Velocity-weakening Friction Law Research Articles

Modelling production-induced dynamic rupture of intra-graben faults and related earthquakes in the North German Basin

Production-induced seismicity occurs in some gas fields of the North German Basin. Increasing effective stress engendered by the pore pressure decline and associated reservoir compaction is considered as the main reason for reactivation of faults. Herein, we use hydromechanically coupled finite element models to investigate how and when a critical state of stress emerges on a fault during pore pressure decline for a setting typical for the North German Basin. Proceeding from this critical state of stress and assuming a velocity weakening friction law the dynamic rupture is modelled. Normal faulting slip is found at the depth of the reservoir nucleating near its top in the hanging wall. A vertical offset of the reservoir at the fault of half its thickness produces the largest earthquake among the cases tested between zero offset and equal to the reservoir thickness, but fault reactivation occurs first for larger offsets. Regarding the relative position of production wells to the fault simultaneous production from both compartments leads to earlier reactivation and larger earthquakes compared to if production is from only one compartment. The frictional properties of the fault are found to have the largest impact on coseismic displacement and stress drop. A crucial role on the timing of rupture initiation and size of the rupture can be attributed to the pre-production stress state.

The Xinmo rockslide-debris avalanche: An analysis based on the three-dimensional material point method

On June 24, 2017, a catastrophic rock avalanche with a volume of 5.08 × 106 m occurred in Xinmo village, Maoxian County, Sichuan Province, SW China. Several studies focusing on the triggering factors, failure mechanism and dynamic process of the Xinmo landslide have been reported in the literature. However, there are few studies with detailed three-dimensional investigations based on numerical modeling that assess the post-failure stage of the landslide. In the present study, the three-dimensional material point method is used to reproduce the kinematics of the landslide to obtain better insight into the disaster by considering the effects of fragmentation and entrainment. Based on this framework, a velocity-weakening friction law is implemented to describe the basal friction between the moving mass and the substrate, and a strain–softening Drucker–Prager constitutive model is used to describe the internal deformation of the moving mass. The entrainment processes obtained with and without the proposed model are compared, and the simulated results generated with the presented models showing the distribution characteristics of the materials in the deposit area match the observed results fairly well. The implementation of a velocity-weakening friction law and a strain-softening Drucker–Prager constitutive model in the material point method may provide valuable insight for the enforcement of physically based risk assessments of “rockslide-debris avalanches”.

MPM evaluation of the dynamic runout process of the giant Daguangbao landslide

Giant landslides can cause significant damage to their dynamic runout processes. Understanding the mechanics of the runout process is essential for landslide risk assessment and mitigation design. This paper investigates the runout process of the 1.16 × 109 m3 giant Daguangbao landslide triggered by the 2008 Ms 8.0 Wenchuan earthquake. The Daguangbao landslide is a typical bedding-plane slide and the properties of basal sliding surface play a key role in the runout behaviors of the landslide. The material point method (MPM) is adopted as a numerical tool of the simulations. A thermal-based velocity-weakening friction law is used to simulate the contact between the sliding body and the basal sliding surface. A strain-softening constitutive model is used to evaluate the damages inside the landslide body and their effects on the runout behaviors of the landslide. Numerical results reveal that landslide mass slides along the bedding-plane as a whole body initially and then disintegrates during the runout process. The calculated duration of sliding is 64 s and the maximum velocity reaches 60 m/s. The friction coefficient of the slip surface decreases sharply as the landslide body starts to move, and a steady-state friction coefficient μ ≈ 0.06 is reached when the velocity exceeds approximately 20 m/s. Friction degradation of the slip surface shows a sensible influence on the final runout distance and the depth of the deposit zone. The dynamic fragmentation of the landslide body, the final runout distance, and deposition topography are also significantly affected by material softening.

