Brittle Part Research Articles

Low‐Viscosity Zones Beneath the Coso Volcanic Field Revealed by Postseismic Deformations Following the 2019 Ridgecrest Earthquake

AbstractThe rheology of materials near fault zones controls the deformation of the fault, thus playing an important role in the rupture propagation of large earthquakes. Here, we model the postseismic deformation in the first 4 years following the 2019 Ridgecrest earthquake, and probe the laterally variable lower‐crustal viscosity and fault afterslip, using a combined model incorporating afterslip and viscoelastic relaxation. Modeling results reveal that laterally variable low‐viscosity zones (1017∼1018 Pa·s) beneath the Coso Volcanic Field are required to explain the observations well. These low‐viscosity materials may reduce the width of the brittle part of the fault, thus affecting the northwestward propagation of the 2019 Ridgecrest earthquake rupture and the spatial pattern of nearby seismicity. Numerical simulations reveal that the postseismic viscoelastic relaxation of the event will cause contractional strain in the upper‐crustal magma reservoirs, which may counteract the extensional strain caused by the coseismic rupture.

Formation of heterogeneous interfaces in the TiAl/Ti2AlNb layered composite and its effect on the fracture toughness

TiAl/Ti2AlNb intermetallic-intermetallic laminated (IIL) composites featuring brittle/ductile heterogeneous interfaces were fabricated through vacuum hot-pack rolling. The microstructures and the phase transformation behaviors of the interfaces of the IIL composites before and after annealing at 900 °C/6 h were investigated. The heterogeneous interfaces are composed of four distinct regions, individually I (βo+γ+α2), II (βo/B2+ω) (brittle part), III (O lath), and IV (equiaxed O) (ductile part) regions from TiAl to Ti2AlNb side. Notably, after annealing, an equiaxed O band approximately 50 μm wide was observed in region IV of the interface. In addition, a significant microhardness variation was observed between regions II and IV of the interface, where region II exhibited higher hardness compared to the TiAl alloy, and region IV displayed lower hardness than the Ti2AlNb alloy. The enhanced fracture toughness of the IIL composites, three times that of the TiAl base alloy, is attributed to the formation of the brittle/ductile heterogeneous interfaces and the layered design incorporating the Ti2AlNb alloy. The corresponding toughening mechanism was further discussed. The brittle II region plays a role in increasing crack branching, while the ductile IV region inhibits the propagation of microcracks and prevents the formation of main cracks. This work highlights the crucial role of the brittle/ductile heterogeneous interface in the toughening of laminated composites. Furthermore, the discovery of the O band provides novel insights into the design of TiAl/Ti2AlNb heterostructures.

Effect of Neutron Irradiation on the Critical Event Size of Cleavage Fracture of the Chinese A508-3 Steel

In order to analyze the influence of neutron irradiation on the critical event of cleavage fracture for the Chinese A508-3 (RPV) steel, the fracture morphology, microstructure and grain size of the irradiated specimens are observed and analyzed by optical microscope (OM) and scanning electron microscope (SEM). The results show that with the increase of neutron doses, the fracture mode of Chinese RPV steel material changes gradually from ductile fracture to ductile-brittle mixed fracture transformation. The brittle part for fracture mode of ductile-brittle fracture is cleavage fracture, and the non-metallic inclusions, microstructure and grain size grades are not significantly different from those of the specimens without cleavage fracture. In the same material, with increasing of neutron doses, the critical event size of the cleavage fracture will be reduced, and the percentage of the grain that satisfies the grain size of the cleavage critical event will increase correspondingly, resulting in an increase of the probability of cleavage fracture of the material. The fine grain with uniform distribution can improve partly the fracture toughness of the material and withstand higher neutron doses under the same conditions.

One-dimensional velocity structure modeling of the Earth's crust in the northwestern Dinarides

