Discontinuous Slip Research Articles

Behavior of soil slopes reinforced with composite-structural piles

Slope stability is a key problem in geotechnical engineering, often addressed through reinforcement methods, such as reinforced concrete piles. However, they have limitations, including high costs and underutilization of steel and concrete properties. This study proposes a new type of composite-structural pile, combining two types of materials with different mechanical behaviors. Centrifuge model tests were performed to explore the deformation and failure behavior of slopes reinforced with the composite-structural pile under vertical loading conditions. The strains and soil pressure of the composite-structural pile were measured to analyze its stress characteristics. The composite-reinforced slope exhibited progressive failure from the top to the toe under vertical loading conditions, featuring a curved, discontinuous slip surface. The slope deformation increased with increasing load and developed to deformation localization. A clear coupling effect was observed between slope deformation localization and local failure. Finite element analysis was performed to evaluate the mechanical characteristics of the composite-structural pile under bending conditions. The strain distribution on the cross-section of the pile was linear for different material parameters. Based on these findings, a method for calculating the stress and strain of composite-structural piles was developed. Centrifuge model tests validated the reliability of the proposed method.

Discontinuous Surface Ruptures and Slip Distributions in the Epicentral Region of the 2021 Mw7.4 Maduo Earthquake, China

Discontinuous Surface Ruptures and Slip Distributions in the Epicentral Region of the 2021 Mw7.4 Maduo Earthquake, China

Regularization analysis of the strong discontinuity-Cosserat finite element method for modeling strain localization in cohesive-frictional materials by spectral theory

An inappropriate numerical approach adopted for modeling the strain localization of geomaterials often leads to ill-posed boundary value problems (BVP). In this article, we apply spectral analysis to study the regularization mechanism of Cosserat finite element method (CFEM) and strong discontinuity-Cosserat FEM (SD-CFEM). The 1D shear layer model and 2D plane strain tests are modeled to conduct the diagnostic spectral analysis. A 2D slope problem is simulated to demonstrate the effectiveness of SD-CFEM in simulating the characteristics of progressive deformation in geomaterials. The numerical results show that CFEM and SD-CFEM not only maintain the eigenvalues as positive, but also make the dominant eigenvectors for different mesh densities possess the identical evolution pattern which is the fundemental regularization mechanism of both methods. The deformation patterns reflected by dominant eigenvectors indicate that SD-CFEM is more robust in modeling strain localization/shear band than CFEM and SD-FEM do because the former can reflect the energy dissipation both in the shear band with a constant width and on the slip line in the shear band. It can be concluded from the displacement evolution process in the shear band that SD-CFEM inheriting the merits of CFEM and SD-FEM can physically and mathematically better simulate the whole deformation process of geomaterials from weak discontinuity (strain localization) to strong discontinuity (slip).

Investigations on the interface-dominated deformation mechanisms of two-dimensional MAX-phase Ti3Al(Cu)C2 nanoflakes reinforced copper matrix composites

Two-dimensional (2D) materials showing the giant advantage over their bulk counterparts are believed to be the ideal reinforcement for metal matrix composites, whereas the deformation mechanism of which is currently unknown. Herein, we investigated the interface effect of 2D MAX phase Ti3Al(Cu)C2 nanoflakes (MAX NFs) obtained by a Cu-atoms-diffusion assisted exfoliation method on the plastic deformation process of Cu matrix. Tensile tests demonstrated a simultaneous enhancement in strength and fracture elongation with the increase of MAX NFs content. The composites exhibited a four-stage deformation process involving an extended “yield plateau” before obvious strain hardening stage. Microstructural examination revealed that the 2D nature of MAX NFs and the coherent interface structure facilitated the nucleation of partial dislocations, which coordinated the initial plastic deformation by gliding and interacting to form Lommer-Cottrel (LC) locks. At high strain levels, both LC locks and MAX NFs served as obstacles for dislocation cross-slip and thus achieved significant forest hardening (or latent hardening) effect, validated by EBSD texture from the in-situ tensile tests and visco-plastic self-consistent simulation. This sort of interface-induced microstructure evolution promoted tortuous micro-cracks along discontinuous slip bands and significant crack bridging and deflection extrinsic toughening mechanisms. The current findings provide a possible strategy of simultaneously enhancing strength and ductility through tailoring 2D geometric shape of reinforcements and their interface with the metal matrix.

