Shear Band Inclination Research Articles

Capturing the transition from diffuse to localised failure in constitutive modelling of partially saturated soils

Localised failures in the form of shear band induce localised deformation and saturation within partially saturated soils. Inelastic responses mainly take place inside the shear band, while the zone outside it usually undergoes unloading processes with much smaller changes in deformation and saturation, as observed in several triaxial tests. The interaction between responses inside and outside shear bands governs the macro behaviour under effects of the hydromechanical coupling. This mechanism, along with properties of shear band (inclination, thickness) and the specimen size, are usually missing in existing classical models based on homogenous assumption. They are incorporated into our approach to correctly capture the post-localisation behaviour of partially saturated soils. In our proposed approach, enrichment terms for kinematics are used in the thermodynamics-based formulation to account for strong variations of hydromechanical responses (stress-strain, suction-saturation) outside and inside the shear band. The proposed formulation results in a size-dependent constitutive structure capable of describing the transition of behaviour from homogeneous to localised stages. The promising features of the proposed formulation are illustrated using data from drained triaxial tests.

DEM-aided study of Coulomb and Roscoe theories for shear band inclination

DEM-aided study of Coulomb and Roscoe theories for shear band inclination

Modeling uplift failure of pipes buried in sand using material point method

Uplift of underground pipelines is frequently encountered in urban tunneling and landslide-prone areas, seriously affecting their structural integrity and serviceability. However, the uplift resistance of pipelines and the failure modes of surrounding soils under permanent ground deformation have not been fully understood. In numerical simulations, the element distortion phenomenon significantly restricts the application of mesh-based numerical methods in addressing such issues. In this paper, the material point method (MPM) is used to investigate the upward movement of pipes buried in dense sand and the mobilization of uplift resistance. Two typical constitutive models are used, and their model parameters are estimated using state index, whose values are dependent on relative density and confining pressure. The post-peak softening characteristics of soil have also been considered and a series of numerical simulations are conducted. The results from physical model tests in the literature are used to verify the numerical model. It is found that the experimental and numerical results agree well with each other in terms of force–displacement relationships and soil deformation patterns. The effects of burial depths on the uplift failure mechanism of pipes are investigated in detail. The numerical results show that for shallow burial conditions, the inclination of shear bands is approximately identical to the maximum dilation angle of sand at the peak resistance and then decreases when the pipe undergoes larger uplift displacement, leading to a reduction of uplift resistance. For deeply buried pipes, the inclination of shear bands does not change in the post-peak phase, but a failure pattern with a series of progressive shear zones gradually forms, which is analogous to the bearing failure modes of foundations. At large uplift displacements, significant flow-around phenomena are observed for various burial depths of the pipe. Finally, the distribution profiles of earth pressure acting on the pipe surface are explored. It is found that the normal pressure concentration area mainly rangesfrom 0°–45° from the pipe crown. In comparison, the tangential contact pressure primarily concentrates on the pipe shoulder within 15°–45° from the crown. Finally, the peak uplift forces and corresponding failure modes within the maximum embedment ratio of 50 are investigated to provide practical guidance for the design of underground pipelines.

Plane strain shear strength of unsaturated fiber-reinforced fine-grained soils

Discrete randomly distributed fibers are commonly used to improve the engineering characteristics of the soil and thus soil properties such as shear strength, compressibility, density, and hydraulic conductivity. Most studies have so far focused on describing the behavior of soils containing randomly distributed fibers under dried or saturated conditions. However, the water table may seasonally fluctuate, thus generating unsaturated soil conditions. Therefore, a better understanding of the hydro-mechanical properties of unsaturated improved soils is of high necessity. In this research, the shear strength parameters of fine-grained soils were evaluated using the biaxial device available at Ruhr Universität Bochum. The applied device was modified to test unsaturated fine-grained soils with various degrees of saturation using axis translation and vapor equilibrium techniques. The experiments were conducted on fine soils containing 0, 0.5, and 1% fiber contents under a wide range of matric suctions. The ductile behavior was more noticeable in samples with lower suctions and higher straw contents. Furthermore, the shear strength of both unreinforced and reinforced fine-grained soils considerably increased by an increase in the suction. Finally, shear band inclination increased by the suction while decreasing by straw content.