Abstract. The studied area of the northwestern (NW) Dinarides is located in the northeastern (NE) corner of the Adriatic microplate and is bordered by the Adriatic foreland, the Southern Alps, and the Pannonian basin. Its complex crustal structure is the result of interactions among different tectonic units, the most important of which are the Eurasian plate and the Adriatic microplate. Despite numerous seismic studies in this tectonically complex area, there is still a need for a detailed, small-scale study focusing mainly on the upper, brittle part of the crust. In this work, we investigated the velocity structure of the crust with one-dimensional (1-D) simultaneous hypocenter–velocity inversion using routinely picked P- and S-wave arrival times. Most of the models computed in the combined P and S inversion converged to a stable solution in the depth range between 0 and 26 km. We further evaluated the inversion results with hypocenter shift tests, high- and low-velocity tests, and relocations. This helped us to select the best performing velocity model for the entire study area. Based on these results and the seismicity distribution, we divided the study area into three subregions, reselected earthquakes and stations, and performed the combined P and S inversion for each subregion separately to gain better insight into the crustal structure. In the eastern subregion, the P velocities in the upper 8 km of the crust are lower compared to the regional velocities and the velocities of the other two subregions. The P velocities between 8 and 23 km depth are otherwise very similar for all three models. Conversely, the S velocities between 2 and 23 km depth are highest in the eastern subregion. The NW and southwestern (SW) subregions are very similar in terms of the crustal structure between 0 and 23 km depth, with slightly higher P velocities and lower S velocities in the SW subregion. High vP/vS values were obtained for the layers between 0 and 4 km depth. Below that, no major deviations of vP/vS in the regional model from the value of 1.73 are observed, but in each subregion we can clearly distinguish two zones separated by a decrease in vP/vS at 16 km depth. Compared to the model currently used by the Slovenian Environment Agency to locate earthquakes, the obtained velocity models show higher velocities and agree very well with some of the previous studies. In addition to the general structural implications and the potential to improve the results of seismic tomography, the new 1-D P and S velocity models can also be used for reliable routine earthquake location and for detecting systematic travel time errors in seismological bulletins.

Estimation of Absolute Stress in the Hypocentral Region of the 2019 Ridgecrest, California, Earthquakes

AbstractStrength of the upper brittle part of the Earth's lithosphere controls deformation styles in tectonically active regions, surface topography, seismicity, and the occurrence of plate tectonics, yet it remains one of the most debated quantities in geophysics. Direct measurements of stresses acting at seismogenic depths are largely lacking. Seismic data (in particular, earthquake focal mechanisms) have been used to infer orientation of the principal stress axes. I show that the focal mechanism data can be combined with information from precise earthquake locations to place constraints not only on the orientation, but also on the magnitude of absolute stress at depth. The proposed method uses relative attitudes of conjugate faults to evaluate the amplitude and spatial heterogeneity of the deviatoric stress and frictional strength in the seismogenic zone. Relative fault orientations (dihedral angles) and sense of slip are determined using quasi‐planar clusters of seismicity and their composite focal mechanisms. The observed distribution of dihedral angles between active conjugate faults in the area of Ridgecrest (California, USA) that hosted a recent sequence of strong earthquakes suggests in situ coefficient of friction of 0.4–0.6, and depth‐averaged shear stress on the order of 25–40 MPa, intermediate between predictions of the “strong” and “weak” fault theories.

The Mechanics of Creep, Slow Slip Events, and Earthquakes in Mixed Brittle‐Ductile Fault Zones

AbstractGeological observations show that fault zone composition varies and often accommodates a mixture of brittle and ductile deformation. There is growing evidence that the nature of this mixture may play an important role in determining whether the fault creeps steadily or slides in slow slip events (SSEs) and/or fast earthquakes. Using numerical experiments of slip events in a fault zone of finite thickness, we explore how the ratio of brittle to ductile material and the absolute friction change resulting from a variation in slip velocity, affect energy partitioning and slip behavior in brittle‐ductile mixtures. We treat brittle material as Mohr‐Coulomb elastoplastic and ductile material as Maxwell viscoelastic. We simulate velocity‐weakening () behavior in the brittle part of the mixture and velocity‐strengthening () behavior in the ductile part using a rate‐and‐state formulation dependent on plastic strain accumulation. We show that: (1) mixtures can exhibit multiple slip behaviors including earthquakes and slow slip, (2) highly brittle mixtures do not tend to generate SSEs while weakly brittle mixtures can generate slow slip over a wider range of compositions, (3) structural features formed during simulated creep, SSEs, and earthquakes share notable similarities with structures observed in natural fault zones. We find that slip‐synchronous strengthening in the ductile portion of the mixture controls whether a rupture propagates as SSEs of yearlong durations. Shorter duration SSEs occur when the length of the plastic shear segments formed during slip is similar to the characteristic weakening distance for an earthquake.