Characterisation of strain localisation under cyclic loading at 450 °C by SEM-DIC in a PM Ni-based superalloy

In this study, the strain localisation under cyclic loading in an advanced powder metallurgy Ni-based superalloy at 450 °C was characterised by SEM-DIC, and the related deformation substructures were characterised by electron channelling contrast imaging under controlled diffraction conditions (cECCI). The results indicate strain mainly accumulates in slip/strain bands due to dislocation slip on the {111} plane, and the strain saturates at 1000 cycles with no evident increase in strain value within strain bands or strain band density from 1000 cycles to 10,000 cycles. Analysis of the strain components in the local coordinates associated with each strain band shows the strain band mainly consists of shear strain ϵxy along the strain band and transverse strain ϵyy normal to the strain band. The strain bands can transmit through, be deflected, or be blocked at grain boundaries depending on the grain boundary characteristics and the neighbouring grain orientation. Comparing the strain bands obtained by SEM-DIC and deformation substructures obtained by cECCI shows that the strain bands originate from underlying continuous slip bands which show the sheared γ′ within the slip bands and dislocation pairs looping around the γ′ precipitates, but the deformation localised in the discontinuous slip bands is not well characterised by SEM-DIC at this lateral resolution of strain.

An interacting wing-crack based semi-analytical meso-scale model for describing elasto-plastic damage behavior of brittle rocks

An interacting wing-crack based mesoscale model was developed for describing the elastoplastic damage behaviors of brittle rocks under compressive loading. In the present model, the main deterioration process of the rock is assumed to be induced by the wing-crack propagation, attributing the macroscopic inelastic strain to the nucleation and growth of tensile ‘wings’ of the initial flaws. The initial flaws are assumed to follow a periodic distribution in space. To account for the interaction between microcracks, a spatial evolution law as a function of the wing length is introduced, and the influences of the wing-crack propagation on the discontinuous slip of the crack surface are taken into consideration. On this basis, the increment of the compliance tensor caused by wing-crack propagation is proposed, and an incremental-based constitutive model is constructed so that the total stress-strain relations involving post-peak softening and residual behavior can be reproduced. Further, through appropriate parameter selection, the proposed model can reasonably simulate the triaxial test results of Taiwan sandstone, and the correctness of the model is effectively validated. Finally, the intrinsic features of the model are explored through a series of parametric analyses, and the macroscopic mechanical behavior and damage evolution of the rock characterized by the model are investigated. The conclusions show that this model is of significant usage to describe the whole strain-stress relation and inelastic strain analysis. It is full of potential to deem various rock macroscale mechanisms to mesoscale crack evolution.

Paraglacial Rock Slope Stability Under Changing Environmental Conditions, Safuna Lakes, Cordillera Blanca Peru

