Shear Rupture Research Articles

The criterion of block media strength and geomechanical back-calculation

Relevance and problematics. The mechanism of block medium and jointed rock mass deformation and breaking differs notably from continuum mechanics ideas, making up the crucial fundamental problem of geomechanics and distinguishing it from other engineering sciences connected with the mechanics ISSN 0536-1028 «Известия вузов. Горный журнал», № 6, 2020 47 of deformable solids. However, due to poor understanding of block media breaking mechanism, rock masses strength is overwhelmingly estimated by means of empirical dependences obtained by simulation in laboratory conditions. It is apparent that this approach does not solve the crucial fundamental problem and the accuracy of predicting mechanical characteristics of jointed rock masses may reach 100%. Research methodology. Based on the earlier theoretical research by the methods of variational, integral, and differential calculus, a new mechanism of block mass breaking at a point was substantiated. It implies translation and rotational character of blocks displacement in a rock mass in the process of its deformation making it possible to substantiate the criterion of jointed rock masses breaking. Research results, analysis and recommendations for use. The research was the first to obtain the block medium strength criterion. It has been shown that block mass strength is made up of the strength along the slip joint and block rotation resistance. Besides, within some range of loads, the ultimate strength of the rock mass is proportional to the tensile strength of a structure block. The work also proposes a range of analytical dependences obtained based on the solid mechanics making which make it possible to back calculate the rock mass strength based on the curvature of the shear rupture surface and assess the full tensor of the plain field of strain by the base axes orientation.

Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure

We are concerned with the numerical solution of a unified first order hyperbolic formulation of continuum mechanics that goes back to the work of Godunov, Peshkov and Romenski [65,68,97] (GPR model) and which is an extension of nonlinear hyperelasticity that is able to describe simultaneously nonlinear elasto-plastic solids at large strain, as well as viscous and ideal fluids. The proposed governing PDE system also contains the effect of heat conduction and can be shown to be symmetric and thermodynamically compatible, as it obeys the first and second law of thermodynamics. In this paper we extend the GPR model to the simulation of nonlinear dynamic rupture processes, which can be achieved by adding an additional scalar to the governing PDE system. This extra parameter describes the material damage and is governed by an advection-reaction equation, where the stiff and highly nonlinear reaction mechanisms depend on the ratio of the local equivalent stress to the yield stress of the material. The stiff reaction mechanisms are integrated in time via an efficient exponential time integrator. Due to the multiple spatial and temporal scales involved in the problem of crack generation and propagation, the model is solved on space–time adaptive Cartesian meshes using high order accurate discontinuous Galerkin finite element schemes endowed with an a posteriori subcell finite volume limiter. A key feature of our new model is the use of a twofold diffuse interface approach that allows the cracks to form anywhere and at any time, independently of the chosen computational grid, which is simply adaptive Cartesian (AMR). This is substantially different from many fracture modeling approaches that need to resolve discontinuities explicitly, such as for example dynamic shear rupture models used in computational seismology, where the geometry of the rupture fault needs to prescribed a priori. We furthermore make use of a scalar volume fraction function α that indicates whether a given spatial point is inside the solid (α=1) or outside (α=0), thus allowing the description of solids of arbitrarily complex shape. We show extensive numerical comparisons with experimental results for stress-strain diagrams of different real materials and for the generation and propagation of fracture in rocks and pyrex glass at low and high velocities. Overall, a very good agreement between numerical simulations and experiments is obtained. The proposed model is also naturally able to describe material fatigue.

Dynamic earthquake rupture modeling considering regional crustal stress conditions in southeastern Korea

The Korean Peninsula is located in a low-seismicity zone at the eastern margin of the Eurasian plate. However, the 2016 Gyeongju and 2017 Pohang earthquakes, which occurred in southeastern Korea, highlight the importance of advanced seismic hazard assessment and mitigation in this region. We successfully performed spontaneous dynamic rupture modeling by considering the crustal stress field in southeastern Korea, constrained by earthquake focal mechanism data, to better understand the seismic hazard in the region. We found that the geologically recognized Yangsan fault trace near the location of the Gyeongju earthquake is not aligned well with the favorable shear rupture directions, given the current crustal stress field in the region. The fault needs to be very weak (i.e., have a low static friction coefficient) to initiate a large earthquake rupture. However, our dynamic model results show that the fault plane constrained by the focal mechanism solution of the 2016 Gyeongju earthquake is more favorably aligned for shear rupture under the current stress condition and that it may be able to produce a relatively large earthquake if the extension of the fault is quite long (~60 km). This type of dynamic rupture modeling study may help to more accurately elucidate the seismic hazard in a low-seismicity zone such as southeastern Korea.

