similar phenomena such as Episodic Tremor and Slip (ETS), icequakes, and repeating earthquakes.

Vehicle Dynamic Control with 4WS, ESC and TVD under Constraint on Front Slip Angles

To enhance vehicle maneuverability and stability, a controller with 4-wheel steering (4WS), electronic stability control (ESC) and a torque vectoring device (TVD) under constraint on the front slip angles is designed in this research. In the controller, the control allocation method is adopted to generate yaw moment via 4WS, ESC and TVD. If the front steering angle is added for generating yaw moment, the steering performance of the vehicle can be further deteriorated. This is because the magnitude of the lateral tire forces are limited and the required yaw moment is insufficient. Constraint is imposed on the magnitude of the front slip angles in order to prevent the lateral tire forces from saturating. The driving simulation is performed by considering the limit of the front slip angle proposed in this study. Compared to the case that uses the existing 4WS, the results of this study are derived from the actuator combination that enhances performance while maintaining stability.

Complex Migration of Tremor Near Cholame, CA, Resolved by Seismic Array Analysis

AbstractTectonic tremor observed along the Cholame and Parkfield sections of the San Andreas Fault has previously been associated with transient slip beneath the seismogenic zone. To study tremor and associated Low Frequency Earthquakes (LFEs), we deployed three dense near‐fault seismic arrays for a period of 3 months in 2018. In early August 2018, the arrays recorded a strong 4‐day‐long deep transient that nucleated in Cholame and propagated toward the northwest. The initiation area is characterized by tremor that persists throughout the transient, while adjacent fault portions located to the northwest host more intermittent tremor. From the rate and location of tremor and LFEs, we infer a deep slip transient, whose along‐strike propagation velocity is ∼8 km/day. Secondary tremor fronts are observed to travel ahead of the main slow slip front at speeds that are times faster. These rapid migrations propagate in slow slip events (SSE) slip‐parallel direction, and are sometimes observed to back‐propagate into previously ruptured segments. High‐resolution images of secondary fronts obtained by using near‐fault borehole stations indicate the active tremor band takes the shape of a narrow strain pulse that is bounded from above by the lower edge of the seismogenic zone. We estimate the stress drops associated with the secondary slip fronts are of the order of a few kPa. Frequency‐dependent analysis suggests the tremor signal is coherent at frequencies as high as 16 Hz, and that the spatial distribution of high‐ and low‐frequency tremor radiators is sometimes complementary.

Effect of Porosity and Permeability Evolution on Injection‐Induced Aseismic Slip

AbstractIt is widely recognized that fluid injection can trigger aseismic fault slip. However, the processes by which the fluid‐rock interactions facilitate or inhibit slip are poorly understood and some are oversimplified in most models of injection‐induced slip. In this study, we perform a 2D anti‐plane shear investigation of aseismic slip that occurs in response to fluid injection into a permeable fault governed by rate‐and‐state friction. We account for porosity and permeability changes that accompany slip, including dilatancy, and quantify how these processes affect pore pressure diffusion, which couples to aseismic slip. Fault response to injection has two phases. In the first phase, slip is negligible and pore pressure closely follows the standard linear diffusion model. Pressurization eventually triggers aseismic slip close to the injection site. In the second phase, aseismic slip front expands outward and dilatancy causes pore pressure to depart from the linear diffusion model. We quantify how prestress, injection rate, permeability and other fluid transport properties affect the slip front migration rate, finding rates ranging from 10 to 1,000 m/day for typical parameters. The migration rate is strongly influenced by the fault's closeness to failure and injection rate. The total slip on the fault, on the other hand, is primarily determined by the injected volume, with minimal sensitivity to injection rate. Additionally, we show that when dilatancy is neglected, slip front migration rate and total slip can be several times higher. Our modeling demonstrates that porosity and permeability evolution, especially dilatancy, fundamentally alters how faults respond to fluid injection.

Coseismic slickenlines record the emergence of multiple rupture fronts during a surface-breaking earthquake