Landslides or landslide-induced impact waves in high mountain lakes represent a high hazard for society, calling for realistic assessments of rock slope stability responsible for the process chain initiation. This task is often hampered by complex interplays of triggers, which effects on slope stability may be delayed by decades or even millennia, while historical records describing slope topography or landslide occurrences are usually shorter and incomplete. This article builds on rarely available detailed historical data describing the site of the 2002 rock avalanche in the Cordillera Blanca, Peru. It caused a dangerous impact wave in the Safuna Alta Lake resulting in a minor flood, but ongoing downstream development significantly increased the risk of a comparable event. Pre-2002 and post-2002 failure slope topography, 70 years long history of glaciation and landslide occurrences were combined with non-invasive field geological surveys and laboratory geotechnical analyses to characterize the distinct morphological parts of the failed slope with reliable engineering geological slope models. Slope stability was calculated for a series of environmental scenarios providing insights into the 2002 rock avalanche failure mechanism and dynamics as well as the role of glacier slope support for its stability. Results show that the rock slope stability is governed by discontinuous slip planes where rock bridges represent the most likely additional resisting forces. The effect of glacier support on the slope stability is limited under full-water saturation of the rocks and due to specific morpho-structural conditions. Importance of the long-term, progressive deterioration of the rock slope strength under paraglacial environment and repeated seismic shaking is illustrated by the fact that even the Little Ice Age maximum glacier extend only had minor positive effect on the pre-2002 rock avalanche slope stability. Despite of that, the slope remained without a major failure for decades or possibly even centuries. Its collapse in 2002 caused retrogressive movements of the adjacent slope, which remains highly unstable until now. Therefore the future safety of the lake would largely benefit from the implementation of a reliable slope movement monitoring system.

Centrifuge model tests on pile-reinforced slopes subjected to drawdown

Piles are generally an effective way to reduce the risk of slope failure. However, previous approaches for slope stability analysis did not consider the effect of the piles coupled with the decrease of the water level (drawdown). In this study, a series of centrifuge model tests was performed to understand the deformation and failure characteristics of slopes reinforced with various pile layouts. In the centrifuge model tests, the pile-reinforced slopes exhibited two typical failure modes under drawdown conditions: across-pile failure and through-pile failure. In the through-pile slope failure, a discontinuous slip surface was observed, implying that the assumption of the slip surface in previous stability analysis methods was unreasonable. The test results showed that drawdown led to instability of the piles in cohesive soil, as the saturated cohesive soil failed to provide sufficient constraint for piles. The slope exhibited progressive failure, from top to bottom, during drawdown. The deformation of the piles was reduced by increasing the embedment depth and row number of piles. In addition, the deformation of soils outside the piles was influenced by the piles and showed a similar distribution shape as the piles, and the similarity degree weakened as the distance from the piles increased. This study also found that the failure mechanism of unreinforced and pile-reinforced slopes induced by drawdown could be described by coupling between the deformation localization and local failure, and it revealed that pile-reinforced slopes could reduce slope deformation localization during drawdown.

Understanding the strength softening of Zr/Mo and Zr/Ti nanostructured multilayers

Zr/Mo and Zr/Ti nanostructured multilayers manifest a peak hardness at the critical layer thickness of ~10 and ~20 nm, respectively. The non-monotonical thickness-dependent hardness is understood in terms of the back stress, which is closely correlated with the dislocation absorption probability by the interfaces. It appears that strength softening occurs as gliding dislocations can be absorbed by interfaces at smaller layer thickness. Furthermore, incoherent interface in the Zr/Mo with discontinuous slip systems is more effective to block dislocation motion than the Zr/Ti with continuous ones, resulting in a higher dislocation storage ability.

Effect of microtextures on the intermediate temperature fracture behavior of additive-manufactured Ni-based overlay

Texture components with specific orientations are found to play important roles in crack and fracture phenomena. In this study, nickel-based alloy overlays with different texture intensities were directly produced by wire and arc additive manufacturing (WAAM) processes. Results of hardness and tensile tests from room to elevated temperatures showed global differences in strength, ductility and cracking susceptibility between the deposit with the Cube texture and the deposit with the Brass texture. The formation mechanism of different textures during WAAM processes was elucidated. Then the deformation of individual texture grains and incompatible deformation among them were analyzed, and their effects on the fracture mechanism at the intermediate temperature were also investigated. During the deformation, the Brass grains, with relatively lower Schmid factors compared to the Cube grains, were hard to activate (111)<1–10> system slip without rotation, which led to significant strain accumulation at the grain interior and boundaries. The incompatible deformation and discontinuous slip transfer between differently orientated grains, especially the Brass grains, induced cracking and exacerbated the ductility within the intermediate temperature range.

