Dynamic Rupture Process Research Articles

Graph theoretical analysis of limestone fracture network damage patterns based on uniaxial compression test

The topological attributes of fracture networks in limestone, subject to intense hydrodynamics and intricate geological discontinuities, substantially influence the mechanical and hydraulic characteristics of the rock mass. The dynamical evolution of fracture networks under stress is crucial for unveiling the interaction patterns among fractures. However, existing models are undirected graphs focused on stationary topology, which need optimization to depict fractures' dynamic development and rupture process. To compensate for the time and destruction terms, we propose the damage network model, which defines the physical interpretation of fractures through the ternary motif. We focus primarily on the evolution of node types, topological attributes, and motifs of the fracture network in limestone under uniaxial stress. Observations expose the varying behavior of the nodes' self-dynamics and neighbors' adjacent dynamics in the fracture network. This approach elucidates the impact of micro-crack behaviors on large brittle shear fractures from a topological perspective and further subdivides the progressive failure stage into four distinct phases (isolated crack growth phase, crack splay phase, damage coalescence phase, and mechanical failure phase) based on the significance profile of the motif. Regression analysis reveals a positive linear and negative power correlation between fracture network density and branch number to the rock damage resistance, respectively. The damage network model introduces a novel methodology for depicting the interaction of two-dimensional (2D) projected fractures, considering the dynamic spatiotemporal development characteristics and fracture geometric variation. It helps dynamically characterize properties such as connectivity, permeability, and damage factors while comprehensively assessing damage in rock mass fracture networks.

On the Unloading‐Induced Fault Reactivation: The Effect of Stress Path on Failure Criterion and Rupture Dynamics

AbstractFault reactivations induced by deep excavation can pose significant challenges to underground construction or resource extraction. Laboratory experiments on rock faults demonstrate that unloading‐induced fault reactivations obey the Coulomb failure criterion derived from loading‐induced events. However, the effect of stress path during unloading on the failure criterion and rupture dynamics of fault reactivations remains poorly understood. Here, we present findings from a series of laboratory experiments aimed at elucidating the effect of the unloading path on the failure criterion and rupture dynamics of fault reactivations. We conducted experiments under various stress conditions, examining two cases of unloading paths. In Case I, we unloaded the minimum principal stress, while in Case II, the maximum principal stress was unloaded. Strain gauges and high‐speed photography were employed to capture the transient dynamic rupture process. Our investigations have yielded new insights into the effect of unloading path on the rupture dynamics when the fault is reactivated. In Case I, we observed fault reactivations resembling those loading‐induced events characterized by forward sliding. Conversely, in Case II, fault reactivations associated with stress reversal produce mild reversed sliding with lower stress drop and rupture velocity. Furthermore, we find that there is a remarkable reduction in static friction for reversed sliding, indicating that the failure criterion for fault reactivation is influenced by the stress path. We demonstrate that enhanced stress heterogeneity, caused by stress reversal, serves as a mechanism for reduced static friction. These findings contribute to our understanding of the mechanisms underlying fault reactivations, particularly those involving reversed sliding.

Source parameters and scaling relationships of stress drop for shallow crustal seismic events in Western Europe

For an ω2-source model, moment-based estimates of the stress drop are obtained by combining corner frequency and seismic moment source parameters. Therefore, the moment-based estimates of the stress drop are informative about the amount of energy radiated at high frequencies by dynamic rupture processes. This study aims to systematically estimate such stress drop from the harmonized dataset at the European scale and to characterize the distributions of the stress drop for application in future stochastic simulations. We analyze the seismological records associated with shallow crustal seismic events that occurred in Western Europe between January 1990 and May 2020. We processed 220,000 high-quality records and isolated the contributions of the source, site, and path contributions using the Generalized Inversion Technique. The source parameters, including the corner frequency, moment magnitude, and stress drop, of 6135 seismic events are calculated. The events processed are mainly tectonic events (e.g., earthquakes of the central Italy 2009–2016 sequence), although non-tectonic events associated with the Groningen gas field and mining activities in Western Europe are also included in the analysis. The impact of different attenuation models and reference site choices are evaluated. Most of the obtained source spectra follow the standard ω2-model except for a few events where the data sampling considered does not allow an effective spectral decomposition. The resulting stress drop shows a positive correlation with moment magnitude between 3 and 4, and a self-similarity for magnitudes greater than 4 with a mean stress drop of 13.8 MPa.