Coseismic changes in slip direction recorded by curved slickenlines on fault surfaces are commonly observed following surface-breaking earthquakes. Such observations represent a dynamic record of seismic slip and may provide a new set of constraints on the evolution of propagating rupture and hence earthquake dynamics. We test this hypothesis by conducting dynamic rupture simulations of the 2011 Mw 6.6 Fukushima-Hamadori Earthquake (Japan). These simulations aim to reproduce the well-documented field observations of curved slickenlines that formed during coseismic fault displacement at the ground surface. We consider relatively simple dynamic rupture models with a dipping fault embedded into a homogeneous or layered elastic halfspace. Among a wide range of model parameters tested, we find a model with shallow (<1.5km) low-velocity layers derived from a regional 3D velocity model combined with a depth-dependent prestress result in curved slip trajectories that closely match slickenline observations. This same model also generates a slip distribution and rupture propagation direction consistent with published inversions constrained by seismological and geodetic data. Furthermore, the characteristics of slickenline curvature are consistent with theoretically predicted earthquake rupture direction. Unlike previous theoretical studies, coseismic changes in rake angle occur due to the emergence of multiple slip fronts within the shallow low-velocity medium. Our results indicate that on-fault geological observations can supplement seismological studies of earthquake rupture evolution beyond traditional datasets.

Onset of sliding across scales: How the contact topography impacts frictional strength

When two solids start rubbing together, frictional sliding initiates in the wake of slip fronts propagating along their surfaces in contact. This macroscopic rupture dynamics can be successfully mapped on the elastodynamics of a moving shear crack. However, this analogy breaks down during the nucleation process, which develops at the scale of surface asperities where microcontacts form. Recent atomistic simulations revealed how a characteristic junction size selects if the failure of microcontact junctions either arises by brittle fracture or by ductile yielding. This work aims at bridging these two complementary descriptions of the onset of frictional slip existing at different scales. We first present how the microcontacts failure observed in atomistic simulations can be conveniently "coarse-grained" using an equivalent cohesive law. Taking advantage of a scalable parallel implementation of the cohesive element method, we study how the different failure mechanisms of the microcontact asperities interplay with the nucleation and propagation of macroscopic slip fronts along the interface. Notably, large simulations reveal how the failure mechanism prevailing in the rupture of the microcontacts (brittle versus ductile) significantly impacts the nucleation of frictional sliding and, thereby, the interface frictional strength. This work paves the way for a unified description of frictional interfaces connecting the recent advances independently made at the micro- and macroscopic scales.

Integrated Chassis Control With Four-Wheel Independent Steering Under Constraint on Front Slip Angles

This paper presents a method to design an integrated chassis controller with four-wheel independent steering (4WIS) under the constraint on front slip angles for electric vehicles (EVs) adopting in-wheel motor (IWM) driving system. To improve lateral stability and maneuverability of a vehicle, direct yaw moment control strategy is adopted. A control allocation method is adopted to distribute control yaw moment into tire forces, generated by 4WIS. If corrective steering angles of 4WIS are added to front steering angles generated by a driver, it can deteriorate control performance because the lateral tire force of front wheels easily saturated and it causes loss of required yaw moment needed to stabilize a vehicle. To cope with the problem, it is necessary to impose constraints on front slip angles. To compensate the loss of control yaw moment caused by the constraint on front slip angles, a constrained control allocation method is presented. Simulation on driving simulation tool, CarSim <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">®</sup> , shows that the proposed integrated chassis controller is capable of maintaining lateral stability and maneuverability without performance deterioration under the constraint on the front slip angles.

Stochastic properties of static friction

The onset of frictional motion is mediated by rupture-like slip fronts, which nucleate locally and propagate eventually along the entire interface causing global sliding. The static friction coefficient is a macroscopic measure of the applied force at this particular instant when the frictional interface loses stability. However, experimental studies are known to present important scatter in the measurement of static friction; the origin of which remains unexplained. Here, we study the nucleation of local slip at interfaces with slip-weakening friction of random strength and analyze the resulting variability in the measured global strength. Using numerical simulations that solve the elastodynamic equations, we observe that multiple slip patches nucleate simultaneously, many of which are stable and grow only slowly, but one reaches a critical length and starts propagating dynamically. We show that a theoretical criterion based on a static equilibrium solution predicts quantitatively well the onset of frictional sliding. We develop an efficient Monte-Carlo model by adapting the theoretical criterion and study the variability in global strength distribution caused by the stochastic properties of local frictional strength. The results demonstrate that an increasing spatial correlation length on the interface, representing geometric imperfections and roughness, causes lower global static friction. Conversely, smaller correlation length increases the macroscopic strength while its variability decreases. We further show that randomness in local friction properties is insufficient for the existence of systematic precursory slip events. Random or systematic non-uniformity in the driving force, such as potential energy or stress drop, is required for arrested slip fronts. Our model and observations provide a necessary framework for efficient stochastic analysis of macroscopic frictional strength and establish a fundamental basis for probabilistic design criteria for static friction.