Strain localization of a frozen sand under different test conditions

In this paper, a series of plane strain tests were conducted on a coarse frozen sand under different temperatures and loading conditions of constant strain rate and stress. With the overall strain fields obtained with particle image velocimetry (PIV) technique, the influence of loading conditions, temperature and strain rate on the strain localization characteristics of the frozen sand was analyzed. It is indicated that, under the same loading conditions, the temperature and strain rate have little influence on the shear band formation process. Both of the single and X shape shear band are observed under different test conditions. The X shape shear bands are more likely to be generated under strain rate lower than the magnitude of 10−3 min−1. When the sand samples are at failure, most part of the strain field is at dilatancy state. The shear band inclination angle and width are inversely proportional to the temperature and independent of strain rate and loading conditions. Further analysis indicated that, within the testing temperature range in this study, the widely accepted Coulomb's solution of unfrozen soils is applicable as the upper bound of the measured shear band inclination angle of the tested frozen sand, and the measured shear band width falls in the range of 10 to 20 times of mean particle size.

Dynamics of prestressed elastic lattices: Homogenization, instabilities, and strain localization

A lattice (or ‘grillage’) of elastic Rayleigh rods (possessing a distributed mass density, together with rotational inertia) organized in a parallelepiped geometry can be axially loaded up to an arbitrary amount without distortion and then be subject to incremental time-harmonic dynamic motion. At certain threshold levels of axial load, the grillage manifests instabilities and displays non-trivial axial and flexural incremental vibrations. Including every possible structural geometry and for an arbitrary amount of axial stretching, Floquet–Bloch wave asymptotics is used to homogenize the in-plane mechanical response, so to obtain an equivalent prestressed elastic solid subject to incremental time-harmonic vibration, which includes, as a particular case, the incremental quasi-static response. The equivalent elastic solid is obtained from its acoustic tensor, directly derived from homogenization and shown to be independent of the rods’ rotational inertia. Loss of strong ellipticity in the equivalent continuum coincides with macro-bifurcation in the lattice, while micro-bifurcation remains undetected in the continuum and corresponds to a vibration of vanishing frequency of the lowest dispersion branch of the lattice, occurring at finite wavelength. Dynamic homogenization reveals the structure of the acoustic branches close to ellipticity loss and the analysis of forced vibrations (both in physical space and Fourier space) shows low-frequency wave localizations. A perturbative approach based on dynamic Green’s function is applied to both the lattice and its equivalent continuum. This shows that only macro-instability corresponds to localization of incremental strain, while micro-instabilities occur in modes which spread throughout the whole lattice with an ‘explosive’ character. In particular, extremely localized mechanical responses are found both in the lattice and in the solid, with the advantage that the former can be easily realized, for instance via 3D printing. In this way, features such as shear band inclination, or the emergence of a single shear band, or competition between micro and macro instabilities become all designable features. The comparison between the mechanics of the lattice and its equivalent solid shows that the homogenization technique allows an almost perfect representation, except when micro-bifurcation is the first manifestation of instability. Therefore, the presented results pave the way for the design of architected cellular materials to be used in applications where extreme deformations are involved.

Mesh bias and shear band inclination in standard and non-standard continua

A severe, spurious dependence of numerical simulations on the mesh size and orientation can be observed in elasto-plastic models with a non-associated flow rule. This is due to the loss of ellipticity and may also cause a divergence in the incremental-iterative solution procedure. This paper first analyses the dependence of the shear band inclination in a biaxial test on the mesh size as well as on the mesh orientation. Next, a Cosserat continuum model, which has been employed successfully for strain-softening plasticity, is proposed to prevent loss of ellipticity. Now, numerical solutions result for shear band formation which are independent of the size and the orientation of the discretisation.

Two-dimensional discrete element simulation of the mechanical behavior and strain localization of anisotropic dense sands

This paper presents a microscopic investigation on the effects of initial anisotropy, drainage condition, and consolidation state on the mechanical behavior and strain localization of dense sands. Discrete element simulations with non-spherical clumps were carried out to simulate drained and undrained biaxial tests of isotropically and K0 consolidated anisotropic sands. In drained tests, the stress–strain relationship shows an initial hardening and subsequent softening behavior, and the peak shear stress decreases as the bedding plane angle increases. K0 consolidation has slight influence on the peak friction angle and does not affect the friction angle at zero dilatancy. In undrained tests, softening behavior occurs when the bedding plane angle is small, while for higher bedding plane angle, the strengthening response takes over. As the bedding plane angle increases, the peak friction angle decreases initially but increases afterwards. The relative displacement and rotation angle of clumps as well as the void ratio distribution within the specimen indicate the appearance of shear band. Shear bands leads to the inhomogeneous deformation field within specimens. Excessive dilation inside of shear band is produced, and it may induce re-contraction behavior under drained condition and may re-increase the pore water pressure under undrained condition. The appearance of shear band reduces the peak shear strength, and the specimen with a low bedding angle results in a larger reduction of shear strength than that from the specimen with a high bedding angle. Particle rotation mode and force chain network change along with the formation of a shear band. As the longest axis of clumped particle varies from vertical to parallel with respect to the loading direction, the majority of particle contacts inside of shear band changes from multi-point mode to single contact mode. The obtained shear band width and inclination angle were computed, and their variations with bedding angle were obtained.