On the fatigue behavior of low-temperature gaseous carburized 316L austenitic stainless steel: Experimental analysis and predictive approach

Low-temperature gaseous carburization is a surface modification method for austenitic stainless steels. In order to investigate the effects of low-temperature gaseous carburization on the fatigue behavior of AISI 316L, fully reversed axial fatigue tests were performed at room temperature on specimens with various remaining case depths. The fatigue performance of AISI 316L could be significantly improved; a 15% higher endurance limit is achieved after low-temperature gaseous carburization. After removal of the outer, brittle part of carburized case by electropolishing, the improvement of the fatigue performance is reduced. Fractography showed that for untreated specimens, fatigue cracks always initiated on the surface. For the carburized specimens, however, the locations of crack initiation sites depend on the applied stress levels. Compressive residual stresses in the case move the crack initiation site to the sub-surface; the lower the applied stress, the deeper the initiation site. A quantitative analysis of the effect on fatigue behavior forms the basis for a life prediction model, which can accurately predict the fatigue life of AISI316L steel after low temperature carburization.

Ridged plains on Europa reveal a compressive past

Europa's young surface implies relatively recent resurfacing. Ridged plains, which make up >50% of Europa's surface, have not yet been fully analyzed for a potential formation mechanism. Because ridged plains dominate Europa's surface, this terrain is key to understanding how Europa has resurfaced and how the resurfacing mechanisms may have evolved through time. In this work, we create a new high-resolution topographic model and a two-layer physical analog model to investigate the formation of ridged plains. We find that the ridged plains most closely resemble the compressional physical analog experiments which generate folds. Specifically, the analog experiments with a brittle layer <1/16th the thickness of the underlying ductile-layer best explain the morphological observations of the ridged plains on Europa. Based on the scaling relationships, we find that at the time of the ridged plains formation, the brittle part of the ice shell of Europa's ice shell was ~200 m thick and the total ice-shell thickness, including both the ductile and brittle parts, was >~3000 m. Compared to the predicted current ice shell thickness, this would imply that Europa's ice-shell has thickened through the visible surface history.

Numerical Analysis of Strain Localization in Rocks with Thermo-hydro-mechanical Couplings Using Cosserat Continuum

A numerical model for thermo-hydro-mechanical strong couplings in an elasto-plastic Cosserat continuum is developed to explore the influence of frictional heating and thermal pore fluid pressurization on the strain localization phenomenon. This model allows specifically to study the complete stress–strain response of a rock specimen, as well as the size of the strain localization zone for a rock taking into account its microstructure. The numerical implementation in a finite element code is presented, matching adequately analytical solutions or results from other simulations found in the literature. Two different applications of the numerical model are also presented to highlight its capabilities. The first one is a biaxial test on a saturated weak sandstone, for which the influence on the stress–strain response of the characteristic size of the microstructure and of thermal pressurization is investigated. The second one is the rapid shearing of a mature fault zone in the brittle part of the lithosphere. In this example, the evolution of the thickness of the localized zone and the influence of the permeability change on the stress–strain response are studied.

After-effects induced by interactions between hydrogen and the martensite transformation in Ni–Ti superelastic alloy

The effects of dynamic interactions between hydrogen and a stress-induced martensite transformation on the recovery of deteriorated tensile properties by ageing in air at room temperature have been investigated for a Ni–Ti superelastic alloy. A specimen is subjected to single stress-induced martensite and reverse transformations immediately after hydrogen charging. Upon tensile testing, brittle fracture occurs in the latter half of the elastic deformation region of the martensite phase after the stress-induced martensite transformation. Upon ageing before the tensile test, fracture occurs during the stress-induced martensite transformation. In addition, the nano- and micro-morphologies of the brittle outer part of the fracture surface of the specimen are changed by ageing. Thus, the tensile properties markedly deteriorate, rather than recover, by ageing. The present results clearly indicate that dynamic interactions between hydrogen and the stress-induced martensite transformation have serious after-effects on hydrogen embrittlement of Ni–Ti superelastic alloy.