Effects of strain rates on shear band and serrated flow in a bulk metallic glass

Effects of different strain rates on the shear band and serrated flow in Ti30.81Cu48.83Ni7.44Zr12.92 bulk metallic glass compressed at the room temperature were investigated. With increasing strain rates, the plastic strain, maximum compressive strength, and numbers and densities of shear bands increases, and the serrated flow in the second stage translates from similar uniformity to heterogeneity. No uniformity serrated flow in the second stage was found to be the combination of the no uniformity serrated flow in the first stage and the uniformity serrated flow in the second stage. The range of the stress drop in the second stage of the serrated flow coming from the discontinuous slip of the primary shear plane, is from 22 ± 1 MPa to 35 ± 1 MPa at different strain rates; the corresponding maximum value of stress drop is 35 ± 1 MPa. The range and maximum value of stress drop is crucial to further understand the mechanism of plastic strain in the metallic glass field.

Interface conditions of roughness-induced superoleophilic and superoleophobic surfaces immersed in hexadecane and ethylene glycol.

Interface conditions are an important property that can affect the drag of fluid flow. For surfaces with different oleophobicity, the boundary slip at the solid–oil interface is mostly larger than that at the solid–water interface. Roughness is a key factor for the wettability of superoleophilic/superoleophobic surfaces, and it has been found to affect the effective value of slip length in measurements. Moreover, there are no studies on the effect of roughness on slip at interfaces between oil and superoleophilic/superoleophobic surfaces. A theoretical description of the real surface roughness is yet to be found. Results show that the effective slip length is negative and decreases with an increasing root mean squared (RMS) roughness of surfaces, as the increasing roughness enhances the area with discontinuous slip at the solid–liquid interface. The underlying mechanisms are analyzed. The amplitude parameters of surface roughness could significantly inhibit the degree of boundary slip on both superoleophilic surfaces in Wenzel state and superoleophobic surfaces in Cassie state immersed in oil. The oleic systems were likely to enhance boundary slip and resulted in a corresponding reduction in drag with decreasing roughness on the solid–oil interfaces.

Acoustic emission during different-type inter-block movements

The article reports the lab experimentation on seismic/acoustic emission during different-type inter-block movements of rock mass. The fact that co-seismic displacement under induced earthquakes occurs along the existing interfaces is the basis for relatively simple tests on a slip-model plant. Using different materials as fracture fillers allowed modeling entire range of probable deformation modes. The deformation modes are conditionally grouped as creep or steady-state slip, unsteady-state slip and regular discontinuous slip or stick-slip. The authors show that statistics of acoustic emission during slip is described using the Gutenberg–Richter law. The strongest “representative” events under shearing occur quasiregularly, with probability much higher than follows from G–R law. The functional relation is found between the acoustic emission energy and the shear velocity.

A range of fault slip styles on progressively misoriented planes during flexural-slip folding, Cape Fold Belt, South Africa

Flexural slip folds are distinctive of mixed continuous-discontinuous deformation in the upper crust, as folding is accommodated by continuous bending of layers and localized, discontinuous slip along layer interfaces. The mechanism of localized, layer-parallel slip and the stress and fluid pressure conditions at which flexural slip occurs are therefore distinctive of shear localization during distributed deformation. In the Prince Albert Formation mudstone sequence of the Karoo Basin, the foreland basin to the Cape Fold Belt, folds are well developed and associated with incrementally developed bedding-parallel quartz veins with slickenfibers oriented perpendicular to fold hinge lines, locally cross-cutting axial planar cleavage, and showing hanging wall motion toward the fold hinge. Bedding-parallel slickenfiber-coated veins dip at angles from 18° to 83°, implying that late increments of bedding-parallel shear occurred along unfavorably oriented planes. The local presence of tensile veins, in mutually cross-cutting relationship with bedding-parallel, slickenfiber-coated veins, indicate local fluid pressures in excess of the least compressive stress.Slickenfiber vein microstructures include a range of quartz morphologies, dominantly blocky to elongate-blocky, but in places euhedral to subhedral; the veins are commonly laminated, with layers of quartz separated by bedding-parallel slip surfaces characterized by a quartz-phyllosilicate cataclasite. Crack-seal bands imply incremental slickenfiber growth, in increments from tens of micrometers to a few millimeters, in some places, whereas other vein layers lack evidence for incremental growth and likely formed in single slip events. Single slip events, however, also involved quartz growth into open space, and are inferred to have formed by stick-slip faulting. Overall, therefore, flexural slip in this location involved bedding-parallel faulting, along progressively misoriented weak planes, with a range of slip increments.