Fracture evolution during rockburst under true-triaxial loading using acoustic emission monitoring

This paper investigates the fracture evolution during rockbursts of granodiorite and basalt that appeared to be representatives of two different rockburst modes under true-triaxial loading using acoustic emission (AE) analysis. In the experiments, with the macroscale ejection and failure features captured and presented by the high-speed video imaging and failed specimens, the inside micro- or meso-scale fracturing was detected and analyzed in detail by AE in terms of intensity, temporal-spatial distribution, and mechanism. The experimental results and AE analyses show that the fracture evolution during rockburst (particularly in granodiorite) exhibits hierarchical characteristics: during early loading, small local microfractures developed progressively and stably mainly by tension and clustered preliminarily; around and after the point of the crack damage stress, large-scale fractures developed and coalesced rapidly and unstably with increasing shear mechanism, and nucleation zones significantly developed; upon rockburst failure, rocks near the free face buckled or fractured and ejected rapidly, and shear ruptures suddenly ran through. The findings help facilitate the rockburst prediction and control.

Effect of Load on the Corrosion Behavior of Friction Stir Welded AA 7075-T6 Aluminum Alloy.

The paper focuses on the corrosion behavior of aluminum joints made by friction stir welding as a function of loading conditions. A four-points bend-beam test, constant loading test, and slow strain-rate test were carried out on AA 7075-T6 alloy in aerated NaCl 35g/L solution at room temperature monitoring the free corrosion potential. The penetration depth of the intergranular attack was deeper after the four-point bent-beam tests compared to all the other testing techniques. Preferential dissolution along the grain boundaries was found in the heat-affected zone and the attack follows the elongated grains structure along the rolling direction. However, no stress-corrosion cracking phenomena were detected. No relevant stress corrosion cracking (SCC) crack embryos propagation was noticed under uniaxial tensile tests—both constant loading and slow strain-rate tests—manly due to the high dissolution rate occurring at the crack tip which promoted premature shear ruptures.

Experiments and nonlinear analysis of the impact behaviour of sandwich panels constructed with flax fibre-reinforced polymer faces and foam cores

As the effects of climate change become more apparent, it is necessary that environmental impact is considered in every aspect of our society, including the design of new infrastructure. The use of natural materials for building construction is one way to improve the sustainability of infrastructure and therefore it is important that the behaviour of structures made with natural materials be investigated extensively and well understood. In this study, the performance of sandwich panels constructed with flax fibre-reinforced polymer faces and foam cores under impact loading is studied experimentally and analytically. The parameters of the tests were facing thickness (1, 2 and 3 layers of flax fabric) and core density (32, 64 and 96 kg/m3). Each specimen was 1220 mm long, 152 mm wide and approximately 80 mm thick and was tested by a 10.41 kg drop weight impact at mid-span. Each specimen was tested multiple times starting at a drop height of 100 mm and increasing the height by 100 mm for each subsequent test until ultimate failure. The results indicate that the ultimate impact energy increases with both core density and face thickness. The four main failure modes observed were: compression face crushing, compression face wrinkling, core shear and tension face rupture. The failure modes observed generally matched those observed during similar quasi-static testing. Additionally, a nonlinear incremental iterative model was developed based on the conservation of energy during an impact event and the nonlinear mechanical behaviour of both the fibre-reinforced polymer faces and foam cores. This novel model accurately predicts the total deflection and face strains based on the energy of an impact.