Complex fault geometry controls dynamic rupture of the 2021 Mw7.4 Maduo earthquake, NE Tibetan Plateau

Geodetic observations and seismic inversions suggest that the 2021 Mw7.4 Maduo earthquake's rupture velocity differs in two directions. However, the dynamic mechanisms underlying these differences remain unclear. To address this issue, we constructed a three-dimensional finite element model implementing heterogeneous fault geometry and real topography and simulated the Maduo earthquake's dynamic rupture process, with the tectonic stress field varying with depth. The results show that the uneven distribution of normal and shear stresses on the fault plane, due to the complex geometry of the seismogenic fault, is the primary factor controlling rupture velocity and slips on the fault plane of the Maduo earthquake. The modelled results reproduced basic kinematic characteristics as indicated by the observation and inversion results of the Maduo earthquake. Our study also suggests that if an earthquake occurs in a region without significant changes in velocity structure and stress field distribution, the complex geometry of the seismogenic fault is responsible for the dynamic rupture process. These findings provide important insights into the rupture behaviour of geometrically complex faults and have important implications for seismic hazard assessments of these complicated fault systems.

Dynamic Rupture Process of the 2023 Mw 7.8 Kahramanmaraş Earthquake (SE Türkiye): Variable Rupture Speed and Implications for Seismic Hazard

AbstractWe considered various non‐uniformities such as branch faults, rotation of stress field directions, and changes in tectonic environments to simulate the dynamic rupture process of the 6 February 2023 Mw 7.8 Kahramanmaraş earthquake in SE Türkiye. We utilized near‐fault waveform data, GNSS static displacements, and surface rupture to constrain the dynamic model. The results indicate that the high initial stress accumulated in the Kahramanmaraş‐Çelikhan seismic gap leads to the successful triggering of the East Anatolian Fault (EAF) and the supershear rupture in the northeast segment. Due to the complexity of fault geometry, the rupture speed along the southeastern segment of the EAF varied repeatedly between supershear and subshear, which contributed to the unexpectedly strong ground motion. Furthermore, the triggering of the EAF reminds us to be aware of the risk of seismic gaps on major faults being triggered by secondary faults, which is crucial to prevent significant disasters.

Numerical simulation study on the spontaneous rupture process and its influencing factors of the 2001 MS 8.1 Kunlun earthquake in China

On November 14, 2001, the MS 8.1 Kunlun earthquake occurred in the west of Kunlun Mountain pass in the East Kunlun fault zone of the Qinghai-Tibet Plateau, China. The field investigation and the results of kinematic inversion indicate that it is a strike-slip earthquake with a complex rupture process. The study of the spontaneous rupture process of this earthquake and its influencing factors is of great significance for understanding the occurrence mechanism of continental large earthquakes. First, based on the results of geological survey and kinematic inversion, a three-dimensional non-planar fault model is established. Then, using the curved-grid finite difference method (CG-FDM), the dynamic rupture process of the 2001 MS 8.1 Kunlun earthquake is numerically reproduced by adjusting the parameters for numerical simulation experiments. On this basis, the influence of background stress field, fault geometry and friction coefficient on the surface slip distribution, seismic moment rate function and rupture velocity are discussed respectively. The results show that the important reasons for the super-long rupture scale and super-shear rupture velocity of this earthquake may be the clockwise rotation of the maximum horizontal principal compressive stress along the NNE ∼ NE direction and the low friction coefficient distribution on the whole fault surface. The difference between the dynamic and static friction coefficients along the fault strike may be non-uniform, and it may be larger on the main fault than that on the secondary fault. This will result in a higher level of stress drop on the main fault, leading to the occurrence of super-shear rupture and the slip distribution with the Kusai Lake as the macroseismic epicenter. The large local geometric variation along the strike of the main fault may also have some influence on the distribution of co-seismic slip and the location of the super-shear rupture. In addition, the numerical simulation results in this paper confirm the conclusion that the East Kunlun fault zone has low friction coefficient.