Micromechanistic origin of irradiation-assisted stress corrosion cracking

A multi-scale study of the micromechanics of dislocation–grain boundary interactions in proton and ion-irradiated stainless steels is presented. Interactions of dislocation channels with grain boundaries result in slip transfer, discontinuous slip without or with slip along the grain boundary. The presence of the irradiation damage enhances the importance of the magnitude of the resolved shear stress on the slip system activated by the grain boundary to transfer slip across it. However, the selected slip system is still determined by the minimization of the grain boundary strain energy density condition. These findings have implications for modelling the mechanical properties of irradiated metals as well as in establishing the mechanism for disrupting the grain boundary oxide, which is a necessary prerequisite for irradiation-assisted stress corrosion cracking.

Numerical investigation of unstable rock failure in underground mining condition

Underground coal mining affects the stress distribution in rock mass and may induce slip failures along large existing rock discontinuities and sizable compressive failures of coal in mining faces and sidewalls. When such failures occur in an unstable and uncontrollable manner, they can be accompanied by a significant release of strain energy from the surrounding rock and potentially create coal burst events. This paper focuses on identifying failure stability of rock and rock discontinuities in terms of their manifestation as stable and unstable manner in coal mining settings. The studies use numerical modeling and consider failure stability of both rock discontinuities in slip and coal material in compression. The influence of the slip failure stability on the compressive failure stability is also investigated. The Universal Distinct Element Code (UDEC) is used with its optional constitutive models the Continuously Yielding joint and the Mohr–Coulomb strain softening model. A laboratory scale numerical model of a double shear test setup is developed and used to assess the ability of the numerical code in detecting the stability during discontinuity slip failures. The studies performed using this model confirmed the ability of the numerical code in differentiating stable and unstable slip failures when using the failure stability criterion based on the relative stiffnesses of loading system and failing discontinuities. Using the numerical double shear test models, criteria and tools are developed for identifying the failure stabilities in larger in situ scale numerical models. The in situ scale models allowed studies of the failure stabilities of existing rock discontinuities under the influence of an advancing excavation. The results show that both stable and unstable slip failures can occur at an existing rock discontinuity depending on the post-failure characteristic of the discontinuity and the loading stiffness of the surrounding rock. The loading stiffness is observed to continuously reduce with increasing mining extent. Additional in situ models are also built to study the effect of coal seam–host rock interfaces on the failure stability of sidewalls and mining faces in coal mining settings. The results show that unstable sidewall failures may occur when a sudden de-confinement is triggered by an unstable slip failure at the coal–rock interfaces. The existence of weak regions along such interfaces can also contribute to unstable compressive failures of mining faces and sidewalls.