Explicit dynamic approach for unbounded domains in frictional contact with Rate and State laws

The paper explores the ability of an explicit time integration procedure to simulate the dynamics of shear rupture between unbounded elastic blocks on frictional interface, modeled with the finite element method. The behaviour of the interface is governed by Rate and State (RS) friction laws, proposed to describe the rate dependent phenomena observed in experiments on rocks and many other materials in sliding contact. The method for the frictional contact between bodies is integrated in the framework of heterogeneous asynchronous time integrator (HATI). Dual formulation, requiring the introduction of Lagrange multipliers, is adopted by dealing in a weak way with the normal contact conditions as well as the tangential frictional conditions expressed in velocity. Taking advantage of the flexibility of the HATI framework, precise formulations of Perfectly Matched Layers (PML) are also incorporated, enabling us to treat semi-infinite media in frictional contact. Simulations concerning an unbounded elastic block on a rigid flat plane, initially compressed and sheared with remote loadings, are carried out. Advantages of the PML are underlined during the preliminary stages of loading as well as during the nucleation and propagation of the shear rupture along the interface. Numerical oscillations inherent from the high non-linearity of the RS friction law, characterized by significant variations of the friction coefficient with small changes in tangential velocity, are drastically reduced thanks to the HATI method.

Block shear failure in welded gusset plates under combined loading

Block shear failure in the base metal of welded steel connections is a potential failure mode affecting many steel structures. However, there are only a few studies on the block shear failure of welded connections under combined shear and axial loading. Combined loading is defined as a simultaneous loading parallel and perpendicular to the weld lines (or an inclined loading) in the plane of the connecting plate. In this research, a nonlinear finite element model is used to study the effect of connection geometry and weld group configuration on the block shear strength of welded connections under combined loading. In current design standards, the block shear failure planes are assumed to consist of shear and tension planes, parallel and perpendicular to the applied load, respectively. The results obtained indicate that for combined loading, inclined failure planes are possible and the state of stress in such planes is a combination of tensile and shear stresses, the extent of which is proportional to the angle of loading. The results are used to describe the behavior of block shear rupture planes in such cases. Finally, to provide a better estimate of block shear strength in welded connections subjected to combined loading, a new equation is proposed that considers the actual shape of displaced block.

Self-similarity of low-frequency earthquakes

Low-frequency earthquakes are a particular class of slow earthquakes that provide a unique source of information on the physical processes along a subduction zone during the preparation of large earthquakes. Despite increasing detection of these events in recent years, their source mechanisms are still poorly characterised, and the relation between their magnitude and size remains controversial. Here, we present the source characterisation of more than 10,000 low-frequency earthquakes that occurred during tremor sequences in 2012–2016 along the Nankai subduction zone in western Shikoku, Japan. We show that the scaling of seismic moment versus corner frequency for these events is compatible with an inverse of the cube law, as widely observed for regular earthquakes. Their radiation, however, appears depleted in high-frequency content when compared to regular earthquakes. The displacement spectrum decays beyond the corner frequency with an omega-cube power law. Our result is consistent with shear rupture as the source mechanism for low-frequency earthquakes, and suggests a self-similar rupture process and constant stress drop. When investigating the dependence of the stress drop value on the rupture speed, we found that low-frequency earthquakes might propagate at lower rupture velocity than regular earthquakes, releasing smaller stress drop.

The Progressive Failure Analysis of Uni-Directional Fibre Reinforced Composite Laminates

ABSTRACTThe three dimensional standard damage model developed by Lavedeze et.al [9, 13] for uni-directional fibre reinforced ply is implemented into the nonlinear solution of NX Nastran within composite solid element to analyze the progressive damage process and ultimate failure of fibre reinforced composite laminates. This ply level meso-damage-constitutive-model takes into account main damage mechanisms including fibre breaking, matrix transverse cracking, and fibre/matrix de-bonding; also considers contributions like plasticity coupling, damage delay effects, and elastic nonlinearity in fibre compression. Dissipated energy and damage status are also introduced to reflect the damage condition on the macrostructural-level. Using the implemented code, simulation is carried out on the uniaxial tension of a [±45]2s laminate with IM6/914 material, wherein the predicted ply shear rupture stress matches the experimental results very well and better than the theoretical predictions in literature. Moreover, a [-45/0/45/90] holed laminate loaded in tension is simulated to show the complex behavior of subcritical damage evolution and failure process in the composite structure. The composite solid element with damage model supported in NX Nastran is shown to be a reliable tool to analyze the progressive failure of uni-directional fibre reinforced composite laminates.

