Plastic Limit Condition Research Articles

Selection of a stress‐based soil compaction test to determine potential impact of machine wheel loads

AbstractThe use of heavy machinery is increasing in agricultural industries, and in particular cotton farming systems in Australia, which induces an increased risk of soil compaction and yield reduction. Hence, there is a need for a technical solution to use available tools to measure projected soil compaction due to farm machinery traffic. The aim of this work was to compare the effects of static and dynamic loads on soil compaction. In this study, three Vertisols (soils commonly used for cotton production in Australia) were selected to examine soil compaction under a range of static and dynamic loads, respectively, using uniaxial compression equipment and a modified Proctor test. In general, soils behaved similarly under static and dynamic loads with no significant difference between bulk density values for all moisture contents with a high index of agreement (d = 0.96, RMSE = 0.056). The results further indicate better agreement between soil compaction produced under static and dynamic loads. Uniaxial compression test (static loads) produced greater compaction compared with the modified Proctor test (dynamic loads), in particular at moisture contents less than the plastic limit condition. The variation in soil compaction for static and dynamic loads was often evident for loads ≥600 kPa, with the greatest soil compaction induced under loads ≥1200 kPa. The findings of this study confirm the suitability of a modified Proctor method to assess soil compaction as an alternative tool under a range of moisture contents and machinery loads for Vertisols.

A Comparison Study between Traditional and Finite Element Methods for Slope Stability Evaluations

ABSTRACT Landslides are amongst the major disasters that have occurred in Karabük, Turkey. Due to the rapid increase in population movement to new habitats in urban areas, the need for engineering structures will increase. This condition has led to the construction of arts, cultural facilities and housing in insecure regions these days. The excavations to prepare the construction site, the external loads due to heavy structures and the changes in coverage of the earth surface are among the reasons for landslides in such areas. In this study, the landslides that occurred due to unsupported excavation for the construction of Karabük university stadium were analyzed using the three softwares like Plaxis, Geoslope and Slide. The study area is critical in terms of slope problems. Mass movement in the stadium occurred in high plasticity clay units containing sand and silt. For this reason, it is necessary to carry out detailed studies before the construction of engineering structures. The landslide considered in the study were analyzed using finite element (FE) analysis and slice method. These approaches are used for evaluating the stability of natural slope by considering a failure mechanism, which is known as the plastic limit condition. Regarding safety factors calculated using the different numerical solutions confirm that the results obtained are similar. In addition, the landslide area is close to the predicted simulation results.

Macroscopic and microscopic behaviors of granular materials under proportional strain path: a DEM study

SummaryUnder the proportional strain loading path, particle assemblies may exhibit various failure modes. Besides the strain localization, the diffuse failure may also occur under certain conditions. The diffuse failure mode corresponds to a homogeneous occurrence of failure with stress states strictly included within the plastic limit condition. This paper emphasizes the influences of the density degree and the rolling resistance under the strain path. A contact model considering rolling friction is adopted in a discrete element method analysis as an approximate means to account for the effects of particle shape. Mechanical responses indicate that loose assemblies without the rolling resistance are more vulnerable to static liquefaction. A sample with a smaller initial void ratio or larger rolling friction coefficient will reinforce the stability of the structure and reduce the likelihood of failure. For microscopic properties, the evolution of coordination numbers, contact forces, force chains and the anisotropies of the assemblies are explored and discussed. Rotational resistance helps increase the shear stress of the granular material, and the microscopic parameters indicate that the assembly has a strong anisotropy and a stable structure to resist the increasing loading.

Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work, involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

Smectite clay microstructural behaviour on the Atterberg limits transition

Abstract Particle space arrangement is a very important factor that determines the physico-mechanical properties of soil. Formations of three-dimensional (3D) structured networks within gelled or flocculated suspension may prevent clay particles and aggregates from building dense aggregates and by encapsulate water within the ultrathin and closed void network, lead to poor sludge dewatering. To better understand the water retention behaviour of smectite-rich clays, a microstructural investigation was conducted on Amcol Australian bentonite in aqueous suspension in near the liquid limit (LL) and the plastic limit (PL). The investigation was conducted with the aid of synchrotron-powered transmission X-ray microscope tomography (TXM), with subsequent computer reconstruction. Images from the microscopy studies were statistically analysed using the STatistical IMage ANalysing (STIMAN) system. The study found that clay particles form a spanned framework in which mineral particles, aggregates and water-filled voids assemble as hierarchic structural elements. The size of these structural elements was larger in the water suspension and subsequently became smaller as an effect of water loss in the suspension > liquid and > plastic limit conditions. The clay suspension structure was almost isometric, with a low anisotropy coefficient: K α – 9%. This parameter increased to K α – 17% in (LL) and increased further in (PL) conditions to K α – 35%. Voids within structural elements were much smaller than the water filled inter-flock voids, with their median diameter 140 nm (suspension), 120 nm (LL) and 90 nm (PL). Significant differences in Atterberg limits values were observed between powder freshly mixed with water and a seasoned sample. Therefore, careful consideration of the sample mineral composition, clay content and genesis must be given due to preparation for geotechnical examination.

Divergence and Flutter Instabilities of Some Constrained Two-Degree-of-Freedom Systems

AbstractIt is now well known that a variety of instability modes can appear before the conventional plastic limit condition is met. In this note, both flutter and divergence instability modes are investigated. First, the criterion for detecting their occurrence is established, and the case of kinematically constrained discrete systems is investigated. Based on an illustrative example, the competition between the occurrences of each of these instability modes is analyzed, showing that the prevalence of a given mode is strongly related to both the loading conditions and the stiffness properties of the material system at hand.

Bifurcation in granular materials: An attempt for a unified framework

Sudden collapse mechanisms strictly inside the Mohr–Coulomb plastic limit condition have been observed in granular materials in the laboratory as well as in the field. The purpose of this paper is to show that the theoretical framework of loss of sustainability is convenient to describe such mechanisms. In this context, the notions of both loading and response variables, which characterize the loading path applied to the specimen considered and its response path, are fundamental. Moreover, by investigating the relation between loading and response parameters, it is established that this framework also embeds the notions of loss of constitutive uniqueness and loss of controllability. Therefore, a unified approach is attempted. Finally, by highlighting the basic role played by the loading parameters, the vanishing of the second-order work is shown to be a proper criterion to detect the occurrence of a bifurcation from a quasi-static regime to a dynamic regime leading to the collapse of the material.

Analysis of failure occurrence from direct simulations

ABSTRACT Stress probes are simulated with the discrete element method (DEM). From these simulations we show that the numerical discrete model presents a non-associative flow rule. As the material is non-associate, sign of the second-order work is checked for stress states included within the plastic limit condition. Conditions of occurrence of failure when the second-order work vanishes are discussed.

Material instability in granular assemblies from fundamentally different models

AbstractThree fundamentally different models: a phenomenological constitutive relation, a micro‐mechanical model and direct numerical simulations by Distinct Element Method (DEM) are compared in this paper. In addition, the local form of Hill's sufficient condition of stability (i.e. the vanishing of the second‐order work d2W) is considered to describe material instabilities in granular assemblies. Stress probes in the axisymmetric plane of stress increments are achieved with all three models to check whether d2W vanishes at different stress–strain states. For all the models, cones of unstable stress directions (cones of stress probe directions for which d2W = 0) are found and they appear for stress states strictly inside the plastic limit condition. Thus, independently of the model, a bifurcation domain exists inside the plastic limit condition which can describe the sudden collapses of sand samples observed in laboratory tests before reaching the Mohr–Coulomb criterion. Taking advantage of the different models considered, the vanishing of the second‐order work is linked to the existence of non‐associated plastic strains and to micro‐mechanical bases. Copyright © 2007 John Wiley & Sons, Ltd.