A Mixed‐Flux‐Based Nodal Discontinuous Galerkin Method for 3D Dynamic Rupture Modeling

AbstractNumerical simulation of rupture dynamics provides critical insights for understanding earthquake physics, while the complex geometry and heterogeneous material properties of natural faults make numerical method development challenging. The discontinuous Galerkin (DG) method is suitable for handling these complexities. In the DG method, the fault boundary conditions can be conveniently imposed through the upwind flux by solving a Riemann problem based on a velocity‐strain elastodynamic equation. However, the universal adoption of upwind flux can cause spatial oscillations in cases where elements on adjacent sides of the fault surface are not nearly symmetric. Here we propose a nodal DG method with an upwind/central mixed‐flux scheme to solve the spatial oscillation problem and thus reduce the dependence on mesh quality. Our method can achieve high scalability in parallel computing under different orders of accuracy. We verify the new method by comparing simulation results with those from other methods on a series of published benchmark problems with complex fault geometries, heterogeneous materials, off‐fault plasticity, roughness, thermal pressurization, and various versions of fault friction laws. Finally, we demonstrate that our method can be applied to simulate the dynamic rupture process of the 2008 Mw 7.9 Wenchuan earthquake along realistic fault geometry, including branches, step‐overs and a previously neglected sub‐parallel fault segment, offering a high potential to systematically explore the influences of fault zone properties on earthquake rupture dynamics.

Dynamic rupture simulations based on interseismic locking models—taking the Suoerkuli section of the Altyn Tagh fault as an example

SUMMARY For simulating the dynamic rupture process in earthquake scenarios, the stress distribution along the fault remains unclear owing to a lack of direct measurements. Regional stress fields are often resolved onto the fault plane to determine the stress distribution along it. To overcome this limitation, we considered different interseismic locking models to better constrain the actual stress distribution. Specifically, we took the Suoerkuli section in the middle of the Altyn Tagh fault, China, and conducted dynamic rupture simulations to obtain possible earthquake scenarios. The surface rupture length and moment magnitude obtained from the simulations were consistent with those of historical earthquakes. Compared with the traditional stress field resolution method, our approach led to better constrained fault rupture extent and distribution characteristics of regional intensity, thereby avoiding overestimations of earthquake damage. We conclude that examining regional seismic hazards and risks based on seismic dynamic rupture simulations that account for the locking ratio of the fault plane is advantageous, and should be encouraged.

Detection of fault zone head waves and the fault interface imaging in the Xianshuihe–Anninghe Fault zone (Eastern Tibetan Plateau)

SUMMARY Fault zone head waves (FZHWs) are an essential diagnostic signal that provides high-resolution imaging of fault interface properties at seismogenic depth. In this study, we validate the existence of a bi-material interface in the Xianshuihe–Anninghe Fault (XAF) zone around their intersection and determine the cross-fault velocity contrast. We employ a semi-automatic workflow to detect and pick FZHWs and direct P waves. In addition, to improve the identification ability of potential FZHWs in the automatic picking process, we adopt a ‘forward-detecting and backward-picking’ strategy combining the short-term average/long-term average (STA/LTA) algorithm with a kurtosis detector. The polarization and characteristic periods of the waveforms are then used to manually refine the picks and evaluate the quality. The results indicate that the average velocity contrast along the southern Xianshuihe Fault is 3–5 per cent, with the northeast side characterizing a faster P-wave velocity, in agreement with tomographic results. A systematic moveout between FZHWs and the direct P waves over a 100 km long fault segment reveals a single continuous interface in the seismogenic zone. The single bi-material fault structure might be conducive to the preparation of large earthquakes and further influences the corresponding dynamic rupture processes.

Rupture-induced dynamic pore pressure effect on rupture

The ordinary elasticity model is often used in dynamic rupture earthquake simulation without incorporating the poroelasticity effect in rocks. In consideration that rocks are porous and saturated, we carry out a two-dimensional simulation of spontaneous rupture in a poroelastic medium with a finite difference time domain scheme. In particular, the influence of the rupture-induced pore pressure on the rupture process is investigated. The fault plane is idealized as an impermeable layer of negligible thickness, and the rupture is assumed to be governed by the slip-weakening friction law. Results show that an impermeable fault plane leads to a rupture-induced pore pressure change, which promotes or hinders the rupture process by altering effective normal compressive stress (normal compressive stress minus pore pressure). It is remarkable that super-shear rupturing will occur when the porosity of the rock around the fault increases to some extent. The comparison with the permeable fault model suggests that the permeability of the fault and the porosity of rocks around the fault significantly influence the dynamic rupture process.