Fault’s hydraulic diffusivity enhancement during injection induced fault reactivation: application of pore pressure diffusion inversions to laboratory injection experiments

SUMMARYIn situ observations of fluid induced fault slip reactivation, as well as the analysis of induced seismicity have demonstrated the complexity of fluid–fault interactions under geological conditions. If fluid flow commonly reactivates faults in the form of aseismic slip or earthquakes, the resulting shear deformation causes strong modifications of the hydraulic properties. In this context, the relationship between slip front and fluid front on deep faults remains not fully understood. In this study, we investigate shear induced fluid flow and hydraulic diffusivity enhancement during fracture shearing in the laboratory. We use a series of injection reactivation tests, conducted under triaxial conditions, at different confining pressures (30, 60 and 95 MPa). The evolution of the fluid pressure along the saw-cut Andesite rock sample was monitored by two pressure sensors, at two opposite locations of the experimental fault. We estimate the history of the effective hydraulic diffusivity (and its associated uncertainties) governing the experimental fault, using the pressure history at two points on the fault. For this, we develop a deterministic and a probabilistic inversion procedure, which is able to reproduce the experimental data for a wide time range of the different experiments. In this study, the hydraulic diffusivity increases by one order of magnitude through the injection experiment. Hydraulic diffusivity changes are mainly governed by the reduction of the effective normal stress acting on the fault plane, with a second-order effect of the shear slip.

Slip bursts during coalescence of slow slip events in Cascadia

Both laboratory experiments and dynamic simulations suggest that earthquakes can be preceded by a precursory phase of slow slip. Observing processes leading to an acceleration or spreading of slow slip along faults is therefore key to understand the dynamics potentially leading to seismic ruptures. Here, we use continuous GPS measurements of the ground displacement to image the daily slip along the fault beneath Vancouver Island during a slow slip event in 2013. We image the coalescence of three originally distinct slow slip fronts merging together. We show that during coalescence phases lasting for 2 to 5 days, the rate of energy (moment) release significantly increases. This observation supports the view proposed by theoretical and experimental studies that the coalescence of slow slip fronts is a possible mechanism for initiating earthquakes.

The mechanical parameters modeling of heavy steel plate snake/gradient temperature rolling with the same roll diameters

The grains in the center of the heavy steel plate can be refined by the snake/gradient temperature rolling, and the deformation penetration, the microstructure, and the properties of the steel plate will be improved. The existing rolling mechanical models are not suitable for the snake/gradient temperature rolling, so it is necessary to establish the mechanical parameters model of the snake/gradient temperature rolling to instruct production. The yield criterion of rolled material was modified based on the idea of equivalent flow stress. The element stress analyses were carried out based on the uniform normal stress and nonuniform shear stress in the vertical sides of each slab. Then the equilibrium equation of the unit pressure based on the slab method was established on this basis. The deformation region was divided into three layers (the top layer, the bottom layer, and the central layer) and maximum four zones (back slip zone, front slip zone, cross shear zone, and reverse deflection zone) according to the temperature distribution and position of the neutral point, and then the 12 zones were formed during the snake/gradient temperature rolling. The boundary conditions of the existence of the back slip zone, the front slip zone, and the cross shear zone were established according to the relationship between the threading angle and the neutral angle. The accurate mechanical parameters model of the rolling force and rolling torque of the snake/gradient temperature rolling with the same roll diameters was set up on this basis. The ANSYS software has been used in the rolling process simulation by many scholars, and the calculating precision has been verified. So the rolling processes were simulated by the ANSYS software to validate the model precision. The results show that the maximum relative deviation of the rolling force analytic model is less than 7% compared with the numerical method, and the maximum relative deviation of the rolling torque analytic model is less than 11% compared with the measured results. The mechanical parameters model can accurately predict the rolling force and rolling torque during the snake/gradient temperature rolling with the same roll diameters, so as to provide a theoretical basis for the design of rolling mill and the setup of the process parameters.

Transition between Macroscopic Steady Slippage and Creep Motion in a System with Velocity-Dependent Friction Stress

We investigate the propagation of a slip front in a visco-elastic body on a rigid substrate. The body is one-dimensional, and the loading stress is applied at one end. By employing a local friction law that has a quadratic form of the slip velocity and gives vanishing friction stress at vanishing velocity or above a certain velocity, we show analytically that macroscopic steady slippage and creep motion can be understood in a single framework. The critical values of the end-loading stress causing macroscopic steady slippage and the slip-front propagation velocity appear are obtained. These values are completely determined by the gradient of the slip velocity-friction curve at the vanishing friction stress. These results are extended to more general friction laws, and found to be consistent with numerical calculations. Furthermore, we discuss some seismological implications based on the analytical and numerical results.