Development of a novel plane strain test apparatus for frozen soils

In this paper, a novel apparatus enable of high controlling accuracy of temperature was developed for plane strain test of frozen soils. A cryostat was used to control test temperature. To improve temperature distribution uniformity of frozen soil specimens, two guiding plates were installed into the cryostat to force cooling air distribute uniformly surround specimen. According to test results, the temperature difference between different monitored points and average temperature can be controlled at ±0.2 °C. By taking Chinese standard sand as study object, compression tests under different axial strain rates were conducted. The images on the surface with strain restrained were captured during loading process, and strain localization evolution was analyzed with PIV technique. It was indicated that, with decrease of strain rate, shear band inclination and width do not change notably, while the strain field distributes more uniformly and concentration of which was decreased.

DEM Investigation of Particle-Scale Mechanical Properties of Frozen Soil Based on the Nonlinear Microcontact Model Incorporating Rolling Resistance

Although frozen soil is in nature the discrete material, it is generally treated as the continuum material. The mechanical properties of frozen soil are so complex to describe adequately by conventional continuum mechanics method. In this study, the nonlinear microcontact model incorporating rolling resistance is proposed to investigate the particle-scale mechanical properties of frozen soil. The failure mechanism of frozen soil is explicated based on the evolution of contact force chains and propagation of microcracks. In addition, the effects of contact stiffness ratio and friction coefficient on stress-strain curve and energy evolution are evaluated. The results show that the nonlinear microcontact model incorporating rolling resistance can better describe the experimental data. At a higher axial strain, the contact force chains near shear band which can give rise to the soil arch effect rotate away from the shear band inclination but not so much as to become perpendicular to it. The propagation of microcracks can be divided into two phases. The stress-strain curve is strongly influenced by contact stiffness ratio. In addition, friction coefficient does not significantly affect the initial tangential modulus. Compared with frictional coefficient, the effect of contact stiffness ratio on stress-strain curve and energy evolution is greater.

A quantitative experimental study on non-homogenous deformation behaviors of nanocrystalline Ni sheet

Abstract A quantitative experimental study on the non-homogenous plastic deformation of fully dense electrodeposited nanocrystalline Ni sheet under a quasi-static uniaxial tensile load was carried out in this paper. The sheet sample exhibited high strength simultaneously with a decrease in tensile strain. To investigate the early failure of the nanocrystalline Ni, the strain fields was quantified with digital image correlation algorithm. Based on the experimental results, the non-homogenous in form of shear bands was analyzed. Some critical points, such as shear band nucleation, broadening process and failure point were recognized. Then the inclination and width of full-developed shear band were discussed quantitatively. Finally, the failure mode, deformation mechanism and some impact factors on the non-homogenous deformation were discussed in detail.

Localized deformation in sands and glass beads subjected to plane strain compressions

In order to investigate shear behavior of granular materials due to excavation and associated unloading actions, load-controlled plane strain compression tests under decreasing confining pressure were performed under drained conditions and the results were compared with the conventional plane strain compression tests. Four types of granular material consisting of two quartz sands and two glass beads were used to investigate particle shape effects. It is clarified that macro stress-strain behavior is more easily influenced by stress level and stress path in sands than in glass beads. Development of localized deformation was analyzed using photogrammetry method. It was found that shear bands are generated before peak strength and shear band patterns vary during the whole shearing process. Under the same test condition, shear band thickness in the two sands was smaller than that in one type of glass beads even if the materials have almost the same mean particle size. Shear band thickness also decreased with increase of confining pressure regardless of particle shape or size. Local maximum shear strain inside shear band grew approximately linearly with global axial strain from onset of shear band to the end of softening. The growth rate is found related to shear band thickness. The wider shear band, the relatively lower the growth rate. Finally, observed shear band inclination angles were compared with classical Coulomb and Roscoe solutions and different results were found for sands and glass beads.