Energy Release Resulting from Sudden Excavation Shape Changes during Two-sided Strainbursts

When tunnels in underground hard rock mines experience strainbursts, the effective shape of the tunnel suddenly changes as part of the rock fails, notches form and the broken rock bulks inside the strainburst volume. For circular tunnels, this dynamic rupture and bulking process causes a shape change with associated displacements and velocities in the surrounding elastic rockmass and at the excavation walls. This process can be approximated for circular tunnel bursting in elastic rock by a shape change from circular to elliptical and Maugi’s solution [1] can be adapted to estimate related displacements and average ground velocities. If these velocities are imposed on a volume of rock or shotcrete with a given mass, the mass can be ejected, and the corresponding kinetic energy can be estimated. When combined with the sudden bulking of the fractured rock, displacements and velocities are magnified between the elliptical shape and the pre-burst (circular) shape of the tunnel. This study focuses on the effect of the combined excavation response with elastic and bulking deformations to assess frequently observed excavation damage processes involving ‘shotcrete rain’ and heave of floor slabs caused by these shape changes. An analytical solution is presented for circular tunnels to estimate the elastic and bulking displacements, the resulting velocities, and energy demands.

Dynamic rupture simulations based on depth-dependent stress accumulation

SUMMARY The depth variation in earthquake rupture behaviour is important for quantitative seismic hazard analysis. We discussed how to set up the initial stress on a fault before an earthquake based on the Mohr–Coulomb criterion considering depth variation. One can assume that the stress is uniformly loaded without exceeding the Coulomb criterion at any depth (stress-constrained condition); however, this implicitly induces a discontinuity of strain in a 1-D layered Earth model. We alternatively assumed that the strain in an upper layer does not exceed that in a lower layer (strain-constrained condition). We numerically demonstrated the dynamic rupture process through 3-D numerical simulations, particularly for the 2019 Mw 4.9 Le Teil (France) earthquake, showing a very shallow ruptured area with ground surface displacement. The rupture extent and seismogenic depth can be controlled by a limited layer at depth, which is favourably loaded in advance. The lateral extension of the rupture propagation at this layer is necessary to trigger the above layer but not enough to trigger the layers below. The depth variation of stress loading before an earthquake would be important for assessing the rupture size of moderate (magnitude 5–6) crustal earthquakes in particular.

Simulation of Dynamic Rupture Process and Near-Field Strong Ground Motion for the Wenchuan Earthquake

ABSTRACT The 2008 Wenchuan earthquake that occurred in the Longmenshan thrust zone is the most serious natural disaster recorded in China’s densely populated areas over the past few decades. Its northeast-trending principal fault—the Yingxiu–Beichuan fault (YXBCF), has a complex, segmentary-cascaded geometry and was dominated by the thrust slip in the southwest section, while the right-lateral slip in the northeast section. Some previous works believe that there may have occurred a supershear rupture in the strike-slip-dominated northeast section. Here we revisited this earthquake by exploring the dynamic rupture mechanism of the principal fault and showed a hypothetical scenario with supershear rupture occurring in its northeast section. We utilized a 3D curve grid finite-difference method to simulate the spontaneous rupture process of the YXBCF and corresponding near-field strong ground motion. An appropriate focal process is obtained using the trial-and-error method within reasonable parameters, and its related responses are validated by geological investigations and geophysical inversions. Besides, a large hypothetical oblique propagating supershear rupture is shown between Beichuan and Nanba in the northeast section of the YXBCF. Its transition mechanism is related to the Gaochuan–Beichuan conjugated fault from the fault geometry perspective, and belongs to the joint action of fault barrier and free surface. Such a supershear scenario is not rejected by observations and could increase the credibility of the occurrence of supershear rupture in the northeast section of the YXBCF during the Wenchuan earthquake.