Non‐Double‐Couple Microearthquakes in the Focal Area of the 2000 Western Tottori Earthquake (M 7.3) via Hyperdense Seismic Observations

AbstractEarthquakes with non‐double‐couple (NDC) components are indicators of geometric fault complexity, anisotropy, tensile failure, and fluid flow effects. NDC earthquakes have been observed in volcanic zones and interpreted as faulting related to fluid effects in the hypocentral region. In this study, we provide evidence of the occurrence of microearthquakes with NDC components in a tectonic zone. Aftershocks of the 2000 Western Tottori earthquake revealed definite NDC components based on a polarity analysis of the first P wave motion data from a hyperdense seismic observation. We modeled these events using both shear faulting with tensile failure and multiple shear ruptures. Six of the eight NDC events were well modeled by shear faults accompanied with an opening tensile crack. These results suggest that pressurized fluid or a weak tensile crack may exist along the rupture zone of the Tottori earthquake.

Rockburst characteristics of several hard brittle rocks: A true triaxial experimental study

Abstract Rockburst is a typical rock failure which frequently threatens both human life and construction equipment during highly stressed underground excavation. Rock lithology is a control factor of rockburst. In this paper, rockburst tests were conducted on rectangular prismatic specimens of six types of intact hard brittle rocks, i.e. granodiorite, granite, marble, basalt, sandstone and limestone, under one-free-face true triaxial loading conditions. With the use of high-speed cameras, an acoustic emission (AE) system and a scanning electron microscope (SEM), rockburst of different rocks was investigated. The results show that the strainbursts of granodiorite, granite and marble were accompanied by tensile splitting near the free face, and consequently were relatively strong with a large amount of fragment ejection and kinetic energy release. For basalt, sandstone and limestone, failure was primarily dominated by shear rupture. The strainbursts of basalt and sandstone were relatively small with minor fragment ejection and kinetic energy release; while no burst failure occurred on limestone due to its relatively low peak strength. Rock strength, fracturing and fragmentation characteristics, and failure modes of different rocks can significantly affect rockburst proneness and magnitude. The AE evolution coupled with SEM analysis reveals that the differences in the inherent microstructures and fracture evolution under loading are the primary factors accounting for different rockbursts in various rock types.

Initial studies on brace-type shear fuses

This paper proposes new brace-type shear fuses (BSFs) connected in series. The BSF consists of a core plate, two filling plates, two perforated cover plates, unbonding material and bolts. It is designed to dissipate seismic energy via yielding mainly under shear. Perforated cover plates make damage of the core plate visible. To analyze BSFs, seven specimens were designed with different number of shear fuses, tension-to-shear strength ratios and radii of shear fuses. In the experiments, it was found that the deformation capacity had positive correlation with number of shear fuses, tension-to-shear strength ratio, and radii of shear fuses. No buckling of the core plates occurred due to the short length of specimen. Fracture modes of all the specimens were shear rupture. Contact between the lateral sides of core plate and filling plates due to flexural deformation was observed, which led to significant increase of force in both tension and compression. In addition, initial stiffness and yield force of BSFs were derived based on the Principle of Virtual Work. A design criterion to avoid direct contact was also proposed for design of BSFs.

Recent Milestones in Unraveling the Full-Field Structure of Dynamic Shear Cracks and Fault Ruptures in Real-Time: From Photoelasticity to Ultrahigh-Speed Digital Image Correlation

AbstractThe last few decades have seen great achievements in dynamic fracture mechanics. Yet, it was not possible to experimentally quantify the full-field behavior of dynamic fractures, until very recently. Here, we review our recent work on the full-field quantification of the temporal evolution of dynamic shear ruptures. Our newly developed approach based on digital image correlation combined with ultrahigh-speed photography has revolutionized the capabilities of measuring highly transient phenomena and enabled addressing key questions of rupture dynamics. Recent milestones include the visualization of the complete displacement, particle velocity, strain, stress and strain rate fields near growing ruptures, capturing the evolution of dynamic friction during individual rupture growth, and the detailed study of rupture speed limits. For example, dynamic friction has been the biggest unknown controlling how frictional ruptures develop but it has been impossible, until now, to measure dynamic friction during spontaneous rupture propagation and to understand its dependence on other quantities. Our recent measurements allow, by simultaneously tracking tractions and sliding speeds on the rupturing interface, to disentangle its complex dependence on the slip, slip velocity, and on their history. In another application, we have uncovered new phenomena that could not be detected with previous methods, such as the formation of pressure shock fronts associated with “supersonic” propagation of shear ruptures in viscoelastic materials where the wave speeds are shown to depend strongly on the strain rate.