Shear Fractures of Extreme Dynamics

Natural and laboratory observations show that shear ruptures (faults) can propagate with extreme dynamics (up to intersonic rupture velocities) through intact materials and along pre-existing faults with frictional and coherent (bonded) interfaces. The rupture propagation is accompanied by significant fault strength weakening in the rupture head. Although essential for understanding earthquakes, rock mechanics, tribology and fractures, the question of what physical processes determine how that weakening occurs is still unresolved. The general approach today to explain the fault weakening is based upon the strong velocity-weakening friction law according to which the fault strength drops rapidly with slip velocity. Different mechanisms of strength weakening caused by slip velocity have been proposed including thermal effect, high-frequency compressional waves, expansion of pore fluid, macroscopic melting and gel formation. This paper proposes that shear ruptures of extreme dynamics propagating in intact materials and in pre-existing frictional and coherent interfaces are governed by the same recently identified mechanism which is associated with an intensive microcracking process in the rupture tip observed for all types of extreme ruptures. The microcracking process creates, in certain conditions, a special fan-like microstructure shear resistance of which is extremely low (up to an order of magnitude less than the frictional strength). The fan-structure representing the rupture head provides strong interface weakening and causes high slip and rupture velocities. In contrast with the velocity-weakening dependency, this mechanism provides the opposite weakening-velocity effect. The fan-mechanism differs remarkably from all reported earlier mechanisms, and it can provide such important features observed in extreme ruptures as: extreme slip and rupture velocities, high slip velocity without heating, off-fault tensile cracking, transition from crack-like to pulse-like rupture mode at variation in loading conditions, dramatic embrittlement of hard rocks at highly confined compression, abnormally low transient strength of hard rocks at high confining stresses, etc. All these questions are discussed in the paper.

Intermittent slipping of landslide regulated by dilatancy evolution and velocity-weakening friction law: an efficient numerical scheme

When a block of dense sandy soil moves downhill, the shear-induced soil dilatancy along the basal shear boundary produces a negative value of excess pore pressure that increases the basal frictional resistance. Dilatancy angle, , the degree to which the basal soil dilates due to the shear, normally evolves during slope failure. A study by other researchers shows that if is constant, the block of dense soil will remain stable (or unstable) sliding when the velocity-weakening rate of the basal friction coefficient of the block is small (or large) enough. Moreover, during unstable sliding processes, the block of dense soil exhibits "periodic" patterns of intermittent slipping. Here, we used a more efficient and accurate numerical scheme to revisit that study. We expanded their model by assuming evolves during slope failure. Consequently, we acquired completely different results. For instance, even though the velocity-weakening rate of the friction coefficient is fixed at the same smaller (or larger) value that those researchers use, the stable (or unstable) steady states of landslide they predict will inversely change to unstable (or stable) when decreases (or increases) with the increase of slide displacement to a value small (or large) enough. Particularly, in unstable processes, the soil block exhibits "aperiodic" styles of intermittent slipping, instead of "periodic". We found out that the stick states appearing later last longer (or shorter) in the case of decreasing (or increasing) . Moreover, because the basic states of landslides with impacts of dilatancy evolution are not steady nor periodic, traditional stability-analysis methods cannot be "directly" used to analyze the stability of such landslides. Here, we broke through this technical problem to a degree. We showed that combining a concept called "quasi-steady-state approximation" with a traditional stability-analysis technique can qualitatively predict the instability onset of the landslides. Through this study, we demonstrated that the combination of Chebyshev collocation (CC) and 4th-order Runge-Kutta methods is more accurate and efficient than the numerical scheme those researchers use.

Two-dimensional landslide dynamic simulation based on a velocity-weakening friction law

Surprisingly, hypermobility (high velocity and long run-out) is a remarkable feature of large landslides and is still poorly understood. In this paper, a velocity-weakening friction law is incorporated into a depth-averaged landslide model for explaining the higher mobility mechanism of landslides. In order to improve the precision of the calculation, a coupled numerical method based on the finite volume method is proposed to solve the model equations. Finally, several numerical tests are performed to verify the stability of the algorithm and reliability of the model. The comparison between numerical results and experimental data indicates that the presented model can predict the movement of landslide accurately. Considering the effect of velocity-weakening friction law, the presented model can better reflect the hypermobility of landslide than the conventional Mohr–Coulomb friction model. This work shows that the application of a universal velocity-weakening friction law is effective in describing the hypermobility of landslide and predicting the extent of landslides.

Frictional velocity-weakening in landslides on Earth and on other planetary bodies

One of the ultimate goals in landslide hazard assessment is to predict maximum landslide extension and velocity. Despite much work, the physical processes governing energy dissipation during these natural granular flows remain uncertain. Field observations show that large landslides travel over unexpectedly long distances, suggesting low dissipation. Numerical simulations of landslides require a small friction coefficient to reproduce the extension of their deposits. Here, based on analytical and numerical solutions for granular flows constrained by remote-sensing observations, we develop a consistent method to estimate the effective friction coefficient of landslides. This method uses a constant basal friction coefficient that reproduces the first-order landslide properties. We show that friction decreases with increasing volume or, more fundamentally, with increasing sliding velocity. Inspired by frictional weakening mechanisms thought to operate during earthquakes, we propose an empirical velocity-weakening friction law under a unifying phenomenological framework applicable to small and large landslides observed on Earth and beyond.