Mechanism for seismic supershear dynamic rupture based on in-situ stress: a case study of the Palu earthquake in 2018

The Palu earthquake, with a magnitude of 7.5, severely devastated the region in Central Sulawesi, Indonesia, but the mechanism of dynamic rupture considering in-situ conditions is not well understood. The in-situ stress field and fault geometry play important roles in the evolution of the supershear rupture. This study investigated the in-situ stress field, critical factors including the inversion of principal stress orientation by the focal mechanism solution, and constraint magnitude using the improved lateral pressure coefficient polygon. Furthermore, the dynamic rupture process is simulated using the finite element method (FEM) considering the strike and in-situ stress magnitudes of the seismogenic fault. The result shows that the principal stress orientation rotates counterclockwise about 15° from north to south, and the northern part of the fault zone is less straight than the fault from Palu Bay to the south, which are two decisive factors for supershear in the north. The damage zones considering the peak acceleration and co-seismic displacement are enlarged in Palu City, which is attributed to the rupture mode. It provides plausible explanations for this supershear event and sheds light on different dynamic rupture processes and seismic hazards that can be predicted by fully understanding the regional in-situ stress field.

Anatomy of resistive switching behavior in titanium oxide based RRAM device

Resistive random access memory (RRAM) devices based on binary transition metal oxides and the application for nonvolatile memory devices are becoming an area of extensive concern. The physical understanding of resistive switching is crucial for RRAM development. In this paper, both experiments and simulated dynamic formation and rupture processes of oxygen vacancy (VO) conductive filament (CF) channels in titanium oxide based RRAM devices are presented. Compared with the Al/TiO2.1/Al device with higher oxygen content, the Al/TiO1.6/Al device shows a lower forming voltage. However, little dependence on oxygen content in TiOx film is shown for other resistive switching parameters, including high resistance state resistance, low resistance state resistance, set voltage, and reset voltage. A numerical physics model is presented to relate the resistive switching behavior with the evolution CF channels in terms of VO morphology and I−V characteristics.

Dynamic Rupture Simulation of the 1833 Songming, Yunnan, China,M8.0 Earthquake: Effects From Stepover Location and Overlap Distance

AbstractStepover structures are widely distributed in natural fault systems. The jump distance is typically easier to identify than both the stepover location and the overlap distance because of the presence of lakes and sedimentary basins around the stepover. Using the curved grid finite‐difference method, we first conducted a 3D spontaneous dynamic rupture simulation of the 1833 Songming earthquake on a continuous model of the western Xiaojiang fault to estimate the regional stress azimuth. Then, we performed rupture process simulations with different stepover structure models on the western Xiaojiang fault to investigate the effects of the stepover location and overlap distance on the dynamic rupture process. In addition, we analyzed the fault strength ratioSand rupture velocity of the preferred fault models and discussed the occurrence of supershear rupture during the Songming event. Finally, we simulated the strong ground motion with the preferred fault models for the 1833 Songming earthquake. Our simulation results suggest that the optimal regional maximum principal stress azimuth during the Songming event was N20°W. Our simulations further reveal that the Qingshuihai stepover is located in the middle of Qingshuihai Lake, and the overlap distance is 6 km; in contrast, the location of the Yangzonghai stepover is located in the southern part of Yangzonghai Lake, and the overlap distance is not constrained. Furthermore, our numerical simulation indicates that the Songming earthquake exhibited supershear rupture; however, this supershear rupture is not sustained and is easily affected by the friction parameters and nucleation location.

Coseismic deformation of the 2021 MW7.4 Maduo earthquake from joint inversion of InSAR, GPS, and teleseismic data

The MW7.4 Maduo earthquake occurred on 22 May 2021 at 02:04 CST with a large-expansion surface rupture. This earthquake was located in the Bayan Har block at the eastern Tibetan Plateau, where eight earthquakes of MS >7.0 have occurred in the past 25 years. Here, we combined interferometric synthetic aperture radar, GPS, and teleseismic data to study the coseismic slip distribution, fault geometry, and dynamic source rupture process of the Maduo earthquake. We found that the overall coseismic deformation field of the Maduo earthquake is distributed in the NWW-SEE direction along 285°. There was slight bending at the western end and two branches at the eastern end. The maximum slip is located near the eastern bending area on the northern branch of the fault system. The rupture nucleated on the Jiangcuo fault and propagated approximately 160 km along-strike in both the NWW and SEE directions. The characteristic source rupture process of the Maduo earthquake is similar to that of the 2010 MW6.8 Yushu earthquake, indicating that similar earthquakes with large-expansion surface ruptures and small shallow slip deficits can occur on both the internal fault and boundary fault of the Bayan Har block.