Failure criteria and flow rules of geomaterials

ABSTRACT Essentially because of the non-associative character of geomaterials plastic strains, many bifurcations leading to various failure mechanisms exist strictly inside the plastic limit condition. The equations of the boundaries of the failure domain and of the cones of unstable stress directions are first exhibited for axisymmetric conditions. Because these bifurcation criteria can be satisfied before the localization condition, the failure mechanism is often of diffuse type. The considered constitutive relations, which are incrementally piece-wise linear or thoroughly non-linear, do not introduce any flow rule. However in a third section it is shown that a flow rule can be exhibited for the octo-linear model in axisymmetry while it disappears for more general 3D conditions. This last result is in agreement with some conclusions issued from discrete element modelling.

Failure criteria and flow rules of geomaterials

ABSTRACT Essentially because of the non-associative character of geomaterials plastic strains, many bifurcations leading to various failure mechanisms exist strictly inside the plastic limit condition. The equations of the boundaries of the failure domain and of the cones of unstable stress directions are first exhibited for axisymmetric conditions. Because these bifurcation criteria can be satisfied before the localization condition, the failure mechanism is often of diffuse type. The considered constitutive relations, which are incrementally piece-wise linear or thoroughly non-linear, do not introduce any flow rule. However in a third section it is shown that a flow rule can be exhibited for the octo-linear model in axisymmetry while it disappears for more general 3D conditions. This last result is in agreement with some conclusions issued from discrete element modelling.

Modelling of slope failure by a material instability mechanism

Abstract Slope stability analysis, based on the continuum mechanics assumption and finite element analysis, generally uses a plasticity criterion to describe the failure mechanism. In this paper we model the failure phenomenon using a material stability criterion based on the sign of the second order work. After a brief and critical review of the classical methods for slope stability analysis, we study a case of material instability experimentally and analytically. Homogeneous stress–strain problems are then investigated ising a non-linear constitutive model. It is shown that unstable stress–strain states are reached strictly inside the plastic limit condition (set of admissible stresses). Theses analyses are then extended and applied to sandy slope problems solved by FEM.

Instabilities in granular materials and application to landslides

Landslides or questions related to slope stability are usually considered in the framework of plastic limit analyses. Recent progress has made it possible to describe some failure modes in the framework of the theories of bifurcation of the strain mode by plastic strain localization and the shear-banding phenomenon. We propose in this paper to reconsider the question of landslide analysis by taking into account an appropriate instability criterion. As soils are strongly non-associated materials, unstable states can be reached strictly inside the plastic limit condition (which defines the set of admissible stresses). In the first part of this paper, we describe the constitutive model. Then Lyapunov's definition of stability allows us to detect unstable stress–strain states from experimental evidence. These unstable states are analysed by considering the sign of the second-order work. The stability analysis, performed for loose and dense sands under plane strain conditions, shows a large domain of instabilities in the stress space. This method is applied to some boundary-value problems by finite elements computations. It is shown finally by examples that such unstable stress–strain states are observed in our FEM modelling of slope problems. Copyright © 2000 John Wiley & Sons, Ltd.

Effects of phase geometry and volume fraction on the plane stress limit analysis of a unidirectional fiber-reinforced composite

Limit theorems of plasticity are applied to unidirectional fiber-reinforced composite materials to determine bounds to plastic limit conditions for the composite in average stress space. For this purpose a representative volume element (RVE), sufficiently large compared to the scale of inhomogenity of the composite, is chosen and analyzed by limit analysis methods.Upper and lower bounds to the plane average stress limit condition for the composite are derived for the following geometries which are presented in descending order of generality.1.(a) Only volume fraction of phases are known.2.(b) Volume fraction and fiber cross-section shape are known, but the size and distribution are arbitrary.3.(c) Deterministic periodic array.The bounds are shown to be improved at the cost of generality of fiber geometry and distribution. An evaluation is made of the effects of fiber volume fraction and distribution geometry on the composite limit condition.