Strain localization at dislocation channel–grain boundary intersections in irradiated stainless steel

The interaction of dislocation channels with grain boundaries in irradiated stainless steel was observed on multiple length scales using scanning electron microscopy (SEM) digital image correlation (DIC) and confocal microscopy (micro-scale), in situ straining and transmission electron microscopy (TEM) (nano-scale), and atomistic modeling (atomic scale). Interactions were divided into three classifications; slip transmission, discontinuous slip, and discontinuous slip that induced grain boundary slip. DIC and confocal microscopy were used to quantify the plastic strain at dislocation channel–GB intersections. In situ TEM was used to image dislocations inside of channels as they interacted with the grain boundary. Slip in the dislocation channels, as observed by TEM, was found to involve cross slip between different slip planes, as well as the possibility of different slip systems activated on parallel slip planes. Atomistic simulations agreed well with experiments on the nature of channel-grain boundary interactions and also showed elevated levels of elastic stress at DC–GB intersections where slip was discontinuous with no slip transmission. The two distinct classifications of discontinuous slip are significant, suggesting two possible cracking mechanisms that both lead to the rupture of the oxide over the grain boundary.

Cessation of viscoplastic Poiseuille flow with wall slip

We solve numerically the cessation of axisymmetric Poiseuille flow of a Herschel–Bulkley fluid under the assumption that slip occurs along the wall. The Papanastasiou regularization of the constitutive equation is employed. As for the slip equation, a power-law expression is used to relate the wall shear stress to the slip velocity, assuming that slip occurs only above a critical wall shear stress, known as the slip yield stress. It is shown that, when the latter is zero, the fluid slips at all times, the velocity becomes and remains uniform before complete cessation, and the stopping time is finite only when the slip exponent s<1. In the case of Navier slip (s=1), the stopping time is infinite for any non-zero Bingham number and the volumetric flow rate decays exponentially. When s>1, the decay is much slower. Analytical expressions of the decay of the flat velocity for any value of s and of the stopping time for s<1 are also derived. Using a discontinuous slip equation with slip yield stress poses numerical difficulties even in one dimensional time-dependent flows, since the transition times from slip to no-slip and vice versa are not known a priori. This difficulty is overcome by regularizing the slip equation. The numerical results showed that when the slip yield stress is non-zero, slip ceases at a finite critical time, the velocity becomes flat only in complete cessation, and the stopping times are finite, in agreement with theoretical estimates.

Strain incompatibilities and their role in intergranular cracking of irradiated 316L stainless steel

This study analyzes the influence of microstructural parameters on strain incompatibilities that develop in irradiated 316L stainless steel and evaluates the influence of the incompatibilities on intergranular cracking. Tensile specimens were proton irradiated to 7dpa at a temperature of 400°C and then strained to 5% in a 400°C supercritical water environment. The surface oxides were removed through an oxide stripping treatment to reveal the dislocation channels for analysis of their interactions with grain boundaries. It was observed that grains with high Schmid factors and low Taylor factors were more likely to have multiple active slip planes, and less likely to have discontinuous slip across grain boundaries. It was also observed that the propensity for slip discontinuity was greater along boundaries that had surface trace inclinations of 50° or higher to the tensile axis. The similar dependencies of slip discontinuity and intergranular cracking on trace inclination, Schmid factor, and Taylor factor and the observation that intergranular cracks occur primarily at grain boundary sites that are most susceptible to slip discontinuity suggest that such strain incompatibilities promote intergranular cracking.

Boundary elements solution of stokes flow between curved surfaces with nonlinear slip boundary condition

AbstractThis work presents a boundary integral equation formulation for Stokes nonlinear slip flows based on the normal and tangential projection of the Green's integral representational formulae for the velocity field. By imposing the surface tangential velocity discontinuity (slip velocity) in terms of the nonlinear slip flow boundary condition, a system of nonlinear boundary integral equations for the unknown normal and tangential components of the surface traction is obtained. The Boundary Element Method is used to solve the resulting system of integral equations using a direct Picard iteration scheme to deal with the resulting nonlinear terms. The formulation is used to study flows between curved rotating geometries: i.e., concentric and eccentric Couette flows and single rotor mixers, under nonlinear slip boundary conditions. The numerical results obtained for the concentric Couette flow is validated again a semianalytical solution of the problem, showing excellent agreements. The other two cases, eccentric Couette and single rotor mixers, are considered to study the effect of different nonlinear slip conditions in these flow configurations. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013