True Triaxial Tests on Cross-Anisotropic Deposits of Fine Nevada Sand

An experimental program was designed to study the effects of cross-anisotropy under three-dimensional conditions on fine Nevada sand using tall prismatic specimens. Eighteen drained tests were performed using a true triaxial apparatus. Specimens were created with both horizontal and vertical bedding planes by dry pluviation, then a freezing technique was used to solidify the specimens while they were mounted in the true triaxial apparatus. The specimens were then sheared at various b-values, where b=(σ2−σ3)/(σ1−σ3), in the three sectors of the octahedral plane. The stress-strain behavior and strength under various loading conditions on the octahedral plane are presented. Results show similar strength results in Sectors I and II. Effects of cross-anisotropy are shown when comparing the friction angles in Sectors I and II with those in Sector III. The strength is highest in Sector I, where the friction angle in triaxial compression (b=0.0, vertical specimen with horizontal bedding planes) is 5.3° higher than the triaxial-compression friction angle in Sector II/III (b=0, horizontal specimen tested with the horizontal bedding planes in the vertical direction). In triaxial extension (b=1.0), the friction angle is 2.5° higher in Sector I/II than that in Sector III. Shear band inclinations in these three sectors were essentially unaffected by the cross-anisotropy.

Influence of relative density, particle shape, and stress path on the plane strain compression behavior of granular materials

Two types of stress path-controlled plane strain compression tests were performed on both loose and dense specimens of angular and sub-angular sands and two rounded glass beads with different particle sizes. Digital image correlation method was used to analyze local deformation developments, especially shear band patterns. The material behavior in response to shearing has been found to be dependent on the relative density, particle shape, and stress path. The results of analysis on local deformation developments showed that the onset of shear bands occurred prior to their peak strengths in both dense and loose specimens. The growth rates of local maximum shear strain along a shear band were approximately consistent with an increasing global axial strain after the onset of shear band. The shear band width was influenced by both the mean particle size and the particle shape. The measured shear band inclination angles were in between those estimated by Coulomb’s and Roscoe’s formulas.

Experimental study of strain localization in sensitive clays

For evaluation of slope stability in materials displaying strain-softening behavior, knowledge concerning the failed state material response is of importance. Here, soft sensitive clay is studied. Such clays behave contractant at failure, which for undrained conditions yields a strain-softening behavior governed by the generation of excess pore water pressure. Strain softening is further linked with material instability and the phenomenon of strain localization. In the case of shear band formation, internal pore pressure gradients are then expected to be present for globally undrained conditions in the sensitive clay due to its low permeability. In the present study, this hypothesis and its implications on the global response and shear band properties are investigated. Utilizing an experimental setup with a modified triaxial cell allowing for shear band formation, the effect of varying the displacement rate is studied. Onset of strain localization is interpreted to occur just before or at the peak shear strength. A strong rate dependency of the softening response is observed. Increasing displacement rates give raised brittleness in terms of the slope of the global softening curve due to accumulating pore pressure. Also, reduced shear band thickness and a shear band inclination approaching 45° are obtained for increasing rates. In the context of slope failure in such materials, the rate dependency in the post-peak state opens up for a large variation in behavior, all depending on time as an important factor.

Orientation of locally drained shear bands in contractant clays

A slip surface or shear band orientation of 45° from the minor principal stress is obtained when contractant clays are numerically analyzed while assuming undrained conditions. This orientation occurs because the shear band is modeled as undrained and with no volume change. However, thin shear bands induce the dissipation of pore water to the outside body, and depending on the degree of local drainage, the incipient shear bands are then no longer at 45°. In drained conditions, the incipient shear band inclination to the minor principal stress is controlled by the friction angle, the dilatancy angle or a combination of both. This paper examines the orientation of a developing shear band, accounting for the effects of local pore water pressure flow away from the shear band to investigate whether the orientation of the band is controlled by the degree of drainage (i.e. volume change) or the mechanisms of shear band orientation under fully drained conditions. The numerical results show that the band’s inclination can be >45° for globally undrained contractant clays sheared at rates of ≤10%/h, rates that are normal in laboratory testing.