Rockburst mechanism in coal rock with structural surface and the microseismic (MS) and electromagnetic radiation (EMR) response

Rockburst is a complex coal and rock dynamic disaster, which poses a serious threat to safe and efficient mining activities. With the increase in the mining depth and strength, rockburst becomes more and more serious. Coal rock contains different types and sizes of structural surface, and its bucking failure is the result of crack propagation and coalescence. In this paper, based on the elastic–plastic mechanics and damage mechanics, we established the elastic–plastic-brittle mutation rockburst model of coal rock with structural surface, introduced the concept of the coal rock volume energy potential function, and researched the relationship between energy accumulation and dissipation during the coal rock dynamic deformation and rupture process to obtain the rockburst energy condition. In addition, the volume element-region-system model of rockburst was established to explain the rockburst evolution process very well. In the external disturbance or high stress state, the coal rock system volume element is destroyed and quickly releases energy to the adjacent volume element. When the adjacent volume element cannot absorb this energy, it is destroyed, and the energy is released quickly. This energy release forms a chain reaction, and the local coal rock is unstable. Eventually, the entire coal rock system is unstable, and rockburst happens. Based on the above theory, the microseismic (MS) and electromagnetic radiation (EMR) characteristics of coal rock in the rockburst evolution process were analyzed. The significance of the study lies in both theory and practice for deeply understanding the rockburst mechanism, as well as for accurate monitoring and early warning.

A unified first-order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones.

Earthquake fault zones are more complex, both geometrically and rheologically, than an idealized infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities and multi-physics coupling within and outside of fault zones, here we present a first-order hyperbolic and thermodynamically compatible mathematical model for a continuum in a gravitational field which provides a unified description of nonlinear elasto-plasticity, material damage and of viscous Newtonian flows with phase transition between solid and liquid phases. The fault geometry and secondary cracks are described via a scalar function ξ ∈ [0, 1] that indicates the local level of material damage. The model also permits the representation of arbitrarily complex geometries via a diffuse interface approach based on the solid volume fraction function α ∈ [0, 1]. Neither of the two scalar fields ξ and α needs to be mesh-aligned, allowing thus faults and cracks with complex topology and the use of adaptive Cartesian meshes (AMR). The model shares common features with phase-field approaches, but substantially extends them. We show a wide range of numerical applications that are relevant for dynamic earthquake rupture in fault zones, including the co-seismic generation of secondary off-fault shear cracks, tensile rock fracture in the Brazilian disc test, as well as a natural convection problem in molten rock-like material.This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

Effects of the Rock Bridge Ligament on Fracture and Energy Evolution of Preflawed Granite Exposed to Dynamic Loads

This paper aims to reveal the mechanical properties, energy evolution characteristics, and dynamic rupture process of preflawed granite under impact loading with different rock bridge angles and strain rates. A series of dynamic impact experiments were conducted along with the separate Hopkinson press bar (SHPB) testing system to analyze and study the overall rock fracture process. Under the impact load, the peak stress of granite increases with the increase of rock bridge angle and strain rate, but the increase gradually decreases. The peak strain also increases gradually with the increase of rock bridge angle, but there is an upper limit value; the total input strain energy increases with the increase of strain rate and rock bridge angle. It is shown that the higher the strain rate, the higher the unit dissipation energy, and the greater the degree of rock fragmentation. For rock under impact loads, the crack first initiates from the wing end of the prefabricated flaw, the preflaw closes gradually, and finally the crack propagates at the locking section leading to the coalescence of rock bridge. With the increase of strain rate, the fragmentation degree of the specimen increases asymptotically, and the average fragmentation size of the specimen decreases with the increase of strain rate. It is suggested that the stability of large rocked slopes is controlled by the locked section, and understanding the fracture evolution of the rock bridge is the key to slope instability prediction.