Nonlinear Drillstring Dynamics Analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control.

A self‐organized model of earthquakes with constant stress drops and the b‐value of 1

The magnitude‐frequency relation and the constant stress drop are fundamental features of earth‐quakes, to which a full physical explanation has yet to be given. We present a model that can reproduce the above two fundamental features simultaneously and spontaneously. The model is two‐dimensionally configured spring‐loaded blocks with a velocity‐weakening friction law. We change widely the dynamic friction parameter, which results in the frequency distributions showing the critical, subcritical and supercritical behaviors. Seismicity near the critical state is characterized by almost constant stress drops and the b‐value of 1, in which a self‐healing pulse maintains its frontal dynamic stress at a level near the static friction in an environmental stress heterogeneity that has evolved through the healing process itself.

A dissipation‐based analysis of an earthquake fault model

We analyze the dynamics of a discrete dynamical model of earthquake faulting, derived from the Burridge‐Knopoff model. The system is shown to exhibit a characteristic event size (L* = 2v2f l2) that separates two distinct regimes in the statistical distribution of event sizes and magnitudes. The dynamics of the system exhibits scaling laws that are in agreement with observed seismic laws. Influence of the frictional rate of dissipation, of the elastic stiffness coupling, and of the system size is investigated. The dynamics of the system is rather insensitive to the numerical treatment of the nonsmooth friction. In contrast, the exact form of the velocity weakening friction law is shown to have a major effect on the dynamics. For friction laws allowing local reversal backslipping, the distribution of the magnitudes does not exhibit a Gutenberg and Richter (GR) distribution, while by precluding backslipping a GR distribution is observed. Two populations of events can be characterized based on dissipation: weakly dissipative events that allow the mechanical energy of the system to increase; and strongly dissipative events that release a large fraction of the elastic potential energy of the system and introduce large stress heterogeneities. A coarse grain analysis in terms of the stored elastic energy and the magnitude of the disorder provides new interesting insights on the dynamics of the model. Weakly dissipative events, which reproduce the seismic laws, are shown to follow a deterministic evolution. A statistical criterion for the initiation of big dissipative events is proposed.

Velocity weakening friction: A renormalization approach

The frictional response when a two‐dimensional elastic body, under a steady antiplane shearing, slides over a rigid frictional surface is solved using a real‐space renormalization technique. The model is mapped onto iterations of the classical Burridge‐Knopoff chain model. A velocity weakening friction law is assumed for the interactions between the rigid interface and the elastic slider. Through the renormalization approach, we specifically study the coupling between the bulk elastic response of the slider and the friction at the interface level. The frictional system is characterized by its mechanical response in terms of mean friction force opposed to a prescribed constant velocity. The response is shown to differ strongly from the interface friction law. Under renormalization, the response converges toward an apparent dynamical Coulomb's friction law, with distinct static and dynamic coefficients. This result provides some new insight in the “ubiquity” of Coulomb's friction law. On the base of this model, the experimental observability of velocity weakening friction laws and their scaling to seismically active system are discussed. The main result is that velocity weakening friction law is scale dependent. Within the assumptions of the model, the friction law at the scale of the system appears to be rather insensitive to the exact form of the friction at local scale on the interface.

Dynamics of earthquakes and fracture

We discuss some new dynamical models of earthquake and crack propagation. For the earthquake model, it is pointed out thet the instability caused by a velocity weakening friction law gives the system chaotic time development and a scaling behavior even when the system is totally uniform and deterministic. For the model of crack propagation, we demonstrate that dissipation can play an important role in the crack propagation by solving the model analytically.

A four-parameter, two degree-of-freedom block-spring model: Effect of the driver velocity

We analyze the effect of tectonic plate velocities in the earthquake pattern using a simple mass-spring model of the Burridge and Knopoff type with two blocks and a velocity-weakening friction law. Previous versions of the two-block model assume a steady driver during slip events (limit of zero driver velocity), which, in some cases makes necessary the introduction of artificial parameters to start the numerical integration of the equations of motion at impending slip of any block. Still maintaining the condition of zero driver velocity during slip, we shall introduce a procedure to start the numerical integration without introducing artificial parameters and this will be done by using a linearized version of the equations of motion valid for small velocities and considering nonzero driver velocity. We also introduce a four parameter model in which the driver velocity enters the equations during the whole simulation, and analyze the effect of the new parameter, the driver velocity, in the displacement and time patterns of blocks motion, directly related to earthquake statistics such as coseismic slips and average repeat times.