A micromechanics-based model for estimating localized failure with effects of fabric anisotropy

This paper presents a micromechanics-based approach to investigate the effects of fabric anisotropy on the behavior of localized failure in granular materials. Based on a micromechanical analysis, the origin of deviatoric stress is decomposed into two components: contact force anisotropy and fabric anisotropy. Using a micro–macro approach, the back stress is interpreted as an contribution to the change of the fabric’s principal direction. The evolution of the back stress is deduced from the stress–fabric relationship and determined with reference to the deviation of the principal directions between the rate of the reduced stress tensor and the actual reduced stress tensor. With this micro–macro framework, a mixed (isotropic–kinematic) hardening model is developed based on the classical isotropic hardening theory. A laboratory simple shear test is first analyzed to validate the proposed model and illustrate the kinematic-hardening mechanism which is usually displayed under non-proportional loading. The analysis further focuses on the anisotropic aspect of localized failure. It has been discovered that the fabric anisotropy can play an important role in the occurrence of shear banding. An increasing degree of fabric anisotropy tends to delay the initiation of the strain localization and result in higher failure strength. The effects of fabric anisotropy have also been illustrated by comparing the theoretical predictions and measured results on the shear band inclination angle, shear strain level and dilatancy at bifurcation.

Comparative Study of Elastoplastic Constitutive Models for Deformation of Metallic Glasses

We present and compare three elastoplastic models currently used for deformation of metallic glasses, namely, a von Mises model, a modified von Mises model with hydrostatic stress effect included, and a Drucker-Prager model. The constitutive models are formulated in conjunction with the free volume theory for plastic deformation and are implemented numerically with finite element method. We show through a series of case studies that by considering explicitly the volume dilatation during plastic deformation, the Drucker-Prager model can produce the two salient features widely observed in experiments, namely, the strength differential effect and deviation of the shear band inclination angle under tension and compression, whereas the von Mises and modified von Mises models are unable to. We also explore shear band formation using the three constitutive models. Based on the study, we discuss the free volume theory and its possible limitations in the constitutive models for metallic glasses.

The orientation and dilatancy of shear bands in a bonded particle model for rock

The elasto-plastic behaviour of porous rock loaded under axisymmetric laboratory conditions and the resultant modes of localised deformation are investigated using Distinct Element Method (DEM) numerical models in which rock is idealised as an assemblage of spherical, unbreakable, cemented particles. These bonded particle models are loaded axially, either in extension or compression tests, using distortional periodic space, while a constant confinement is maintained laterally using a simulated flexible membrane. The emergent elasto-plastic bulk behaviour observed in the numerical simulations is qualitatively similar to that observed for natural rock and includes (i) pressure and stress-state sensitive elasticity, (ii) a positive correlation between friction coefficient and dilatancy factor, and (iii) yield/failure envelopes that depend on the third stress invariant. The shear band orientations and kinematics in the DEM models are quantitatively compared with localisation theory. Average shear band inclinations, defined as the angle between the shear band normal and the greatest compressive stress direction, are a few degrees greater than predicted by theory in compression tests, and over ten degrees greater in extension tests, differences which are attributed to differently shaped yield surfaces in model and theory. Nevertheless, the transition from dilational shear bands at low confining pressure to compactional shear bands at high confining pressure is successfully predicted by localisation theory. Compactional shear bands can develop, at least during localisation, in the absence of particle size reduction (i.e. crushing) provided that the material can accommodate pore reduction by particle rearrangement.

Evolution of shear banding in fully dense nanocrystalline Ni sheet

Compared with the coarse-grained counterpart, nanocrystalline (NC) metals have higher strength simultaneously with a decrease in ductility, strain localization is a main factor contributed to the early failure of NC metals during plastic deformation. This work deals with the study of shear banding in fully dense electrodeposited NC Ni sheet with sample dimensions at tens of millimeters under quasi-static uniaxial tensile load through the use of a strain gage calculated by digital image correlation technique. Shear band nucleation, broadening process and failure point were recognized. It is identified that maximum shear strain happens in the middle of the shear band where crack initiates first in this experiment. This indicates that the shear banding induces the failure of the NC Ni sample. Meanwhile, physical characteristics of the shear band, such as inclination and width of single full-developed shear band, were determined quantitatively. The results show that the inclination of shear band is about 63°, as well as the width of shear band is in sub-micrometer range. To investigate the micro-mechanisms during the shear banding process in the NC Ni sample, in situ tensile testing in a transmission electron microscope was conducted, the results suggest that grain boundary migration and grain coalescence are the main carriers during the propagation of shear band.