Performance of geosynthetic-reinforced soil foundations across a normal fault

This paper presents a series of model tests on geosynthetic-reinforced soil (GRS) foundations across a normal fault. The aim was to evaluate the performance of reinforced foundations as a mitigation measure for surface faulting hazards. Experimental tests modeled a 3-m thick foundation in prototype subjected to a fault displacement up to 90 cm. Test variables included the number of reinforcement layers, reinforcement stiffness and location, and foundation height. Digital image analysis techniques were applied to determine the ground settlement profile, angular distortion, shear rupture propagation, and mobilized reinforcement tensile strain at various magnitudes of fault offset. Test results revealed that compared with the unreinforced foundation, reinforcement inclusion could effectively prevent the shear rupture propagating from the bedrock fault to the ground surface. It also spread the differential settlement to a wider influential zone, resulting in an average reduction of 60% in the fault-induced angular distortion at the ground surface. The maximum angular distortion decreased as the foundation height, number of reinforcement layers, and reinforcement stiffness increased. Relationships between the maximum angular distortion and maximum mobilized reinforcement tensile strain with fault displacement were therefore established. Based on the findings from this study, design suggestions and implications are discussed.

Do stopes contribute to the seismic source?

Parameters such as source location, seismic moment, energy, source size, and stress drop are routinely calculated from mining-induced seismic data. Seismic moment tensors are inverted less routinely because their calculation is more complex and their accuracy depends on the network geometry, among a number of other factors. The models utilized in the source parameter calculations, the most well-known of which is the Brune model, were developed for the global seismicity problem and assume a solid, homogeneous Earth model. However, the tabular orebodies in South African gold and platinum mines are mined extensively and the excavations (stopes) can extend for many kilometres. The seismic source mechanisms on deep-level gold mines are generally compatible with shear failure (Hoffmann et al., 2013), whereas the source mechanisms of events at intermediate-level bord and pillar mines in the platinum district are more compatible with pillar failure and accompanying stope closure (Spottiswoode, Scheepers, and Ledwaba, 2006; Malovichko, van Aswegen, and Clark, 2012). In this paper we investigate the influence of the stope on seismic inversions for the scalar moment, corner frequency/source radius, stress drop through numerical modelling using WAVE3D. The main objective is to determine whether the source parameters calculated from the recorded waveforms are due to a combination of the stope and shearing sources, rather than being related only to a shear source in the host rock. The modelled source is shear rupture in the footwall of a stope. The results show that the stope appears to have an appreciable effect on the seismic inversions. The seismic moment and source radius of the shear source in the stope are larger for the model with a stope compared to the model with no stope. The stress drop for the case with a stope is less than the applied stress drop, which could be an effect of the apparently larger source. This work provides a possible explanation of the second corner frequency often observed in the spectra of seismograms recorded in South Africa platinum mines. This has implications for the accurate determination of source parameters and the assessment of the intensity of shaking in stopes.

Numerical Investigation of the Pre-collapse Behavior and Internal Damage of an Unstable Rock Slope

This paper describes the results of a 2D and 3D numerical modeling carried out on an unstable natural rock slope (volume = 110,000–335,000 m3) located in north-eastern Italy (Friuli Venezia Giulia Region). It was aimed at investigating the mechanical behavior and internal rock mass damage of the unstable slope before the collapse. The numerical simulations testify that the stability condition of the slope is close to the limit equilibrium (strength reduction factor, SRF = 1.03–1.13), as demonstrated by the considerable rock mass damage observed on the field. The overall mechanical behavior of the slope is mainly governed by the kinematic conditions of the secondary internal blocks, which, in turn, depend on the geometry and mechanical properties of the major discontinuities that delimit the adjacent blocks. Slope failure is achieved through internal rock mass damage represented by internal shear and tensile ruptures localized in correspondence with over-stressed zones. The failure mechanism is characterized by sliding along pre-existing discontinuities and inner damage in the form of the enucleation of shear bands that originate internal secondary failure surfaces and/or damaged rock mass zones. The stress–strain modeling predicts intense slope deformations in zones where rock mass damage actually occurred. This paper emphasizes the decisive connection between the geomechanical field survey and numerical modeling. The comparison of surface geological data acquired on the field with the mechanical indicators obtained from the numerical analyses can significantly improve knowledge of the rock mass damage process that involves unstable slopes approaching failure condition.