Double-difference relocation of the 29 January 2011 ML 4.5 Oroszlány earthquake and its aftershocks and its relevance to the rheology of the lithosphere and geothermal prospectivity

In the central part of Hungary, an earthquake with the local magnitude of 4.5 occurred near the town of Oroszlany, on 29 January 2011. The main shock and its more than 200 aftershocks were recorded by a significant number of three-component seismic stations, which enabled us to perform multiple event location on the event cluster. We applied the double difference, HypoDD method to relocate the aftershock sequence in order to identify the pattern of active faulting. We used the extended International Seismological Centre location algorithm, iLoc to determine the initial single event locations for the aftershock sequence and applied multiple event location algorithm on the new hypocenters. To improve both location precision and accuracy, we added differential times from waveform cross correlation to the double-difference multiple event location process to increase the accuracy of arrival time readings. We show that both HypoDD collapses the initial, rather diffuse locations into a smaller cluster and the vertical cross-sections show sharp images of seismicity. Some of the relocated events in the cluster are ground truth quality with a location accuracy of 5 km or better. Having achieved accurate locations, we further examined the extent of the seismogenic zone. We investigated the relationship between geothermics and seismicity through strength profiles constructed for the study area. The aftershocks of the Oroszlany earthquake are dominantly in the range of 5–10 km, fitting well to the extent of the thin brittle part of the crust. It shows that the events are well in accordance with a thermally attenuated lithosphere and elevated geothermal gradient in the upper crust and basin sediments. These findings underline the geothermal prospectivity of the Panonian Basin. © 2017, Akademiai Kiado.

Geology and Structure Analysis of Palanpur-Danta Area, North Gujarat Using Remote Sensing and GIS

In this research paper, The GIS and remote sensing data for allowing detection of structural features, such as faults, offers opportunities to improve, mapping and identifying the areas that are likely to be locations of faulting. Faults are weakness zones in the brittle part of the lithosphere, along which the movement can take place in response to an induced stresses. When faults undergo displacement, depending on geological and structural conditions, strain markers could be formed on the fault surface. Computer technology, such as computer-based geographic information system (GIS), supplies a different method for data storage, integration, analysis, and display. The combination of remote sensing and GIS provides an optimum system for various geological investigations such as fault mapping.

Scattering attenuation profile of the Moon: Implications for shallow moonquakes and the structure of the megaregolith

We report measurements of the attenuation of short period seismic waves in the Moon based on the quantitative analysis of envelope records of lunar quakes. Our dataset consists of waveforms corresponding to 62 events, including artificial and natural impacts, shallow moonquakes and deep moonquakes, recorded by the four seismometers deployed during Apollo missions 12, 14, 15 and 16. To quantify attenuation and distinguish between elastic (scattering) and inelastic (absorption) mechanisms we measure the time of arrival of the maximum of energy tmax and the coda quality factor Qc. The former is controlled by both scattering and absorption, while the latter is an excellent proxy for absorption. Consistent with the strong broadening of seismogram envelopes in the Moon, we employ diffusion theory in spherical geometry to model the propagation of seismic energy in depth-dependent scattering and absorbing media. To minimize the misfit between predicted and observed tmax for deep moonquakes and impacts, we employ a genetic algorithm and explore a large number of depth-dependent attenuation models quantified by the scattering quality factor Qsc or equivalently the wave diffusivity D, and the absorption quality factor Qi. The scattering and absorption profiles that best fit the data display very strong scattering attenuation (Qsc≤10 ) or equivalently very low wave diffusivity (D≈2km2/s) in the first 10km of the Moon. These values correspond to the most heterogeneous regions on Earth, namely volcanic areas. Below this surficial layer, the diffusivity rises very slowly up to a depth of approximately 80km where Qsc and D exhibit an abrupt increase of about one order of magnitude. Below 100km depth, Qsc increases rapidly up to approximately 2000 at a depth of about 150km, a value similar to the one found in the Earth’s mantle. By contrast, the absorption quality factor on the Moon Qi≈2400 is about one order or magnitude larger than on Earth. Our results suggest the existence of an approximately 100km thick megaregolith, which is much larger than what was previously thought. The rapid decrease of scattering attenuation below this depth is compatible with crack healing through viscoelastic mechanisms. Using our best attenuation model, we invert for the depth of shallow moonquakes based on the observed variation of tmax with epicentral distance. On average, they are found to originate from a depth of about 50km±20km, which suggests that these earthquakes are caused by the failure of deep faults in the brittle part of the Moon.