The effect of Poisson's ratio on the creation of tensile branches around dynamic faults

It is common for the fractured zone around dynamic faults to contain tensile cracks. The effect of Poisson's ratio (ν) on the creation of these cracks was investigated in this study as a function of the dynamic minimum strain energy density criterion (MSED-Criterion). In addition, the effect of rupture speed (c), friction coefficient (f), fault inclination angle (β) and confining stress (Ko) were taken into account. The MSED-Criterion permits the study of the creation of tensile cracks in brittle and ductile shear zones. It was found that by increasing Poisson's ratio, the rock behavior transfers gradually from brittle to ductile and as a consequence, the branching angle and fracture toughness increase. Whenever the rock mass tends towards ductile behavior, the possibility of creating tensile branches decreases. Ductile shear zones can sustain stresses greater than brittle zones before tensile branches are formed around dynamic faults. The branching angle of tensile cracks is directly proportional to (ν, c, β, f and Ko) and it varies between approximately 77° and 115°. These cracks are formed in the extensional side of a dynamic fault and they tend to grow towards the maximum far-field stress. The results of this study can be used in the field of earth science and earthquakes to identify the formation of tensile branches around dynamic shear ruptures and they were explained depending on experimental results and field observations of other studies.

Development of nail-anchor strengthening system with iron-based shape memory alloy (Fe-SMA) strips

This work discusses the development process of a direct fastening technique for strengthening steel members using iron-based shape memory alloy (Fe-SMA) strips. First, several lap-shear tests were performed to examine the efficiency of five nail-anchor systems in terms of load-carrying capacity, slippage, and convenience of installation. To this end, 3D optical digital image correlation (DIC) measurements (using an ARAMIS system) and numerical simulation were conducted. Different failure modes including tensile rupture of the strips, shear rupture of the nails, and/or sliding of the strips were observed and discussed. The optimum nail-anchor system was then determined. This system has a very short anchorage length of approximately 50 mm and only 12 nails (i.e., 3 × 4). Second, to demonstrate the efficiency of the proposed system, a steel I-beam was strengthened with the selected nail-anchor system and activated using an infrared heating (IRH) technique. The SMA-strengthened beam was subjected to static and then high-cycle fatigue loadings with a loading ratio of R=0.2 for 2.5 million cycles without any failure or damage, indicating reliable performance of the system. Owing to the larger coefficient of thermal expansion of the Fe-SMA material compared to that of steel, it was observed that a decrease and increase in the environmental temperature resulted in an increase and decrease of the pre-stress level in the Fe-SMA strip, respectively (i.e., an inverse correlation).

Experimental evidence for wall-rock pulverization during dynamic rupture at ultra-high pressure conditions

The mechanisms triggering intermediate and deep earthquakes have puzzled geologists for several decades. There is still no consensus concerning whether such earthquakes are triggered by brittle or ductile mechanisms. We performed a deformation experiment on a synthetic lawsonite-bearing blueschist at a confining pressure of 3 GPa and temperatures from 583 to 1,073 K. After deformation, the recovered sample reveals conjugated shear fractures. Garnet crystals are dissected and displaced along these narrow faults and reveal micro- and nanostructures that resemble natural pulverization structures as well as partial amorphization. Formation of such structures at low confining pressures is known to require high tensile stresses and strain rates and is explained by the propagation of a dynamic shear rupture. The absence of shearing in the pulverized wall rock is taken as evidence that these structures pre-date the subsequent heat-producing frictional slip. In analogy to observations at low pressure we infer that the garnet structures in our experiment result from rapid propagation of a shear fracture even at the high pressure exerted on the sample and thus suggest that brittle deformation is possible at lower crustal to upper mantle depths.