Fundamental solutions of a crack impinging upon an interface slippage in laminated anisotropic bodies

Intra-ply or inter-ply slippages are commonly seen at the crack tip impinging upon an interface in laminated anisotropic bodies. An interface slippage could occur in the form of yielding (e.g., a well-bonded ductile layer with plastic yielding) or debonding (e.g., a weak, sliding-free one) along the interface direction. This paper presents a fundamental solution for a crack in one individual brittle part impinging normally upon the interface slippage with the neighboring brittle part of laminated anisotropic materials under tensile loading. A superposition method is employed to explicitly solve the problem which combines the solution of a crack in a perfectly bonded elastic homogeneous medium, the solution of a continuous distribution of dislocations which represent slippage at the interface and an appendix solution which offsets the stress on the crack faces induced by the dislocations. This procedure reduces the problem to a singular integral equation which can be numerically solved by using Chebyshev polynomials. The validity of the present solutions is numerically verified where the traction-free condition on the crack faces and the equilibrium of shear stress along the interface slippage can be really satisfied. Numerical implementations are performed to analyze the influence of interface slippage on cracking and stress redistribution in laminated anisotropic bodies. It is found that interface yielding or interface debonding redistributes the stress ahead of the crack tip in the neighboring uncracked part. The presence of interface yielding or debonding lowers the high stress concentration in the tensile stresses ahead of the crack tip. It is also concluded that interface debonding appears to be more effective in lowering the stress concentration than interface plastic yielding.

1D Velocity Structure and Characteristics of Contemporary Local Seismicity around the Tehri Region, Garhwal Himalaya

Abstract A 1D velocity model of the Tehri region in the Garhwal Himalaya is estimated from the travel‐time inversion of 145 well‐located local events having 1177 P and 1090 S arrivals. The velocity model consists of six layers up to 24 km depth, with P ‐ and S ‐wave velocities ranging from 4.42 to 6.78 km/s and 2.41 to 3.71 km/s, respectively. The depth of the Moho, estimated using travel‐time curves of crustal phases, is about 46 km. A low‐velocity layer deciphered between 12 and 14 km depths is ascribed to fractured basement thrust representing the upper surface of the Indian plate. Using the proposed velocity model, 1457 events are relocated. About 70% of the locatable events occur in the Inner Lesser Himalaya between the Main Central thrust (MCT) and the Srinagar thrust. The postulated depth of the basement thrust in the vicinity of the MCT is about 10–12 km. The depth distribution of events delineates the geometry of the seismically active Main Himalayan thrust (MHT) below a 300‐km‐long segment of the MCT. The MHT is composed of two shallow‐dipping fracture zones that seem to represent seismically active thrust zones dipping in opposite directions. Two seismicity zones, at 10 and 15 km depths with a 5 km vertical separation, define a flat‐ramp‐flat type structure of the MHT in the vicinity of the MCT. The postulated front of the underthrusting Indian plate is at a depth of about 15–18 km. The lower‐flat seismicity zone bifurcates into two, indicating further slicing of the lower‐flat zone. The postulated thickness of the brittle part of the underthrusting Indian crust is about 20 km in the vicinity of the MCT.

General selection of lattice shape in ductile-reinforced brittle structures for increased stiffness

Ductile reinforcements are used in brittle structures to increase the overall stiffness and strength. However, the optimum lattice shape geometry according to which the ductile reinforcements must be laid down, has not been generally established. In this work, a ductile isotropic lattice structure is constructed from a unit cell and the brittle matrix is “filled” in the empty spaces thereafter. In homogeneous stress conditions, the brittle part will experience the same applied remote stress as is felt by the ductile lattice. The statistical theory of brittle failure is invoked to bring home the point that the unit cell area of the lattice is arbitrary (for a given total area) and hence the lattice shape geometry does not influence the probability of survival of the structure. Therefore, a suitable geometry shape (triangle or square) maybe chosen to further enhance the overall stiffness at a given probability of survival. It has been concluded that an (equilateral) triangular lattice is better suited compared to a square lattice if the ductile reinforcement lattice bars have the same stiffness. The technique and conclusion is generally true for any choice of brittle and ductile materials. Also, the conclusion holds true for both compressive and tensile loading.

Mid-crustal detachment beneath western Tibet exhumed where conjugate Karakoram and Longmu–Gozha Co faults intersect

Models for how shortening is accommodated in the India–Asia collision vary between an end member in which largely rigid blocks are extruded eastwards between lithospheric-scale strike-slip faults and an end member in which a hot, weak mid-crustal layer aids distributed deformation. Here the mode of crustal deformation is evaluated by studying the intersection of two main conjugate strike-slip faults at the west end of the Tibetan plateau. Our field mapping suggests that these faults, the right-lateral Karakoram fault and the left-lateral Longmu–Gozha Co fault, an eastward continuation of the Altyn Tagh fault, may be connected by a large-scale, east-dipping listric normal fault, exposing a wedge of mid-crustal rocks in its footwall. Pseudosection modeling of matrix and porphyroclast rim compositions from footwall metamorphic rocks yield late-syntectonic pressures of 640±100 MPa and temperatures around 600±50°C. Extensive networks of narrow granitic dikes give U–Pb zircon ages as young as 13.7±0.2 Ma, suggesting that footwall rocks remained hot until the late Miocene and were not exhumed until after this time. We infer >40 km heave across the Angmong fault, and suggest that it absorbs effectively all of the slip across the Longmu–Gozha Co fault (which it appears to truncate), so the Longmu–Gozha Co fault is seemingly confined to the upper crust. Similar mechanical decoupling likely occurs throughout the plateau, with strike-slip faulting in western Tibet limited to the upper, brittle part of the crust.

Fault slip analysis and late exhumation of the Tauern Window, Eastern Alps

Exhumation of the Eastern Alps from the early Tertiary to the late Miocene was localized mainly in the Tauern Window, a thermal and structural dome located in front of the Dolomites indenter. Stress inversions based on new structural investigations over the entire Tauern Window indicate a regional zoning of the paleostress field with a predominance of strike-slip states of stress in the core of the investigated area, and dominant extensional regimes in the eastern and western borders of the dome. Few inverse fault structures have been highlighted. We propose a two-stage deformation history in order to explain the different types of structures that characterise the ductile and the brittle domains. During the first stage of exhumation of the Tauern Window, corresponding to the folding event, the brittle crust was probably dominated by N-S shortening and compression. The second stage of exhumation was marked by normal faulting at the borders of the dome and strike-slip faulting in the core. During the second stage, the brittle part of the crust that was previously affected by compressive structures belonging to the first stage was eroded. Normal faulting associated to E-W extension along the eastern and western borders of the Tauern Window was accommodated by strike-slip faulting located in the core of the Tauern Window, yielding E-W extension and N-S shortening. The orientation of the extensional axes and the nature of the stress tensors are similar to the ones inferred for the late-stage, brittle overprint of the internal basement massifs of the Central Alps pointing to a possible common, large-scale, state of stress acting well beyond the area of the Eastern Alps.

Repeated hydrothermal quartz crystallization and cataclasis in the Bavarian Pfahl shear zone (Germany)

Field and microstructural data of the Pfahl shear zone in north-eastern Bavaria (Germany) reveal the intimate spatial-temporal connection between fragmentation, fluid influx and quartz crystallization. These processes and their interaction led to complex-structured quartz units: (i) a dense network of early quartz veins, (ii) two domains of fine-grained reddish to grayish quartz masses, (iii) an extended central zone of massive white quartz, and (iv) late cross-cutting closely spaced parallel fractures and partly open quartz veins.The fine-grained quartz domains result from repeated and coeval cataclasis, fluidization and quartz precipitation. Material transport in these domains is at least partly governed by the flow of mobile fluid-quartz-particle suspensions. The complex internal meso-to microstructures of the massive white quartz are generated by repeated processes of fragmentation and grain growth. In general, the brittle part of the Pfahl shear zone represents a key example of cyclic dissolution/precipitation and fragmentation on large scale.

Strain localization due to structural softening during pressure sensitive rate independent yielding

AbstractAfter giving a complete analytical solution for the strain softening model associated to Mohr-Coulomb non associated elasto-plastic flow rule (MC-model), the paper demonstrates that this rheology possesses a finite limit load which allows solving for strength drop as a boundary value problem. The MC-model produces a non-dimensional strength drop, which depends on three parameters: the orientation of the shear band versus the least principal stress axis outside the band α0, the peak friction angle φ and the dilatation angle Ψ. The maximum reduction of strength obtained with that strain-softening model is on the order of the confining stress p0. For this weakest regime, the effective friction of the shear band drops from μini = 0.85 at peak to μss = 0.64 at the end of the softening phase. In this model, which considers thick shear bands, the weakest regime is not obtained for an orientation corresponding to the exact Coulomb orientation. Instead, the orientation of the weakest shear zone systematically deviates from the coulomb orientation by an angle, which rises with its internal friction angle. The characteristic shear strain needed to achieve steady state is quantified semi analytically and in the range of parameters valid for Earth, this strain is found to be of the order of 7–8%. These numbers are typical of what is observed in the laboratory, which give us confidence on that MC-model is a good and probably the simplest model to localize strain in numerical codes aimed at modeling the brittle part of the Earth.